ACHIEVING DIFFRACTION-LIMITED ANGULAR RESOLUTIONS in the OPTICAL THROUGH SPECKLE STABILIZATION by MARK STANLEY KEREMEDJIEV A

ACHIEVING DIFFRACTION-LIMITED ANGULAR RESOLUTIONS IN THE OPTICAL THROUGH SPECKLE STABILIZATION

By MARK STANLEY KEREMEDJIEV

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2011 °c 2011 Mark Stanley Keremedjiev

2 ACKNOWLEDGMENTS In the process of doing the research and writing this dissertation, I have had a lot of help along the way. My research would not have gotten very far without the aid of my advisor,

Stephen Eikenberry. On day one he handed me a great project idea that I am fortunate to have worked on. His advice, guidance and excitement for the ﬁeld have been an inspiration. Anthony Gonzalez deserves quite a bit of recognition for all of the help he has given me. His expertise in extragalactic matters enabled me to pursue research interests more attuned to my particular tastes. Beyond that, his insights into academia and comments on various proposals and papers throughout the years have been extremely helpful.

The instrumentation-side of things would not have gotten very far without the guidance of Nick Raines. He has been indispensable in offering advice, ideas and plain old fashion common sense when putting my instrument together. Without him and the other engineering folks on the fourth floor, my project would have likely taken years longer to finish. Reba Bandyopadhyay is someone I would like to thank for long discussions on the mechanics of actually being a scientist. In addition to that, she has also provided valuable editing advices and research project ideas. I would like to thank the staff at the Kitt Peak National Observatory and the William Herschel Telescope. Installing a new instrument can always be tricky and both facilities were more than helpful when problems arose. I would particularly like to thank Dick Joyce, Di Harmer and Ian Skillen for their assistance. In addition, Bruno Femenia deserves credit for helping me with EMCCD issues. Joe Carson’s fundamental question: “how does SPIFS compare to Lucky for imaging?” was essential to the results found in Chapter 7. He was also a great observing partner for the first week-long SPIFS-POC run at the KPNO 2.1-meter. On the software end of things, I would like to thank Craig Warner for allowing me to use his prototype FATBOY data analysis software. Eric Ford deserves credit for his insightful comments on GPUs and endless patience helping me learn to program CUDA. Related to that, Nathan De

3 Lee’s comments on C++ programming in general helped get the SPIFS-POC running. I thank Jian Ge for allowing me the use of his optical bench when the SPIFS-POC was in its infancy. The ofﬁce staff in our department have been extremely supportive and helpful during

my tenure and kept me from spending a huge amount of time buried under paperwork. I also thank Brandi Boniface for helping with the international shipping of SPIFS. The department’s computer coordinator, Ken Sallot, has been an asset and I owe him particular thanks for getting a construction crew to leave early so as not to make noise during my defense. My ofﬁce-mattes Ji Wang and Soung-Chul Yang have been good friends throughout graduate school and our weekly lunches have been a good break from the routine of staring at a screen day in and day out. Justin Crepp and Dimitri Veras were both helpful in advising how to navigate the ins and outs of graduate school and in particular, Justin’s advice to write up

everything as you go along saved a tremendous amount of time when I sat down to write this dissertation. I also thank my friend Doug Bishop for our long conversations and providing a useful, outside insight on many matters. I would be remiss if I did not acknowledge the SPIFS-POC “corporate sponsor” the Gregory Marshall Blond Salon. The hairspray they provided has been extremely helpful in characterizing system performance and probably saved me a bit of a headache in justifying the purchase of beauty products with a federal grant... I think it is also important to mention two individuals who really got me excited about professional science. The ﬁrst is Ives Idzerda at Montana State University. When I was thinking

about leaving the ﬁeld, he put me to work as an REU in his lab and showed me that experimental science is truly amazing. The second person is Jim Houck at Cornell University. Conversations with him made showed me what real science is and how it should be done. My family deserves special recognition for supporting me the whole way through. My parents, George and Barbara, have endorsed my efforts from day one and were always there to listen. My sister, Helen, has also been a friend in this whole process as we both have tried to get through the experience known as “graduate school”.

4 But I especially thank my wife, Lauren, for being both a sounding board and grounding rod for my thoughts. Our countless hours talking about the mechanics of graduate school, my research and life in general has kept me sane (you always know how to make me laugh). Thank you all! The research in this dissertation was partially supported by NSF grant AST-0917758.

5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ...... 3

LIST OF TABLES ...... 9

LIST OF FIGURES ...... 10

ABSTRACT ...... 13

CHAPTER 1 INTRODUCTION ...... 14 1.1 Current Speckle-Based Systems ...... 14 1.2 Speckle Stabilization ...... 18 1.3 Using Speckle Stabilization to Probe the Masses of SMBH ...... 21 2 SIMULATIONS OF SPECKLE STABILIZATION ...... 24 2.1 Simulation Design ...... 24 2.2 Simulation Results ...... 26 2.2.1 Core FWHM ...... 26 2.2.2 Strehl Ratios ...... 27 2.2.3 Guide Star Magnitudes ...... 28 2.2.4 Off-axis Guiding ...... 30 2.3 Simulations of SS 433 ...... 33

3 DESIGN, DEVELOPMENT AND TESTING OF THE SPIFS-POC ...... 37 3.1 Principal Components and Performance ...... 37 3.1.1 Speckle sensor ...... 37 3.1.1.1 Timing ...... 38 3.1.1.2 Read noise ...... 38 3.1.2 Fast steering mirror ...... 41 3.1.3 Science detector ...... 46 3.2 Optical Design ...... 46 3.3 Mechanical Design ...... 49 3.4 Turbulence Generator ...... 55

4 CONTROL LOOP ...... 57 4.1 Overall Loop Design ...... 57 4.2 Speckle Selection Algorithm ...... 58 4.3 Loop Speed and Optimization ...... 65 4.3.1 2D Cross Correlations ...... 65 4.3.2 Using a GPU to Speed Up Convolution Calculations ...... 66 4.3.2.1 Method and results ...... 66

6 4.3.2.2 Discussion ...... 67 4.4 Driver Initialization ...... 69 4.5 Windowing ...... 70 4.6 Detector Rotation and Solution ...... 72 4.7 Final Loop Speed and Code Options ...... 73 4.8 Initial Lab Results ...... 74 5 OBSERVATIONS WITH THE SPIFS-POC ...... 77

5.1 2009A/B Observations at the KPNO 2.1-m ...... 77 5.2 2010A Observations at the WHT ...... 79 5.2.1 Single Star Observations ...... 80 5.2.2 Observations of WDS 14411+1344 ...... 83 5.3 System Accuracy ...... 85

6 FUTURE PLANS AND DEVELOPMENT OF THE S3D ...... 87 6.1 Loop Speed and Latency ...... 87 6.2 FSM Accuracy ...... 88 6.3 High Speed Shutter ...... 90 6.4 Science Channel and ADC ...... 90 6.5 S3D ...... 92

7 A COMPARISON BETWEEN LUCKY IMAGING AND SPECKLE STABILIZATION FOR ASTRONOMICAL IMAGING ...... 94 7.1 Methods ...... 94 7.1.1 Speckle Stabilization Simulations ...... 94 7.1.2 Comparison Between Methods ...... 96 7.2 Results ...... 99 7.2.1 Read Noise Limit ...... 102 7.2.2 Photon Counting ...... 103 7.2.3 Optimal Lucky Imaging ...... 106 7.2.4 1024x1024 pixel2 Detectors ...... 108 7.3 Discussion ...... 110

8 THE FUTURE OF SMBH DETECTION VIA KINEMATIC MODELING AS ENABLED BY ELTS ...... 111 8.1 Extremely-Large Telescopes ...... 111 8.1.1 Theoretical Improvements Over Existing Facilities ...... 112 8.1.1.1 10-meter resolutions ...... 112 8.1.1.2 ELT diffraction-limited resolutions ...... 113 8.1.2 K-band CO Bandheads ...... 114 8.1.3 H-band CO Bandheads ...... 117 8.1.4 Calcium Triplet Lines ...... 118 8.1.5 Number of Galaxies ...... 120

7 8.1.6 First-Generation Instruments on ELTs ...... 122 8.2 SPIFS Impact on SMBH Measurements ...... 125 8.3 Rest-Frame J-band Spectral Features ...... 126 8.3.1 Observational Requirements ...... 127 8.3.2 Observational Conﬁrmation ...... 130 8.3.2.1 Observations and Data Reduction ...... 131 8.3.2.2 Results ...... 132 8.4 Discussion ...... 135

9 DISCUSSION AND CONCLUSIONS ...... 137

9.1 Simulated and Actual Performance ...... 137 9.2 Scientiﬁc Potential of SS ...... 138 9.3 Advantages to Speckle Stabilization ...... 139 9.3.1 Comparison to Adaptive Optics ...... 139 9.3.2 Comparison to Standard Speckle Imaging ...... 140 9.3.3 Space-based Platforms ...... 141 9.4 Future Directions for Speckle Stabilization ...... 142 REFERENCES ...... 143 BIOGRAPHICAL SKETCH ...... 148

8 LIST OF TABLES Table page 2-1 Summary of SS Performance Simulations ...... 34

4-1 List of stars and parameters used for speckle testing ...... 59

4-2 Comparison between BP and 2DCC ...... 60

4-3 Effects of the various windowing parameters ...... 72

4-4 Components of loop speed ...... 74 7-1 Summary of simulation results ...... 108

8 8-1 ELT K-band resolutions and distances at which typical (1 × 10 M¯) SMBH should be observable...... 114

8-2 List of galaxies, their SMBH masses and corresponding redshifts ...... 116

8-3 ELT H-band resolutions and distances at which SMBH should be observable...... 118 8-4 Observed galaxy properties ...... 132

9 LIST OF FIGURES Figure page 1-1 Demonstration of simulated seeing limited images...... 16

1-2 Stabilized-speckle system conceptual schematic...... 19

1-3 Cross sections of PSFs produced by speckle stabilization and in the seeing limit. .... 20

2-1 Simulations FWHM vs. wavelength ...... 27

2-2 Simulations of Strehl ratios vs. wavelength ...... 28

2-3 Strehl ratio versus guide star magnitude as a function of r0 ...... 29 2-4 Required guide star magnitudes ...... 31

2-5 Effect of guide star offset on FWHM ...... 32 2-6 Effect of guide star offset on Strehl ratios ...... 33

2-7 Optical spectrum of SS 433 used for the SPIFS simulations ...... 35 2-8 Spectra extracted from a simulated SPIFS datacube for SS 433 ...... 35 2-9 Simulated false color image of SPIFS-resolved jet outﬂows from SS 433 ...... 36 3-1 Measurement of the cycle times produced by the Andor iXon 860 ...... 39 3-2 Plot of variance versus signal for multiple EM gain values ...... 40

3-3 Read noise as a function of EM Gain ...... 40 3-4 Plot of FSM ringing between shifts ...... 43 3-5 Example of the two-step solution ...... 44 3-6 Damped harmonic oscillator ﬁts to the ringing data ...... 45

3-7 Ringing solution applied to a 16-pixel shift ...... 46 3-8 ZEMAX drawings of the optical design for the SPIFS-POC ...... 50 3-9 The theoretical performance of the optical system as determined by ZEMAX ..... 51

3-10 SolidWorks drawing of the holder for the EMCCD camera optic ...... 52 3-11 SolidWorks drawing of the entire SPIFS-POC ...... 53

3-12 SolidWorks drawings of the SPIFS-POC handing card ...... 54

3-13 Artiﬁcial speckle pattern produced by the hairspray phase screen ...... 55

10 4-1 Difference image of 2DCC and BP ...... 61 4-2 Contour plots of the correlation between speckle locations selected with the BP and 2DCC ...... 62

4-3 Cumulative distribution speckle locations differences ...... 63

4-4 Comparison of GPU and CPU performance for computing raw FFTs ...... 68

4-5 Comparison of GPU and CPU performance for computing full FFTs ...... 69 4-6 Images of in-lab speckle stabilization ...... 75

4-7 Cross sections of the PSFs produced in laboratory speckle stabilization ...... 75 5-1 Images of the SPIFS-POC on observing runs ...... 78

5-2 SPIFS-POC observations of 65 tau Cyg ...... 79 5-3 Observations of two PSF stars with both SPIFS on and off ...... 81

5-4 Observations of the binary star WDS 14411+1344 ...... 84 5-5 Analysis of the accuracy of the SPIFS-POC ...... 86 6-1 Plot of PSF cross-sections as a function of latency ...... 88 6-2 Simulated SS PSF cross-sections using data from the EMCCD ...... 89

6-3 PSF cross-section as a function of fraction of images used ...... 91 6-4 Plot of differential refraction as a function of wavelength ...... 92 7-1 Cross sections of the PSF produced by Speckle Stabilization ...... 96 7-2 Comparison between SS and SS+S with SAA and Lucky Imaging ...... 101

7-3 Comparison between Speckle Stabilization and no-read-noise SAA and Lucky Imaging 104 7-4 Comparison between techniques in the case of photon counting ...... 105

7-5 Comparison between speckle stabilization and OLI ...... 107 7-6 Comparison between SS and OLI for 1024x1024 pixel2 detectors ...... 109 8-1 Plot of SMBH Mass versus limiting observable redshift for Keck and the three ELTs in K-band ...... 116

8-2 Plot of SMBH Mass versus limiting observable redshift for Keck and the three ELTs using various line diagnostics ...... 119

8-3 Mass function of observable SMBH as a function of SMBH mass for Keck and the ELTs ...... 121

11 8-4 Plot of total number of SMBH observable as a function of telescope aperture diameter . 122 8-5 Plot of SMBH Mass versus limiting observable redshift for the four ﬁrst generation instruments for the ELTs ...... 124

8-6 Plot of SMBH Mass versus limiting observable redshift with SPIFS ...... 126

8-7 Mass function of observable SMBH including galaxies observable by SPIFS ...... 127

8-8 Y and J-band spectra of the galaxies in the sample ...... 133 8-9 J-band spectra of NGC 7619 and the best-ﬁt models ...... 134

12 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulﬁllment of the Requirements for the Degree of Doctor of Philosophy ACHIEVING DIFFRACTION-LIMITED ANGULAR RESOLUTIONS IN THE OPTICAL THROUGH SPECKLE STABILIZATION By Mark Stanley Keremedjiev May 2011 Chair: Stephen S. Eikenberry Major: Astronomy

I present results from a new observational technique for ground-based astronomy called speckle stabilization. This technique is similar to other speckle-based techniques and is capable of producing diffraction-limited images in the optical, but has the added advantage of being able to employ an integral ﬁeld spectrograph. Performance simulations show that a speckle stabilization system on a 10-meter class telescope should be capable of achieving resolutions as ﬁne as 15 milliarcseconds in the optical. I also show that guide stars can be as faint as 16th magnitude and be located up to 30 arcseconds away. I present the design, fabrication and assembly of a prototype instrument the Stabilized sPeckle Integral Field Spectrograph

Proof of Concept (SPIFS-POC) and describe the algorithms and programming necessary to control such a system and discuss optimization efforts. I compare speckle stabilization to other methods, including lucky imaging, and find that in certain circumstances, speckle stabilization is able to match or even outperform lucky imaging by up to a factor of 3 in signal-to-noise. Finally, this dissertation also covers the scientific gains speckle stabilization should be able to achieve. In particular, I address impacts on research in the field of super-massive black holes and demonstrate that the technique will fill an important niche in detecting the kinematic influence of SMBH on their host galaxies, aiding in the detection of the highest and lowest mass SMBH.

13 CHAPTER 1 INTRODUCTION When the Hubble Space Telescope was first conceived, there was no question of the scientific value of the data it would produce. This was not because it was a large or expensive mission; it was because astronomers knew being able to avoid the detrimental effects of atmospheric turbulence would produce the sharpest astronomical images anyone had ever seen. This assumption has since been confirmed and the Hubble Space Telescope (HST) remains one of, if not the most, over-subscribed facilities in modern astronomy. A large portion of this demand is due to the amazing ability to produce images at the theoretical resolution limit (or diffraction limit) of the telescope. Developing new techniques to achieve similar results from the ground is the purpose of this Ph.D. dissertation.

1.1 Current Speckle-Based Systems

In an ideal world, the angular resolution a telescope can achieve is directly proportional to the aperture diameter of the telescope. This relationship is given by θ ≈ λ/D where θ is the angular resolution, λ is the wavelength of light observed and D is the telescope diameter. This intuitively makes sense as telephoto lenses for cameras are able to produce much sharper images than the lens in a camera-phone. However, we do not live in an ideal world. The laws of physics are much more complicated than this ﬁrst order estimation and one of the key factors is atmospheric turbulence. At various altitudes in the sky, there are many turbulent layers. This turbulence is caused by physical phenomena such as wind shear, temperature gradients and pressure inhomogeneities.

There are many effects stirring the atmosphere and the result is a completely chaotic system. This chaos results in pockets of atmosphere at different temperatures and pressures from the pockets around it. Since the refractive index of the atmosphere is dependent on these parameters, it means that there are subtle differences in refractive indices throughout the atmosphere. This turbulence has a dramatic effect on image quality and as coherent light passes through the atmosphere, it gets refracted and bent so that the wavefront at the telescope pupil is highly distorted. When

14 an exposure of a star is taken, much of the high-angular resolution information is lost and the observer is left with a “seeing-limited” observation. The key parameter that determines the

resolution limit in seeing then becomes the Fried parameter r0 – a measure of the size of a

coherent pocket. So the resolution equation becomes θ = λ/r0. When the coherent pocket is larger, the resolution is better and vice-versa. This is why “good seeing” results in higher quality images. What further compounds the turbulent effects is that the conditions are not static. If images of a star are taken fast enough, the atmospheric turbulence produces a pattern of “speckles” at the image plane of a telescope (see Figure 1-1 (a)). As the turbulence proﬁle between the telescope and its target shifts and changes, typically on timescales of a few to a few tens of milliseconds, the speckle pattern also evolves and shifts. Thus, the average image of a star propagated through

the atmosphere signiﬁcantly blurs on timescales of 1-second (Figure 1-1 (b)). This is why astronomers often take focus exposures of a few seconds, in order to “average over the seeing”. While standard tip/tilt systems can improve this spread, they use the centroid of the entire energy envelope for steering, resulting in typically 10% improvement over the seeing, but still losing the highest angular resolution information. What is of note, however, is that each individual speckle within the pattern contains information about the target source at angular scales as high as the diffraction limit. This has led to the speckle-based techniques discussed below and is the basis of speckle stabilization. Diffraction-limited images in the optical regime remain difﬁcult to achieve using

conventional adaptive optics techniques. Therefore, obtaining resolutions matching or beating the HST requires clever techniques. One of the earliest attempts to overcome atmospheric turbulence

in the optical was through the speckle shift-and-add (SAA) method developed by Bates & Cady (1980). In this technique, the fact that the atmosphere is coherent for ≈ 10 − 30 ms (Kern et al.,

2000) is exploited by taking thousands of images with exposure times on the same order as the

coherence time. In the resulting speckle patterns, the highest quality speckle is found and the

15 Figure 1-1. Demonstration of simulated seeing limited images. (a) represents a short exposure (≈ 10 ms) while (b) is a long exposure (≈1 second). Images were produced with the code explained in Chapter 2. They simulate observations on a 10-meter telescope with seeing of r0 = 15 cm. Both images have the same scale. In the “seeing disk” on the left, the high-spatial-frequency information has largely been “blurred out” by time-averaging effects. images are stacked on top of one another such that the best speckles are always in the same location. The results of such work is a diffraction-limited core atop a diffuse halo of light. Lucky imaging (LI) is a recent technique that borrows the fundamental approach of the SAA but further improves the image quality. It was ﬁrst proposed by Fried (1978) and has been implemented by several groups with such instruments as LuckyCam, FastCam and AstraLux

(Law, 2007; Oscoz et al., 2008; Hormuth et al., 2008). The idea behind the technique is relatively simple. Since the turbulence pattern is chaotic and obeys a power-law distribution best-described by Kolmogorov (1941), temporal ﬂuctuations in the turbulence mean that occasionally near diffraction-limited images naturally occur. These pockets are normally short lived lasting only a few tens of milliseconds and occur only ≈ 10% of the time on 2.5-meter class telescopes. Therefore, to exploit these high quality pockets LI takes tens of thousands of images but only keeps the highest quality images. These high-quality images are then shifted and added to one another in the same way as the SAA method. The result is a PSF similar to SAA but with higher

Strehl ratios (Baldwin et al., 2001; Tubbs et al., 2002; Law et al., 2006; Law, 2007).

16 The reason why this technique has only recently been employed has to do with advances in detector technology. When Fried (1978) ﬁrst proposed the idea of lucky imaging, detectors were slow and to get the required signal-to-noise ratios involved observations spanning many

nights. The advent of Electron-Multiplying CCDs (EMCCDs) has enabled LI to become a reality. These detectors are both highly sensitive and able to read out quickly. A 512 x 512 pixel2 EMCCD is able to read out at 100 Hz as opposed to a traditional detector which read outs at <1 Hz. Therefore it is possible to get tens of thousands of images in less than an hour. The ﬁrst group to perform lucky imaging was Baldwin et al. (2001), who achieved near diffraction-limited

angular resolutions on the 2.56-m Nordic Optical Telescope at 0.8µm. Since that time there have been observations of binary star systems (Law et al., 2005, 2006, 2008), exoplanet host stars

(Daemgen et al., 2009) and many other scientiﬁc targets.

While Lucky Imaging has been successful at achieving diffraction-limited angular resolutions in the optical, this feat is limited to telescopes with apertures less than 4-meters in diameter. The reason for this is the fraction of usable images decreases as a function of telescope diameter such that at 4-m or larger, the fraction of usable images approaches zero. However, Law et al. (2009) developed a way to increase the usefulness of Lucky Imaging to these larger telescopes: using Lucky Imaging in conjunction with an Adaptive Optics system. Current AO systems are very successful at correcting atmospheric turbulence in the NIR much of the time. AO systems achieve this by using a deformable mirror correcting for turbulence at rates as high as 1 kHz. However, turbulence is more signiﬁcant in the optical

and requires corrections > 1 kHz. Additionally, the number of terms requiring correction is signiﬁcantly higher in the optical meaning that visible AO systems would require many more actuators than are currently employed. While none of these facts pose a theoretical reason optical AO is impossible, it is not practical with current technology.

What Law et al. (2009) noted however, is that even with these shortcomings, AO still

produces nearly diffraction-limited images some of the time in the optical. Furthermore, the

fraction of the time AO succeeds in correcting optical images is similar to the fraction of time

17 diffraction-limited images occur in Lucky Imaging on 2.5-meter telescopes. As such, if a LI system is put behind an Adaptive Optics system and only the best AO-corrected speckle patterns are used, diffraction-limited images should be possible on larger telescopes. This concept was

proven by Law et al. (2009) at the Palomar 200-inch telescope using the existing facility AO system and achieved the highest angular resolution ever recorded in optical observations.

1.2 Speckle Stabilization

A natural evolution of these speckle techniques is to find a way to do integral field spectroscopy (IFS) at diffraction-limited resolutions. In this dissertation, I describe an instrument concept, feasibility study and on-sky tests for a new observational technique called Speckle Stabilization (SS) (Eikenberry et al., 2008; Keremedjiev et al., 2008, 2010). SS will enable, under certain observational conditions and constraints, low-to-modest-Strehl diffraction-limited imaging spectroscopy from large ground-based telescopes in the optical bandpass (e.g. r’, i’, and z’ bands). When coupled with an integral field spectrograph, SS is capable of exploring

important scientiﬁc niches which are not currently available using existing high angular resolution techniques such as adaptive optics or lucky imaging. At the same time, speckle stabilization is relatively straightforward and feasible using existing, relatively-inexpensive technology. The Stabilized sPeckle Integral Field Spectrograph (SPIFS) is effectively a real-time SAA system coupled with an IFS (Eikenberry et al., 2008). Previous speckle techniques (SAA and LI) generally rely on off-line post-processing to recover the high-spatial-frequency information but this in turn typically limits them to simple imaging, using the same detector for “science” as for speckle sensing. In the SS technique, we propose to use a fast steering mirror (FSM) to stabilize the position of the brightest speckle in real-time. This then enables us to feed a stable image with a diffraction-limited core into an alternate “science channel” (such as an integral ﬁeld spectrograph) via pickoff and/or dichroic mirrors. This then decouples the high-speed (and typically lower-sensitivity) speckle sensing from the “science channel,” enabling analyses

18 Figure 1-2. Stabilized-speckle system conceptual schematic. Shows the primary layout and how the science channel is decoupled from the speckle sensing channel.

requiring long exposures with more sensitive “slow” detectors (i.e. spectroscopy, polarimetry, etc.). I present an ideal, cartoon-level schematic for a speckle stabilization system in Figure 1-2. Light from a telescope ﬁrst encounters a fast-steering mirror (FSM) and is then relayed to the remainder of the instrument after passing through an atmospheric dispersion corrector (ADC).

A dichroic (or, alternately, a small “pickoff” mirror) relays the “science beam” to the science instrument, while the remainder of the light continues into the “speckle sensor”. The speckle sensor consists of optics and an EMCCD– essentially identical to a speckle-imaging system. However, rather than simply recording the speckle patterns for eventual off-line analysis, the speckle camera images are analyzed in real-time to identify the location of the brightest speckle in the system. This information is then used to generate a command signal to the fast-steering mirror which keeps this brightest speckle stably located at a constant position on the output focal plane.

19 Figure 1-3. Cross sections of PSFs produced by speckle stabilization and in the seeing limit. The code used to produce these PSFs is described in Chapter 2. Note that there is a sharp, diffraction-limited core sitting atop a seeing limited halo.

The process of using a FSM to stabilize speckles effectively achieves a real-time shift-and-add

of the speckle patterns. While all other speckles are still moving in an uncontrolled manner, averaging out to a smooth “halo”, the stabilized speckle produces a steady diffraction-limited “core” which is then analyzed and recorded by the science instrument, much as an adaptive optics (AO) science instrument analyzes/records an AO-corrected image. I show a cross section of the PSF produced by speckle stabilization in Figure 1-3 and demonstrate that SS produces a sharp, diffraction-limited core atop a diffuse halo. When compared to the seeing limit in red, it is clear SS produces high Strehl ratios and higher resolutions. This approach overcomes one of the major limitations of traditional speckle imaging: the speckle sensor system is decoupled from the “science instrument” in such a way that the science instrument can effectively carry out high-sensitivity observations of targets using techniques ranging from standard imaging to integral-ﬁeld spectroscopy to polarimetry, etc. The latter can

20 all be accomplished using high-sensitivity, “low-speed” CCD detectors (as opposed to the noisier high-speed CCDs for standard speckle imaging discussed more in Chapter 7). This dissertation primarily focuses on the development of the Stabilized sPeckle Integral

Field Spectrograph Proof Of Concept (SPIFS-POC) instrument. In Chapter 2 I will show the theoretical simulations that demonstrate SS potential. Much of this chapter is an adaptation of

Keremedjiev et al. (2008). In Chapter 3 I cover the mechanical and optical design while Chapter 4 is on the control loop. I discuss the on-sky observations of the instrument in Chapter 5 and comment on future directions for the technique in Chapter 6 (much of the content appeared in Keremedjiev et al. (2010)). In Chapter 7, adapted from Keremedjiev & Eikenberry (2011), I compare speckle stabilization to other speckle imaging techniques and discuss strengths and weaknesses.

1.3 Using Speckle Stabilization to Probe the Masses of SMBH

The era of Extremely-Large Telescopes (ELT) is rapidly approaching and the many advances planned for these facilities have the potential to revolutionize our understanding of the Universe. One particular area of research that has the potential to benefit greatly from these developments is the field of supermassive black holes (SMBH). Much of our understanding of the properties of SMBH comes from detailed modeling of kinematic profiles based on data acquired with integral field spectrographs (IFS). To constrain the mass of a SMBH requires an understanding of the stellar mass (from surface brightness profiles) and velocity information from spectroscopy. Having kinematic information as a function of distance from the center of the source enables estimates of the mass with fewer assumptions than with reverberation mapping or scaling relations. Since van der Marel (1994) proposed that STIS on the Hubble Space

Telescope could be used to derive black hole masses, high-spatial resolutions in conjunction with spectroscopic information have proven to be essential to work in this ﬁeld. Dozens of these measurements using HST and AO+IFS observations on ground based telescopes have been made by Gebhardt et al. (2000); Pinkney et al. (2003); Davies et al. (2006); Cappellari et al. (2009); McConnell et al. (2011) and others. However, due to instrumental/facility constraints and the

21 time-consuming nature of the observations, there are still many questions left unanswered. This provides an excellent opportunity for Stabilized sPeckle Integral Field Spectroscopy (SPIFS) to shine. The high resolutions achievable with SPIFS when deployed on an 8 or 10-m class telescope mean it will be an excellent tool for the study of SMBH properties as well as current outstanding questions.

The MBH − σ relationship (Ferrarese & Merritt, 2000; Gebhardt et al., 2000), a correlation between the mass of the central black hole in a galaxy and the velocity dispersion of stars in the host galaxy, has been one of the fundamental discoveries in our understanding of SMBH properties. The relationship drives research into the coevolution of galaxies and their SMBH as the black hole sphere of inﬂuence R = GMBH/σ (Peebles, 1972) is too small (on the order of 10 pc) to inﬂuence the larger rotation of the host galaxy on kpc scales.

6 8 The relation is well characterized for SMBH masses of 10 −10 M¯ but at both the high and low mass end of the MBH − σ relation there are lingering questions that require new observations to address. One such issue is the disjoint between SMBH masses predicted by the MBH − σ relation and the mass predicted by the black hole mass-galaxy luminosity MBH − L relation (Kormendy & Richstone, 1995; Magorrian et al., 1998). Part of the divergent mass estimated by the two techniques is driven by the intrinsic scatter in both correlations which increase at higher mass (Law, 2007), but the fact that we do not measure galaxies with σ much greater than

400 km/s (Sheth et al., 2003) indicates a point at which the MBH − σ relation plateaus. Since the MBH − L relation does not have the same limitation at high luminosity, the two theories 9 predict different masses at MBH > 10 M¯. A recent example of this disjoint can be found in the investigation of NGC 1332 by Rusli et al. (2011) where there is an order of magnitude difference between black hole masses predicted by the two relations.

At the low mass end of the MBH − σ relation there is debate over whether intermediate mass 3 5 black holes (those with 10 − 10 M¯) exist. Evidence of black holes at the boundary between the 5 two at MBH ≈ 10 M¯ has been found by Greene & Ho (2007); Filippenko & Ho (2003); Peterson et al. (2005); Barth et al. (2004) in AGN using single epoch observations and reverberation

22 5 mapping. For black holes with masses < 10 M¯, Gebhardt et al. (2005) use kinematic modeling 4 and detect a 2 × 10 M¯ IMBH in G1, a stripped galaxy core around Andromeda. In the globular 4 cluster Omega Centauri Noyola et al. (2010) detect a ≈ 5 × 10 M¯ IMBH, but van der Marel & Anderson (2010) dispute this claim with proper motion modeling and place an upper limit on

3 the black hole mass at < 7 × 10 M¯. As the debate continues over the existence of IMBH, their location on the MBH − σ relation also remains and open issue. Consequently, these questions at the high and low mass limits hinder efforts to develop a

comprehensive black hole mass function (BHMF). Once a full understanding of the MBH − σ relation is available at all mass ranges, then a BHMF can be constructed. It then becomes useful

to see if the BHMF changes over cosmic time and such information will provide valuable insight into SMBH and galaxy formation and evolution.

To address the most massive SMBH, understand the nature of IMBH (or lack thereof) and develop a BHMF, we need access to high angular resolution IFS instrumentation. While STIS on HST has been repaired and current AO-fed IFU work has been conducted on some local galaxies, it is difﬁcult to get the necessary time to conduct these complicated and time-intensive observations. Furthermore, the sample size is strongly limited by the resolving power of the telescope aperture. An effective means to address these issues is through new telescopes, instrumentation and techniques. In Chapter 8 of this dissertation, I will address how SPIFS and the advent of extremely large telescopes will impact this research. Since they both present the capability to measure SMBH at

higher angular resolutions it is important to see where they compliment one another. Finally, I will summarize the ﬁndings in Chapter 9 and discuss the overall beneﬁts of speckle stabilization

as noted in Eikenberry et al. (2008). For this investigation, I assumed H0 = 73.0km/s/Mpc

(Freedman & Madore, 2010) and a ﬂat ΛCDM with ΩM = 0.3.

23 CHAPTER 2 SIMULATIONS OF SPECKLE STABILIZATION In order to understand how a speckle stabilization system would perform in real-world astronomical observations it is necessary to conduct simulations of the various parameters exploited by this technique. In this Chapter, I demonstrate that SS is sound from a theoretical perspective and that the technique has unique features making it highly competitive in high-angular resolution observations. Much of the work presented in this chapter is based on my ﬁndings presented in Keremedjiev et al. (2008). In §2.1 I cover how the simulations were conducted and what parameters they investigate. In §2.2, I present results showing FWHM, Strehl ratios, limiting guide star magnitudes and guide star offset information. Finally in §2.3, I address the speciﬁc case of the microquasar SS 433 and show how SS will enable unique

measurements of jet properties. 2.1 Simulation Design

To simulate the capabilities of a SS system, I have carried out a range of simulations using model atmospheres with Kolmogorov-spectrum turbulence (Kolmogorov, 1941) in the Interactive

Data Language (IDL). The fundamental idea behind the code is that the wavefront W(α,β) at the pupil plane is the integral over all frequencies. This can be described in one dimension as:

Z ∞ p ω(α) = Φ(k)e−i(2πkα)dk (2–1) −∞

Here Φ(k) is the phase amplitude, k is the wave number and α is the position. To modify this to account for errors due to turbulence, I add a random phase error in the exponent denoted by θ(k):

Z ∞ p ω(α) = Φ(k)e−i(2πkα−θ(k))dk (2–2) −∞ p As a result, the wavefront can be described as the Fourier Transform of Φ(k)eiθ(k) which is how the code simulates observations. The adaptive optics group at the Jet Propulsion Laboratory

has extensively used similar algorithms and veriﬁed their accuracy in comparison with actual

performance results with the Palomar Adaptive Optics system (PALAO).

24 More speciﬁcally, I began the simulations by deﬁning a phase map which characterizes a Kolmogorov turbulence screen projected onto the pupil of the telescope. To achieve a Kolmogorov-like turbulent spectrum, I require that the turbulent wavefront amplitude as a

function of spatial frequency k goes as

−5/3 −11/3 Φ(k) = 0.023br0 k (2–3)

Here r0 is the Fried parameter (the atmospheric turbulence coherence length) such that 6/5 r0 ∝ λ where λ is the wavelength of the observed light. The term b is a normalization factor of order unity used to make the simulations match observational results. I used a value b = 0.7 since we found this provided the best agreement between our simulations and observational results. Using these terms, I deﬁne a two-dimensional “normalization array” in phase space (k-space) characterizing the spatial frequencies sampled across the aperture.

I generate another array of random phase values θ(k) ranging from −π to +π, and produce

a complex array equal to e−iθ(k). I then multiply the normalization array by this array of randomly-phased complex unit vectors to assign each component of the wavefront its proper power sampled from the Kolmogorov power spectrum. The resulting array is then Fourier

transformed and the output is a turbulent 1024x1024-pixel wavefront phase map ω(α,β)

sampled from a Kolmogorov power spectrum. I deﬁne this phase map over a square aperture 3 times the telescope diameter. This guarantees oversampling of the ﬁnal point spread function (PSF) and also sets the outer length scale of the turbulence we can simulate. For completeness, my simulations also include seven layers of atmospheric turbulence. Each layer is independent from the others and is assigned a weight and altitude according to values given by Le Louarn

(2002). I then deﬁne an amplitude mask for the pupil A(x,y) matching the dimensions of the

phase map φ(α,β). A(α,β) is set to 1 for every location in the unobscured telescope pupil,

and 0 everywhere else. It is assumed for the purposes of these simulations that the secondary

mirror obscures 1/3 of the pupil. The ﬁnal wavefront map is then given by W(α,β) =

25 A(α,β)e−iφ(α,β). We then determine the resulting point spread function according to PSF(x,y) =

|FFT(W(α,β))|2, where x and y are the angular positions at the telescope focal plane. The result is a stellar speckle pattern.

Because the physical scale of the simulations is deﬁned to be wavelength independent, a correction is applied to compare different wavelengths. The output of my simulations

assumed that the diffraction-limited FWHM was 3-pixels across for each λ. Therefore, since

the diffraction limit scales as λ, I needed to expand the images to match physical results. The

base wavelength was set to λ = 0.5µm. For any image corresponding to a longer wavelength, I

stretched the image out from the center by a factor of λ/0.5µm using a linear interpolation. To simulate speckle stabilization, I found the “best” speckle in each of these distinct frames using a 2D cross-correlation between the speckle pattern and an ideal PSF (the speciﬁc algorithm performing this task is described in detail in Chapter 5) This ideal PSF was produced using the same code but with no turbulence applied. I then shifted the images according to the location of the best speckle as deﬁned by the maximum value in the cross-correlation and summed them. To contrast to seeing-limited observations, I simply added the frames on top of one another with no shifting whatsoever. A simple “sanity check” was also performed to measure the consistency of this code. As noted above, standard seeing-limited images consist of simply summing the individual speckle patterns with no speckle stabilization. Thus, summing many of these images should yield a PSF with FWHM ≈ λ/r0. I summed 100 such exposures for various telescope apertures and seeing conditions and found the simulated “seeing-limited” PSFs do in fact closely match the expected FWHM.

2.2 Simulation Results

2.2.1 Core FWHM

I simulated 100 speckle patterns for a range of wavelengths 0.5µm < λ < 1.0µm for both

5-meter and 10-meter class telescope. The resulting FWHMs of the core from shifting and adding

the speckle patterns as a function of wavelength is given in Figure 2-1. The FWHM of each

26 PSF was found via ﬁtting a 2-dimensional Gaussian across the core of the PSF. For comparison,

the theoretical FWHM given by optical theory (θ = 0.98λ/D) is overplotted in green. As hypothesized, our simulations conﬁrm that the core of the PSF is in fact at the diffraction-limit of

the telescope.

A B

Figure 2-1. FWHM in mas as a function of wavelength for r0 = 15cm for both 5-meter and 10-meter class telescopes, along with the theoretical diffraction-limited FWHM. The slight discrepancies between theory and simulation are primarily due to sampling effects near the diffraction-limit and the tuning parameter b in the simulations.

2.2.2 Strehl Ratios

To measure the Strehl ratios for speckle stabilization PSFs on the two telescopes, I produced

more speckle patterns assuming a range of r0 values between 10cm and 20cm. Strehl was measured by comparing to an ideal PSF also produced by the code. I used the FWHM of the ideal PSF to deﬁne an aperture where pixels intensity would be measured. For this investigation I deﬁne the Strehl ratio as the intensity within the aperture measured for the SS image divided by the intensity measured within the aperture of the ideal image. I present the resulting Strehl ratios for the 10-meter telescope simulations on the right of Figure 2-2. As expected, performance improves with increasing r0– effectively, the light is divided amongst fewer speckles. Furthermore, we see that SS achieves > 1% Strehl ratio in decent seeing conditions and that in good seeing conditions (r0 = 20 − 25cm, slightly higher than the median GTC site r0 of 18 cm) SS will achieve Strehl ratios > 2 − 3%.

27 On the left of Figure 2-2, I present the results of simulations for a 5-meter class telescope.

Because the telescope entrance pupil is divided into fewer r0-diameter patches than in the 10-m case, larger fractional energy is present in each speckle. As a result, the Strehl values are 2-3x higher than in the 10-meter case at a given r0. It is worth noting, however, that the total energy in the central core Strehl×D2 is greater for the 10-m telescope.

These values are broadly consistent with lucky imaging observations. Tubbs et al. (2002) measured Strehl ratios of ≈ 0.06 in Lucky Imaging observations when using 100% frame selection on a 2.5-m telescope in the i’ ﬁlter. We also ﬁnd that the SS PSF is quite similar to lucky imaging PSFs produced in real observations with 100% frame selection i.e. a

diffraction-limited core atop a diffuse halo.

A B

Figure 2-2. (a) SS Strehl ratios as a function of r0 and wavelength for a 5-meter telescope. (b) SS Strehl ratio as a function of r0 and wavelength for a 10-meter telescope.

2.2.3 Guide Star Magnitudes

A critical issue for speckle stabilization is the kind of sky coverage can it attain. There are a number of factors which determine the answer to this issue, the ﬁrst of which is the

required guide star brightness. To investigate SS sky coverage, I simulated Strehl ratio as a function of guide star magnitude using 1,000 speckle patterns for a 10-meter telescope. The

speckle patterns had four different Fried parameters r0 =10, 15, 20 and 25cm. To simulate the effects of observing, each speckle pattern was normalized to match the ﬂux in a 2ms

28 exposure of stars ranging in magnitude from 0

In Figure 2-3, I show that SPIFS will be able to use guide stars as faint as 15th magnitude

in typical seeing conditions (r0 ≈ 15cm) on a 10-m telescope without signiﬁcant degradation of Strehl ratios. In other words, guide star shot noise only becomes an issue for stars of ≈ 14 − 15 mag or fainter. This is 1.5-2 magnitudes fainter than would typically be usable for adaptive optics correction. This is expected since AO systems split the wavefront-sensing light into > 200 Shack-Hartmann cells and must measure the centroid for each of these. SS, on the other hand, only requires an accurate location of the brightest speckle, which contains ≈ 1 − 2% of the total ﬂux (several times brighter) for typical turbulence conditions.

Figure 2-3. SS Strehl ratio versus guide star magnitude as a function of r0 on a 10-m telescope.

The simulations used in Figure 2-3 assume 100% frame selection. If a high-speed shutter

is used such that only the best 10% of images are used (akin to lucky imaging) it is possible that

fainter guide stars may be usable. The basic idea would be that the shutter opens only when we

29 have a useful detection of a speckle centroid effectively discriminating against “noise-only” contributions to the science PSF, due to intermittent clouds, variable seeing, or simply “unlucky”

realizations of the turbulent spectrum combined with a marginally-bright guide star. Figure 2-4(a)

shows the resulting performance as a function of guide star magnitude for a 10-m telescope. We can see that the shutter approach with fainter guide stars will actually improves the image quality of the SPIFS technique with faint sources at the expense of integration time. This improvement in image quality occurs because the shutter is only open for speckle patterns with the highest Strehl ratios resulting in an improvement in the overall SS image. It also signiﬁcantly improves sky coverage (by 50-100%) while still maintaining the high angular resolution which

is the primary driver for SPIFS. We also note that the shutter will be a critical feature for observing under varying seeing conditions. This will be the rule rather than the exception for real

observations (while the simulations here assume a constant value of r0 for the sake of simplicity). Additional advantages to shuttering are discussed in Chapter 6.

2.2.4 Off-axis Guiding

The ﬁnal critical parameter for estimating SS sky coverage is the range of off-axis angles over which we can achieve useful near-diffraction-limited PSFs. For sky coverage, the number of available guide stars (equivalent to the number of patches on the sky reachable by SPIFS) goes

roughly as N ∝ 1/Flim where Flim is the ﬂux of a star at the limiting magnitude. Meanwhile, the 2 useful solid angle on the sky reachable by SPIFS for each patch goes as θmax , where θmax is the maximum useful off-axis angle from the guide star. To accurately simulate offset guide star effects, I created a strip of turbulence for each of the seven simulated layers of atmosphere. Each strip was comprised of three Kolmogorov phase

screens set next to one other. Because each phase screen is completely independent of the others there is a non-physical disjoint at the boundary between images. However, the simulations are sampling an inherently random system and the disjoint should not affect the results. Therefore an off-axis angle from the guide star shifts the projection of the pupil different amounts on each

turbulent phase map effectively simulating a volumetric turbulent structure. I then sampled offset

30 A B

Figure 2-4. (a) Pseudo-Strehl ratio versus guide star magnitude in the case of a high-speed shutter employing a signal-to-noise threshold for allowing light to enter the science channel. (b) Open shutter fraction versus guide star magnitude for the same situation. (c) Fractional energy in the core versus guide star magnitude (equal to the produce of the curves in a and b). While the total energy continues to drop with magnitude, note that the contrast between the core and the associated halo of the PSF remains high for fainter guide stars using this approach (as compared to Figure 2-3). locations ranging from 1” to 120” with 100 speckle patterns produced at each offset. Simulations were conducted for three wavelengths (λ = 0.5,0.75,1.0µm) and three seeing conditions

(r0 = 10,15,20cm) for a 5- and 10-meter telescope. The results are presented the results in Figures 2-5 and 2-6. From the Figure 2-5, we can see that SS PSFs show very little FWHM degradation over off-axis angles as large as 20” in radius under normal seeing conditions at most telescope facilities. We can also see in Figure 2-6 that the Strehl ratios degrade with off-axis angle, but that

31 Figure 2-5. SPIFS FWHM as a function of offset from guide star. Each panel corresponds to a different r0. The dotted line denotes the value given by the guide star for each iteration and provides a constant comparison against the science channel. Note that the small differences between “guide” and “science” Strehls ratios at zero offset are due simply to different realizations of the same noise distribution in the Monte Carlo simulations. The dramatic dip in FWHM for 0.7µm in the r0 = 10cm case is simply due to the ﬁtting routine for the FWHM; it assumes the FWHM is < 100” so it returns non-physical results when the true FWHM is > 100”.

at θmax ≈ 20”, the PSFs maintain ≈ 60% of the on-axis Strehl value. Thus, I adopt θmax = 20” as a working estimate for the off-axis patch size. Based on these results, I can estimate the approximate sky coverage for SS. For 15th mag guide stars and 20” useful radius, we can expect sky coverage of ≈ 50% for low Galactic latitudes, with the fraction being higher (≈ 100%) towards the inner Galaxy, and lower (≈ 12%) towards the Galactic anti-center. For 16th mag guide stars, the sky coverage increases to > 30% even towards the Galactic anti-center. For high Galactic latitudes, the sky coverage fraction

32 Figure 2-6. SPIFS Strehl as a function of offset from guide star. Each panel corresponds to a different r0. The dotted line denotes the value given by the guide star for each iteration and provides a constant comparison against the science channel. Note that the small differences between “guide” and “science” Strehl ratios at zero offset are due simply to different realizations of the same noise distribution in the Monte Carlo simulations. naturally drops, but remains > 3% for 15th mag stars (> 7% for 16th mag) even at the Galactic polar cap. Thus, we conclude that the SS sky coverage will be very competitive with natural guide star adaptive optics systems, and even with laser guide star systems near the Galactic Plane.

A summary of Strehl ratios and expected sky coverage is given in Table 2-1. 2.3 Simulations of SS 433

In this section, I wish to clearly demonstrate the scientiﬁc potential of SPIFS. To do this,

I have simulated observations of the microquasar SS 433 using the above code. SS 433 is the

ﬁrst known example of a Galactic relativistic jet source, and thus the forerunner of modern

33 Table 2-1. Summary of SS Performance Simulations 10-m Telescope 5-m Telescope Parameter r0 = 15cm r0 = 20cm r0 = 10cm r0 = 15cm FWHM (0.75µm) 12.7 mas 13.0 mas 26.8 mas 27.8 mas Strehl (0.75µm) 0.009 0.013 0.013 0.024 Guide star mag 15.0 15.5 15.5 16.0 Off-axis angle θmax ≈ 20” θmax ≈ 20” θmax ≈ 20” θmax ≈ 20” Sky Coverage Galactic Plane ≈ 12% ≈ 20% ≈ 20% ≈ 30% Sky Coverage Galactic Cap ≈ 3% ≈ 5% ≈ 5% ≈ 7%

microquasar astrophysics. The optical spectrum of this object shows a number of strong, broad emission lines of the Balmer and He I series, as well as several lines at unusual wavelengths.

These latter have been identiﬁed as redshifted/blueshifted Balmer and He I emission from

collimated jets with intrinsic velocities of ν ≈ 0.26c (Abell & Margon, 1979) and an example

spectrum is presented in Figure 2-7. Furthermore, the Doppler shifts of these features change with time in a cosinusoidal manner, leading to the label of “moving lines”. This behavior is now widely accepted to be a symptom of precession of the jet axis in SS 433 on a timescale of ≈ 164 days (Margon, 1984). While radio observations with VLBI can resolve the radio jets and track their proper motions, the optical jets arise much closer to the compact object and are thus only observable via their spectral features. Spatially resolving these jet lines would

provide tremendous insights into the physical conditions in the relativistic jets. Based on the

kinematic model for SS 433 (summarized in Eikenberry et al. (2001)), we expect the jets to appear approximately 22 milli-arcseconds from the compact object. Note that this is not resolvable by current AO systems on 10-meter-class telescopes operating at the short end of their bandpass. Since SS 433 has a magnitude of I = 12 mag, it is a highly suitable target for SPIFS observations. I created a simulated SS 433 SPIFS image using a 10-meter telescope with median r0 = 15cm based on actual optical spectra of SS 433. I used the simulation software to generate multi-wavelength PSFs and simulated speckle stabilization using SS 433 itself as the guide star with a dichroic diverting the “science” light to the an integral ﬁeld spectrograph. I then convolved the resulting PSFs with an input spectrum dissected into an assumed “core + 2 jets”

34 Figure 2-7. Optical spectrum of SS 433 used for the SPIFS simulations. Note that both the approaching and receding jets are redshifted compared to rest-frame H due to relativistic time dilation effects. The feature between the stationary line and the blue jet is a stationary HeI line.

Figure 2-8. Spectra extracted from a simulated SPIFS datacube for SS 433 at the spatial locations of the central compact object and the two jets. Note that the blue/red jet components are cleanly separated at the resolution of SPIFS.

35 morphology with separations determined from the parameters of the kinematic model to create a simulated datacube (including sky background and shot noise) assuming a brief 1-hour on-source integration. I present three resulting spectral “slices” from the datacube centered on the core and each of the 2 jets in Figure 2-8. Note the signiﬁcant spectral diversity between the three spectra, allowing the clear identiﬁcation of the spatial locations from which particular features predominantly arise- the critical factor for these observations. Finally, we selected 3 spectral channels from the data cube and coded them red (for the wavelength channel of the red jet), blue (for the wavelength channel of the blue jet), and green (for a continuum wavelength between the two) to create a false-color simulated “image” of the spatially-resolved jets in SS 433 (Figure 2-9). These simulations reveal that it should be possible to spatially resolve the optical jets of SS 433 using the technique of speckle stabilization. Since no other technique currently exists that is capable of this feat, it presents an interesting science case which SS is well-suited to address.

A B

Figure 2-9. (a) False color image of SPIFS-resolved jet outﬂows from SS 433, with red (for the wavelength channel of the red jet), blue (for the wavelength channel of the blue jet), and green (for a continuum wavelength between the two). (Right) Continuum subtracted difference images made from the 3 images in the left composite. Note the clean separation of the jet component, which are separated by ≈45-milliarcseconds on the sky in this simulation.

36 CHAPTER 3 DESIGN, DEVELOPMENT AND TESTING OF THE SPIFS-POC The performance simulations done in Chapter 2 show that the concept of speckle stabilization is on sound theoretical grounds and enabled Professor Eikenberry and I to apply for a National Science Foundation Small Grant for Exploratory Research (SGER) to take the project to the next level. The proposal was a success and using the money from the SGER I was able to design and build the Stabilization sPeckle Integral Field Spectrograph Proof Of Concept instrument (SPIFS-POC) to observationally verify the validity of speckle stabilization. In this chapter, I detail the physical design, fabrication and integration of the instrument, and describe in lab characterizations of various components. In §3.1 I describe the principal components of the SPIFS-POC as well as their performance. §3.2 covers the optical design of the system while §3.3

discusses the mechanical design. Finally, §3.4 address the building of a turbulence generator for simulations. 3.1 Principal Components and Performance

Overall, the SPIFS-POC had to be built on a tight budget (<$100,000) while meeting stringent design requirements. To demonstrate the validity of SS, the overall requirement was that there be separate speckle sensing and science channels, the optics Nyquist sample the diffraction-limit in the optical and that the instrument be able to interface with multiple telescopes.

3.1.1 Speckle sensor

The heart of the SPIFS-POC is the speckle-sensing detector. For this component, we opted to purchase the Andor iXon DU-860 electron-multiplying CCD (EMCCD). When purchased in 2007, these detectors were still relatively new. EMCCDs are advantageous for speckle sensing

because they have high frame rates (up to 500 fps) and are sensitive to single photon events. These advantages are made possible by the electron-multiplication process which is similar in many ways to a photomultiplier tube. When a standard CCD is read out, the charges are moved

along the detector to the shift register where the pixels are read out one at a time. In an EMCCD

37 when the charge is moved across the shift register toward readout, the charges are accelerated and “slammed” into the reservoir. As a result each electron produces more electrons and after multiple shifts, a cascade effect occurs where a single photon event may produce hundreds

of electrons for readout. How many additional electrons each count produces depends on the electron multiplication gain (EM gain) which is determined by the voltage potentials that “slam” the charges into each reservoir. The Andor iXon DU-860 used in the SPIFS-POC is a 128 x 128 pixel2 EMCCD with

24µm pixels. The supporting documentation supplied with the detector claims that the system is capable of readout out at 500 Hz with a read noise ≈ 0.2e−/pixel at an EM gain of 300. To better understand the performance limits of the SPIFS-POC, I opted to test these values directly.

3.1.1.1 Timing

I needed to verify that both the read times and cycle times were as reported in the Andor literature. To do this I set the system to take thousands of exposures at various integration times.

While the detector was accumulating these images, I measured the time elapsed with a stop watch. Then, by taking the measured time and dividing it by the number of exposures, I could derive the cycle time and the read time. Since thousands of frames were used and the total operation times were > 40 seconds, my error contribution was small. The results of these tests are given in Figure 3-1. There the cycle time measured closely matches exposure time plus read time. In fact, the measured difference between the two is < 10µsec. Therefore, the detector meets speciﬁcations in terms of exposure times and read out times.

3.1.1.2 Read noise

For read noise, I tested the parameter in a relatively straightforward manner. I accomplished this by measuring signal versus variance for multiple EM gain settings. The slope of these

measurements in the linear regime gives the system gain (Howell, 2000). To get signal versus variance, I took ﬂat exposures with variable integration times such that I had exposures ranging

from under-sampled to saturated. I then calculated the signal (median bias-subtracted intensity)

and variance for each image.

38 Figure 3-1. Measurement of the cycle times produced by the Andor iXon 860. The red line denotes the case of no read-out time, hence the only contribution to the cycle is the exposure time. The black line is the measured cycle time and the dotted line is the read time of the detector. The residuals between the Ideal+Read Time and Measured are less than 10µsec.

I give a plot of variance versus signal for the different EM gain values in Figure 3-2 and present the linear fits to the linear regime of the plots in Figure 3-2. From the figure, I show that where the linear regime actually occurs depends on the EM gain value and that there is a trend between decreasing slope as a function of EM Gain. What is interesting is that the size of the linear regime also increases with EM gain and at EM gain = 250 nearly the entire dynamic range of the detector is linear. I present the slopes of the fits (read noise) versus EM gain in Figure 3-3. The two curves denote different bias measurements for the EMCCD and they are consistent with one another. These data confirm Andor’s statement that the effective gain of the DU-860 converges to

0.2e−/pixel at high EM gains. This extremely low read noise indicates that the detector should be sensitive to faint targets at high EM gains.

39 Figure 3-2. Plot of variance versus signal for multiple EM gain values (EM Gain = 0 is the case where only the normal detector gain is present). The ﬁts are all to data which appear to be in the linear regime of the data. Slope of the ﬁts provide read noise information.

Figure 3-3. Read noise as a function of EM Gain. The data appear to converge toward 0.2e−/pix at high EM gain. The two different curves are from different bias measurements.

40 3.1.2 Fast steering mirror

Once the speckles are detected with the EMCCD, the next important task is to stabilize them onto a ﬁxed location. For this task, a fast steering mirror (FSM) is required. The initial requirements were that the FSM be capable of operating at 1 kHz and have a mirror diameter of at least 1-inch. After some investigation, we selected the Optics in Motion OIM-102. This

2-inch FSM is operated through voice coils and is purported to be capable of operations at >1 kHz for small angular motions. We opted for a gold coating to the mirror as our observations will primarily be λ > 0.5µm and the gold coating has a higher reﬂectivity at these wavelengths. Since the FSM is driven by voice coils, the system accepts analog input voltages to drive

motions. To control such motions, I outﬁtted our control computer with a National Instruments 6731 digital-to-analog card for signal processing. The card has 4 output channels capable of ±10volts with 16-bit resolution. Since the output of the card is a SCSI interface, I built a custom cable to interface with the FSM’s 15-pin connector.

While the advertised parameters for the FSM are adequate, I undertook lab tests to verify performance. The ﬁrst parameter I tested was the precision. To measure precision, I shined a laser off the FSM into the EMCCD. I then commanded the FSM to move to various locations across the EMCCD. I recorded these motions at 500 Hz and measured the centroid of the laser spot in each frame. The stability of the spot location between motions gives a measure of

precision. I found the laser spot was precise to 1.91µrad. This value closely matches the OIM

reported precision of 2µrad. While this experiment conﬁrmed that the FSM was quite precise, it revealed a major problem: the FSM has a long settling time and “rings” about the desired position. This characteristic is presented in Figure 3-4. Ringing occurs for all motions and appears to be inherent to the FSM. What is interesting to note is that for motions between 2 and 64 pixels, the shape of the ringing appears to be constant. The only difference appears to be the amplitude

of the ringing. While ringing that quickly damps out would not normally hinder speckle

41 stabilization, the fact that this damping takes between 10-20 ms is unacceptable for closed-loop performance. To optimize the operational speed of the FSM, we needed to implement a solution designed

to compensate or correct for the ringing. Professor Eikenberry suggested such a solution in the form of a two-step function used by Bifano & Stewart (2005). The basic idea is that if the ringing can be represented by a damped harmonic oscillator, it should be possible to use destructive interference to remove the ringing. To determine if this solution is appropriate for the FSM, the ringing must obey the following form:

³ ´ x(t) = A 1 − e−t/τ cos(ωt) (3–1)

Here there are three key parameters, A the amplitude of the signal, τ the decay time and

ω the angular frequency of the mirror related to the resonant frequency f by ω = 2π f . If ω is independent of amplitude, a generic solution can be applied to damp out the ringing. A two-step solution works by first commanding the mirror to move to a particular location some fraction of the total move. When the mirror reaches 1/2 of its phase, a second motion command is issued for the remainder of the motion. This second command is perfectly out of phase with the first such that it destructively interferes with the “ringing” from the first motion. The result is a two-step drive that causes discrete, non-ringing steps. I present an example of how the solution works in Figure 3-5 and show how the sum of the two commands destructively interfere to produce a discrete motion. The downside to this solution, however, is that it imposes a minimum cycle time equal to one-half the resonant frequency.

To determine if there is indeed a single ω for all motions, I conducted measurements of the ringing. This was done by shining a laser off the FSM and stepping the mirror between two locations several times. I recorded these motions with the EMCCD, giving high time sampling of the data. The resulting measurements and ﬁts are presented in Figure 3-6. I found that there

was indeed one ω that could be used to describe the ringing of the FSM and its value was 9.51

ms. To determine the optimal amplitude for the ﬁrst step, I ran a small optimization routine where

42 Figure 3-4. Plot of FSM ringing between shifts. Data from 9 different cycles is folded to accentuate the overall shape of the ringing. The median of the 9 cycles is represented by the solid lines. The different lines represent different requested pixel shifts.

43 Figure 3-5. Example of the two-step solution. The red curve is the initial command given to the FSM and the blue curve is the second command. The two destructively interfere to produce the black curve. various amplitudes were simulated and the one that produced the smallest residual ringing was adopted. For the SPIFS-POC FSM, the optimal amplitude for the ﬁrst step is 0.80.

With a theoretical solution in place, I applied it to the data. The solution’s effect on the data is evident and I present the result of applying the two-step solution to a 16-pixel shift in Figure 3-7. Here the ringing is greatly diminished and damps out quickly resulting in motions that require < 6 ms to stabilize from the initial command. This solution to the ringing issue greatly sped up the routine, but it brought to light the fact that the fastest the FSM could operate was at 200 Hz (5 ms cycle time). This is significantly slower than advertised and will be discussed more in Chapter 4 and Figure 3-7 also shows that the solution is not perfect. There is still a bit of an overshoot when the mirror first moves to its final location. While this overshoot is less than 1/2 in the case of no ringing solution, it still affects the data and will be addressed in Chapters 5 and 6.

44 Figure 3-6. Median data from Figure 3-4 with damped harmonic oscillator fits to the data. What is interesting about the fits is that I find ω is indeed independent of the amplitude of motion. This is important because it means a generic solution can be applied to solve for all motions. 45 Figure 3-7. Ringing solution applied to a 16-pixel shift. Note that there is still a residual overshoot of ≈ 2 pixels but that the ringing has been damped out resulting in motions that require < 6 ms to stabilize from the initial command.

3.1.3 Science detector

Since the SPIFS-POC was built merely to test the concept of speckle stabilization, an integral ﬁeld spectrograph would be prohibitively expensive to build for demonstration purposes. As a result, a standard optical science detector was used for the testing observations. Speciﬁcally, the SPIFS-POC used a Santa Barbara Instruments Group (SBIG) ST-237. The detector has 640 x

480 pixels2 at 8µm per pixel. The read noise is 15e− per pixel and full-frame read out requires 14 seconds. In many ways this detector is sub-optimal for future science observations, but it is useful for proof-of-concept testing.

3.2 Optical Design

I conducted the optical design of the SPIFS-POC in ZEMAX. The basic requirements for

the optics were that:

1. The focal planes of the detectors Nyquist sample the diffraction-limit in i’ band

2. The instrument should accept an f/15 beam from the telescope

46 3. The distance between the FSM and the EMCCD be maximized so that minimal motions are required to move the FSM

4. Theoretical image quality from the optics had to have Strehl ratios > 90% for 0.70µm < λ < 0.90µm In keeping with the aim to build SPIFS-POC with limited funds, I decided to use all off-the-shelf optical components (i.e. no custom fabricated optics). This helped make the optical design a bit simpler as I was able to use the commercial lens information stored in the ZEMAX database to test a variety of optical layouts. One of the ﬁrst difﬁculties in meeting the optical requirements was with maximizing the

distance between the FSM and the EMCCD. In theory the minimum step size should be equal to

σRMS where σRMS is the angular scatter in the FSM from §3.2.b. When σRMS = 1.91µrad is used, I ﬁnd that the optimal distance between the FSM and the EMCCD is 12 meters. This distance is impractical both due to size constraints and because there are no off-the-shelf lenses with a 12-m focal length. The largest achromatic optic I was able to ﬁnd was the 50107 lens from Edmund

Optics with a focal length of 1.5247 meters. At this distance, each pixel corresponds to 8σRMS– good for reducing residual error in FSM precision but sub-optimal for minimizing the amplitude of motions. Using the EO 50107 camera optic as the backbone of the design, I needed two more major

optics for the system: a camera for the SBIG and a collimator. The collimator needed to match strict requirements to ensure that the correct plate scale was in place at the EMCCD detector plane. Because the ﬁrst run with the SPIFS-POC was scheduled for the KPNO 2.1-m telescope,

the optics needed to convert the telescope plate scale PStelescope = 6.55 arcsec/mm to the detector plate scale of PSdetector = 1.64 arcsec/mm. Since

fcollimator PSdetector = · PStelescope (3–2) fcamera this means that the optimal focal length for the collimator is 381 mm. There are several

achromatic doubles that have nearly this focal length, however when they were simulated in

ZEMAX chromatic aberration became signiﬁcant. Chromatic aberration in SPIFS-POC is more

47 pronounced than in typical speckle imagers because of the long focal length of the EMCCD camera optic. To compensate for this, off-axis mirror and other solutions were considered. The optimal solution was found in the form of a super-achromat– a three optic lens system.

CVI-Melles Griot stock a 250 mm focal length super-achromat (YAP-250-50) that meets the requirements and we selected it for the SPIFS-POC. While 250 mm is shorter than the optimal focal length, plate scale at the detector is directly proportional to the focal length of the collimator. As a result, a shorter focal length results in a smaller plate scale- i.e. the SPIFS-POC will over-sample the data rather than under sample with this optic. The camera optic for the SBIG was a 400 mm achromatic doublet (LAO-400-40 from CVI-Melles Griot) that met speciﬁcations. The SPIFS-POC uses a standard beam-splitter to separate light from the science and guiding channels. We chose this implementation to minimize complexity in the system. I purchased two λ/10 fold mirrors from Edmund Optics to make the system more compact when placed on the telescope. Both mirrors were gold coated as they are downstream of the FSM and the gold coatings have better reﬂectivity.

I give ZEMAX drawings of the optical design in Figure 3-8. In (a) I present the optical path for light headed to the EMCCD while (b) has the path for light going into the SBIG. The various optical components are labeled and show how the instrument should be laid out. I give the performance of the optical system in Figure 3-9. Along the left column, the spot diagram (a), encircled energy (c) and Strehl ratios (e) of the EMCCD optics are given. I ﬁnd that diffraction-limited performance is expected for the SPIFS-POC sampling and that Strehl ratios greater than 90% can be expected at all relevant wavelengths.

On the right column of Figure 3-9 I show the spot diagram (b), encircled energy (d) and Strehl ratios (f) of the SBIG optics. Here the performance is not as good. While the spot diagram is tight, the encircled energy does not match the diffraction limit and Strehl ratios drop below 90% at wavelengths longer than 0.8µm. While this performance is sub-optimal for high precision photometric work, for proof-of-concept demonstrations where the primary concern is high

48 angular resolutions, these Strehl ratios will suffice as they do not significantly degrade resolving power. For the various observing runs, I ordered two sets of filters. The first were standard, broad

band Sloan ﬁlters from Astrodon in r’, i’ and z’. The second set consisted of narrow band ﬁlters

including: a 10 nm Hα filter and a 10 nm red continuum narrow band filter (ordered from Astrodon) and two 3 nm narrow band filters centered on the O I line at 844.6nm and a continuum filter at 835 nm (custom ordered from Custom Scientific). 3.3 Mechanical Design

With the optical components and their relative locations decided, the next important phase was that of mechanical design. The SPIFS-POC needs to be transportable and easy to assemble as it is a visitor instrument. I carried out the design work in SolidWorks 2009 SP2 and gave finished drawings to the UF Physics and Astronomy Machine Shop for fabrication. The SPIFS-POC needs to fit into a relatively compact volume (≈ 1m3) since its first run

on the KPNO 2.1-m was going to be a Cassegrain focus. I designed the SPIFS-POC to hang off a single mounting plate that attaches to the telescope. Using values from the optical design in ZEMAX, I designed optical holders to place the components at their required distances. I give an

example of a lens holder in Figure 3-10. These custom optics holders were designed so that the lenses could be bolted to the instrument and replaced if needed. A single aluminum plate with custom drilled holes served as the optical bench upon which all the components rest. Nearly all the bolts were of the same size to reduce the complexity of on-site assembly and shipping. Two 1” gussets run along half the instrument and provide a rigid structural support. Additional support is given by standard optical mounting posts that are bolted into the base-plate

and the top plate. Furthermore, I designed the housings so that all of the necessary electronics and computers could be bolted to the instrument as well. The net result is that only two ethernet cables and one power cable are required to operate the SPIFS-POC.

I present design drawings of the ﬁnal instrument in Figure 3-11. The instrument is relatively

compact given the long focal lengths of the multiple optics and has ﬁnal dimensions of 48” x

49 A

Figure 3-8. ZEMAX drawings of the optical design for the SPIFS-POC. In (a) the optical design for light passing to the EMCCD is presented whereas (b) shows the optical path of light passing to the SBIG. (0) is the telescope focal plane (1) is the collimator (2) is the location of the FSM (3) is where the beamsplitter is (4) is the camera for the EMCCD (5) and (6) are fold mirrors (7) is the detector plane of the EMCCD (8) is the camera for the SBIG and (9) is the focal plane of the SBIG. 50 A B

C D

E F

Figure 3-9. The theoretical performance of the optical system as determined by ZEMAX. Along the top row, the spot diagram (a), encircled energy (b) and Strehl ratios (c) of the EMCCD optics are given. On the bottom row (d), encircled energy (e) and Strehl ratios (f) of the SBIG optics are given.

51 Figure 3-10. SolidWorks drawing of the holder for the EMCCD camera optic. The drawing denotes the four components that make up the holder as a whole.

42” x 27”. To move the instrument around, I also designed a handling cart that was made out of

Unistrut and I show the design for the cart in Figure 3-12. All told there were 72 different custom parts for the SPIFS-POC, but given the simple design and small number of bolt types, the system is easy to assemble on-site. I added two additional components for the subsequent observing run at the William Herschel Telescope. The first was a motorized filter wheel (59-769) from Edmund Optics. It is capable of storing five 50mm filters in its magazine. The filter wheel can either be manually moved or be commanded by computer with included drivers. The second modification for observations at the WHT was the interface for the telescope. Observations with the SPIFS-POC in 2010A at the WHT were performed in the Ground-Based High-Resolution Imaging Laboratory (GHRIL) lab. This laboratory actually simplified the design requirements for the observing run. The GHRIL is a lab located on the Naysmith platform of the telescope and has an optical bench situated after a derotator. Therefore, to make SPIFS-POC compatible with the telescope only required designing a few blocks for the main plate to sit atop the optical bench such that the optical axes were aligned.

52 Figure 3-11. The entire SPIFS-POC. (a) is the instrument as it would appear to the user and (b) is an inside view. The circular plate in (a) bolts onto the mounting plate at Cassegrain focus at the KPNO 2.1-m. In (b), all of the main components are labeled to show their location. Note the similarity to the optical design given in Figure 3-8. 53 A

Figure 3-12. SolidWorks drawings of the SPIFS-POC handing card. In (a) I show the cart design and in (b) I show how the instrument ﬁts into the cart so that it can be mounted on the telescope. 54 3.4 Turbulence Generator

One of the ﬁnal components necessary to properly test the system is a turbulence generator. The optimal way to produce turbulence and generate speckle patterns is to place a phase screen in the optical. Unfortunately phase screens are prohibitively expensive for the purpose of this project, so other solutions needed to be investigated.

The ﬁrst potential solution I investigated was to use a heat-source. By producing heat in the optical path, the different refractive indices from air pockets of different temperatures produces speckles. I tested this in the lab with a heat gun used for shrink-wrapping wire covers. While the heat gun produced speckle patterns, the coherence length was shorter than the fastest read out speeds of the EMCCD (> 500Hz). These coherence patterns were too fast for testing and are also faster than the real coherence length of the atmosphere.

Figure 3-13. Artiﬁcial speckle pattern produced by the hairspray phase screen. Note that there are multiple speckles of varying intensity. When the phase screen is rotated, the speckle pattern changes and moves about the entire detector with both low and high order changes.

A second option that I decided to pursue was that of using a sheet of glass and hairspray.

Thomas (2005) noticed that properly deposited hairspray on glass has similar properties to a

Kolmogorov turbulence spectrum. Speciﬁcally, they found that putting down one even coat then

55 spraying on a second before the ﬁrst has fully dried produces a decent phase mask. The ﬁrst coat acts as low order turbulence while the second coat works for high order turbulence. Thomas

(2005) speculated that the amphomer compound in the hairspray is what makes the turbulence appear Kolmogorov. Given that this is a potentially easy solution to a difficult problem, I decided to test for myself. The Gregory Marshal Blond Salon in Gainesville, Florida donated hairspray for the purpose of scientific inquiry and a Plexiglass wheel that previously served as an entrance window was donated by the FLAMINGOS-2 team. I experimented with the hairspray and found that it does indeed produce a decent turbulence pattern. I present an example of the speckles produced by shining a laser through the phase screen in Figure 3-13. Time sampled turbulence was produced when I hooked-up the phase screen up to a stepper motor and gradually rotated it. Adjusting the rotation speed enable me to tune the coherence length of the “speckle patterns” to match atmospheric predictions. Rampy et al. (2010) recently confirmed the Kolmogorov nature of the turbulence produced by these methods. They also found that while hairspray works well, there are additional practical advantages that can be gained by using clear spray paint. Notably the phase screen is no longer water soluble and that better control in producing the phase screen can be exercised.

56 CHAPTER 4 CONTROL LOOP One of the critical components for operation of the SPIFS-POC is the control loop. The coding for the control loop needs to be able to detect speckles, send information to the hardware, iterate on particular locations and do all of this in the fastest possible time. In §4.1, I give the overall loop design and computational requirements of speckle stabilization. §4.2 addresses the speckle selection algorithm and why I chose to employ 2D cross correlations. I discuss loop speeds and the optimization of the speckle selection routine in §4.3 and I cover how driver initialization impacts computation times and in §4.4. I address how windowing can improve the efﬁciency of the FSM operation §4.5. The rotation of the EMCCD detector is covered in §4.6, ﬁnal loop speed is in §4.7 and I present initial lab results in §4.8.

4.1 Overall Loop Design

I modeled much of the control loop after the lucky imaging data reduction pipeline of Law

(2007). In Law (2007), their algorithm analyzed speckle patterns taken from an EMCCD to ﬁnd the location “best speckle” and shifted and added onto one another via a drizzle routine. In many ways this is exactly what the SPIFS-POC requires except instead of shifting and adding the images, shift information is sent to the FSM for real time stabilization. The overall loop architecture is as follows:

1. Acquire a speckle pattern with the EMCCD

2. Identify the location of the “best speckle”

3. Convert the location from pixel units to voltages

4. Output voltages to the FSM and stabilize the speckle pattern

5. Take a new exposure

6. Repeat the loop The system operates in a closed loop fashion where each motion is dependent on the

previous one such that solutions are iterated on with each step. A closed loop approach is

57 advantageous as it can correct for any system errors in the conversion of location to voltages and does not require a ﬁxed mapping of the detector onto voltage space. The minimum loop speed is deﬁned by the coherence length of the atmosphere. This time

is generally given by t0 ≈ r0/v (where r0 is the Fried parameter and v is the bulk wind velocity of the dominant turbulent layer (Kern et al., 2000)) and is on the order of 30 milliseconds. Since there should be two motions per speckle location, the loop needs to operate at > 70Hz. To optimize routine speeds and ensure that the computation is minimally impacting the loop time, all of the code was written in C++. Since at the time of purchase, drivers for all of the components were only available in Windows Vista, that is the operating system of choice. The

computer running the loop is a Dell T7400 Workstation with dual Intel Quad Core processors at 2.33 GHz. There are 8 Gb of RAM and three 15,000 RPM SAS 150 Gb hard drives in a RAID 0

conﬁguration– i.e. data are split amongst the different hard drives to minimize write times. The actual C++ code was written in Microsoft Visual C++ 2008 Edition.

4.2 Speckle Selection Algorithm

In order for speckle stabilization to function, an effective and robust algorithm for selecting the “best speckle” must be employed. There are many different techniques to select the best speckle, but the two most prominent methods that I investigated are the 2D cross correlation method (2DCC) and the Brightest Pixel method (BP). 2DCC was adapted from a method developed by Law (2007) for the lucky imagining system LuckyCam. With this method, I convolve an assumed, ideal PSF (generated either through simulation or previous data) with the speckle pattern. The inverse Fourier transform of this convolution results in a 2D cross-correlation that provides the location of the best match between speckles and ideal PSF.

Law (2007) used this method because it analyzes the speckle pattern at the resolution of the diffraction limit and, in theory, should ﬁnd the best overall match in quality not just brightness. The Brightest Pixel method is as straight-forward as it sounds. With this technique, I

determine the brightest pixel in the speckle image and assume that location is also the location of

the brightest speckle.

58 For the on-sky version of the speckle stabilization algorithm, a centroid will be calculated around the location for either BP or 2DCC to determine sub-pixel steering information. However, for the purposes of my tests I did not employ centroid information because sub-pixel shifts do

not actually improve the image quality in any way that affects the results in post processing. Furthermore, while it is possible to drizzle the data as Law (2007) has done, drizzling routines are slow and have little effect on the analysis done here. To compare the methods, I used data collected at the Kitt Peak 2.1 meter telescope in June of 2009 (described in Chapter 5.1). During this observing run, I obtained thousands of speckle images of stars at varying magnitudes. The current analysis is limited to i’ observations where there was a range of 7 magnitudes in brightness. The list of stars used for this analysis, including their V-band magnitudes, exposure lengths, and number of exposures are given in Table 4-1. The

range in exposure lengths and target magnitudes covers the parameter space of speckle exposures the SPIFS-POC will employ and provides and excellent opportunity to test optimal algorithms. The primary discriminants I use to determine which algorithm is superior are the FWHM and Strehl ratios of the of the stacked PSF cores. Other factors to consider for real operation are the length of time the algorithm takes to ﬁnd the best speckle and the requisite number of photons to get enough information for speckle selection.

Table 4-1. List of stars, v magnitudes and exposure parameters used for speckle testing.

Star V mag Exp Length (ms) Nexp hd122574 7.0 1 ms 100,000 hd122574 7.0 5 ms 90,000 hd173416 6.057 10 ms 70,000 18 Del 5.522 10 ms 40,000 14 and 5.22 10 ms 40,000 hr4905 1.77 1 ms 200,000 hr4905 1.77 5 ms 100,000

I calculated the locations of the best speckles for every image using both the 2DCC and BP methods. For 2DCC an artiﬁcial, diffraction-limited i’ image was produced using the simulation

code outlined in Chapter 2.1. I used the best speckle locations to shift-and-add data in IDL using

a program I wrote for the task. In simulating SS I assumed there was no instrumental delay, i.e.

59 every image is assumed to have been shifted to the optimal location given by either algorithm. Furthermore, no data were thrown out as the current version of SPIFS lacks a shutter. FWHM were measured by fitting a Gaussian to the central core and Strehl ratios were measured by summing the flux within a diffraction-limited aperture centered on the core and dividing it by the total flux of the summed image.

The results of the analysis are given in Table 4-2. From these results, there are some interesting findings. The first finding is that PSFs produced by 2DCC tend to have higher Strehl ratios than BP indicating better image quality. However the BP PSFs, on average, tend to have tighter cores (smaller FWHM) than 2DCC. What is interesting about this result is that the FWHM for BP have significant scatter, varying between 1.3 pixels to 4.4 pixels with a mean of 2.908±0.997 pixels. For 2DCC, on the other hand, the mean is 3.113±0.529 pixels. So while the mean values are similar, the scatter in the 2DCC method is much less. In fact, data for the faintest data set (HD 122574 at 1 ms) are particularly troubling. The FWHM for the BP method are a factor of 2 smaller than the diffraction limit (which is 2.1 pixels). Since the data were all reduced in the same way, this indicates something unusual is going on with the BP method in the limiting case of faint guiding.

Table 4-2. Comparison between BP and 2DCC in both FWHM and Strehl ratios for the same data sets. FWHM are in pixels and x and y denote the direction of ﬁt. Brightest Pixel 2D Cross-Correlation Star FWHM x FWHM y Strehl Ratio FWHM x FWHM y Strehl Ratio HD 122574 (1 ms) 1.31±0.06 1.53±0.07 0.0193±0.0008 2.31±0.11 2.46±0.08 0.0219±0.0010 HD 122574 (5 ms) 2.34±0.18 2.53±0.14 0.0165±0.0015 3.10±0.12 3.11±0.11 0.0175±0.0016 HD 173416 3.23±0.16 2.96±0.03 0.0141±0.0002 3.58±0.19 3.28±0.05 0.0146±0.0002 18 Del 3.53±0.11 3.29±0.23 0.0148±0.0010 3.80±0.11 3.58±0.21 0.0151±0.0010 14 and 4.41±0.19 3.11±0.10 0.0137±0.0002 4.66±0.17 3.49±0.11 0.0140±0.0002 HR 4905 (1 ms) 2.37±0.06 2.93±0.09 0.0207±0.0010 2.77±0.05 3.31±0.08 0.0216±0.0010 HR 4905 (5 ms) 3.16±0.04 3.56±0.05 0.0145±0.0002 3.45±0.06 3.88±0.05 0.0146±0.0002

To disentangle the results, a couple of other analyses are necessary. In Figure 4-1 I present a difference image of the BP result and the 2DCC result for the same set of data. While there are signiﬁcant differences, one of the most striking is that the center-most pixel is negative while the rest of the diffraction-limited core is positive. This indicates that only the very center pixel

60 Figure 4-1. Difference image of 2DCC and BP. The brighter regions denote and excess in the 2DCC PSF. Note the one dark pixel at the center. This shows the peaked nature of the BP method and indicates that it is prone to selecting spurious pixel artifacts produced by clock induced charge. is brighter in the BP method while the entire core from the 2DCC is overall more luminous. Therefore, in some instances, the BP method is likely targeting spurious detections– events where only one pixel is activated from stray photons or noise. With enough of these single-pixel events being used for image stacking, it causes a tighter but non-physical FWHM as well as a correspondingly lower Strehl ratio. I produced contour plots of the degree of correlation between speckle locations determined by each of the two methods for all of the speckle images to analyze the discrepancy between the sets further . The result is given in Figure 4-2. If the two techniques found the best speckle to be in the same location, there would only be a straight line with a slope of one. While it is clear that much of the time the two techniques are in general agreement, there is signiﬁcant scatter indicating that BP and 2DCC are ﬁnding different speckles for stabilization.

61 Figure 4-2. Contour plots of the correlation between speckle locations selected with the two methods. The ﬁgure on the left is for speckle locations in the x direction while the ﬁgure on the right is for the y direction. If there were complete agreement between the two methods, the result would be a straight line of slope equal to one.

To determine how often the results diverge, I plot the fraction of images with a particular pixel offset between the two selection methods in Figure 4-3. Since the diffraction-limited FWMH for these observations was 2.1 pixels, anything beyond 4 pixels different is over 2λ/D away i.e. not the same speckle. Through this analysis, I find that the two methods only agree on exactly the same location less than half of the time with a significant spread for the different stars. In the best case scenario, the two methods agree to within 2λ/D 80% of the time, but in the worst case that number falls to < 50%. Also from the Figure 4-3, I find that there is a clear trend between guide star brightness and agreement between methods. In the faintest cases (HD 122574 at 5 ms and HD 122574 at 1 ms) there is much less agreement than in the brightest cases (HR 4905 at 5 ms and HR 4905 at 1 ms). As such, this confirms the earlier analysis where BP was found to be heavily influenced by single pixel events. Given that BP seems to be affected by single pixel events, it is important to try to determine the cause of these artifacts. As detailed in §1 of Chapter 5, cosmic rays are unlikely to be the primary driver. This is because of the low number of cosmic ray events and the fact that cosmic

62 Figure 4-3. Cumulative distribution of images where the difference between speckle locations determined by the two methods are less than or equal to a given pixel offset. Note that greater than 4 pixel different is over 2λ/D away. The total number of images used for the analysis is 640,000. ray strikes cover several adjacent pixels. The next possibility that I examined is if this is a √ property resulting from noise. EMCCDs produce an extra 2 noise in addition to regular photon noise when operating at EM gains >> 1. This means that in the case of faint exposures, the noise could cause the PSF to have an unusual shape where a single pixel could be emphasized. To test this possibility, I used the simulated speckle data from Chapter 2 and I tested two cases where the guide star on a 2.5-meter telescope was 5th and 15th magnitude and added noise terms to simulate the Andor iXon used for these exposures. For this test, I used both the 2DCC method for image reconstruction as well as the BP method. What I found was that the measured FWHM was nearly identical for both methods at both magnitudes. In ruling out image noise, I found that there has to be a different cause for the spurious pixel events. Another possibility is clock-induced charge (CIC). When charges are moved across the detector to readout, there is a small probability that these shifts will produce extra charges

63 through impact ionization. With a normal CCD, the CIC is usually washed out by the read noise or dark current. However, with an EMCCD where the read noise is very low and exposure times are very short, CIC can have a substantial effect on the ﬁnal image.

To test whether CIC was affecting my data, I ﬁrst looked at my dark frames. In a given dark frame with an exposure time of 1 ms at an EM Gain of 100, the variance in counts is ≈ 5. However, the maximum values read out are between 30-40 counts. This means there are

individual, random pixels that are > 8σ above the noise in any given dark frame. I then looked at on-sky exposures of faint targets like HD 122574 and discovered that in these faint exposures, while the speckles are well above the noise threshold, they are only ≈ 50 counts. As a result,

random CIC is not necessarily larger than the actual speckles, but the superposition of CIC with any part of a speckle pattern will cause that pixel to be the brightest one by a signiﬁcant margin.

Because CIC is random, it is more likely that CIC will occur on top of a random part of the speckle pattern as opposed to the brightest part. When an image is then stacked based solely on the brightest pixel, the CIC will cause a random part of the speckle pattern to be the brightest pixel. This effect tends to dissipate with brighter targets as the difference in counts between the various parts of the speckle pattern are many hundreds of counts meaning the brightest part of a speckle is much greater than the sum of CIC and any other part of the image. Therefore, this would explain why the PSFs are much sharper for the BP method when observing faint targets. 2DCC manages to avoid being affect by CIC by sampling the best speckle which is designed to cover several pixels and averages over CIC randomness.

Therefore, this analysis has revealed four interesting points that unambiguously demonstrate 2DCC is the superior method for ﬁnding best speckles:

1. There are signiﬁcant differences between the speckles selected by the two methods

2. 2DCC is sensitive to the entire PSF, not just the brightest pixel

3. BP produces overly narrow, unrealistic FWHM due to clock induced charge

4. 2DCC produces higher Strehl ratios at all magnitudes over BP

64 As such, 2DCC has been adopted as the de facto speckle selection algorithm employed by SPIFS-POC.

4.3 Loop Speed and Optimization

As mentioned above, speckle lifetimes are on the order of 30 ms or less (Kern et al., 2000) and because of this fact, the SPIFS-POC needs to be able to operate as fast as possible. Since I

have shown that correcting the FSM for its ringing already produces nearly 5 ms of lag (Chapter 2.1.2) it is important that every other component of the system be optimized for speed.

4.3.1 2D Cross Correlations

In §4.2, I demonstrated that the 2D cross-correlation method is the superior technique for speckle selection. However, while it produces superior speckle selection, the downside is the increased computational requirements over the brightest pixel method which takes << 1 ms. Cross-correlations are computationally expensive as they require Fourier transforms to execute. The ﬁnal image is the result of F −1 [F (specklepattern) × F (idealPSF)] meaning three transforms are needed. To optimize this routine, I employed several tricks. The ﬁrst is that the F (idealPSF) never changes as the ideal PSF is constant in time. Therefore this Fourier transform can be calculated in advance and stored thus reducing the convolution time by 1/3. Next, the Fastest

Fourier Transform in the West (FFTW) (Frigo & Johnson, 2005) routine was used for the actual Fourier transform calculations. FFTW is a publicly available subroutine written in C. The performance of FFTW is superior to other free Fourier transform code and is even competitive with platform-speciﬁc codes. An additional trick was to cut out quadrant swapping. The ﬁnal output of the cross-correlation is an array where the quadrants have been swapped. Reconstructing the array is time consuming

and inefﬁcient. Rather than perform this reconstruction, I generated a look-up table such that when the location of the best-speckle is determined in the raw output I plug that value into the table and ﬁnd what the actual location of the best speckle is in detector space.

65 The result of all these improvements in the 2DCC selection algorithm is that it takes the computer 1.33 ms to calculate the 2D cross-correlation.

4.3.2 Using a GPU to Speed Up Convolution Calculations

One recent development in inexpensive computing has been the rapid growth in power of graphics processing units (GPU). GPUs are cards designed to speed up graphical calculations to allow for better screen refresh rates at high resolutions. They are particularly popular in the computer gaming community but have recently found traction in research fields. GPUs are based on the idea that a simple chip, with simple architecture can be cloned many times over and placed onto one card. These cards are then programed with highly parallelized code to utilize the ability to perform very simple operations rapidly. However, until 2007 when the NVIDIA corporation released their 1.0 version of the Compute Unified Device Architecture (CUDA) for public use, it was prohibitively difficult to use GPUs for anything other than graphics processing. CUDA is designed so that programmers can use the highly parallel nature of their cards for open-ended programming. Of interest to the SPIFS-POC project, the CUDA software development kit (SDK) also includes cuFFT– a set of programs designed to execute Fast Fourier Transforms on the cards in an optimal fashion.

Ford (2009) investigated the utility of CUDA-enabled GPUs and found that there was up to a factor of 200x increase in speed for algorithms solving planetary orbits. This kind of power for Keplerian simulations is vital to the study of exoplanet dynamics and greatly reduces solving times. These impressive results might be applicable to the SPIFS-POC algorithms. The current cross-correlation time of 1.33 ms is fast but since the algorithm is dependent on a series of

2-dimensional FFTs, it is plausible that a GPU would be able to reduce the calculation time. 4.3.2.1 Method and results

To test whether the SPIFS-POC could beneﬁt from a GPU, I purchased an NVIDIA

GTX-280 GPU implemented by e-VGA. The card has 1 GB of RAM and contains 240 processor cores. The card was installed in the Dell T7400 Workstation running the SPIFS-POC

66 control code. The best way to compare the GPU is to use the CPU as a benchmark. The CPU benchmarks were acquired by running the previously described Fastest Fourier Transform in the

West 3.10 code (Frigo & Johnson, 2005).

I executed two tests to determine the utility of the GPU for 2D FFT processing. First, I generated a single FFT plan, allocated memory once and put a for loop around the actual execution code to get a sense of the absolute speed of the FFTs. I chose to use N pixels on a side ranging from 4 to 2048, where N is always a factor of two– as this is the optimal case for both routines. I show the result in Figure 4-4. The CPU outperforms the GPU for operations smaller than ≈ 104 elements, but beyond that, the GPU is always faster by a factor of nearly 20x. The GPU appears to ﬂat-line at 0.15 ms/FFT for the small transforms. It is likely that this occurs because not all cores are utilized in the small FFT cases and the algorithms cannot run any faster.

The CPU, on the other hand, rises at a steady rate. The second set of tests involves data transfer. While the GPU can perform very fast executions, it requires that the data be transferred onto the card’s internal memory. This obviously takes time and I opted to investigate just how much of an edge the GPU loses in accounting for this limitation. In these tests, I created arrays in a separate C++ program, then passed to CUDA for execution. For comparison, I ran FFTW in a similar manner. The results of these tests are given in Figure 4-5. When accounting for data transfer, it is clear that the GPU under-performs the CPU when the arrays are smaller than 105 elements. Greater than this threshold, the GPU attains 10x increase in performance speed.

4.3.2.2 Discussion

While I have not conducted the ﬁnal step of the investigation, full convolutions, it is clear

that the GPU is not suitable for dramatically improving the speed of the SPIFS-POC algorithm. On both plots, a dotted blue line denotes the size of the SPIFS-POC 128x128 pixel2 EMCCD array. In the case of raw computational speed, the GPU barely edges out the CPU but in the

case where data transfer issues are addressed, it under-performs the CPU for my application.

67 Figure 4-4. Comparison of GPU and CPU performance for computing raw FFTs. Memory is only allocated before the executions began. The dotted blue line denotes the size of a 128x128 array.

Therefore the small nature of the EMCCD image would not benefit from the highly parallel nature of the GPU architecture and SPIFS-POC would actually run slower through the GPU. Furthermore, it appears that in general, GPUs do not currently provide a significant benefit for FFTs on any size less than ≈ 104 elements. They provide the best increases in speed for large arrays. These findings are largely consistent with Merz (2007) who performed similar, albeit more detailed, investigations of this question with an NVIDIA Quadro FX 4600. The FX 4600 in an industrial-grade GPU with 112 processors resulting in about half the computing power of the GTX-280. This is reflected by the fact that Merz (2007) comes to the same conclusions as this investigation, but found that threshold to be about a factor of two times more pixels for the FX 4600. GPUs are extremely powerful tools, and in the cases of large image convolutions, they provide a tremendous reduction in computation time. However, on smaller scales they provide

68 Figure 4-5. Comparison of GPU and CPU performance for computing full FFTs. Memory is allocated before each execution and data is transferred from a host program to the FFT program. The dotted blue line denotes the size of a 128x128 array. little utility. It is likely that this new technology will develop further and it is worth following the progress for use in astronomical instrumentation. 4.4 Driver Initialization

A parameter that is easy to overlook when speed is not an issue is driver initialization. Normally hardware takes only a few milliseconds to initialize so it is rarely noticed. Unfortunately with the SPIFS-POC routine, these initializations can be quite time consuming and greatly reduce the efﬁciency of the code. A prime example of the importance of proper driver initialization is with the EMCCD. The ideal program would have the EMCCD execute an exposure whenever the loop is ready to start over again. However, the detector does not support a continuous mode whereby arbitrary exposure requests can be sent at any time. As a result, to take an exposure at an arbitrary time requires reinitializing the camera– a task which takes up to 10 ms. The solution which best presented itself was to run the detector in what Andor calls the “kinetic” mode. The detector is

69 set to continuously take images of a particular exposure time and in real-time the control code can grab the most recent image from the image buffers. This mimics the desired result but has the downside of phasing errors. If the request for the most recent image is made just before the most

recent image is available, the code will grab the previous image which could have been taken an exposure time plus a read time in the past. This represents an extreme hypothetical case and in general the “kinetic” mode is much faster than single exposure mode. As a counter example to the efﬁciency of “kinetic”-style modes, the digital-to-analog card performed best under opposite circumstances. In an early version of my code I thought the system could save time by running in a continuous mode– i.e. initialize the driver once and feed commands to the FSM whenever they were available. Unfortunately in practice I found that when the commands were sent through the DAC, the on-board buffering actually produced nearly 10

ms of additional delay. Therefore, the optimal conﬁguration for the DAC is to re-initialize the card every cycle. This requires 1.7 ms which adds to the loop cycle budget but it is a factor of 5 faster than in continuous mode and requires no additional syncing.

4.5 Windowing

Due to the sub-optimal properties of the FSM, it is important to try to limit its motions. While much of the ringing mentioned in Chapter 2.1.2 can be damped out, there is still a small overshoot that depends on the amplitude of motion. Additionally, while the FSM slews quickly to a target, it still takes time to reach a given location. So between these two concerns, it becomes useful to limit the extraneous motions imposed upon the FSM. One way to possibly prevent the FSM from jumping from one extreme location to the next is to “window” the available space the FSM can move to. This would optimally be achieved by selecting the best speckle, centering on it and then conﬁning the accessible area from which the next brightest speckle would be selected. To ensure that the system does not select a poor region of the overall speckle pattern and hold that location, there would be a reset built-in where after N exposures the whole image is used once again to ﬁnd the best speckle.

70 There is a large range of possible windowing values and number of exposures that can be used for this purpose, but I examine six practical cases:

1. Window=64x64 pixels2, N = 10

2. Window=64x64 pixels2, N = 100

3. Window=32x32 pixels2, N = 10

4. Window=32x32 pixels2, N = 100

5. Window=16x16 pixels2, N = 10

6. Window=16x16 pixels2, N = 100 To test the windowing, I used data collected during the KPNO 2.1-m observing run described in Chapter 5.1. The high-time resolution speckle data taken from the EMCCD were used to simulate the performance of the SPIFS-POC algorithm. I simulated this effect by assuming a particular image (depending on the N parameter) is the “ﬁrst” image in a particular sequence. I then placed a window on the location of the best speckle and further best speckles in

N subsequent images had to be located in this region. The images were then shifted and added based on the confined information. Rather than attempt to calculate Strehl ratios, I employed a simple flux ratio which was referenced to a “seeing” limited image composed by stacking all the speckle images with no shifting. I placed a diffraction-limited aperture n the peak of the “seeing” limited image and the flux within that aperture was defined as the baseline. I also applied the same aperture to images produced by stacking speckle patterns through shift and add. I define the

ratio of the fluxes f luxspeckles/ f luxseeing as the flux ratio and use it as a proxy for Strehl ratios. In the optimal case, I want the window and N values to have high flux ratios as well

as preserving the resolution gains. I give the results of these test in Table 4-3. My analysis reveals that windowing has almost no effect on resolution whatsoever. This means the only real parameter of concern is the ﬂux ratio. In all of the N = 100 cases, the ﬂux is reduced by >10%,

which is too large a hit for an already low Strehl ratio system. N > 10 suffers from too high a

71 degradation in ﬂux ratios while N < 32 over-constrains the image. This means that the 32x32 window with N = 10 provides an optimal windowing algorithm.

Table 4-3. All simulations assume a 2 ms lag between actual speckle pattern and commands sent to the FSM– a nearly ideal SS system. Window Iterations Star FWHM FWHM Res Gain Res Gain Flux ratio (x) (y) (x) (y) 64x64 10 hr4905 3.44 3.96 14.2 11.4 3.98 64x64 10 hd122574 3.08 3.13 15.2 15.2 4.07 64x64 10 bd2512 2.73 2.99 14.2 15.9 4.36 64x64 100 hr4905 3.44 3.94 14.2 11.5 3.93 64x64 100 hd122574 3.07 3.17 15.3 15.2 4.07 64x64 100 bd2512 2.72 2.98 14.2 15.9 4.32 32x32 10 hr4905 3.40 3.91 14.3 11.6 3.71 32x32 10 hd122574 3.04 3.09 15.4 15.4 3.85 32x32 10 bd2512 2.69 2.96 14.3 16.0 4.28 32x32 100 hr4905 3.37 3.89 14.5 11.6 3.38 32x32 100 hd122574 3.05 3.06 15.4 15.5 3.47 32x32 100 bd2512 2.70 2.97 14.3 15.9 3.72 16x16 10 hr4905 3.35 3.87 14.5 11.8 3.11 16x16 10 hd122574 2.97 3.09 15.8 15.6 3.16 16x16 10 bd2512 2.66 2.98 14.5 16.0 3.77 16x16 100 hr4905 3.36 3.85 14.5 11.8 2.58 16x16 100 hd122574 2.91 2.97 16.5 16.0 2.39 16x16 100 bd2512 2.67 3.03 14.4 15.7 2.83

4.6 Detector Rotation and Solution

When performing tests of the system, offset errors kept cropping up. After careful analysis,

I found that the reason these error kept occurring was because there was a ≈1-2 degree rotation of the EMCCD detector in its housing. Normally this is something that can be calibrated out in post processing, but for SS it needs to be accounted for in real time. If not, there will be a disjoint between commands sent to the FSM and the physical location of the best speckles. As a check to make sure this was not due to the optics or a curvature issue, I commanded the FSM to move to every pixel location on the detector and recorded the resulting, real position.

This test demonstrated that there is a rotation and that ﬁeld curvature is not a signiﬁcant issue for the optical system.

72 While at first it appears that a simple rotation matrix will easily solve to system, there are non-trivial difficulties that make this solution non-ideal. The first problem is that the gain values are different for the x and y directions, i.e. the pixels per volt in x is not the same as pixels per volt in y. As a result, there is an implicit difference in axis definitions making the system non-Cartesian. Second, due to difficulties in optical alignment, the rotation axis is not aligned with the voltage zero points. Therefore this offset (also dependent on the different axes gains) has to be accounted for. To solve for the rotation I went for a simpler solution. The system can be described as:

x0 = x + c1y (4–1)

y0 = y + c2x (4–2)

In this case x0 and y0 are the actual pixel shifts on the detector while x and y are the requested pixel shifts. Since the rotation appears to be linear, c1 is the slope of a ﬁt between the number of pixels shifted in x due to a motion in y. c2 is the opposite: the slope of a ﬁt between the number −1 of pixels shifted in y due to motion in x. If the gains were the same, c1 = (c2) .

Using this matrix, it is possible to solve for x and y in terms of x0,y0,c1 and c2. This solution is optimal because x0 and y0 are known from the speckle selection algorithm and c1 and c2 can be found through measurement. When this solution is applied to the control loop, the residual rotation errors accounts for less than one pixel offset and the FSM can be directed to exact pixel locations.

4.7 Final Loop Speed and Code Options

When all the corrections and optimizations are applied to the SPIFS-POC control loop, the system is capable of running at a maximum of 125 Hz. A breakdown of the various loop components is given in Table 4-4. I note that this does not include any time for speckle exposure. When speckle exposure times are included, the loop speed is <125 Hz. While this meets the minimum requirement of

> 70 Hz, it only does so by a few ms. This is troubling because 30 ms is a generous estimate of

73 Table 4-4. The timings of the various components that make up one cycle time. Component Time (ms) FSM ringing correction 4.50 Speckle Selection 1.33 Driver initializations 1.70 Other system overheads 0.50 Total 8.03

the coherence time of speckle patterns. If the wind speed increases or r0 decreases, the coherence time can drop to 10 ms or less. An additional feature that is included in the SPIFS-POC control code is spooling. While the EMCCD is acquiring speckle data, it is able to spool the data to the hard disk in real time with no noticeable drop in performance. The user interface also allows the user to implement EMCCD cooling as well as adjustment of the EM Gain. 4.8 Initial Lab Results

To ensure that all the components were working properly and communicating with one another, I tested the bench top version of the SPIFS-POC with the turbulence generator described in Chapter 3.4. The turbulence generator turned slowly with a laser shining through it to produce

speckle patterns. I present the lab testing results in Figure 4-6. A variety of speeds for the loop were tested but for the images in Figure 4-6 the loop speed was 63 Hz (this is slower than the optimal 125 Hz because of exposure times as well as the fact the version of the code used was not completely optimized). In the left panel, a “seeing” limited halo is produced with SPIFS-POC off. In the right image a similar halo is present but with a sharp, “diffraction-limited” spike in the center. Total integration time for both images was 100 seconds to average over turbulence produced by the phase screen. A more quantitative approach is given in Figure 4-7 where a 1D slice through the brightest part of the image is presented. The left panel contains a slice when SPIFS-POC is off. A roughly Gaussian-shaped PSF is present and has a measured FWHM of 9.4 pixels. In the right panel, with

speckle stabilization on, a similar broad halo is present, but a sharp, diffraction-limited spike is

on top. Fitting a Gaussian to the spike reveals it has a FWHM of 2.6 pixels– nearly a factor of

74 A B

Figure 4-6. Images of in-lab speckle stabilization. In (a) SPIFS-POC is off and the speckle pattern is smeared out over the course of 100 seconds of integration producing a seeing limited image. (b) SPIFS-POC on with the same exposure time. The result is a sharp spike in the center surrounded by a diffuse halo similar in size to the left image.

A B

Figure 4-7. Cross sections of the PSFs produced in laboratory speckle stabilization. In (a) SPIFS-POC is off and in (b) SPIFS-POC is on with the same exposure time. The result is a sharp spike denoted in red.

75 four improvement in spatial resolution. The FWHM of the spike is consistent with the FWHM of typical speckles in the turbulence generator. The turbulence roughly simulates good seeing on a medium telescope in terms of speckle density. A larger halo would be expected in actual observations meaning that the phase mask does not produce very much low order turbulence. From these ﬁgures, it is clear that SPIFS-POC functions in the laboratory and provides a concrete example of speckle stabilization in action.

76 CHAPTER 5 OBSERVATIONS WITH THE SPIFS-POC Our research group successfully used the SPIFS-POC on three separate observing runs.

The ﬁrst two were at the Kitt Peak National Observatory 2.1-meter telescope and were primarily aimed at initial testing and tuning of system parameters. A third run at the 4.2-meter William Herschel Telescope was conducted to test closed-loop operating and attain high-angular resolutions. In this chapter, I discuss on-sky observations made by the Stabilized sPeckle Integral Field Spectrograph Proof-Of-Concept (SPIFS-POC) instrument. In §5.1 I discuss the observations

conducted at the KPNO 2.1-meter telescope. §5.2 covers the 4.2-meter WHT observations and ﬁnally, in §5.3 I present a performance evaluation of the SPIFS-POC.

5.1 2009A/B Observations at the KPNO 2.1-m

In the left of Figure 5-1, I present a photograph of the ﬁnished instrument as mounted on

the KPNO 2.1-m telescope and provide an annotated schematic of the instrument in the right of Figure 5-1 where the locations of the various components are shown We conducted the ﬁrst set of 2.1-m observations with the SPIFS-POC in 2009A (June 8th - June 14th) and the second in 2009B (August 6th - August 10th) for a total of 11.5 nights . These observations were primarily characterization runs designed to test the overall functionality of the system and assess the validity of the design. In 2009A I was accompanied by Dr. Joseph

Carson and acquired speckle data from stars of various brightnesses. Table 4-1 summarizes the targets observed. The information from these data were used to tune the system for future speckle

stabilization and much of the analysis given in Chapter 4.2 and Chapter 4.5 is based on these observations. The 2009B run allowed me to test loop-closure. Unfortunately, due to insufﬁciently optimized code, the functioning loop speed was 50 Hz for this run. Furthermore, the combination of this slow loop speed and poor seeing conditions at the KPNO 2.1-m (average seeing of 1”.5)

resulted in low-quality corrections.

77 A B

Figure 5-1. On the left: photo of the SPIFS-POC mounted on the KPNO 2.1-m telescope. On the right: photo of the key components of the SPIFS-POC with labels.

Despite poor observing conditions, observations of the binary star system 65 tau Cyg proved encouraging. We used the SPIFS-POC to observe this system in a closed-loop mode at 50 Hz (the low speed was largely due to driver initialization issues discussed in Chapter 4.4). While this loop speed is signiﬁcantly slower than the coherence time of the atmosphere we were able to improve the image quality enough over seeing to discern the location of a known companion. I present an image of this binary star both in the seeing-limited and speckle stabilized case in the z’ ﬁlter in Figure 5-2. The system has a known separation of 0”.77 and a position angle of 236.55 deg. Both observations were 100 seconds long and we took them in seeing of 1”.6. The left image (a) is a seeing limited image with the SPIFS system turned off. On the right (b), we present the image with speckle stabilization enabled. The two stars (which have a three magnitude difference in brightness) are cleanly resolved at a separation and position angle matching previously published results (Mason et al., 2001). To produce the image in (b), a seeing-limited PSF was subtracted from the primary star to emphasize the secondary in the residuals. The physical separation and orientation match known values to within 2σ and hint at

78 A B

Figure 5-2. SPIFS-POC observations of 65 tau Cyg. The left image (a) is a seeing limited image with the SPIFS system turned off. On the right (b), we present the image with speckle stabilization enabled. the high angular resolution potential of SS. These results proved essential to being given time in 2010A for the WHT. Besides partially successful loop closure, one of the key tests I was able to conduct was to produce an estimate of the effect of cosmic ray strikes on the observations. Between observations of BD 2512 and HD 122574, I had 300,000 speckle images to analyze. In all these images, the typical brightest pixel in a “best-speckle” was between 1,000 and 2,000 counts. Therefore, saturation would be indicative of a cosmic ray. I searched the data and found only one saturation event in the whole sample. This would indicate that cosmic ray events are not a major issue for speckle stabilization. This is not unreasonable given that the exposure times are much less than 1 second and that the area of the detector is 0.09 cm2.

5.2 2010A Observations at the WHT

We used the SPIFS-POC in the GHRIL lab at the William Herschel Telescope on the nights of April 28th - May 1st, 2010. Professor Stephen Eikenberry joined me for this observing run where the proposed goal was to look at symbiotic stars. Unfortunately throughput issues

79 prevented us from having adequate ﬂux for speckle stabilization on our science targets. One of the primary reasons we did not collect as many photons as expected was that the fold mirror sending light into the GHRIL has a very low reﬂectivity (Ian Skillen, private conversation). A

second reason was that our observation run coincided with the calima (dust storms blown from Africa) which caused up to a magnitude of extinction. Additionally, the de-rotator which was not accounted for in observation planning is simulated to have a throughput of 90%, but this value has not been empirically tested (Rey, private conversation). As a result, we were constrained to observe brighter targets but were still able to acquire a great deal of useful speckle stabilization data on single and double stars. Because of improvements in the code, we were able to close loop at 100 Hz. Additionally the better seeing at the site (≈0”.5) meant that speckle patterns were longer-lived and thus easier to stabilize.

Using multiple binary and double-star systems separated by many arcseconds, we were able to calculate the plate scale and orientation of the two detectors. For the EMCCD, we found the plate scale to be 18.3 mas/pix and for the SBIG the plate scale came out to 22.2 mas/pix. The relatively close agreement between these two values matches my aim in design as the

diffraction-limit for a 4.2-meter telescope at 0.8µm is ≈40 mas. Therefore, the SPIFS-POC plate scale Nyquist-samples this resolution. 5.2.1 Single Star Observations

In Figure 5-3, I present cross-sections of stellar PSFs produced with speckle stabilization on and off. I acquired the data with the SBIG science camera through a 3 nm ﬁlter center on 846 nm. I took three ten-second images and present the median averages of the results. The speckle data acquired with the EMCCD for stabilization ﬁlled a broader wavelength range spanning Sloan z’

and loop speed was 100 Hz. The top row depicts observations of PSF Star 1 while the bottom row is of PSF Star 2.

In the left-most images of Figure 5-3, cross-sections of seeing-limited (speckle stabilization

off) observations are presented. On top of these cross-section, Gaussian ﬁts to the data are also

80 Figure 5-3. Observations of two PSF stars with both SPIFS on and off. The top row presents observations of PSF Star 1 and the bottom row presents observations of PSF Star 2. The dotted lines in all images correspond to the Gaussian ﬁts. The FWHM value quoted in each plot is in units of pixels.

81 presented. A Gaussian ﬁt provides a good estimation of the shape of the PSF and indicates that seeing for Star 1 was 0”.432 and seeing for Star 2 was 0”.522. The middle and right ﬁgures show the result of SS. As predicted by my simulations in

Chapter 2 (Eikenberry et al., 2008; Keremedjiev et al., 2008), there is a sharp peak sitting atop a halo. The halo is of size comparable to the seeing-limit. The middle panel demonstrates the fact that a single Gaussian fit is not sufficient to characterize the PSF and results in an RMS nearly three times greater than the fit to the seeing-limited case. The largest residuals to the fit are seen in the excess fluxes in the central parts of the PSF. These excesses are signatures of speckle stabilization. The rightmost panels of Figure 5-3 present a fit of two Gaussian functions atop one another. The fit was made by simultaneously solving for both functions using mpfitfun from the IDL

Astronomy User’s Library1 . This fit is much better and yields additional information about the SS PSF. While there is still some excess in the center of the PSF, the fit produces an RMS nearly identical to the single Gaussian fit of the seeing-limited data. In particular, the FWHM of the stabilized speckles is 133 mas for Star 1 and 165 mas for Star 2. This means speckle stabilization produced a factor of 3.25 improvement in resolution over seeing for Star 1 and 3.16 times better resolution in Star 2. In fact, the cores have FWHM only 3-4 times greater than the diffraction-limit at this wavelength. However, given that there is excess flux at the center of the stabilized speckle PSFs in Figure

5-3 not ﬁt by a Gaussian shape, I measured the FWHM making no assumptions about the overall

shape of the core. To make this measurement, I first subtract off the halo so that only the sharp core remains. I then found the half maximum of the peak intensity and performed a linear fit to the data around that point. This fit gave me the pixel location half maximum and performing the fit for the other side of the PSF gives me a direct measure of the FWHM. For Star 1, the FWHM is 85 mas and for Star 2 it is 99 mas. Therefore, the direct measurement of the FWHM produces

1 http://idlastro.gsfc.nasa.gov/

82 a tighter core than assuming a Gaussian shape. This is expected as the ﬁts seen in Figure 5-3 do not account for the peak intensity. Using these values, I ﬁnd that the SPIFS-POC was able to ≈5 times better resolution than the seeing limit for both stars. It also means that Star 1 was approaching 2λ/D. Another interesting note from Figure 5-3 is the fact that the FWHM of the underlying PSF in the SPIFS-on case is larger than the seeing limit. In both cases, the halo is 1.3 times wider than the seeing limit. This effect is expected in the event of speckle stabilization and was predicted in Keremedjiev et al. (2008).

5.2.2 Observations of WDS 14411+1344

In addition to observations of single stars, we conducted observations of the known binary star system WDS 14411+1344. These observations were important to conduct because cleanly resolving binary components in an otherwise unresolved system unambiguously demonstrates whether or not the technique works. WDS 14411+1344 is a binary star system with well-characterized orbital parameters. At the time of observation, the system was expected to have a separation of 0”.543 and a position angle of 294.35 degrees.

In Figure 5-4, I present an image of the star with SS off and SS on. The data presented were acquired with the SBIG camera in the narrow-band 846 nm ﬁlter. Exposures were 5 seconds long and the images used for analysis were the median averages of three exposures. The system has been displayed with the same intensity scale so that differences are more readily apparent. In (a) of Figure 5-4, I show that in the seeing limit, the two stars are clearly unresolved. While there is elongation in the direction of the semi-major axis, there is no way to distinguish between the two components. On the right side, speckle stabilization clearly resolves the system.

Analysis of the image reveals that the measured separation is 0”.577 and a position angle of 294.62 degrees. Therefore there is a good agreement between the observed system parameters and the theoretical expectations.

83 A

Figure 5-4. Observations of the binary star WDS 14411+1344. (a) comprised of two images. The left image is the seeing-limited observation while the right image is the SPIFS-on observation. The scale of the ﬁgure is the same for both images. To heighten the resolving power of SPIFS, we present a contour plot of the same image in (b). From these ﬁgures, we can see that SPIFS was clearly able to resolve to two components of the binary system while in the seeing-limit, they are blurred. The measured separation was 0”.577.

84 5.3 System Accuracy

As a way to characterize the performance of the SPIFS-POC, I examined the accuracy of the system. In particular, I want to see how often the best speckle was actually located at the desired position. To accomplish this, I spooled data from the EMCCD to the hard-drive while speckle stabilization was in progress. Tests of spooling both in the lab and on the mountain revealed

no apparent difference in data quality when spooling was enabled. Spooling is advantageous because, as mentioned above in Chapter 4.7, the EMCCD is acquiring data continuously, not just when the loop is ready. As a result, with short exposure times <0.5 ms there are >4 frames per loop. Using this oversampled data, I can determine what fraction of the time SPIFS-POC was centered on the best speckle and how accurate the FSM was in getting there.

I give the results of this analysis in Figure 5-5. On the left, I show a histogram of the offset between the nominal speckle stabilization and the actual location of the best speckle. For the SPIFS-on case (the solid line) there is a clear spike at 1 pixel offset that dominates the histogram.

The right part of Figure 5-5 is the cumulative distribution of the offsets and from these data we clearly see that the offset is < 2 pixels more than half the time.

I also plot the seeing-limited case (dotted line) in Figure 5-5. We took the seeing-limited data from the same star, just before the we acquired the SPIFS on data. As such, we expect atmospheric conditions to be nearly identical. With the seeing-limit, the data are markedly different. There is a wider distribution in offsets and the peak occurs around 5 pixels. Looking at the cumulative distribution in the lower plot, I show that in the seeing-limit the offset is < 7 pixels only half the time. The difference between these two data sets highlights the fact that our speckle stabilization system does bring the best speckles to the center of the FOV much more often than in the seeing limit. This means the SPIFS-POC was functioning in a successful closed-loop mode. However, the histograms in Figure 5-5 also show speckle stabilization was not functioning at optimal levels. Having offsets of 1 pixel or more only serves to degrade the image quality and is likely

85 Figure 5-5. Analysis of the accuracy of the SPIFS-POC. On the left is a histogram of offset values between the best-speckle and the optimal SS location. The solid line is for SPIFS on and the dotted line is for SPIFS off. On the right we show the cumulative distribution of the data. one of the key reasons why the 2010A observations only achieve 3λ/D performance (although this will be discussed in more detail in Chapter 6). As an interesting check, I note that the half-point for the cumulative distribution in both cases (2 pixels for SPIFS-on and 7 pixels of SPIFS off) roughly matches the half-width half maximums measured in Figure 5-3 (for SPIFS on, the HWHM was ≈3 pixels and for the seeing limit it was ≈10 pixels). Therefore the half point values appear to correlate with the sharpness of the core in the ﬁnal image.

86 CHAPTER 6 FUTURE PLANS AND DEVELOPMENT OF THE S3D From the previous chapters, I have been able to demonstrate that speckle stabilization is a viable technique for producing images at higher resolution than the seeing limit. Specifically, the sharp cores in the single-star observations and the ability to resolve WDS 14411+1344, show that SS has the potential to acquire high spatial resolutions in the optical. However, I note that there are several limitations with the current system (SPIFS-POC) and it will likely be the next generation of SS instrument, the Stabilized Speckle Science Demonstrator (S3D), that will have high scientific merit. This future instrument will apply the lessons learned from the SPIFS-POC and enable scientific inquiries to be undertaken. In this chapter, I will discuss potential upgrades and improvements to the SPIFS-POC. In

§6.1 I will address loop speed and latency effects and in §6.2 I will address FSM accuracy. §6.3 covers the gains possible through the employment of a high speed shutter and §6.4 address a new science detector and atmospheric dispersion corrector ADC. Finally in §6.5 I discuss how the S3D will incorporate these improvements as well as its timeline.

6.1 Loop Speed and Latency

One of the ﬁrst, obvious limitations of the SPIFS-POC is the closed-loop speed of the entire system. During the 2010A run, in addition to 100 Hz, I tested the loop at 50, 70 and 80 Hz. At all these other speeds, little-to-no improvement was observed over the seeing limit. This seems to indicate that the best speckle lifetime is on the order of 10 ms in general agreement with Kern et al. (2000). As a result, the ideal loop should work at least twice as fast, meaning a system

capable of functioning at >200 Hz. As a way to demonstrate this point, I show the effect of latency in the PSF for SS in (a) of

Figure 6-1. Here, using on-sky speckle data taken with the EMCCD, I have simulated lag in the system. The effect of lag was reproduced by ﬁnding the best speckle every n images and use that location to shift and add all subsequent speckle images until n occurs again. By changing n, I can

simulate lags from 2 ms up to several minutes.

87 Figure 6-1. On the left, plot of PSF cross-sections as a function of latency. WE note that the peak ﬂux decreases while the FWHM increases as a function of lag. To highlight this, we present a ﬁt to FWMH as a function of lag on the right. The trend appears roughly linear with a slope of 1.422 mas/ms.

In Figure 6-1 I present a range between no lag and 20 ms of delay (50 Hz). It is clear that the Strehl ratio changes dramatically as a function of lag, but so does the FWHM. In (b) of Figure

6-1 I show the dependence of FWHM on latency. There appears to be a linear trend between the two and a reduced squares ﬁt yields FWMH(mas) = 1.4 × lag + 55 (here lag is measured in milliseconds). This implies that increasing the speed by a factor of 2 over the current operational loop time of 10 ms for SPIFS-POC increases the sharpness by 10%. However slowing the system down by a factor of two results in a 20% degradation in FWHM.

6.2 FSM Accuracy

Since these FWHM are constructed from shifting and adding speckle data taken with the EMCCD, the PSFs should look identical to the ones produced through speckle stabilization on the SBIG. However, there is a large discrepancy between the two. In fact, the SS core appears to be a factor of two larger than in the theoretical, shift-and-add case.

To determine why there was such a discrepancy between the two data sets, I conducted

simulations to attempt to reproduce the SS PSF with speckle data. When analyzing the

88 Figure 6-2. PSF cross-section of our speckle stabilization simulation using data from the EMCCD. We used a lag of 10ms in addition to a random offset to FSM positions. The data match our results from Figure 5-3 fairly closely and demonstrate the current limitations of the SPIFS-POC. differences between the two methods, I found one parameter that shifting and adding speckle data in software does not take into account: uncertainty in the FSM steering. If the FSM does not move to exactly the desired location, the error would manifest itself in the form of random offsets in the SAA location and thus widen the FWHM of the PSF. As revealed in Figure 5-5 (and noted in the ringing solution of Chapter 3.1.2), when speckle stabilization is turned on there is still a 2 pixel inaccuracy in pointing up to half the time. I simulated this inaccuracy by using a Gaussian weighted randomness in the FSM steering with σ = 2 pixels. To force the speckle data to match the SS data as closely as possible, I also factored in a latency of 10 ms. The resulting PSF is presented in Figure 6-2 and it appears that the simulation reproduces the quality of observations acquired with active speckle stabilization.

Therefore, my tests reveal that speeding up the system and increasing the accuracy of the

FSM can greatly improve system performance. What is interesting is that these two factors are

89 related since the FSM is responsible for both the stabilization inaccuracy as well as the largest fraction of the SS loop time (which is devoted to compensating for ringing). The next generation of SPIFS will therefore replace the FSM with one that is both faster and more accurate, resulting

in dramatically sharper FWHMs as well as higher Strehl ratios. 6.3 High Speed Shutter

In addition to a new FSM, a potential upgrade worth investigating is the installation of a high-speed shutter (HSS) for the science channel. If a shutter capable of opening and closing at >200 Hz were employed, S3D would effectively be able to do real time lucky imaging. This would be accomplished by rapid assessment of the quality of speckle patterns to determine whether the shutter should be open or closed. Various thresholds could be used so that only high quality data pass through to the science channel. I have simulated the effect of a HSS in Figure 6-3 and see there is a dramatic difference in the Strehl ratio as a function of image quality. In fact, the peak value of the top 1% of images

is some four times greater than with 100% of images used. This, of course, is not altogether surprising given that lucky imaging teams have been exploiting this fact as the basis of their instruments. However, it does mean that a high-speed shutter could greatly improve the image quality in a SS system.

6.4 Science Channel and ADC

Another important improvement that needs to be made over the SPIFS-POC is replacing the science channel. The SBIG ST-237 currently used is good for testing and proof-of-concept, but has a high read noise, long read out time and a small field of view. Therefore, for the next generation SS tool, we require a proper science imager. There does not have to be an IFS in place as the technique still needs more refinement before such an investment can be justified. The

continued use of narrow band ﬁlters can mimic the results of an IFS just with more on-sky time required. Related to high quality imaging is the need for an atmospheric dispersion corrector (ADC).

Atmospheric dispersion occurs because there is a small refractive index to the Earth’s atmosphere

90 Figure 6-3. PSF cross-section as a function of fraction of images used. The PSFs have all be normalized such that they all simulate the same total number of images used. It is clear that using only 1% of the images results in the highest-Strehl images while using 100% (as in the SPIFS-POC) results in lower Strehl ratios. We note, however, that FWHM is not strongly dependent on the fraction of images used, so 100% of images used still has the resolutional gains of 1% used.

and it disperses the light. Under normal, seeing-limited conditions at low airmass atmospheric dispersion is not usually a large effect. However, at high angular resolutions it must be taken into account. To demonstrate the severity of the issue I have calculated the differential refraction as a function of wavelength for three different airmasses. The calculations are based on equations in Filippenko (1982) and I plug in values for La Palma speciﬁcally. Temperature and pressure values were taken from Lombardi et al. (2006) and Lombardi et al. (2007) respectively. The

resulting differential refraction is presented in Figure 6-4. This Figure clearly demonstrates the need for an ADC. Even at low airmass, the offset between 0.5µm and 1.0µm can be nearly 0”.5. Since the pixel scale will be <<0”.5, this issue needs to be addressed.

91 Figure 6-4. Plot of differential refraction as a function of wavelength for three different airmasses at La Palma. Note that even at low airmass, the offset can be as great as 0”.5.

6.5 S3D

From the above sections, it is clear that with relatively minor modifications to the SPIFS-POC, it could turn into a scientifically valuable instrument capable of near diffraction-limited angular resolutions in the optical from the ground. It has already produced resolutions of 3λ/D on the 4.2-m WHT and on larger telescopes it is possible that the next generation instrument will be able to observe targets with resolutions as fine as 15 mas.

The next envisioned step for SS is the Stabilized Speckle Science Demonstrator (S3D). Professor Eikenberry and I have written and submitted an NSF ATI proposal for funding to build the S3D which aims to incorporate all of the improvements from above. The ﬁrst such upgrade will be a piezo stack FSM capable of > 1 kHz operation from Physik Instrumente. The proposal also calls for a high quality 2k x 2k detector. There are several potential vendors that supply this type of CCD, but the S3D will beneﬁt enormously from increased sensitivity, decreased noise and a faster read out. The goal for the upgraded system will be closed loop operation at >250 Hz-

easily compensating for the variable speckle patterns. The eventual inclusion of an integral ﬁeld

92 spectrograph will only increase the scientific potential of SS, but that will likely be the generation of instrument after S3D. Finally, the S3D even has a place for the SBIG detector. At the high resolutions the S3D will be operating at, both the EMCCD and science channel will have a very small field of view. From observing experience, I know that simply finding the targets and steering them onto the EMCCD was a major time consumer. Being able to rapidly find the target and move it into place would decrease overheads enormously. This is where the SBIG fits in. It will become an acquisition camera for the S3D and will sample a wide FOV. It is a good use for the system and a solid way to re-purpose old equipment.

93 CHAPTER 7 A COMPARISON BETWEEN LUCKY IMAGING AND SPECKLE STABILIZATION FOR ASTRONOMICAL IMAGING Since the current SPIFS-POC and its replacement the S3D both have optical imagers for their science channel, it is worth comparing speckle stabilization to traditional speckle techniques like SAA and lucky imaging purely in imaging mode. I note that there are inherent differences between SS and speckle techniques and my goal is to determine if these differences result in a significant advantages for one or the other. One of the differences I am interested in is the number of readouts each technique requires. SS only needs to read out the science camera a few times during observations, whereas lucky imaging has to read out thousands of times. Even though the read noise on the EMCCDs employed by speckle teams is typically very low (on the order of 0.2e−/pix), it is still present and I hypothesize it can become a significant noise term when observing faint targets. Another term I think might have an effect on sensitivity is the additional √ 2 noise term present in images taken with an EMCCD. This stochastic noise is introduced in the readout process and can only be worked around in photon-counting mode. Therefore, I present simulations to determine if a Speckle Stabilization imager has the capability to overcome these features of lucky imaging and SAA systems in a way that is advantageous to an observer. In §7.1 I address the framework devised for comparison and in §7.2 I present the results and discussion. In §7.3 I summarize the major findings and outline the advantages and disadvantages to the various techniques. 7.1 Methods

7.1.1 Speckle Stabilization Simulations

To compare Speckle Stabilization to SAA and Lucky Imaging, we need to ensure our estimations of the various parameters are accurate. We chose to conduct our comparison with a simulated 2.5-meter telescope. This particular size was chosen because at larger apertures, while Lucky Imaging and SS both produce the same spatial resolutions in the core, the Strehl ratios

and usable fraction of speckle images for Lucky Imaging decreases dramatically. As a result, a

94 2.5-meter telescope is one where Lucky Imaging is highly effective in terms of Strehl ratios and resolution gain. Strehl ratios of 0.3 are common in Lucky Imaging observations in a 2.5-m telescope, but we need to have a good understanding of the Strehl ratio of SS at this aperture size. To simulate the Speckle Stabilization capabilities, we have carried out a range of simulations using model atmospheres based on the turbulence spectrum of Kolmogorov (1941). The adaptive optics group at the Jet Propulsion Laboratory has used a similar algorithm extensively and has verified its accuracy in comparison with actual performance results with the Palomar Adaptive Optics system (PALAO). The code used to produce the SS PSF is the same code detailed in Chapter 2. Five hundred distinct speckle patterns (frames) were produced to form an SDSS i’=0 mag star as produced by a 2.5-meter telescope. Each speckle pattern was sampled at five different wavelengths (0.70µm, 0.75µm, 0.80µm, 0.85µm, and 0.90µm) to account for the broadband nature of the imaging. To simulate Speckle Stabilization, we found the “best” speckle in each frame using a 2D cross-correlation between the speckle pattern and an ideal PSF. This ideal PSF was produced using the same code but with no turbulence applied . We then shifted the images according to the location of the best speckle and stacked them. To contrast to seeing-limited observations, we simply added the frames on top of one another with no shifting whatsoever. We present the results of the simulations in Figure 7-1. There we demonstrate that the stabilized image core has a FWHM similar to the diffraction-limited case. Analysis reveals that the SS PSF is only 6% wider than the diffraction-limited case. Strehl was measured by comparing to an ideal PSF also produced by the code. We used to FWHM of the ideal PSF to define an aperture where pixels intensity would be measured. The Strehl was measured as the intensity within the aperture measured for the SS image divided by the intensity measured within the aperture of the ideal image. This gives a Strehl ratio of 0.085 which is similar to the Tubbs et al. (2002) measured Strehl ratios of ≈ 0.06 in Lucky Imaging

95 Figure 7-1. Cross sections of the PSF produced by Speckle Stabilization, the seeing limit, and the diffraction limit. The diffraction-limited image has been arbitrarily scaled to demonstrate that the SS PSF has a similar FWHM. Note that the seeing-limit has a similar FWHM to the extended halo of the speckle-stabilization image. observations when using 100% frame selection (SAA). Therefore we ﬁnd these simulations conﬁrm that the SS PSF is quite similar to the SAA PSFs produced in real observations. 7.1.2 Comparison Between Methods

In order to compare SS to SAA and Lucky Imaging, we will examine theoretical signal-to-noise ratios as a function of target magnitude. Since we wish to make the comparison as realistic and direct as possible, we use parameters from current Lucky Imaging systems like LuckyCam, AstraLux and FastCam (Law, 2007; Hormuth et al., 2008; Oscoz et al., 2008) and use a comparable standard CCD for Speckle Stabilization. Current Lucky Imagers use EMCCDs of sizes around 512 x 512 pixels2, so we will model a standard CCD of this size for the SS as

96 well. We note that the EMCCD used for the actual speckle stabilization would be a 128 x 128 pixel2 CCD and is thus capable of much faster readouts. To perform the comparisons between the two techniques, we employ the following equation

for Lucky Imaging:

ωαβ f T S/N = q Exp (7–1) 2 2(ωαβδ f TExp + ωnpix(α fskyTExp + DTExp + nExpr )) Here f is the number of photons per second received from a star of a given magnitude at a 2.5-meter telescope in the Sloan i’ ﬁlter. The fraction of photons that are transmitted through the optics of the system is α which we assume to equal 0.5. The fraction of photons that are present in a diffraction-limited core is given by δ. We assume that there are perfect optics producing an Airy pattern– as a result, we assume δ = 0.838. The Strehl ratio is given by β. For Lucky Imaging we assume a Strehl of 0.30 for this telescope diameter at 1% frame selection and Strehl=0.20 for 10% frame selection (Baldwin et al., 2001; Tubbs et al., 2002; Law, 2007; Baldwin et al., 2008). For SAA (100% frame selection) we assume Strehl of 0.085– the Strehl calculated from our simulations in §2.1 as SAA has a similar PSF to SS. The total time on source is TExp

and is determined by the number of exposures, nExp times exposure length tExp. We assume

nExp = 50000 and tExp = 0.030 seconds meaning the total time spent “on source” is 1500 sec. An exposure time of 30 milliseconds is used because the coherence length of the atmosphere,

generally given by t0 ≈ r0/v (where r0 is the Fried parameter and v is the bulk wind velocity of the dominant turbulent layer (Kern et al., 2000)), is on the order of 30 milliseconds. There is no time assumed for the read out as all current Lucky Imaging systems use frame-transfer EMCCDs and a 30ms is greater than or equal to the read out time for a 512 x 512 pixel2 EMCCD (Law, 2007; Hormuth et al., 2008; Oscoz et al., 2008).

We also use the term ω, which is the fraction of near diffraction-limited images kept,

which we assume to be 0.01 and 0.10 for Lucky Imaging cases and 1.0 for SAA. This choice

97 of ω = 0.01 and 0.10 for Lucky Imaging was made because we wanted to examine the case of best-possible Strehl improvement as well as more typical Lucky Imaging parameters. √ In the noise term, the 2 is a result of the stochastic processes involved in the readout of an

EMCCD. We assume Nyquist sampling so that the central core of the source covers four pixels,

meaning npix = 4. We use fsky to include the effects of sky background. For this model, we assume dark time and use i0 = 19.9 mag/arcsec2 for the sky level. We use D as a measure of dark current and adopt of value of 0.002 e−/pix/sec. Finally r is the read noise is assumed to be 0.2 e−/pix. We chose 0.2 e−/pix because lab tests of our own Andor iXon DU 860 at EM Gain of 300 converged to this value as does the

documentation that came with our camera. We use EM Gain=300 for two reasons. The ﬁrst is that this is a typical value used by non-cryogenic EMCCDs for Lucky Imaging (Femenia,

B. private correspondence). The second reason is that the Solis program written by Andor for the camera will not allow the user to select gain values higher than this number and strongly encourages using EM Gain lower than 300. We note, however, that through the use of the Andor Software Development Kit it is possible to attain higher EM Gain levels through custom written code and discuss the ramiﬁcations of higher levels in §3.1. A similar equation is used for Speckle Stabilization:

ωαβδ f T S/N = q Exp (7–2) 2 ωαβδ f TExp + ωnpix(α fskyTExp + DTExp + nExp,SSr ) The equation is mostly the same as Eqn. 1, but there are several subtle differences in the parameters. In the SS case, ω = 1.0 since no images are thrown out. We also use a Strehl ratio of 0.085 for SS as determined from our simulations above in §2.1. A read noise of 5 e−/pix was √ assumed for the science channel, but the 2 term disappears for the SS calculations. To directly compare these two methods, we need to ensure that the time spent by the telescope per target is the same. By doing this, we deﬁne efﬁciency as the signal-to-noise

(S/N) achieved per observing interval. Where the observing interval is deﬁned as TExp,SS = tExp,SS ∗ nExp,SS. For the SS observations, the number of exposures is calculated by nExp,SS =

98 TExp,Speckle/(tExp,SS + treadout,SS). In this case, tExp,SS is the time it takes to saturate an image or

TExp,Speckle, whichever is smaller. We assume a pixel is “saturated” when there have been 64000

photon events. We have ﬁxed treadout,SS at 1 second as this is the typical time it takes to read out a 512 x 512 pixels2 standard CCD. In its current form, SS acts like SAA as both have similar PSFs and Strehl ratios. Comparisons between these two techniques are valid, but SS compared to the higher Strehl Lucky Imaging cases make less sense. While the low-contrast images are still of high scientiﬁc value, one way to boost the Strehl ratios of Speckle Stabilization systems is the installation of

a high-speed shutter in front of the science camera (Keremedjiev et al., 2010). With a shutter fast enough to open and close at > 100 Hz, a speckle stabilization system would be able ensure only high-Strehl data find their way onto the detector. In this way, a SS would act like a real-time Lucky Imaging selection algorithm. Therefore, we also include models which include a high-speed shutter to compare to the lower frame-selection, higher-Strehl Lucky Imaging data. We refer to this technique as Speckle Stabilization + Shutter (SS+S). The only modifications to Eqn. (2) needed to characterize a shutter-based system are that we change ω = 0.01 and 0.10 to reflect the fraction of Lucky Imaging images typically selected, but conversely we would also get the higher Strehls, b = 0.30 and 0.20. Although for dark current, we would still use the full observing interval as the detector continues to accumulate dark charge with the shutter closed. One further note we wish to address is that of guide stars. For these models, we assume that there is a bright guide star near enough that there is little or no degradation in the image quality of the analysis star. We make this assumption because we are only interested in the theoretical limits of these two techniques and to probe the faint magnitudes of these tests requires a bright, nearby guide star for both techniques. 7.2 Results

We calculated the results of equations (1) and (2) for stars from i’=0 to i’=30 mag and

present the results in Figure 7-2. There are six curves in the top part of the ﬁgure. The red lines

represent Lucky Imaging and SAA while the black lines denote SS and SS+S. A blue dashed line

99 is plotted at S/N = 3– a common detection threshold. In the bottom part of the ﬁgure we present

the efﬁciency ratio, deﬁned as (S/NSS)/(S/NLucky), as a function of magnitude. Values less than 1 denote cases where Lucky Imaging has higher signal-to-noise per observing interval and values greater than 1 denote cases where SS has higher signal-to-noise per observing interval. A blue dashed line is also plotted to show where the two techniques are equal. Here we demonstrate that the technique of speckle stabilization has advantages and disadvantages as compared to Lucky Imaging. For most of the models, SS and Lucky Imaging √ have the same shape and are offset by a factor of ≈ 2. This is to be expected as in the √ non-saturated, non-photon starved middle ground, the biggest difference is the additional 2 term in the noise for Lucky Imaging. Where the noticeable differences occur are in the bright and faint ends. At the bright end, we see that SS and SS+S have bright cut-off points. This occurs

because SS requires integration times long enough to allow the system to stabilize speckles. The current SS prototype operates at 100 Hz and future plans are in the works to operate at 500 Hz

(Keremedjiev et al., 2010). Therefore, we will use 100 Hz as a baseline and require 10 cycles (with the shutter open) to have elapsed to get the minimum necessary corrections. This means we

deﬁne the minimum exposure time as ωTExp,SS = 0.1. Using this convention, we see that SAA can observe targets brighter than i’=6.87, Lucky Imaging at 10% frame selection can observe targets brighter than i’=7.80 and Lucky Imaging at 1% frame selection can observe targets brighter than i’=8.24 whereas the corresponding SS and SS+S techniques cannot. At the fainter end, advantages to SS and SS+S become heightened. We see that speckle

stabilization techniques have higher efficiencies and sensitivities than Lucky Imaging (again where efficiency is defined as S/N per observing interval). Sensitivity is the difference in

magnitudes at the 3σ detection level. Specifically, SS is 3.35 times more efficient and 1.42 magnitudes more sensitive than SAA at the SAA detection limit. SS+S at 10% selection is 2.40 times more efficient and 1.10 magnitudes more sensitive than corresponding Lucky Imaging and

SS+S at 1% selection is 1.28 times more efﬁcient and 0.31 magnitudes more sensitive than the

corresponding Lucky Images. While these values are not excessively large, they are interesting.

100 Figure 7-2. Comparison between SS and SS+S with SAA and Lucky Imaging. Also plotted is a blue line denoting S/N = 3, a common detection limit. On the lower part of the plot are the ratio between S/NSS and S/NLucky. These ratios are the efﬁciency ratios. Also plotted on the lower plot in blue is a line denoting an efﬁciency ratio of 1– where both systems perform the same.

101 The fact that the difference becomes more pronounced with higher frame selection points to the fact that both sky background and read noise are more signiﬁcant in Lucky Imaging than in Speckle Stabilization.

These results are fairly robust. Changing most of the shared parameters like f , α, telescope diameter, etc have little impact on the overall results– doing so only shifts the functions vertically or horizontally. Modifying the saturation limits also has little impact as it only affects where and how large the plateau exists for brighter targets. The biggest factors are the Strehl ratios and the read noise terms.

7.2.1 Read Noise Limit

From the above analysis, we see that SS is able to produce higher S/N values and reach fainter magnitudes. However, this advantage is not particularly large. As a result, we chose to look at modifications that can be made to Lucky Imaging and SAA systems to improve their efficiency. The first modification we examine is adjusting the read noise. One of the primary advantages of L3CCDs and EMCCDs over conventional CCDs is the they have very little read noise. This attribute is a result of the electron multiplication process where very high gain values (10-10000) are involved. This means that a real photon strike results in a very large measurement– far greater than the noise of the electronics. While this fact gives these CCDs very √ high sensitivities, it is also the reason for their additional 2 noise term. In the cases where exceptionally high gain values (g >> 300) are employed, it is possible to reduce the read noise to effectively zero (although this generally requires the use of cryogenically cooled cameras as dark current can have dramatic effects). Therefore, we decided to compare SS to Lucky Imaging in the limiting case where read noise equals zero. We present the results

in Figure 7-3. For the 1% frame selection Lucky Imaging data, there does not appear to be any truncation all the way down to the detection limit. In the SS+S 1% data, a truncation around i’=20 still occurs when sky background begins to affect the data. These models show that no

read noise Lucky Imaging is actually a factor of 1.28 times more efﬁcient than SS+S at the SS+S detection limit and is 0.41 magnitudes more sensitive.

102 Looking at the SS vs. SAA case, however, a slightly different picture emerges. Here the read noise in the SS data is less prevalent and sky background appears to affect both models. SS manages to be 1.36 times more efﬁcient and 0.36 magnitudes more sensitive, but we note that

these values are about a factor of two less than with standard read noise in the EMCCD. The case of 10% frame selection actually is somewhat of a hybrid of these two extremes as SS+S and Lucky Imaging models move toward convergence at the faint end. Therefore, we see that reducing the read noise to zero removes much of the advantage of Speckle Stabilization techniques over their partner speckle imaging techniques. In fact, at 1% image selection, Lucky Imaging is both more sensitive and efﬁcient than SS+S.

7.2.2 Photon Counting

Here we address photon counting mode as a way to mitigate some of the advantage of Speckle Stabilization. With data collected from an EMCCD, it is possible to do photon counting in post-processing whereby a pixel either measures one photon or none. This scenario √ is advantageous because it overcomes the additional 2 shot noise usually associated with electron multiplication. It is only useful, however, in cases where there is extremely little flux per exposure. Once more than one photon per pixel per exposure occurs, the advantage is mitigated. To model the photon counting case, we assumed that when there was < 1 photon/pixel/frame, √ we would switch on photon counting and drop the extra 2 term in the noise. For cases where the counts were higher than this, we assumed standard Lucky Imaging analysis. We present the photon counting case in Figure 7-4. The location where photon counting switches on is immediately apparent in the figure a this is the location where the S/N of the speckle techniques jumps in a discontinuous fashion. When this occurs, Lucky Imaging data exactly match the SS and SS+S data for a few magnitudes. In the 1% selection case, Lucky Imaging actually tracks SS+S all the way down to the detection limit and even slightly out-performs it with a factor of 1.12 boost in efficiency and an increase of 0.14 magnitudes in sensitivity.

103 Figure 7-3. Comparison between Speckle Stabilization with and without shutter and no-read-noise SAA and Lucky Imaging. In the case of Lucky Imaging, there is no truncation in the function presented. Also plotted is a line denoting S/N = 3, a common detection limit. The lower part of the plot is the same as Figure 7-2, but in this case, the dotted black line is the ratio of the S/N SS+Shutter to Lucky Imaging.

104 Figure 7-4. Comparison between techniques in the case of photon counting. The discontinuous jumps in the speckle imaging data are due to the point where photon counting becomes active. Also plotted is a line denoting S/N = 3, a common detection limit. The lower part of the plot is the same as Figure 7-2.

105 The 10% and 100% frame selection, however, are not as efficient or as sensitive as their corresponding SS+S and SS models. This is largely due to the fact that the read noise term is still present and becomes dominant at these fainter magnitudes. Specifically, SS+S is 1.76 times more efficient and 0.70 magnitudes more sensitive than Lucky Imaging at 10% frame selection and SS is 2.44 times more efficient and 1.04 magnitudes more sensitive than SAA. Overall, this shows that photon counting is a valuable way to get more information out of Lucky Imaging data, and can be used to observe fainter targets with much higher sensitivity. 7.2.3 Optimal Lucky Imaging

From the previous sections, it is clear that there are circumstances in which Lucky Imaging and SAA are able to mitigate the positive gains of Speckle Stabilization. As such, we discuss the case of an Optimal Lucky Imager (OLI). To maximize the effectiveness of a Lucky Imaging system, the ideal design would be an extremely low read noise system with photon counting performed for fainter targets. We examine this case in Figure 7-5 where read noise is zero and photon counting enabled. Our models reveal that an OLI is both more efficient and sensitive for Lucky Imaging than SS+S and has nearly equivalent performance when comparing SAA to SS. In particular we find OLI is 1.80 times more efficient at the detection limit and 0.96 magnitudes more sensitive than SS+S with 1% frame selection and 1.29 times more efficient and 0.32 magnitudes more sensitive with 10% frame selection. However, on average, SS+S is still marginally more efficient at brighter magnitudes. SS and SAA have nearly the same properties in terms of sensitivity and efficiency. Overall, this means that with fairly few modifications, it is possible to optimize a Lucky Imaging system so that it is maximally efficient and sensitive.

Furthermore, one issue we have not addressed in our simulations is an inherent advantage to Lucky Imaging: because all the analysis is done off-line, in post processing image selection algorithms can be tuned to maximize S/N and Strehl ratios. The observer can also decide at what point to enable photon counting in post processing as well. This gives Lucky Imaging much more

ﬂexibility with respect to data products and is part of the optimization process.

106 Figure 7-5. Comparison between speckle stabilization and OLI. The discontinuous jumps in the speckle imaging data are due to the point where photon counting becomes active. Also plotted is a line denoting S/N = 3, a common detection limit. The lower part of the plot is the same as Figure 7-2.

107 Table 7-1. Summary of simulation results. E is deﬁned as the efﬁciency ratio at the limiting magnitude of the Lucky Imaging system. ∆S is the increase in sensitivity of SS over Lucky Imaging. SS 100% SS+S 10% SS+S 1% Simulation Eff. ∆S (mag) Eff. ∆S (mag) Eff. ∆S (mag) Standard 3.35 1.42 1.54 2.40 1.10 1.26 1.28 0.31 1.39 No Read Noise 1.36 0.36 1.28 1.11 0.12 1.34 0.787 -0.41 1.33 Photon Counting 2.44 1.04 1.33 1.76 0.70 1.33 0.896 -0.14 1.28 OLI 0.964 -0.04 1.10 0.778 -0.32 1.20 0.556 -0.96 1.24 1024 x 1024 1.81 0.66 1.86 1.63 0.57 2.11 1.15 0.17 2.22

7.2.4 1024x1024 pixel2 Detectors

To be thorough, we look at one ﬁnal case to show the potential of Speckle Stabilization.

This ﬁnal case increases the size of the detectors to 1024 x 1024 pixels2 enabling wide-ﬁeld imaging. At this size, the advantages of a Speckle Stabilization system becomes heightened. This is because the read out times for a 1024 x 1024 pixels2 Lucky Imaging system are currently quite long at ≈ 100ms. This means even in frame transfer mode, 30ms integrations still require 100ms

to read out. To highlight this point, in Figure 7-6 we demonstrate the comparison between an OLI system and a SS system both with 1024 x 1024 pixels2 detectors. For the SS detector, we assume a read out time of 4 seconds. In this case, because the readout times are so long for an EMCCD of this size, Speckle

Stabilization has an advantage in both sensitivity and efficiency for both the shutter and non-shutter cases. When comparing SS+S to Lucky Imaging, we find that SS+S is 1.15 times more efficient at the faintest magnitude and 0.17 magnitudes more sensitive with an average efficiency ratio of 2.22 with 1% frame selection. For 10% frame selection, these values are 1.63 times more efficient at the Lucky Imaging detection threshold and 0.57 more sensitive. In the case of SS and SAA, we find SS is 1.81 times more efficient and 0.66 magnitudes more sensitive. We note that being able to use a detector of this size has great scientific potential. At 30 mas pixel sampling, a 1024 x 1024 pixels2 detector would have a FOV of 30 arcsec. While this

kind of FOV is a bit larger than the isoplanatic patch, Keremedjiev et al. (2008) have shown that

speckle stabilization is effective out to offsets as large as 30 arcseconds and would be of high

scientiﬁc value.

108 Figure 7-6. Comparison between speckle stabilization and OLI for 1024x1024 pixel2 detectors. The discontinuous jumps in the speckle imaging data are due to the point where photon counting becomes active. Also plotted is a line denoting S/N = 3, a common detection limit. The lower part of the plot is the same as Figure 7-2.

109 7.3 Discussion

We ﬁnd that Speckle Stabilization is a viable competitor to current Lucky Imaging systems when used solely for imaging in certain circumstances. The results from all of our models and simulations are presented in Table 7-1. Both SS and Lucky Imaging have their own strengths. In general, SS is more sensitive and

efficient than speckle imaging at the faintest magnitudes with normal frame selection meaning it could be well-employed for faint object work. Additionally, for most mid-magnitude targets SS √ and SS+S is a factor of 2 times more efficient owing to the lack of the additional noise term. As a counter, there are several cases in which speckle techniques are superior. We find that the Lucky Imaging techniques are the only way to observe the brightest stars with any usable S/N. Our work has also revealed that simple modifications to traditional Lucky Imaging systems can greatly improve their performance and completely mitigate the advantage of a SS system at the faint end. The most effective alterations are approaching zero read noise and using photon counting techniques beyond a particular threshold. When these features are implemented, we found the Lucky Imaging was both more sensitive and efficient than Speckle Stabilization at the faint end. We highlight again that the main advantage to Speckle Stabilization is long exposures for IFS work, but this Chapter has revealed SS is also useful from an imaging perspective. Overall the differences are fairly minor between the output products, but as telescope time is a valuable commodity it is useful to have instruments in place that are able to perform efficient observations. We find that speckle stabilization is one way to achieve this aim, but similar goals can be met by modifying existing Lucky Imaging systems. While SS is still in its infancy, instruments like

SPIFS will be able to reveal some of the potential of this technique and help solve outstanding issues in astrophysics.

110 CHAPTER 8 THE FUTURE OF SMBH DETECTION VIA KINEMATIC MODELING AS ENABLED BY ELTS Given that one of the primary advantages to speckle stabilization is its ability to use an integral ﬁeld spectrograph at diffraction-limited resolutions in the optical, the possibility of measuring the masses of SMBH is quite appealing. As noted in Chapter 1.3, there are many unanswered questions involving the high and low mass ends of the MBH − σ. Resolving these issues will aid in the development of a complete black hole mass function and enable astronomers to probe the evolution of supermassive black holes. In this Chapter, I examine

how SPIFS, extremely large telescopes and other techniques can enable new SMBH mass

measurements via kinematic modeling of stellar content. This Chapter compliments a previous examination by Batcheldor & Koekemoer (2009) who looked at variety of spectral features and telescope apertures to determine general requirements of future telescopes and facilities. In particular, they found a 16-m space-based telescope to be the ideal tool for measuring SMBH masses over 90% of cosmic history. In this paper, we restrict our study to the planned ground-based ELTs and their instruments to determine redshift limits and estimate the number of accessible targets. We also restrict our study to stellar kinematics as these observations are possible to conduct in nearly every non-active galaxy.

8.1 Extremely-Large Telescopes

It is possible that in the next ten years Extremely Large Telescopes will be taking ﬁrst light data. There are currently three projects that are in various stages of development and represent

the the initial tools of this new class. These projects are the Giant Magellanic Telescope (GMT), the Thirty Meter Telescope (TMT), and the European-ELT (E-ELT) with diameters of 24.5 meters, 30 meters and 42 meters respectively.

111 At time of writing, the GMT is an effort being pursued by private institutions and is currently projected to be completed around 2018.1 The TMT, originally a venture from the California Institute of Technology and University of California schools now includes a broad international collaboration and also projects a completion date of 2018.2 The E-ELT is a project being developed by the European Space Agency and its partner contries; they too claim the telescope will be completed in 2018.3

8.1.1 Theoretical Improvements Over Existing Facilities

In this section, we will examine the theoretical improvements possible in SMBH research via the stellar kinematic modeling technique on ELTs. When coupled with adaptive optics

systems, these increased telescope apertures have dramatically improved angular resolutions and sensitivities over 10-m class telescopes. For the purposes of this cursory investigation, we assume that the AO systems being developed will produce similar Strehl ratios as existing AO facilities. 8.1.1.1 10-meter resolutions

The ﬁrst case we consider is how SMBH mass measurements will be improved on ELTs at existing, 10-meter angular resolutions (≈ 100 mas). Since performing these observations are

often time consuming (typically one night or more per object), it is useful to examine how the increased diameter/collecting power of the ELTs will increase the efﬁciency of SMBH mass measurements when the angular scales are the same. Based on their apertures, the GMT, TMT and E-ELT will collect 6, 9 and 17.6 times more light than a current 10-meter telescope respectively. When considering surface brightness from extended sources in the photon-limited case (where all the noise terms from sky background, read noise, etc. are negligible as compared to the signal from the source) the signal-to-noise in an observation is related to the effective area of the primary aperture A and the integration time t by

1 http://www.gmto.org/

2 http://www.tmt.org/ 3 http://www.eso.org/public/teles-instr/e-elt.html

112 √ S/N ∝ A ·t. Since the pixel scale of the observations are constant across the different apertures, the increase in area means an equally proportional decrease in observing time to attain the same S/N per resolution element. An additional result of the same pixel scale is that as long as the

detectors have similar performance, then sky background and read noise should be the same for the observations. The only difference would be that noise from dark current would be reduced due to the shorter exposure times required. Therefore, all other parameters being equal, current observations of SMBH in the K-band that take ≈ 4 hours including sky (Davies et al., 2006; Nowak et al., 2007; Cappellari et al., 2009;

Krajnovic´ et al., 2009), will take 40 minutes, 27 minutes and 14 minutes on the GMT, TMT and E-ELT respectively to reach the same S/N for the same angular scales. In fact, the S/N will even be marginally higher owing to the fact that shorter exposures mean less noise from dark current.

8.1.1.2 ELT diffraction-limited resolutions

The second major advantage to larger apertures is that diffraction-limited angular resolutions

scale linearly with telescope diameter. So the GMT, TMT and E-ELT are capable of 2.45, 3.00 and 4.25 times better spatial resolution than the Keck or Gran Telescopio Canarias Telescopes (19.4, 15.8 and 11.3 mas in K-band respectively). For comparison, the Hubble Space Telescope is

able to achieve spatial resolutions of ≈50 mas at 0.6µm. We now investigate the case where SMBH mass measurements are conducted at the diffraction-limit of the telescope. When observing galaxies, the relevant ﬂux value is surface brightness and for our analysis we assume that the galaxy core is resolved and the surface brightness is smoothly varying such that at higher resolutions there are not dramatic changes in the surface brightness proﬁle. We also assume that the plate scale varies such that the same number of pixels are illuminated per diffraction-limited resolution element (i.e. Nyquist sampling). Therefore, since surface brightness and sky background are both dependent on the area of sky per resolution element Ωres and in turn Ωres ∝ 1/A, then the signal to noise per resolution element on a 10-meter telescope is the same as on a 30-meter telescope per observing interval

113 8 Table 8-1. ELT K-band resolutions and distances at which typical (1 × 10 M¯) SMBH should be observable. Note also that the distance is the comoving distance. Note that these distance values assume that there are spectral features that can be observed to measure the mass. If the redshift limits of the CO bandheads are employed, then all of the 8 9 redshift limits for all telescopes at both 1 × 10 M¯ and 2 × 10 M¯ are 0.0331. 8 9 1 × 10 M¯ 2 × 10 M¯ Telescope θ(mas) Dist (Mpc) z Dist (Mpc) z GMT 19.4 137 0.0335 642 0.163 TMT 15.8 168 0.0414 818 0.209 E-ELT 11.3 239 0.0591 1.26 × 103 0.334

(although the advantage to the 30-meter case is that it will have more resolution elements at a higher spatial sampling). This implies that an eight hour observation on a 10-meter telescope will have the same S/N per 100 mas element as an eight hour exposure on a 30-meter telescope with 33 mas per element. Therefore in the time it takes to get SMBH mass measurements on current telescopes, diffraction-limited angular resolutions on ELTs will be achieved at the same S/N.

8.1.2 K-band CO Bandheads

Assuming diffraction-limited angular resolutions are possible, new science becomes possible. The ﬁrst possibility we examine is the distance limit at which we should be able to measure a SMBH via the stellar kinematic modeling method for characteristic SMBH in K-band

observations. To estimate this value, we need to know what is the black hole sphere of inﬂuence

2 given by R = GMBH/σ (where σ is the velocity dispersion at R). For our investigation, we

use the σ value at the effective radius and can solve for R using parameters from the MBH − σ 8 relationship of Gultekin¨ et al. (2009). For a characteristic black hole mass of 1 × 10 M¯ with a velocity dispersion of 183 km/s, the black hole’s sphere of influence is 12.3 pc. With knowledge of the physical scale that needs to be resolved, we use the diffraction-limited angular scale of the telescope to find the comoving distance for the given angular size distance. Assuming the sphere of influence fills at least one resolution element, we find the distances given in Table 8-1. From these values, we can see that the ELTs will be able to perform mass

8 measurements of 1 × 10 M¯ SMBH well past the Virgo cluster and even past the Coma cluster.

114 To demonstrate the limiting distance out to which these telescopes will be able to explore, we also consider particularly massive SMBHs. Higher mass SMBH produce larger spheres of inﬂuence and are thus observable at larger distances via the stellar kinematic modeling technique.

9 For our models, we assume the largest SMBH are ≈ 2 × 10 M¯ which is where the M − σ relationship appears to break down (Sheth et al., 2003; Law, 2007; Gultekin¨ et al., 2009). While larger SMBH have been detected, most are in active galaxies which use different mass estimates

than are within the scope of this paper. At this limit, we get a σ = 400 km/s and a sphere of inﬂuence equal to 53.7 pc. Assuming the black hole sphere of inﬂuence is resolved by one

resolution element yields the values of column 5 in Table 8-1. When we convert these distances to redshift values (columns 4 and 6, Table 8-1) we find that using the E-ELT we will be able to observe characteristic galaxies out to z = 0.0591 (lookback time of 0.759 Gyr) and in the most massive cases, we will be able to observe z = 0.334 (lookback time of 3.57 Gyr). It should be noted however, that the K-band CO bandheads used to measure SMBH kinematic influence range from 2.294 < λ < 2.383µm. When we factor this into wavelength range of 2.03 < λ < 2.37µm, which is the K-band in the Mauna Kea Observatories near-infrared (MKO-NIR) filter set (Simons & Tokunaga, 2002), we find that at z = 0.0331 the CO bandheads

8 will be completely shifted out the K-band. Therefore, characteristic (1 × 10 M¯) SMBH mass measurements on GMT will be at the resolution limit of the telescope, but for TMT and E-ELT it will not be possible to measure these black hole masses at the maximum distances allowed by the

telescope due to redshift. Furthermore, there will be no possibility of measuring the most distant,

9 massive SMBH (2 × 10 M¯) resolution allows on any of the ELTs. We calculate the limiting redshift for a range of SMBH masses and present the results

in Figure 8-1. For reference, we have also included the redshift limits expected by the Keck Telescopes as well as the masses and redshifts of some previously observed systems. The

parameters of the observed SMBH plotted in Figure 8-1 are given in Table 8-2. Note that this

sample only includes objects observed with AO-fed IFSs in the K-band. Through Figure 8-1,

115 Figure 8-1. Plot of SMBH Mass versus limiting observable redshift for Keck and the three ELTs. All three telescopes reach the same redshift limit of z = 0.0331 for high masses when the CO bandheads are no longer in the K-band. The diamonds are SMBH masses that have been measured using K-band CO bandheads on existing facilities.

Table 8-2. SMBH mass measurements for a variety of systems determined by K-band integral ﬁeld spectroscopy. The redshift of the host galaxy and references are also provided.

Galaxy BH Mass (M¯) z Reference NGC 3227 1.35 × 107 0.003859 Davies et al. (2006) NGC 4486a 1.25 × 107 0.000500 Nowak et al. (2007) NGC 4151 4.5 × 107 0.003319 Onken et al. (2007) NGC 1316 1.5 × 108 0.005871 Nowak et al. (2008) NGC 5128 5.5 × 107 0.001825 Cappellari et al. (2009) NGC 524 8.3 × 108 0.007935 Krajnovic´ et al. (2009) NGC 2549 1.4 × 107 0.003466 Krajnovic´ et al. (2009) NGC 3368 7.5 × 106 0.002992 Nowak et al. (2010) NGC 3489 6.00 × 106 0.002258 Nowak et al. (2010) we demonstrate that resolution will not be the limiting factor for the most massive SMBH measurements and that current observations of SMBH on 8 and 10-meter class telescopes are approaching the expected redshift limits.

116 We have made all of these calculations assuming the MKO filter set. It is possible to use different K-band filters with longer wavelength coverage to increase the accessible parameter space. In particular, if a K-band filter like the FLAMINGOS-2 HK spectroscopic filter is used,

the long wavelength cutoff is λ = 2.51µm (Raines, private conversation). Using this wavelength as an upper limit increases the usable redshift for the ﬁlters to z = 0.0942 and greatly increases the volume of space accessible by the K-band CO bandheads. However, we note that the MKO

filters were selected to cut off at 2.37µm because thermal background becomes significant beyond this wavelength. So while it might be possible to use these longer wavelengths, it may not be practical as additional noise terms become significant. 8.1.3 H-band CO Bandheads

While the K-band CO bandheads may be of little utility beyond z = 0.0331, a potential solution emerges in the McConnell et al. (2011) observations of NGC 6086. Because their K-band data had high thermal background noise, they used CO bandheads in H-band to measure

the mass of the SMBH at the center of this Brightest Cluster Galaxy. Their work represents the

9 ﬁrst attempt to use features in the H-band and they report a SMBH mass of 3.6 × 10 M¯. Given that the MKO-NIR H-band ranges from 1.49µm < λ < 1.78µm (Simons & Tokunaga, 2002) there are several CO features spanning nearly all of the H-band; however the dominant CO feature is a 6-3 second-overtone bandhead at 1.619µm (Hinkle, 1978; Meyer et al., 1998). For our investigation, we assume that the 1.619µm CO feature needs to be observable to estimate SMBH mass. Using this assumption, the H-band CO features can be used to measure SMBH masses out to z = 0.0994 where it then shifts out of the MKO-NIR ﬁlter band.

While the dominant 1.619µm CO feature increases the limiting redshift from SMBH mass

measurements through H-band observations, it has additional utility in the K-band. At a higher redshift of z = 0.254 the feature becomes observable in the K-band and can again be used to estimate SMBH masses. This added beneﬁt continues until a redshift of z = 0.464 pushes it out of the K-band.

117 8 Table 8-3. ELT H and K-band resolutions and distances at which typical (1 × 10 M¯) SMBH should be observable using the 1.619µm CO feature. N/A is used when the maximum redshift is still less than 0.254, the requisite redshift for the feature to move into the K-band. Note that the distance is the comoving distance. H-band CO in H-band H-band CO in K-band 8 9 8 9 1 × 10 M¯ 2 × 10 M¯ 1 × 10 M¯ 2 × 10 M¯ Telescope θ(mas) Dist (Mpc) z Dist (Mpc) z θ(mas) Dist (Mpc) z Dist (Mpc) z GMT 15.0 185 0.0455 399 0.0994 19.4 N/A N/A N/A N/A TMT 12.2 229 0.0564 399 0.0994 15.8 N/A N/A N/A N/A E-ELT 8.74 328 0.0813 399 0.0994 11.3 N/A N/A 1.27 × 103 0.337

Using H-band resolution limits (15.1 mas on GMT, 12.4 mas on TMT and 8.84 mas on the E-ELT) for the CO features when they are in the H-band and the K-band resolutions for the ELTs when the feature is redshifted into the K-band, we calculate redshift limits particular SMBH masses should be measureable out to. The results are presented in Figure 8-2.

8 In Table 8-3 we summarize the limits for SMBH with masses of ≈ 1 × 10 M¯ and ≈ 9 2 × 10 M¯. We note that only the E-ELT will be able to beneﬁt from the 1.619µm feature being 9 redshifted into the K-band for SMBH with masses of ≈ 2 × 10 M¯. However, from Figure 8-2 we show that for SMBH with masses greater than this value, GMT and TMT will be able to observe some targets. Therefore, while SMBH out to z = 0.337 should be measurable, there is a gap between 0.0994 < z < 0.254 where no strong, near-IR CO line tools exists to probe SMBH masses.

8.1.4 Calcium Triplet Lines

A further line diagnostic we consider to probe SMBH masses at larger distances is the calcium triplet feature (8498A˚,8542A˚,8662A˚) used to measure SMBH via IFS at optical wavelengths when redshifted into the J-band. Since the MKO-NIR J-band is deﬁned as

1.17µm < λ < 1.33µm (Simons & Tokunaga, 2002), at z > 0.377 all of the calcium triplet features will be located in the J-band. If only the longest wavelength feature is used, the requisite minimum redshift becomes z = 0.351. Since current AO systems are capable of diffraction-limited angular resolutions at Strehl ratios of 10% in the J-band (van Dam et al.,

2006), the J-band could be used to measure the kinematic inﬂuence of SMBH at higher angular

118 Figure 8-2. Plot of SMBH Mass versus limiting observable redshift for Keck and the three ELTs. Four different line diagnostics are presented to show the total range of redshifts accessible by the various telescopes. Use of the 1.619µm CO feature in the H-band is denoted by the “CO(H) in H-band” curve and when the feature is redshifted into the K-band, the curve is denoted by “CO(H) in K-band”. Use of the optical calcium triple lines in the J-band is given by the “CaT in J-band” curves. The gap between 0.0994 < z < 0.254 is where no line diagnostics exist to measure SMBH mass via the kinematic modeling technique. The offset between the H and K-band curves is due to the different limiting resolutions afforded by the wavelength regimes. resolutions than in the K-band or H-band. This is because the diffraction-limit for J-band is 9.26 mas on GMT, 7.56 mas on TMT and 5.40 mas on E-ELT. Using these resolution limits to calculate distance and redshift limits as above, we present the results in Figure 8-2. The calcium triplet results are denoted by the “CaT in J-band” curves and we see that the calcium triple feature will only be useful for the most massive galaxies

9 (MBH > 10 M¯). However, in observing these most massive galaxies we will be able to measure SMBH masses out to z = 0.565 where the calcium triplet feature gets shifted out of the J-band.

119 It is possible that the calcium triplet features could be observed in other, shorter bandpasses like Y-band, but for the purposes of this investigation, we limit the analysis to J-band. We made this choice because the J-band currently has AO corrections with Strehl ratios >0.20 and the AO

systems for the ELTs are expected to match this performance as well. At shorter wavelengths, the Strehl ratios drop off dramatically and the ability to measure SMBH masses at Strehl ratios lower than 0.20 is less certain. So in using all of the different line diagnostics we ﬁnd three interesting results:

1. SMBH masses should be measurable out to z = 0.565

2. There is a gap between 0.0994 < z < 0.254 where none of these features can be used to probe SMBH masses

3. The distance limit for the most massive SMBHs is generally set by the availability of line diagnostics and not telescope resolution 8.1.5 Number of Galaxies

Since we now know the volume of space accessible for each SMBH mass, we wish to determine the total number of SMBH observable to further compare the various telescopes and their capabilities. To calculate these totals, we used the mass function from Bell et al. (2003)

derived from the 2MASS survey for all galaxies. Since this is a galaxy stellar mass function, we convert it to a black hole mass function using the fact that there is a relationship between galaxy

mass and SMBH mass (Kormendy & Richstone, 1995). While there is signiﬁcant scatter in this relationship, we only use it as an estimate of the number of galaxies accessible. Therefore, we

assume the Kormendy & Richstone (1995) ratio of MSMBH/MGalaxy = 0.0022. When we combine this SMBH mass function with the volume of space accessible for each SMBH mass we get a mass function of observable SMBH masses and present the results in

Figure 8-3. From this figure, we can see that the ELTs will allow nearly two orders of magnitude more SMBH masses to be measured. Specifically, if we integrate under these curves, we find

that using all of the line diagnostics available, Keck should be able to access a total of ≈ 2 × 104

SMBH via kinematic modeling. GMT, TMT and E-ELT will be able to access ≈ 3 × 105,

120 Figure 8-3. Mass function of observable SMBH as a function of SMBH mass for Keck and the ELTs. The notches are the result of where the break in redshift due to a lack of usable spectral features for SMBH mass measurement occurs.

≈ 7 × 105 and ≈ 6 × 106 targets respectively. These large target sets will enable population statistics of the SMBHs in various galaxy morphologies and the construction of a complete BHMF. Furthermore, the larger number of targets available means the likelihood of detecting unusual objects at the high and low mass ends of the M − σ relationship also increases. If we continue with this analysis one step further, we can produce a plot of number of

galaxies observable versus telescope diameter. This analysis is presented in Figure 8-4. While the ﬁgure does indicate that smaller telescopes should be able to carry out this research, the

sensitivity limits of the smaller apertures is likely to be more of a limiting factor. We also note that these results are independent of sight-lines. The number of actually observable targets could be much less due to the physical location of the telescopes, obscuration from the Galactic disk and other Galactic phenomena.

121 Figure 8-4. Plot of total number of SMBH observable as a function of telescope aperture diameter. The vertical dashed lines speciﬁcally denote 8-m, 10-m, 24.5-m, 30-m and 42-m apertures.

8.1.6 First-Generation Instruments on ELTs

While we have calculated the redshift limits and number of SMBH observable based solely on the resolution afforded by the larger primary mirrors, this is an ideal case and does not take into consideration instrumental limitations. We now examine how planned instrumentation for the ELTs will modify the results. Nearly all the planned instruments will use a suite of adaptive optics systems to get the best possible Strehl ratios and the development of these instruments ensure that the increased advantage of the larger apertures is not solely to collect more photons. In the realm of SMBH kinematic measurements, the key factors are angular resolution, spectral resolution and the ability to perform integral ﬁeld spectroscopy. Current SMBH measurements in the near-IR are done with instruments like SINFONI at VLT and OSIRIS at Keck (Davies et al., 2006; Nowak et al., 2007; Larkin et al., 2006; Krajnovic´ et al., 2009). The IFSs on these instruments each have angular resolutions of 100 mas and spectral resolutions

122 of R ≈ 4500. At a minimum, advances in SMBH research on ELTs will need to match these requirements. Unfortunately for GMT, there are currently no plans for instruments that will be able to

outperform or even match existing systems4 . The closest fit is NIRMOS with R ≈ 75005 , but it is not totally clear if this first generation instrument will have an IFU, but even if it does, the angular resolution will only be 200 mas– not even as fine as existing systems. For TMT there are two planned instruments capable of measuring the kinematic influence of SMBHs. The first is IRIS (Larkin et al., 2010), a near-IR IFS with R ≈ 4000 designed to be among the first generation of instruments for the telescope. It is planned to have 4, 10, 25 and 50 mas resolution settings for flexibility in observing. The entire FOV is expected to be 3”.

The second instrument capable of measuring SMBH on TMT will be IRMOS (Eikenberry

et al., 2006b), a near-IR multi-object IFU planned for later deployment in the second or third generation. It will be able to simultaneously observe a least 10 different, 2” fields with 1000 < R < 10000 at 50, 24 and 16 mas angular resolutions. While the resolution is not as fine as with IRIS, this instrument has the capacity to measure the masses of SMBH in 10 galaxies at a time enabling the black hole mass properties of clusters and dense fields to be quickly analyzed. Similar to TMT, E-ELT will also have two instruments capable of measuring SMBH kinematics. In this case HARMONI (Thatte et al., 2010) will be akin to IRIS. It will have 4, 15 and 50 mas spaxels, but has a tunable resolution of 4000 < R < 20000. The expected Strehl ratio on this system from laser tomographic AO is expected to be 0.6. For E-ELT, EAGLE will have 75

mas angular resolutions at resolutions ranging from 4000 to 10000 and is being designed with 20

different ﬁelds in mind (Cuby et al., 2010). The encircled energy within the 75 mas is expected to be > 0.3 meaning this instrument will certainly be useful for SMBH kinematic measurements.

4 http://www.gmto.org/CoDRpublic

5 http://www.gmto.org/codrfolder/GMT-ID-01477-Section 13.5 NIRMOS .pdf/download

123 Figure 8-5. Plot of SMBH Mass versus limiting observable redshift for the four ﬁrst generation instruments for the ELTs. The gap between 0.0994 < z < 0.254 is where no line diagnostics exist to measure SMBH mass via the kinematic modeling technique.

We present a plot of the redshifts accessible for the instruments as a function of SMBH mass in Figure 8-5. We show that IRIS and HARMONI will be able to probe SMBH kinematics with the highest resolutions meaning they will produce the most detailed measurements as well as some of the most distant measurements of SMBH. This is largely due to the fact that the smallest spaxel scale (4 mas) corresponds to a Nyquist sampled diffraction-limit in J-band. While we also see that IRMOS and EAGLE will not be able to probe quite as far due to their coarser sampling, the capability of observing SMBH in multiple galaxies at once will dramatically increase the

5 population statistics of SMBH masses in the more conventional mass range 10 M¯ < MBH < 9 10 M¯. The planned instruments on the ELTs certainly have the capability to measure the masses of SMBH in a large number of galaxies. While it appears GMT will have to wait for future instrumentation, TMT and E-ELT will be able to probe the kinematic inﬂuence of SMBH seemingly from day one.

124 8.2 SPIFS Impact on SMBH Measurements

From the above sections I have shown that ELTs will greatly increase the number of targets available for SMBH mass measurements, however the gap in redshift between 0.0994 < z < 0.254 and the resolution limits of near-IR observations reduce the entire parameter space accessible. A possible way to close the redshift gap and increase the number of SMBH

accessible, particularly in the local universe, is with SPIFS. Since SPIFS has diffraction-limited angular resolutions at optical wavelengths, it will be useful for increasing the total number of SMBH mass measurements possible in the local universe.

Since SPIFS will function between 0.6µm < λ < 1.0µm, it will be able to use the calcium triplet feature to measure the masses of SMBH. As a result of the 1.0µm cutoff, the maximum redshift it will be able to use the calcium triplet line is z = 0.177. This cuts the redshift gap for the near-IR nearly in half. In Figure 8-6, I present the limiting redshifts speckle stabilization will be able to achieve in measuring SMBH masses. I also include what SPIFS should be able to

achieve if used on ELTs as well. While SPIFS on an ELT will have lower Strehl ratios than on 10-meter telescopes, it should still provide diffraction-limited angular resolutions and can be used to measure SMBH masses.

From these curves, I produce a new SMBH mass function and present it in Figure 8-7. The first noticeable difference between this figure and Figure 8-3 is that the curves are shifted upward to reflect the increased number of black holes measurable. The second notable difference is that the notches have a different, less pronounced shape. This is because the gap in redshift has been reduced. When I integrate under these curves, I find that a 10-meter class telescope should be able to measure ≈ 1 × 105 SMBH and that GMT, TMT and E-ELT should be able to measure

≈ 2 × 106, ≈ 3 × 106 and ≈ 1 × 107 SMBH respectively using all line diagnostics on all the telescopes. Therefore SPIFS would enable nearly a factor of ﬁve increase in the total number of SMBH measurable over the near-IR instruments alone. What is interesting to note, however is that the remaining “gap” in accessible redshifts is

somewhat artiﬁcial. This is for two reasons, the ﬁrst is that it is possible for SPIFS to work at

125 Figure 8-6. Plot of SMBH Mass versus limiting observable redshift for Keck and the three ELTs. The lines are the same is in Figure 8-2 except for the addition of the SPIFS curve. The redshift gap where no line diagnostics exist to measure SMBH mass via the kinematic modeling technique has been reduced to 0.177 < z < 0.254. wavelengths longer than 1µm and with the right combination of detectors, SPIFS could nearly reach the J-band. Secondly, there are many other lines in the optical, like Hα, that could be used in the SPIFS bandpass at z ≈ 0.2 reducing or eliminating the gap entirely. Therefore it is possible that with SPIFS, SMBH at all redshifts up to z = 0.565 could be measured. However, for this investigation, I simply limited the analysis to lines currently employed in SMBH mass measurements through kinematic modeling.

8.3 Rest-Frame J-band Spectral Features

In principle, measurements of J-band rest-frame features offer an additional way to probe the kinematic inﬂuence of SMBHs. The apparent advantage of the J-band that is that the shorter wavelengths enable higher spatial resolutions. These higher resolutions could

126 Figure 8-7. Mass function of observable SMBH as a function of SMBH mass for Keck and the ELTs including galaxies observable by SPIFS. The notches are the result of where the break in redshift due to a lack of usable spectral features for SMBH mass measurement occurs. potentially enable SMBH to be observed at higher redhshifts and/or bridge the current gap between 0.177 < z < 0.254.

8.3.1 Observational Requirements

An important question to address is what requirements would have to be met to conduct measurements of SMBH with rest-frame J-band features? Wallace et al. (2000) performed an extensive survey of nearby stars to characterize their spectra in the J-band at R ≈ 6000. They were able to detect many metal lines in their spectra including Al I, Mn I, He I, Ti I and C I.

These features, however, are not very strong. Most of the equivalent widths (Wλ ) are ≈ 2A˚ with the largest measurements being ≈ 3A.˚ Given that the calcium triplet feature has Wλ =≈

8A(˚ Garcia-Rissmann et al., 2005) and the K-band CO bandheads have Wλ =≈ 14A(˚ Mannucci et al., 2001), these results immediately point to the fact that long integration times will be required.

127 Rayner et al. (2009) also observed many nearby stars and found that features could be detected at R ≈ 2000 using the 3.0-m IRTF. Davies et al. (2010) took the observations one step further and found that metallicity could be derived from J-band observations of red

super-giants (RSG) at R ≈ 2000. They surmised that J-band observations of RSG could be used to characterize metal abundances in distant galaxies and estimated that in two nights of observation on a 10-m class telescope, one could get S/N ≈ 100 for Fe I, Mg I, Si I and Ti Ions from a RSG at 40 Mpc where it would have an apparent J magnitude of 19. To determine the necessary integration times, we use observations of SMBH kinematics from the calcium triplet line (CaT) as a starting point. Comparisons between CaT lines and

atomic J-band features make logical sense because any broadening observed in the features is indicative of kinematic inﬂuence.

An important parameter we will use to estimate the necessary integration times is the S/N of

the line (S/Nline). The easiest way to calculate this value is from the equivalent widths Wλ and is given by:

Ã√ !1/2 S/N ·W FWHM2 + ∆λ 2 S/N = cont. λ · (8–1) line ∆λ ∆λ

Here S/Ncont. is the signal to noise ratio of the continuum near the feature, Wλ is the line equivalent width, FWHM is the full width half maximum of the line and ∆λ is the width of a

resolution element.

We estimate the requisite S/Nline for the calcium triplet features in kinematic observations using values from the literature. Pinkney et al. (2003) were able to successfully measure SMBH

in galaxies using S/Ncont = 30 for STIS on HST. Their spectral resolution was R = 3800 meaning ∆λ = 2.2A˚. We use Wλ = 7.7A˚ for CaT in normal galaxies from Garcia-Rissmann et al. (2005). We estimate the FWHM from the velocity dispersion of a galaxy with a SMBH mass of

8 1 × 10 M¯ using parameters from the Gultekin¨ et al. (2009) M − σ relation. This gives σ = 183 km/s and thus a line width of 5.2A.˚ Putting these values into Equation 8–1, we ﬁnd that Pinkney

et al. (2003) should have achieved a S/Nline for the calcium triplet of ≈165.

128 If we assume that this is the necessary S/Nline to characterize SMBH kinematics, we can

work backwards to estimate the S/Ncont. needed in the J-band. For J-band lines, we will use the same spectral resolution as STIS (R = 3800) giving ∆λ = 3.2A˚. For the line strength, we use the value of Wλ = 2.0A˚ which is the approximate strength of lines for RSG according to Wallace 8 et al. (2000); Davies et al. (2010). The line width for a 1 × 10 M¯ black hole at 1.25µm is 7.6A.˚ We also include a dilution factor because while RSG contribute signiﬁcantly to the overall spectrum of a galaxy in the J-band, there are other sources of continuum. Therefore, as an upper limit we assume that half the light of the galaxy is from RSG meaning that we apply a dilution factor of two to the line strength. When we incorporate all these values, we ﬁnd that we will need

to reach a S/Ncont. = 340 for measuring the kinematic inﬂuence on SMBH.

Next we need to turn the S/Ncont. into an estimation of integration times. We assume observations are carried out on a 10-m telescope with a spatial resolution of 100 mas/pixel (the same angular resolution currently used in K-band SMBH mass measurements). We used

flux values from Cox (1999) for an assumed surface brightness near the black hole sphere of influence of 13.0 mags/arcsec2. Total system efficiency (telescope+instrument) is based on the OSIRIS instrument at Keck which has a measured efficiency of ≈ 0.10. Without taking into account read noise, dark current or sky background we employ Poisson statistics for noise and find that an integration time of 2.8 × 106 seconds (780 hours) is required to reach the minimum

5 S/Ncont. necessary. For a 30-m and 42-m telescope, this drops to 3.1 × 10 seconds (86 hrs) and 1.6 × 105 seconds (44 hrs) respectively. Since these numbers only reﬂect on-source time, they

do not include the requisite sky observations which will double the required telescope time for a standard source-sky pattern. Therefore, while it is theoretically possible to measure SMBH in the J-band, it is not efﬁcient. We emphasize again that these calculations assume 100 mas spatial resolution– a resolution already employed by K-band observations of SMBH. Because of this fact, the

≈200x increase in integration time required to achieve the exact same science as a four hours of

K-band observation (Davies et al., 2006; Cappellari et al., 2009) makes the J-band inefﬁcient for

129 measuring SMBH masses. We also note that to harness the higher angular resolutions possible in the J-band would require four times longer exposures than quoted above.

Finally, we note that Davies et al. (2010) found there is a relationship between Wλ and metallicity in many J-band lines. While this is desirable from an abundance characterization perspective, it poses an additional problem for SMBH detections. To avoid introducing additional systematic errors, this fact requires the metallicity of stars in the core of the target galaxy be known beforehand and that stars of similar metallicity to the target galaxy be observed for calibration. When one considers the long exposures necessary and the additional calibration difﬁculties, the J-band becomes unappealing for SMBH detections. So while it is theoretically possible to conduct this work in the J-band, it is not practical.

8.3.2 Observational Conﬁrmation

As an independent check to the claims made above, we have conducted observations of

local galaxies to detect rest-frame J-band features. Mannucci et al. (2001) performed a study of rest-frame J-band spectra of galaxies but their observations were met with limited success. They reported spectra of non-active, nearby galaxies in the J-band. They conducted observations of 25 galaxies (five galaxies of five different morphological types across the Hubble diagram) to produce composite spectra of E, S0, Sa, Sb, and Sc galaxies. Their final median averaged J-band spectra had a S/N ≈ 30 and a spectral resolution of R ≈ 300. They did not identify any features in the J-band data citing the fact that their J-band data were of lower quality than their H and K-band spectra and that J-band stellar spectral analysis is in its infancy. Therefore, our observations seek to examine local galaxies at higher spectral resolution and

S/N than previously obtained and see if any features are clearly discernible. The presence or lack of features can help constrain the analysis in §3.1. It should be noted, however, that these observations are not meant to provide a comprehensive survey of local galaxies in the J-band. We conduct these observations as a probe to see if anything interesting has been missed by previous

work and determine if more follow-up observations are well-motivated at this spectral resolution.

130 8.3.2.1 Observations and Data Reduction

We acquired our data at the Kitt Peak Mayall 4-m telescope between September 5-8, 2008. We used the Florida Image Slicer for Infrared Cosmology and Astrophysics FISICA (Eikenberry et al. 2006)– an integral ﬁeld unit (IFU) for the FLAMINGOS instrument (Elston et al. 2003) to observe the targets. FISICA was selected primarily because the aperture of the IFU can

effectively be used as a large-throughput spectroscopic slit while maintaining good spectral resolution. Because FISICA is an image slicing IFU with 22 individual slices, it does not suffer the throughput losses of a fiber-fed IFU and therefore its 16”x33” area has 1.5 times more light gathering power than the slit in the LonGSp spectrograph (Vanzi et al. 1997) used by Mannucci et al. (2001). This property allows us to better characterize the overall flux of the galaxy. Spectroscopic information was obtained with the JH filter, which obtains data simultaneously for the J and H bands, on FLAMINGOS which resulted in a spectral resolution of R ≈ 1400. We selected the galaxies for these observations to be representative of non-active, local

galaxies. We constrained the semi-major axis to be between 1’.5 and 3’.0 so that the maximum amount of flux would be collected in our 16”x33” aperture. Additionally, we selected galaxies sufficiently bright (J < 11 in Vega taken from 2MASS) so that a S/N> 25 would be achieved with 45 minutes of on-source observation. Finally, we examined the literature on our candidates to screen any unusual characteristics. For our final list, we targeted seven galaxies for observations. However, owing to cloudy, variable conditions during the run, we only observed four targets meeting the requirement of S/N> 25 for this study. We present these galaxies and their relevant

observational properties in Table 8-4. Our science exposures were 300 seconds long and we took them in an ABBAAB

science-sky pattern to account for the time variable nature of the infrared sky background. Because of the ﬂexure in the FLAMINGOS system, we acquired ﬂat and HeNeAr calibration lamp data after each set of three science exposures. Then we obtained spectra of a telluric absorption star of similar airmass for absorption line calibration.

131 Table 8-4. The semi-major axis length is denoted by a. J magnitudes are taken from the 2MASS survey (Skrutskie et al. 2006). Redshifts, z, were acquired from the NASA/IPAC Extragalactic Database (NED). Object Type a J mag z Exp. Time S/N (arcmin) (Vega) (minutes) NGC 7619 E 2.9 8.992 0.012549 45 70 NGC 6824 Sb 2.1 9.228 0.011294 35 34 NGC 83 E 1.6 10.279 0.020771 45 25 NGC 13 Sc 2.7 10.667 0.016038 45 24

We performed initial reduction of the data with the Florida Analysis Tool Born of Yearning for high quality spectroscopy data (FATBOY) reduction package (Warner et al. 2008). Using FATBOY, we first flat field corrected with lamp flats. Next, we matched each science exposure to its corresponding off source sky frame (taken 10’ away) and performed sky subtraction. After sky subtraction,we rectified the spectral images and aligned the wavelengths using flat and lamp data. From the resulting, calibrated slices, we extracted raw spectra. We calibrated for telluric absorption by dividing galaxy spectra by standard G0-5 V stars. Then we multiplied the galaxy

spectra by a blackbody corresponding to each calibration star’s intrinsic temperature. To produce the composite spectra, we co-added spectra from the image slices. However, not all slices produced usable data and blindly summing them would introduce substantial errors. To select the best spectra for summing, the S/N was calculated for each slice in the

1.22µm < λ < 1.24µm. For NGC 7619, only slices with S/N>10 were added. For NGC 6824 we used a cutoff of S/N>9 and for NGC 83 and NGC 13 we chose S/N>7. 8.3.2.2 Results

We present the ﬁnal, reduced, rest-frame spectra for NGC 7619, NGC 83, NGC 13, and

NGC 6824 in Figure 8-8. Data between 1.1µm < λ < 1.15µm of the observation frame have been omitted due to heavy contamination by sky lines. All four galaxies, spanning a wide range in Hubble types (two early type galaxies, an Sb galaxy, and an Sc galaxy), appear to contain featureless continua with similar slopes. The featureless nature of the continuum at R ≈ 1400

and S/N> 25 is consistent with previous ﬁndings from Mannucci et al. (2001) at R ≈ 300

132 Figure 8-8. Y and J-band spectra of the galaxies in our sample. Data between 1.1 < λ < 1.15µm have been omitted due to sky contamination. The offsets are arbitrary scalar shifts, but are plotted in order of decreasing S/N. and S/N> 30. Therefore, at almost ﬁve times greater spectral resolution, we ﬁnd no clearly discernible features.

In Figure 8-9, we present comparisons between our best-quality spectrum of NGC 7619 and current galaxy stellar population models produced by Maraston (2005) and Bruzual & Charlot (2003). To use the models, we need both the metallicity and age of each galaxy; however, these values have only been published for NGC 7619. Bregman et al. (2006) found NGC 7619 to be 14.4 ± 2.2 Gyr old and have Z = 0.21 ± 0.03. Using these parameters, and assuming an e-folding time of 1 Gyr for a Saltpeter IMF, we can produce model galaxy spectra. Both models have very low resolution, R ≈ 250, so we reduced the resolution of our data correspondingly. Because our data have not been ﬂux calibrated we also scaled the model to match the ﬂux levels of our data.

The ﬁt was found by minimizing the χ2 difference between our data and a constant times the

2 2 model ﬂux. For Maraston (2005) χmin = 1.24 and for Bruzual & Charlot (2003) χmin = 1.09. Both the degraded and full resolution, together with the models are presented in Figure 8-9.

133 Figure 8-9. J-band spectra of NGC 7619 in black and the Maraston (2005) model that best ﬁts its properties in red and the Bruzual & Charlot (2003) model in blue. The upper spectrum is the full resolution result and the lower spectrum is a degraded version of the NGC 7619 spectrum to match the resolution of the models.

At high resolution, both models closely match the continuum and at the degraded resolution there is nearly a perfect match. Therefore, our observations confirm the overall shape of both models and demonstrate that either model is sufficient to characterize the J-band. Our data can be used to constrain future higher resolution models of galaxy spectra, but show that such models will likely continue to be featureless at R ≈ 1400. Because no obvious features are present in our reduced spectra, we decided to calculate our detection limits. To do this, we elected to add artificial features to NGC 7619’s spectrum

and ﬁnd the line equivalent widths necessary to meet a 3 or 5σ detection threshold. We assumed the features were in absorption, Gaussian in shape, and had a FWHM equal to the resolution limit of our data (R ≈ 1400). Examining our spectra in Figure 8-8 we see that there are two

noise regimes to our data. There is a noisier section blue-ward of 1.215µm and a cleaner section red-ward. Therefore, we chose to ﬁnd our limiting EW in both regimes. The 3 and 5σ errors in

134 both sections were determined by measuring the variance in the data after a linear continuum ﬁt had been subtracted and multiplying by the appropriate constant. We then calculated what the required EW of an artiﬁcial feature is to ensure that detection thresholds are exceeded.

By performing this test, we revealed that in the noisy part of the spectrum we should have

been able to detect features with EW > 0.94A˚ at the 3σ conﬁdence level and would have detected

features with EW > 1.6A˚ at the 5σ level. In the cleaner part of the spectrum, we should have

been able to detect features with EW greater than 0.56A˚ at the 3σ level and would have detected

features with EW > 0.93A˚ at the 5σ level. We note that these results are roughly consistent with

the ﬁndings of Wallace et al. (2000) as well as the analysis of our previous section. Many of the strongest stellar features detected in observations of stellar J-band features have an EW≈ 2A˚. Since some dilution of these stellar absorption features is expected on the galactic scale, we

conclude that they are right below our detection limits. Our observations demonstrate that in the local universe, emission and absorption lines remain elusive for current medium-resolution, near-IR instruments at S/N< 70. Therefore, it is possible that instrumentation matching or exceeding the Wallace et al. (2000) R ≈ 3000

observations, such as FLAMINGOS II at Gemini South (Eikenberry et al., 2006a), NIRSPEC on Keck (Magorrian et al., 1998), or LUCIFER at the LBT (Mandel et al., 2007) will be able detect spectral features in local galaxies. Since our S/N > 50 J-band spectra contain no discernible features at 2700 seconds of on-source integration with an R = 1300 spectrograph on a 4-m telescope with a 528 arcsec2

aperture, we can conﬁrm the ﬁndings from §8.3.1 that the J-band requires extremely long integration times to detect any usable features.

8.4 Discussion

With advances in instrumentation like SPIFS and a new class of telescopes just on the horizon, the ﬁeld of SMBH research looks to beneﬁt enormously. Our analysis has revealed that the calcium triple feature and H-band CO bandhead features can be used in conjunction with current line diagnostics to measure the masses of SMBHs in a much larger volume of space.

135 9 ELTs will enable us to measure SMBH out to z = 0.565 for massive (≈ 2 × 10 M¯) SMBH and we will be able to observe out to z ≈ 0.1 for more characteristic galaxies. Our investigation has also revealed that there is a gap between 0.177 < z < 0.254 where no line diagnostics currently

exist to measure the kinematic inﬂuence of SMBH on their host galaxies. However, despite this small exception in the volume of space accessible by ELTs, many questions about supermassive black holes become answerable.

These high resolutions will enable the high and low-mass ends of the MSMBH − σ relationship to be fully probed and enable a complete black hole mass function to be determined. With lookback times on the order of Gyrs, we can start to directly measure the evolution of the

BHMF as a function of time. Furthermore, having > 107 potential targets means we will be

able to gain a much more reﬁned understanding of the intrinsic scatter in the M − σ relation and

rectify the discrepancies with other relations like the M − L relationship. In general, our findings agree with Batcheldor & Koekemoer (2009) as we find similar redshift limits for the ELTs. Our work, however, also estimates the total number of galaxies observable by these telescopes and takes into account what redshift ranges should be accessible. Unfortunately, we find that rest-frame J-band features are too observationally demanding to be effective for SMBH research. Between theoretical calculations and observational constraints, we find the features are exceptionally difficult to detect. If targets in the redshift range of 0.177 < z < 0.254 are absolutely essential to observe, it is possible that one week per object on an ELT could be conceivable, but it is likely we will have to wait for other advances in visible

AO or the JWST to address those issues. In the short term, the hundreds of hours needed for proper observations of rest-frame J-band features to measure SMBH make it the features largely unsuitable for these types of observations.

136 CHAPTER 9 DISCUSSION AND CONCLUSIONS In this dissertation I have shown that speckle stabilization is a viable technique that has the potential to achieve angular resolutions as high as the diffraction limit in the optical. As a result, interesting possibilities in terms of supermassive black hole research and other topics open up.

9.1 Simulated and Actual Performance

In Chapter 2, I demonstrated that SS has promising potential in terms of angular resolutions achievable and image quality. While I found that Strehl ratios would be low ≈ 2% on 10-m class telescope, the angular resolution of ≈ 15 mas is unmatched. This is important because an observer can always increase integration times to account for lower flux but no amount of sky time will increase the resolution. What is also worth noting is that because SS only requires one good speckle of operation, it loosens the requirements on the guide stars. Because of this fact, I found that the guide star can be as far away as 20” and as faint as 16th magnitude for a 10-m telescope in moderate seeing (r0 = 15 cm). All told, until visible AO becomes common, speckle stabilization will be the only way to get diffraction-limited angular resolutions in conjunction with integral field spectroscopy. Besides the theory, in Chapter 5, I also demonstrated that SS with the SPIFS-POC actually produces angular resolutions ≈5x better than seeing. An important confirmation of this fact was with observations of the binary star system WDS 14411+1344 (Figure 5-4) where in the seeing-limited case the two stars were blended, but when using SS, they were clearly separated. I also found that while the SPIFS-POC was a useful demonstrator of SS potential, it was not

effective for science operations. The main limiting factor on this instrument was the fast steering mirror which had signiﬁcant ringing requiring a long time to compensate for. The next generation of speckle stabilization, the S3D will remedy this issue by having a better FSM. The S3D will also likely be able to acquire interesting science results as it will have a high-quality science camera and a high-speed shutter to increase Strehl ratios. All told, the potential of speckle

stabilization is just beginning to be realized.

137 9.2 Scientiﬁc Potential of SS

As shown above, SS will yield observations which are characterized by a modest Strehl ratio diffraction-limited core with a smoother halo on the same approximate angular scale as a seeing disk. This Strehl regime, of course, means that SS, despite its excellent spatial resolution, will probably not be a great tool for high-contrast imaging or milli-magnitude-precision photometry

in crowded fields. However, it will offer the ability answer questions like “Does this particular spectral feature come from Point A or Point B in this field?” at unprecedented spatial resolution. While this may seem a modest accomplishment, a great deal of astronomical discovery space is contained in the answers to that question. Particular lines of research which would benefit tremendously from the speckle stabilization technique include:

· Black hole mass measurements in galaxy cores (Chapter 8) · X-ray binaries (Chapter 2) · Quasar host-galaxy properties

· Star formation properties of galaxies at z>2 · Searches for black holes in globular clusters (Chapter 8)

· Properties of stars in tight binaries · Binarity in star-forming regions · Solar system planets and moons · Asteroid and comets More speciﬁcally, in Chapter 2 I showed how SPIFS on a 10-meter class telescope will be able to resolve the optical jets of the microquasar SS 433. This will enable a deeper understanding of jet and compact object astrophysics.

Chapter 8 speciﬁcally addressed the potential of speckle stabilization for the purpose of measuring the kinematic inﬂuence of SMBH on the host galaxy to estimate its mass. I found that on current 10-m class telescopes, the technique will be able to measure masses out to z = 0.177

9 5 for MSMBH = 10 M¯ and will have access to a total of ≈ 10 objects. The high resolutions of SS will greatly open up the parameter space of black holes accessable and aid in the search for

138 IMBHs in globular clusters as well as characterizations of the most massive black holes with

9 MSMBH > 10 M¯. This technique will compliment the ELTs in development and it will be possible to answer outstanding questions about the M − σ relationship and aid in the construction

of a complete black hole mass function. 9.3 Advantages to Speckle Stabilization

It is important to put the value of speckle stabilization in context of other high-resolution techniques like adaptive optics, lucky imaging or HST. In particular, since all of these techniques can enable near-diffraction-limited observations from ground-based telescopes, the critical issue is what regions of observational “phase space” will SPIFS reach that current techniques do not.

I ﬁrst look to adaptive optics techniques, then move to lucky imaging, and ﬁnally turn to the Hubble Space Telescope (HST). 9.3.1 Comparison to Adaptive Optics

The ﬁrst and most obvious response to this question would be that AO does not work at

visible wavelengths– it is restricted to λ > 1µm. However, as with most broad generalizations, this statement is not strictly true. While the overwhelming majority of astronomical adaptive

optics systems have been designed primarily for operation at λ > 1µm, many of them do provide some performance at shorter wavelengths. Furthermore, future systems are being planned which

will be oriented towards extending their operational focus shortwards of 1µm. However, all of these “Visible-AO” systems share some common, limiting characteristics. In order to carry out adaptive correction at these shorter wavelengths, the AO systems need faster responses and larger numbers of wavefront sensor elements and deformable mirror actuators. This generally drives up the cost of the system. Furthermore, dividing the guide star light up so ﬁnely (both spatially and temporally) means that a very bright guide star is needed to provide

sufﬁcient photons. This in turn dramatically reduces the sky coverage of Visible-AO systems. The introduction of laser guide stars can improve the sky coverage, but this also dramatically increases the cost and complexity of the AO system.

139 Speckle stabilization, on the other hand, is relatively inexpensive and simple. It only needs to track the brightest speckle, which contains typically ≈ 2% of the light under typical conditions on a 10-meter-class telescope (see Chapter 2). This is in sharp contrast to Visible-AO systems, which divide the guide star light into ≈ 1000 wavefront elements– all of which must receive enough light to measure a centroid on millisecond timescales. This difference (2% versus 0.1%) enables SPIFS to use guide stars which are ≈ 20 times fainter than Visible AO with natural guide stars effectively increasing the sky coverage (and thus, number of reachable targets) by a similar factor of ≈ 20. So, Visible-AO (Vis-AO) systems may eventually match or exceed SPIFS performance in terms of angular resolution and Strehl ratio; however, such systems are still, generally speaking, in their early development stages. Furthermore, they are likely to take quite a few years to reach fruition due to their cost and complexity, and will typically have much poorer sky coverage without lasers. In addition, even if/when these systems are developed, it is likely that their cost and complexity will mean that they are available at only a few observatories, whereas the simplicity of SS would make it an attractive alternative for reaching similar wavelengths/resolutions at greatly reduced cost and on a faster timescale for many telescopes. What is also interesting to note is that as Visible-AO becomes possible on 10-meter class telescopes, it will still be some time before Visible-AO is possible on ELTs. Therefore, SS has the potential to be used on ELTs to achieve diffraction-limited angular resolutions in the optical in the time before Vis-AO comes to fruition.

9.3.2 Comparison to Standard Speckle Imaging

Much of Chapter 7 addressed this issue with direct comparisons between SAA and LI to speckle stabilization. I modeled observations on a 2.5-meter class telescope to assess the strengths and weaknesses of the two techniques. While the differences are relatively minor, I found that speckle stabilization is a viable competitor to current Lucky Imaging systems.

Specifically, I find that Speckle Stabilization is 3.35 times more efficient (where efficiency is defined as signal-to-noise per observing interval) than shift-and-add and able to detect targets

140 1.42 magnitudes fainter when using a standard system. If a high-speed shutter is employed to compare to lucky imaging at 1% image selection, speckle stabilization is 1.28 times more efﬁcient and 0.31 magnitudes more sensitive.

However, when I incorporate potential modifications to lucky imaging systems I find the advantages are significantly mitigated and even reversed in the 1% frame selection cases. In particular, I find that in the limiting case of Optimal Lucky Imaging, that is zero read noise and photon counting, I find Lucky Imaging is 1.80 times more efficient and 0.96 magnitudes more sensitive than speckle stabilization. For the cases in between, there is a gradation in advantages to the different techniques depending on target magnitude, fraction of frames used and system modifications. Overall, however, I find that the real strength of lucky imaging is in observations of the brightest targets at all frame selection levels and in observations of faint targets at the 1%

level. For targets in the middle, speckle stabilization regularly achieves higher S/N ratios. Beside direct imaging mode, it is important to note that speckle stabilization has fundamental advantage in that the science channel is decoupled from the speckle sensor. This allows for long exposures which mean the science channel can be filled by an integral field spectrograph or polarimeter. While there is talk of doing lucky spectroscopy (Mackay 2010, private conversation), it is still in its infancy and has not been demonstrated to be feasible. Furthermore, even if lucky spectroscopy were to succeed, it would still have all the noise issues outlined in Chapter 7. Therefore this decoupling gives SS a unique advantage in the field of astronomical observations and give it an edge of speckle-based techniques.

9.3.3 Space-based Platforms

A ﬁnal comparison I consider is that of SS versus the Hubble Space Telescope. Like SS,

HST has diffraction-limited performance in the optical bandpass. Furthermore, HST has much higher Strehl ratios than SS and nearly 100% sky coverage– two extremely powerful advantages which can easily lead one to wonder “Why even bother with SPIFS when we have HST?”.

Fortunately, there are in fact several positive answers to this question. First of all, SS has the potential for signiﬁcantly higher angular resolutions than HST. Regardless of its other

141 advantages, HST is only a 2.5-meter telescope. This means that SS will have superior resolution in its diffraction-limited core even on 3-4-meter telescopes, and ≈ 4 times better resolution on 10-m-class telescopes. Secondly, adding an IFS in the form of SPIFS will provide an integral

ﬁeld spectroscopic capability which is neither currently-available nor planned for HST. Thus, while HST will have better raw sensitivity (due to its high Strehl ratios– not to mention ultra-low space-environment background), SPIFS reaches parameter space, particularly in terms of high angular resolution and integral spectroscopy, not covered by HST. 9.4 Future Directions for Speckle Stabilization

Speckle stabilization is just starting to be realized. As a result, there are many potential directions and modifications that will make the technique more competitive in the coming years. A particular direction that is worth investigating is that of putting a SS system behind and adaptive optics system. Much in the same way that Law et al. (2009) were able to realize added benefits to lucky imaging from this, SS might also be able to get higher Strehl-ratios and increased efficiency. It will also be interesting to see what SS will be able to do on ELTs and the science it will be able to access. Speckle stabilization has the potential to answer many outstanding questions in astronomy. In this dissertation, I have shown that it is both theoretically and experimentally valid and that in the next few years the techniques should be getting scientific returns.

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147 BIOGRAPHICAL SKETCH Mark Keremedjiev was born in Doylestown, Pennsylvania in June of 1984. Although he grew up in Bozeman, Montana as his parents moved there in 1988. Under the stars and mountains of the Big Sky state he grew an appreciation for astronomy and nature. Mark attended Cornell University where he did research with Professor Jim Houck, Dr. Lei Hao and Dr. Greg Sloan and received a BA with honors in Astronomy. He rowed varsity lightweight crew and also received the Cranson W. and Edna B. Shelley Awards for Excellence in Undergraduate and Graduate Research in Astronomy. Mark has spent the last four and a half years in Gainesville, Florida at the University of

Florida working on his Ph.D. in Astronomy. He has been active in the department’s Graduate Astronomy Organization and served as President from 2009-2010. Mark is an avid triathlete and has completed two half-Ironman races on the road to a full Ironman. He is happily married to Lauren Young and looks forward to a long and prosperous future with her.

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