Infrared Imaging with COAST
John Stephen Young
St John’s College, Cambridge and Cavendish Astrophysics
A dissertation submitted for the degree of Doctor of Philosophy in the University of Cambridge 26 March 1999
iii
Preface
This dissertation describes work carried out in the Astrophysics Group of the Department of Phys- ics, University of Cambridge, between October 1995 and March 1999.
Except where explicit reference is made to the work of others, this dissertation is the result of my own work, and includes nothing which is the outcome of work done in collaboration. No part of this dissertation has been submitted for a degree, diploma, or other qualification at any University.
This dissertation does not exceed 60,000 words in length.
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Acknowledgements
Many people say that this is the only page of a PhD. thesis worth reading. I hope that is not the case here. This is, however, the only page not written in the passive voice, and the only one which might make you smile.
Above all, I would like to thank my supervisor, Professor John Baldwin, for always being available to give advice and encouragement, and for assisting with many hours of alignment and even more hours of observing. The shortbread was much appreciated! Many thanks are also due for his reading of this thesis.
It has been a pleasure to work with all of the members of the COAST team. None of the work described in this thesis would have been possible without the NICMOS camera built by Martin Beckett. I would like to thank him for taking the time to explain it to me. I am also grateful to Craig Mackay for revealing some of the undocumented features of CCD controllers. I would like to thank Chris Haniff for many useful discussions, and for reading Chapter 8. Peter Warner was always willing to hack the Nord software to accommodate the infrared system, and participated in most of the observing with COAST. David Burns wrote the original versions of most of the analysis software. Donald Wilson contributed his expertise to the artificial star and mirror drives used in the IR beam combiner. Thanks to Richard Wilson for help with the Betelgeuse stuff. Peter Lawson also participated in the WHT run which yielded the Betelgeuse data. Amanda George and Debbie Pearson took the photographs of COAST. All of the above, plus John Rogers, Roger Boysen, and David St-Jacques contributed to the very enjoyable COAST meetings on Friday afternoons.
Of those outside Cambridge, I would like to thank Professor Michael Scholz for supplying model Mira CLVs, and Dr. Joseph Lehar for modifying his versions of the Caltech VLBI model-fitting software.
My office mates deserve a mention for putting up with me. Keith and Mat should go first, for 1 surviving all 3 2 years of me (and the canteen food). Klaus, Youri, Firouzeh, Dave, Marcel and Anja all helped to brighten things up too.
Special thanks are due to my long-time housemates Matt, Emma (honorary housemate), Tim, Steve, and Anna. I also want to thank Dave, Pip and Fred for keeping me in touch with the real world.
I owe the largest debt of gratitude to my family. Thanks to Mum, Dad and Suzanne for love and support from afar, and to my grandparents for the same from slightly closer.
To my family
The Cambridge Optical Aperture Synthesis Telescope x Contents
1 Introduction and Historical Perspective 1
1.1Highresolutionimaging...... 1
1.2Historyofopticalstellarinterferometry...... 3
1.3Historyofinfraredstellarinterferometry...... 4
1.4Thiswork...... 5
2 Infrared Detectors for Interferometry 7
2.1Detectorprinciples...... 7
2.2Performance...... 8
2.2.1 Quantumefficiency...... 8
2.2.2 Readnoise...... 9
2.2.3 Readout time ...... 9
2.2.4 Linearity...... 9
2.2.5 Darkcurrent...... 9
2.2.6 Wellcapacity...... 10
2.2.7 Arraysize...... 10
2.3NICMOScamera...... 10
2.3.1 NICMOSdevice...... 10
2.3.2 Dewar...... 11
2.3.3 Interfacebox...... 11
2.3.4 CCDcontroller...... 11 xii CONTENTS
2.3.5 Hostcomputer...... 11
2.4 Pixel readout ...... 12
3 Optical Systems 15
3.1 Components of an optical/infrared interferometer ...... 15
3.1.1 Telescopes...... 15
3.1.2 Acquisition/autoguiding...... 16
3.1.3 Pathcompensation...... 16
3.1.4 Correlator...... 16
3.2Possiblecorrelatordesigns...... 17
3.2.1 All-on-onev.pair-wisebeamcombination...... 17
3.2.2 Image plane v. pupil plane combination ...... 18
3.3Alignmentproblems...... 23
3.3.1 Generalproblems...... 23
3.3.2 Infrared-specificproblems...... 24
3.4Alignmentsolutions...... 28
3.4.1 Measuring the pupil positions ...... 28
3.4.2 Referencedirections...... 30
3.4.3 Focusingtheartificialstar...... 31
3.4.4 Schemeforfineadjustmentofthebeamdirections...... 33
3.4.5 Resultsandsummary...... 36
3.5Performance...... 37
3.5.1 Optical throughput ...... 37
3.5.2 Fringe visibility ...... 42
3.5.3 Spectral response ...... 42
3.5.4 Closurephases...... 45
3.5.5 Path stability ...... 46
3.5.6 Conclusions...... 46 CONTENTS xiii
4 NICMOS3 Infrared Camera 47
4.1Samplingrequirements...... 47
4.2 Readout of the NICMOS array ...... 49
4.2.1 NICMOSfeatures...... 51
4.2.2 Extrinsicnoise...... 53
4.3Futureimprovements...... 55
4.4Summary...... 59
5 Stellar Observations, Data Reduction and Analysis 61
5.1 Introduction ...... 61
5.2Observations...... 62
5.2.1 Telescopealignment...... 62
5.2.2 Findingfringes...... 62
5.2.3 Recordingfringedata...... 63
5.3 Visibility amplitude estimation ...... 67
5.4Closurephaseestimation...... 70
5.5Capellaobservationsanddatareduction...... 71
5.6Imagereconstruction...... 72
5.7 Model fitting ...... 75
5.7.1 Effectivetemperatures...... 76
5.8Conclusions...... 78
6 The Wavelength-dependent Morphology of Betelgeuse 81
6.1 Introduction ...... 81
6.2Observationsanddatareduction...... 82
6.2.1 Measurements with COAST at 1.3 µm...... 83
6.2.2 MeasurementswithCOASTat905nm...... 84
6.2.3 MeasurementswiththeWHT...... 84 xiv CONTENTS
6.3Results...... 85
6.3.1 Fourierdata...... 85
6.3.2 Images...... 90
6.3.3 Asymmetries...... 90
6.3.4 Apparentsizesandlimb-darkening...... 97
6.4Discussion...... 100
6.4.1 Asymmetries...... 100
6.4.2 Infraredlimb-darkening...... 106
6.5Conclusions...... 107
7 Cyclic Variations in the Angular Diameter of χ Cygni 109
7.1 Introduction ...... 109
7.1.1 Miravariables...... 109
7.1.2 DiameterchangesofMiras...... 110
7.2Observationsanddatareduction...... 110
7.2.1 MeasurementswithCOAST...... 110
7.2.2 MeasurementswiththeWHT...... 111
7.3Results...... 114
7.4Discussion...... 118
7.5Conclusions...... 119
8 Mira Variables 121
8.1 Introduction ...... 121
8.2Observationsanddatareduction...... 121
8.3Results...... 122
8.3.1 Simplemodels...... 122
8.3.2 Asymmetries...... 124
8.3.3 Photosphericdiameters...... 128 CONTENTS xv
8.3.4 Variationwithphase...... 133
8.3.5 Effectivetemperatures...... 133
8.3.6 Linearradii...... 135
8.4Discussion...... 135
8.4.1 Asymmetriesandlimb-darkening...... 135
8.4.2 Previously-published angular diameters ...... 137
8.4.3 Effectivetemperatures...... 137
8.4.4 Linearradiiandpulsationmodes...... 138
8.5Conclusions...... 142
9 Conclusions 143
9.1Thefuture...... 145 xvi CONTENTS List of Figures
2.1Circuitforcalculationofresetnoise...... 12
2.2DCScircuitry...... 14
3.1Imageplanebeamcombiner...... 19
3.2Exampleofatemporalfringepattern...... 20
3.3Pupilplanebeamcombiner...... 20
3.4Powerspectrumofthree-baselinedata...... 22
3.5 Layout of the optical components inside the COAST building ...... 25
3.6 Beam-splitter unit ...... 26
3.7PhotographoftheIRbeamcombiner...... 27
3.8 Effect of pupil shift with defocused artificial star ...... 29
3.9Setupforfocusingartificialstar...... 32
3.10Centroidcoordinateplottedagainstbeamangle...... 34
3.11 Angular displacements due to a thin prism ...... 35
3.12 Non-parallel-sided beam-splitter and compensating plates ...... 36
3.13Powerspectraofinternalfringesandstellarfringes...... 43
3.14 Transmission curve of J bandfilterandtelluricabsorptionfeatures...... 44
4.1Real-timecodein“observe”...... 52
4.2Powerspectrumofthree-baselinedataonCapella...... 53
4.3 Data stream from fast readout cycle ...... 54
4.4Noisefeaturesduetopick-upatspecificfrequencies...... 56 xviii LIST OF FIGURES
4.5Residualnoisefeatures...... 57
4.6 Plot of signal against read number for successive reads with only occasional resets 58
5.1Stellarfringes...... 63
5.2 Histogram of visibilities ...... 65
5.3 Cumulative average visibility ...... 66
5.4 Multi-summed power spectra ...... 68
5.5 Illustration of the integration method for visibility amplitude estimation ..... 69
5.6 uv coverageforCapellaobservations...... 71
5.7ImageofCapella...... 74
5.8 Two-component model for Capella ...... 77
6.1 Visibility curve and closure phases for Betelgeuse at 1.3 µm...... 86
6.2 Visibility curves and closure phases for Betelgeuse at 905 nm ...... 88
6.3 Visibility curve for Betelgeuse at 700 nm ...... 89
6.4ClosurephasesforBetelgeuseat700nm...... 89
6.5COASTinfraredimageofBetelgeuse...... 92
6.6WHT700nmimageofBetelgeuse...... 93
6.7 Visibility functions and intensity profiles for Hestroffer limb-darkened models . . 94
6.8 Brightness distributions for the best-fit models for Betelgeuse at 700 nm and 905 nm 98
6.9 Best-fit two-parameter limb-darkened disk model for Betelgeuse at 1.3 µm.... 101
6.10 Blackbody hotspot model ...... 102
6.11SyntheticTiOspectrum...... 105
7.1 Visibility curve for χ Cygat905nm...... 114
7.2 Gaussian plus one unresolved feature model for χ Cyg...... 115
7.3 Variation of diameter with pulsation phase for χ Cyg...... 117
7.4 Light curve for χ Cygat905nm...... 117
8.1 Visibility curves and closure phases for T Cep and χ Cyg...... 125 LIST OF FIGURES xix
8.2 Visibility curves for R Cas and o Cet ...... 125
8.3 J bandcentre-to-limbintensityprofilesforMiramodels...... 131
8.4Stellarradiusplottedagainstpulsationperiod...... 139
8.5 Stellar radius plotted against pulsation period for Miras from van Belle et al. (1996) 141 xx LIST OF FIGURES List of Tables
3.1Reflectivityofmirrorcoatings...... 39
3.2 Transmission of optical components ...... 40
3.3 Predicted IR throughput of COAST ...... 41
3.4QuantumefficiencyofNICMOSdevice...... 41
5.1 Two-component model for Capella ...... 76
5.2 Predicted and observed separation and position angle for Capella ...... 76
5.3 Synthetic V J coloursforG-andK-typegiantstars...... 78
6.1LogofBetelgeuseobservations...... 82
6.2 Best-fit disk plus one unresolved feature models for 905 nm 97/11/21 COAST data 95
6.3Best-fitdiskplusoneunresolvedfeaturemodelsfor700nmWHTdata...... 96
7.1 Log of χ Cygobservations...... 112
7.2 Apparent angular sizes for χ Cyg...... 113
8.1LogofMiraobservations...... 123
8.2One-parametermodelsforMiras...... 126
8.3 Adopted uniform disk diameters for calibrator stars ...... 126
8.4Best-fitdiskplusoneunresolvedfeaturemodels...... 129
8.5 Best-fit disk elliptical disk models ...... 129
8.6 Fundamental properties of Mira models ...... 131
8.7Diameterscalingfactors...... 133 xxii LIST OF TABLES
8.8 Photospheric angular diameters for Miras ...... 134
8.9 Mean photospheric angular diameters for Miras ...... 134
8.10EffectivetemperaturesforMiras...... 135
8.11LinearradiiofMiras...... 136 Chapter 1
High Resolution Infrared Imaging: Introduction and Historical Perspective
1.1 High resolution imaging
The detail which can be seen by conventional optical and infrared telescopes is limited by tur- bulence in the Earth’s atmosphere. In the absence of an atmosphere, and with flawless optical components, the imaging performance of a telescope would be limited by diffraction from the fi-
θ : λ= λ nite primary mirror. The diffraction limit for a circular aperture is given by = 1 22 D,where is the light wavelength and D is the aperture size, i.e. the limit is inversely proportional to the size of the aperture in wavelengths. Thus the angular resolution of a diffraction-limited 10 m telescope λ in the visible part of the spectrum ( = 500nm) would be 12 milliseconds of arc.
The diffraction-limited resolution of a 10 m telescope is insufficient for many astrophysical prob- lems. Binary systems in which the two constituent stars are close enough to interact would appear as single images, and the disks of all but the nearest, most evolved single stars would remain unresolved. Higher angular resolution is essential for understanding the early and late stages of stellar evolution, and for imaging the inner regions of active galactic nuclei. However, telescopes with large one-piece mirrors are hugely expensive and time-consuming to build. It is difficult to imagine telescopes with mirrors much more than 10 m in diameter being constructed within the next ten years.
Radio astronomers ran into this problem much earlier. Because radio wavelengths are one hundred thousand times longer than optical wavelengths, the diffraction-limited resolution of the world’s largest radio antennas is still one minute of arc. The solution is to combine the signals from physically separated radio dishes. The van Cittert-Zernicke (VCZ) theorem states that the degree of coherence between the parts of a wavefront received at two separate points from a distant source is the Fourier transform of the brightness distribution of the source. The VCZ theorem tells us that it is not necessary for all parts of a telescope mirror to be present at once. Thus it is possible to use an array of small telescopes to synthesise a much larger telescope. The synthesised telescope 2 CHAPTER 1. INTRODUCTION AND HISTORICAL PERSPECTIVE will have the angular resolution of a single-mirror telescope the size of the largest separation in the array. This technique, called aperture synthesis, was pioneered at the Mullard Radio Astronomy Observatory (MRAO) in the 1950s and 1960s.
The superposition of the parts of a wavefront received at two separated telescopes produces an interference pattern. Hence a telescope which works in this way is called an interferometer.The contrast, or visibility, of the interference pattern (or fringe pattern) is directly related to the degree of coherence of the two wavefronts, and has both an amplitude and a phase. The interference pattern produced by a pair of telescopes is analogous to the pattern of light and dark fringes produced in a Young’s slit experiment. A two-element interferometer is sufficient to measure the angular size of an object, but more telescopes are needed for imaging through the atmosphere.
The individual telescopes making up an interferometer cannot be arbitrarily large, as all ground- based optical and infrared telescopes (not just the elements of an interferometer) suffer from image degradation caused by the atmosphere, which can drastically reduce the contrast of interference fringes. The image distortions are caused by both spatial and temporal variations of refractive index in the turbulent air above the telescope, called seeing. Hence the atmosphere acts as a constantly changing lens which distorts the image. The refractive index variations cause variations in optical path, and hence distortions of the phase of an incoming light wavefront (e.g. from a star) across an aperture. The phase variations may be characterised by a spatial scale and a timescale.
The spatial scale is a length r0 (Fried 1966), equal to the diameter of a circular aperture over which the RMS variation in the phase of a light wavefront is one radian. Thus r0 is roughly the size of the largest telescope which is unaffected by the atmosphere. At visible wavelengths this size is only about 10 cm.
The timescale of the refractive index variations can be derived by assuming that an unchanging screen of turbulence is blown across the telescope by the wind. This yields a characteristic time t0 in which the RMS phase variation, relative to that of the undistorted wavefront, is one radian. At visible wavelengths, t0 is typically 5 ms at good sites. This is the longest exposure time which will
“freeze” the seeing. If a short exposure (i.e. < t0) image is made with a telescope whose primary mirror is larger than a few times r0, the resulting image is a speckle pattern, consisting of an image of the target convolved with a random pattern of bright “speckles”.
To obtain diffraction-limited resolution for long-exposure images, the optical train of the telescope must include Adaptive Optics (AO), i.e. a system to measure the wavefront distortions introduced by the atmosphere, plus a deformable mirror to correct the wavefronts. The wavefront must be measured and corrected before it has changed significantly, i.e. in a time less than t0. The number of degrees of freedom needed for the deformable mirror, and hence the number of measurements which must be made in each time interval, increases with the size of the telescope aperture. In order to measure the wavefront distortions when the target is faint, an AO system must observe a nearby bright point source through the same column of atmosphere as the target of interest. There may be no real stars sufficiently close to a particular target to act as references, in which case a guide “star” can be generated artificially using powerful lasers. Even without laser guide stars, AO systems are complicated and expensive. Nevertheless, during the last few years a number of systems have come into routine use at observatories world-wide. 1.2. HISTORY OF OPTICAL STELLAR INTERFEROMETRY 3
The simplest form of AO system is tip-tilt correction, which only corrects the mean tilt of the wavefront across the telescope aperture. This is equivalent to taking out the mean image motion. Tip-tilt correction is particularly useful for optical interferometry, since it allows the aperture size
to be increased to 3r0 without seriously reducing the visibility of the interference fringes.
Even if the wavefront distortions across all of the telescopes making up an optical interferometer were completely corrected, the visibility phases would contain no information about the astro- nomical target. This is because the atmosphere randomly perturbs the paths of light rays from the source to the different telescopes in the array, i.e. the atmosphere adds a random phase to the signal from each antenna. However, the sum of the phases around a triangle of three antennas remains unaffected by the atmosphere. This quantity, called the closure phase (Jennison 1958), is vital to provide the phase information needed to reconstruct images.
Atmospheric turbulence places strict constraints on optical interferometers. The individual tele- scopes must not be larger than a few times r0, so that the images from the telescopes, which are superposed to form a fringe pattern, do not break up into a number of speckles. Measurements of
the contrast of the fringe pattern must be made in a time < t0, otherwise the pattern would become blurred. The coherence length must also be longer than the atmospherically-induced optical path fluctuations (otherwise there would not always be fringes), thus a narrow optical bandwidth must be used. All of these constraints restrict optical aperture synthesis to bright targets.
Use of the standard statistical theory of atmospheric turbulence (Kolmogorov 1941) leads to the conclusion that r0, and hence t0 (which is proportional to r0 divided by the wind speed), increase with wavelength as the 6/5 power (Fried 1966). Also the optical path variations caused by the atmosphere are a smaller number of wavelengths in the infrared, and so a wider fractional band- width can be used. The combination of these effects is the potential for the signal-to-noise in a fringe measurement to increase as λ4 :6, if the optimum telescope size and fractional bandwidth are employed. For this reason, it is preferable to operate an interferometer at infrared, rather than optical, wavelengths. However, early experiments used visible light, as suitable infrared detectors were not available.
1.2 History of optical stellar interferometry
The use of interferometry to obtain high angular resolution at optical wavelengths was in fact proposed by Fizeau in 1868, decades before interferometry was used in the radio. The first exper- iment was performed by St´ephan in 1874, who failed to resolve any stars with an interferometer constructed by masking all of a large telescope but two small apertures, spaced 50–65 cm apart. St´ephan correctly concluded that all stars had angular diameters much smaller than 0.16 seconds of arc. The first astronomical angular diameter measurements were made by Michelson, who measured the diameters of Jupiter’s moons in 1891, and the diameter of the red supergiant star Betelgeuse in 1921. The latter measurement required the use of two mirrors at either end of a 20 foot beam mounted on the 100 inch Hooker telescope. These measurements were made by varying the spacing of the two apertures until the observer determined that the interference fringes (watched by eye) had disappeared. In practice the fringes often disappeared because of optical 4 CHAPTER 1. INTRODUCTION AND HISTORICAL PERSPECTIVE misalignments and bending of the telescope structure, hence the experiment was very difficult to perform. Similar problems affected the dedicated 50 foot interferometer which was subsequently constructed (Pease 1931). Further development in this field was stalled until the 1970s by the lack of detectors suitable for fringe measurement.
The entire history of aperture synthesis at optical and infrared wavelengths has been closely linked to the development of required technology in the areas of opto-mechanics, opto-electronics, and computing. The relevant theory and image reconstruction techniques were developed in the 1950s and 1960s for radio interferometry. The early 1980s saw the introduction of infrared detectors which were sufficiently sensitive to detect the small numbers of photons collected by stellar inter- ferometers in the permitted integration times. Because of the potential for better signal-to-noise in the IR compared with visible wavelengths, several of the two-element stellar interferometers built subsequently were designed to operate in the infrared.
1.3 History of infrared stellar interferometry
All of the infrared interferometric telescopes described here had one feature in common. None were designed to combine the light from more than two telescopes simultaneously, and hence they could not measure closure phases or make images. Nevertheless all of the telescopes listed below have been successful at making stellar diameter measurements, which have led to significant astrophysical results. The instruments have also contributed to the understanding of the practice of interferometry at IR wavelengths.
The first-generation of infrared interferometers included the Interf´erom`etrea2T´ ` elescopes (I2T, Di Benedetto 1985) at the Observatoire de Calern in Provence, and the University of Wyoming’s Infrared Michelson Array (IRMA, Benson 1991). Both operated at a wavelength of 2.2 µmand used single-element InSb detectors (the I2T could also operate in the visible). The Infrared Optical Telescope Array (IOTA, Dyck et al. 1995), with larger telescopes located on a better site in Ari- zona, is the successor to IRMA, run by a consortium of US and French institutions. IOTA is now capable of operating at wavelengths between 1.0 and 2.4 µm, thanks to the recent incorporation of a NICMOS3 detector.
The most recent stellar interferometer to commence operations is the Palomar Testbed Interfer- ometer (Colavita et al. 1995). This interferometer operates at 2.2 µm, and was built by the Jet Propulsion Laboratory to experiment with the new technique of dual-star astrometry. Two stars are observed simultaneously in order to accurately measure their relative positions. This method will be used on the forthcoming Keck interferometer to search for planets orbiting nearby stars, by attempting to detect the orbital motion of the parent star.
The interferometers mentioned above all detect near-IR photons incoherently, after the light beams from different telescopes have been interfered to form a fringe pattern. Several other experiments have used heterodyne detection techniques (as used by sub-millimetre and radio telescopes) at µ wavelengths of 10 m. Two early experiments (Johnson et al. 1974; Assus et al. 1979) were 1.4. THIS WORK 5 forerunners of the successful Infrared Spatial Interferometer (ISI, Danchi et al. 1988). Heterodyne detection is generally noisier than incoherent detection at shorter wavelengths, and this thesis is only concerned with the 1–3 µm wavelength range.
Because of bright limiting magnitudes, all of the targets observed by optical and near-infrared interferometers thus far have been stars, particularly cool, late-type stars (which are large enough
to be resolved on baselines 20 m). The peaks of the (approximately) black-body spectra of stars µ with effective temperatures 3000 K are at wavelengths near 1 m, and so IR interferometers can operate in the band which maximises the detected flux. More importantly, the infrared region (above 1 µm) is relatively free of spectral lines, so an appropriate band may be used to image the “true” surface of the star. A potential problem with this application is that cool stars are enveloped
by dust, but fortunately the optical depth of a 1000 K dust shell is minimised in the near-infrared. At shorter wavelengths there is significant scattering by the dust grains, whereas at wavelengths longer than about 3 µm, thermal emission from the dust begins to dominate. Hence observations at 5–10 µm can be used to determine the spatial distribution of the circumstellar dust.
Dust also obscures young stellar objects (YSOs) in nearby star-forming regions. Many YSOs should be bright enough to be imaged by future aperture synthesis arrays. The cores of active galactic nuclei are yet more ambitious targets, but the best chance is at IR wavelengths: AGN are typically several magnitudes brighter in the infrared than in the visible. For example, the core of NGC 1068, one of the brightest AGN, has a K band (2.2 µm) magnitude of 8.0 (McCarthy et al. 1982). The astronomical targets accessible to IR interferometers are discussed in more detail by Dyck and Kibblewhite (1986).
1.4 This work
The first optical/IR aperture synthesis image from separated telescopes was made at visible wave- lengths, in 1995 (Baldwin et al. 1996), using the Cambridge Optical Aperture Synthesis Telescope (COAST). COAST is the first optical interferometer specifically designed to produce images, by measuring closure phase as well as visibility amplitude.
COAST was designed to work at visible wavelengths. The aim of this project was to add the capability of imaging at near-infrared wavelengths, following on from the work of Beckett (1995). The project was made possible by the arrival of new detector technology, discussed in Chapter 2.
This work describes the problems encountered in modifying COAST to operate as an imaging telescope in the near-infrared, and the solutions employed in overcoming these problems. Many of the solutions have more general applications in interferometry.
The effectiveness of the solutions is clearly demonstrated by the number of astronomical results obtained with the working COAST IR system. These results, described in Chapters 5–8, include high-quality images of Capella and Betelgeuse, and a large number of diameter measurements of Mira variables. The astrophysical implications of these results, combined with high angular resolution observations at visible wavelengths, are also discussed. 6 CHAPTER 1. INTRODUCTION AND HISTORICAL PERSPECTIVE
Chapter 2 is a brief review of the principles of operation of modern infrared array detectors, required in order to follow the discussion in later chapters.
Chapter 3 describes the optical systems of a typical stellar interferometer, with particular em- phasis on beam-combining schemes which could be used at infrared wavelengths. The relative merits of the different schemes when a noisy detector is used are discussed. The pupil plane beam combiner chosen for IR operation at COAST is described, as are the fundamental problems in aligning such a system. Possible solutions to these problems are discussed, including the methods finally adopted at COAST. These procedures have been used at COAST to accurately align the four-way IR beam combiner and maintain its alignment throughout the observing season.
Chapter 4 discusses the readout mode used for the NICMOS3 camera at COAST to sample pupil plane fringes at up to 2.5 kHz. The functionality of the software used to control the NICMOS array and store fringe data is described.
Chapter 5 describes the procedures used when observing with COAST in the infrared, illus- trated by observations of the binary star Capella. I discuss the methods for extracting visibility amplitudes and closure phases from the raw data, and subsequently using them to reconstruct an image of the astronomical target.
Chapter 6 is concerned with contemporaneous high resolution imaging of the M-type supergiant star Betelgeuse in a number of wavebands from 0.7–1.3 µm, performed with COAST, and with the William Herschel Telescope by the technique of non-redundant masking. The implications for the possible origin of the “hotspots” frequently detected on Betelgeuse are discussed.
Chapter 7 presents the results of a programme to monitor the angular diameter of the Mira variable star χ Cygni. This programme was carried out with COAST and the William Herschel Telescope, over a period of 17 months.
Chapter 8 describes a programme to make near-continuum (1.3 µm) diameter measurements of a sample of Mira variables with COAST, and the implications of the measurements for the effective temperatures, physical diameters and pulsation modes of the sample stars.
Chapter 9 is a summary of the most important ideas from each chapter. Developments planned for the IR instrumentation at COAST are discussed, with suggestions for future astronomical pro- grammes. Chapter 2
Infrared Detectors for Interferometry
Infrared interferometry is limited by detector performance, so I shall continue by describing the principles of operation of infrared detectors, and how these principles impinge upon the design and performance of real detectors. I will discuss the importance of each aspect of detector per- formance for stellar interferometry, identifying the limits imposed by the detector on how faint or complex a source can be imaged by aperture synthesis. Finally, I will describe the mechanical and electronic components which make up the NICMOS3 camera system used at COAST, and examine the processes involved in first addressing a pixel of the NICMOS array, then reading the signal stored at that pixel.
2.1 Detector principles
All IR detectors suitable for use in interferometers operating at wavelengths between one and five microns are based on semiconductors, and detect individual photons directly. An incoming photon with energy greater than the bandgap energy is absorbed within the semiconductor material, ex- citing a bound electron into the conduction band. The remaining net positive charge behaves as a positively-charged particle, called a hole. Thus a electron-hole pair is created, which can carry a measurable electric current (a photocurrent).
λ Infrared detectors must have low bandgap energies, as photons with wavelengths longer than c =
hc=Ebandgap are not detected. This cut-off wavelength (which is temperature dependent) is about
1.05 µm for silicon, and so more exotic materials must be used for most of the infrared region.
: µ Popular choices include InGaAs, which is sensitive up to 1.7 µm, InSb (λc = 5 4 m) and HgCdTe, whose composition can be tuned to give a cut-off wavelength in the range 2.4–4.8 µm (Joyce 1992).
The simplest form of semiconductor detector is a photoconductor. An applied electric field causes a photocurrent when incident photons generate electron-hole pairs within the semiconductor. The photocurrent is sensed by measuring the voltage across a series resistor. However, this voltage is sensitive to changes in the external resistance or in the intrinsic resistance of the semiconductor. Instead, most high-performance detectors use the photovoltaic effect: a diode junction is created 8 CHAPTER 2. INFRARED DETECTORS FOR INTERFEROMETRY within the semiconductor and biased to create an electric field across the junction. The photocur- rent discharges the diode capacitor, and so the voltage across the diode at the end of an integration gives the accumulated signal.
Arrays of detectors are desirable for efficient direct imaging, but are necessarily much more com- plex than single pixel detectors. A possibility is to use small arrays of self-contained detect- ors, each with its own readout circuitry, but these are expensive and the pixels cannot be closely packed. Shared addressing and readout circuitry must be manufactured in silicon, as the techno- logy to make complex integrated circuits in other semiconductors is still immature. Thus high- performance infrared arrays employ hybrid designs, where a detector layer is bonded to a silicon layer containing the readout circuits.
A hybrid device may use a Charge-Coupled Device (CCD)1 as a readout circuit. The CCD is used to transfer the charge from the pixel of interest to a shared readout circuit. Alternatively the device may be a direct-readout array, in which each pixel has its own readout circuit in the silicon layer. A set of switches called a multiplexor allows any individual readout circuit to be connected to the output of the device. Both types of hybrid array are difficult to manufacture, as differential thermal expansion between the two layers can cause the array to break apart. Partly as a result of this, such IR arrays are very expensive.
2.2 Performance
As discussed in the previous chapter, stellar interferometers operate in a photon-starved regime.
The fringe patterns must be measured in integration times shorter than t0 (which is typically tens of milliseconds in the near-infrared). These constraints determine which of the limitations of IR detectors are important for interferometry.
2.2.1 Quantum efficiency
The Quantum Efficiency (QE) of a detector is the fraction of incident photons (with appropriate wavelengths) which are detected. The QE is the product of the probabilities that:
1. A photon incident on the front surface of the detector will reach the photon-sensitive semi- conductor layer. This depends upon the design of the device.
2. A photon will generate an electron-hole pair within the semiconductor. This depends on the composition and temperature of the semiconductor.
3. An electron-hole pair will be detected by the readout circuitry. This depends on the design of the diode junction and readout circuit.
1In this context, CCD refers to a readout circuit which operates by charge transfer, which should not be confused with visible wavelength detectors, usually referred to as CCDs, which have the photon-sensitive region and the (charge- coupled) readout circuit combined in a single silicon integrated circuit. 2.2. PERFORMANCE 9
Because only a few photons may be incident on the detector during each integration time, the QE of the detector is crucially important. The quantum efficiency and read noise of the detector limit the faintest target for which fringes can be detected by an interferometer. Modern direct-readout arrays typically have quantum efficiencies in the range 20–80%.
2.2.2 Read noise
This is the component of the noise on the signal from a single pixel which is independent of the signal level. Read noise arises from the process by which the charge stored on the diode capacitor is converted to the final signal. If the readout procedure is optimised, the read noise is usually limited by electronic noise in the amplifier(s). The smallest signal which can be detected goes as the square of the read noise.
2.2.3 Readout time
Long readout times are usually needed to take out the effects of high frequency changes in bias voltages etc., and so the time taken to read out a pixel with the minimum read noise can be tens or hundreds of microseconds. If measuring a fringe pattern requires a large number of pixel reads, the total readout time can approach or exceed t0, leading to blurring of the fringe pattern.
2.2.4 Linearity
Infrared detectors which use the photovoltaic effect are non-linear, i.e. the output signal is not proportional to the number of photons detected. As arriving photons discharge the diode capacitor, the bias across the junction, and hence its capacitance, decreases. Thus the detector is non-linear.
This non-linearity is important for all applications of IR detectors, but the relationship between detected photons and output signal is monotonic, and so can be calibrated.
2.2.5 Dark current
Dark current is the signal received which does not originate from the target of interest. It has two components: electron-hole pairs are generated thermally within the semiconductor material, as well as by arriving photons. To minimise the resulting signal, IR detectors are normally operated at low temperatures. There is a further contribution to the dark signal from background radiation incident on the detector. In the infrared, at wavelengths longer than 2 µm, most of the background is thermal radiation from objects at room temperature within the field of view of the detector.
The intrinsic dark current is almost always negligibly small for the short exposures used in inter- ferometry, but the thermal background signal can be a problem if the detector sees large areas at room temperature. 10 CHAPTER 2. INFRARED DETECTORS FOR INTERFEROMETRY
2.2.6 Well capacity
This is the signal needed to saturate the detector, i.e. to discharge the diode capacitor. The well capacity is determined by the bias applied to the diode junction, and is of little importance to inter- ferometric applications in the near-infrared. At longer wavelengths, thermal background radiation can saturate array detectors in the time it takes to read them out.
2.2.7 Array size
Larger format arrays increase the speed at which astronomical surveys can be carried out. Infrared
arrays with 1024 ¢ 1024 pixels are now available, and 2048 square arrays are promised in the very near future. However, interferometers can work satisfactorily with single element detectors or with small (128 square) arrays, depending upon the fringe measurement scheme chosen.
2.3 NICMOS camera
This thesis is concerned with the operation of COAST in the infrared, using the IR camera system built by Martin Beckett. I will now describe the components of this system. The processes of addressing and reading a pixel of the array are explained in the following section. For more details the reader is referred to Beckett (1995).
2.3.1 NICMOS device
The camera uses a NICMOS3 detector chip, manufactured by Rockwell International. The device was designed for use in the Hubble Space Telescope, hence its acronym, which stands for Near-
Infrared Camera and Multi-Object Spectrograph. It is a hybrid direct-readout array with 256 ¢ 256 40 µm square pixels, although the array is in fact operated as four 128 square quadrants. The detector material is HgCdTe, with a cut-off wavelength of 2.4 µm. The quantum efficiency of the µ NICMOS3 is 50% for wavelengths from 1.0 m to the cut-off wavelength. The device in use at COAST is an engineering grade chip, which has a large number of inoperative pixels.
Each pixel has a detector diode within the HgCdTe layer, which is electrically connected to its own unit cell in the silicon layer by indium bonds. The unit cell circuit contains a Field-Effect Transistor (FET) with very high gate resistance, so that the voltage across the diode at the end of an integration can be read without any of the charge leaking away. This property of non-destructive reads can be used to reduce the effective read noise, by making multiple reads of the same signal level.
The silicon layer also contains the multiplexor, a matrix of switches which can connect any pixel in the array to an output amplifier, which provides the final signal from the detector chip. 2.3. NICMOS CAMERA 11
2.3.2 Dewar
The NICMOS device is mounted in an standard Oxford Instruments liquid-nitrogen-cooled dewar, which has two functions:
¯ Cool the NICMOS device itself, to minimise the intrinsic dark current.
¯ Ensure that the photo-sensitive parts of the device see only cold surfaces in addition to the desired input light beam, to minimise the thermal background signal.
The second requirement includes cooling of the interference filter used to select the spectral band for observing.
2.3.3 Interface box
Cables link the NICMOS device inside the dewar to an external electronic circuit, designed to interface the chip to a standard controller (Astromed 3200) intended for visible-wavelength CCD cameras. The interface box has the following functions:
¯ Select a particular quadrant of the NICMOS device, as the CCD controller can only handle one at a time.
¯ In conjunction with the CCD controller, implement Double-Correlated Sampling (DCS) to reduce the read noise. The operation of DCS is described in the next section.
¯ Incorporate a source follower based upon an n-channel FET, for compatibility with the con- troller.
2.3.4 CCD controller
Operating a direct-readout array is much simpler than controlling a CCD, as only very simple analogue circuitry is required — the minimum is just that needed to digitise the final signal. The controller must also generate digital signals to control pixel addressing and readout within the IR device.
The controller has two components, a Digital Drive Electronics (DDE) unit, controlled by a simple RISC (Reduced Instruction Set Computer) microprocessor on an expansion card inside a Personal Computer (PC). The two components communicate via a 16-bit RS-422 bus.
2.3.5 Host computer
The IBM-compatible personal computer’s purpose is to load and run programs on the RISC pro- cessor, in order to operate the NICMOS array. The PC provides a simple user interface, and 12 CHAPTER 2. INFRARED DETECTORS FOR INTERFEROMETRY
RC VN
Figure 2.1: Circuit for calculation of reset noise. See text. is responsible for storing image data or for transferring it to a Norsk Data mini-computer by a custom parallel link, in real-time (i.e. while the camera is being operated).
2.4 Pixel readout
A pixel is addressed by clocking two shift registers in the multiplexor, using digital signals from the CCD controller. It is not possible to address a particular pixel without first skipping the pre- ceding rows, then the preceding columns on the desired row. It is the controller in the COAST camera system which limits the rate at which rows and columns can be skipped.
To reset a pixel, it is connected to a bias voltage (supplied by the CCD controller) through the multiplexor, thus charging up the diode capacitor. During an integration, photons are incident on the chip, and the resulting photoelectrons discharge the capacitor. At the end of the integration,
the voltage remaining across the capacitor must be measured in order to read the final signal level. Ô When the reset switch is released after the reset there is an uncertainty of kTC in the charge on the capacitor, where k is Boltzmann’s constant, T is the temperature of the NICMOS device, and C is the capacitance of the diode junction. This uncertainty leads to kTC, or reset, noise. Reset noise is caused by thermal motions of charge carriers in a circuit with finite resistance. Consider the circuit in Figure 2.1 (this argument is taken from Rieke 1994). C and R are equal to the capacitance and resistance of the diode junction respectively. This circuit has one degree of freedom, the noise 1 voltage VN, which has an associated thermal energy of 2 kT when in thermodynamic equilibrium. 1 2
The energy stored in the capacitor is 2CV , hence «
1 ª 2 1 : C V = kT (2.1) 2 N 2
The charge on the capacitor is given by Q = CV ,so «
ª 2 = QN kTC: (2.2)
In the NICMOS device the reset noise is about 100 electrons RMS, which would be the major noise contribution if not corrected. Fortunately, the correction is easily made, by measuring the reset 2.4. PIXEL READOUT 13 level immediately after the reset, before the integration begins. The drawbacks of this technique
are that twice as much time is spent reading each pixel, and that the effective read noise for the Ô differential measurement is a factor of 2 greater than that for a single read.
The controller contains dedicated electronics for removing reset noise when it is used with a CCD camera. This technique of Double-Correlated Sampling (DCS) cannot be used to remove reset noise with a direct readout array, but is nevertheless useful for reducing the noise from other sources which is associated with any single read of a pixel.
The DCS circuits are shown in Figure 2.2. The interface box incorporates a potential divider, driven from the same bias voltage supplied to the NICMOS device, to provide a reference voltage. The interface also contains a low noise FET switch which can connect either the NICMOS or the reference to the controller. The reference voltage, or “dummy pixel” is set to approximately the level of a real pixel immediately after a reset. The controller contains positive and negative unity gain amplifiers, an integrator, and an analogue-to-digital converter (ADC).
During the first half of the DCS cycle, the reference is connected, the positive amplifier is selected, and the signal is integrated for a fixed time (5–50 µs). For the second half of the cycle, the signal from the NICMOS is integrated for the same time, but through the negative amplifier. Finally the voltage at the integrator output is digitised. Thus a differential measurement of the real and dummy pixels is made (this differential measurement should not be confused with that used to remove reset noise, which involves the entire DCS procedure twice, once straight after a reset, then again after the desired integration time). The final signal is in fact proportional to dummy minus real, to ensure that the result increases with decreasing pixel charge (recall that arriving photons discharge the diode capacitor).
The integration procedure averages out any high frequency noise, and since the reference is sup- plied by the bias voltage used for the real pixels, slow drifts in the bias supply are cancelled out by the differential measurement. Using the DCS procedure with 20 µs integration times, and measur- ing the reset level to remove kTC noise, the COAST NICMOS system has a typical read noise of 23 electrons (Beckett 1995). 14 CHAPTER 2. INFRARED DETECTORS FOR INTERFEROMETRY
NICMOS Interface Controller
+V
x(+1) Dummy
ADC
NICMOS Output NICMOS x(-1)
0V
Figure 2.2: DCS circuitry. The diagram is from Beckett (1995). Chapter 3
Optical Systems
This chapter describes the optical components of COAST, especially those specific to infrared operation. The difficulties associated with aligning these many components are discussed. An alignment procedure which has been used successfully at COAST is presented. After alignment by this method, the beam combiner can produce fringe patterns with very high visibilities.
Various aspects of the performance of the beam combiner are discussed, including optical through- put, visibility losses, and closure phase errors.
3.1 Components of an optical/infrared interferometer
I shall now briefly describe the optical components of a generic visible/infrared interferometer and their functions, illustrated by the example of COAST. For more information on the design of COAST, see Baldwin et al. (1994).
3.1.1 Telescopes
The purpose of the telescopes is to collect light from the target of interest, and produce small- diameter light beams which can be steered into the other components of the interferometer. The
part of the telescope mirror which is actually used must be 3r0 in diameter, so that the resulting image is a single speckle.
Since June 1998, COAST has had five telescopes, which can be arranged in many different con- figurations, on foundations along the arms of a Y. The maximum baseline which will fit on the site is 100 metres. Each telescope is a fixed 40 cm Cassegrain design, illuminated by a steerable flat mirror which tracks the astronomical target. The telescope produces a 25 mm diameter collimated light beam, which is steered into an optics laboratory through alloy pipes. 16 CHAPTER 3. OPTICAL SYSTEMS
3.1.2 Acquisition/autoguiding
The field of view of the telescopes, looking through the long light pipes from inside the optics building, is just a few seconds of arc. The size of this field is comparable to the pointing accuracy of the telescopes, and so each telescope incorporates a wide-field video camera for acquisition purposes.
For aperture diameters comparable to or larger than r0, the fringe contrast will be drastically reduced by wavefront distortions caused by the atmosphere above the telescopes, unless the mean tilt of the wavefront is removed (Tango and Twiss 1980). For this purpose, each telescope also incorporates a piezo-actuated fast steering mirror, driven by error signals from a CCD camera operating at frame rates of up to 250 Hz, which is located inside the optics building. This CCD system is also used for acquisition.
3.1.3 Path compensation
To form interference fringes in white light, the light beams which are combined must have travelled equal paths from the source. In a stellar interferometer, the relative paths for the beams from the different telescopes change continuously as the target moves across the sky. The interferometer must incorporate a path compensation system to take out these variations.
At COAST, path compensation is performed by reflecting the beams from movable mirrors moun- ted on trolleys, which run on precisely-aligned rail tracks. The position of the mirrors on each trolley are continuously monitored by a laser interferometer, and kept at the desired position by a servo-controlled loudspeaker voice coil. The trolley is driven along the track to keep the voice coil displacement small.
3.1.4 Correlator
The correlator consists of a beam combiner and optical or infrared detector(s). The beam combiner is an optical system designed to form interference pattern(s) which can be measured by the chosen detector system. The correlator must be designed to allow the visibility amplitudes and phases on all of the interferometer baselines to be measured, with the capability of measuring the phase on at least three baselines simultaneously, in order to measure a closure phase.
All of the components of the interferometer, except the correlator, will serve for observations at both visible and near-infrared wavelengths, providing that the effective telescope aperture is reduced for operation at the shorter wavelengths. However, an interferometer optimised for a narrower spectral region would probably use different coatings on its optical surfaces to those employed in a general-purpose design.
COAST has two beam combiners, one which operates at visible wavelengths (650–950 nm), and an alternative combiner, optimised for infrared wavelengths, which was added later. The IR beam 3.2. POSSIBLE CORRELATOR DESIGNS 17 combiner is the subject of the remainder of this chapter.
Selection of one of the two beam combiners is achieved by means of four dichroic mirrors moun- ted on a kinematic slide. These can be slid into position to intercept the light beams from the four telescopes, after path compensation, in order to reflect infrared light into the IR beam com- biner. A fraction of the visible wavelength light is transmitted through the dichroic mirrors. The dichroics may be removed so that all wavelengths propagate in this direction. These light beams meet partially-aluminised glass plates which reflect the central portion of the beams into the vis- ible beam combiner (recall that only a fraction of the telescope aperture may be used at optical wavelengths). The outer parts of the pupil are directed onto the autoguider CCD camera.
3.2 Possible correlator designs
3.2.1 All-on-one v. pair-wise beam combination
Consider a beam combiner which has M input light beams from M telescopes. Two extreme
possibilities for the design of the beam combiner are as follows. The M beams may all be mixed
µ= together to form a single fringe pattern, containing M ´M 1 2 sets of fringes. Each set must have
a unique spatial or temporal frequency, so that the fringes on different baselines may be separated.
µ= This is all-on-one beam-combination. Alternatively, M ´M 1 2 separate fringe patterns may be formed, each from a single pair of beams. These are not the only choices of beam combiner design: hybrid schemes, such as that used at the Navy Prototype Optical Interferometer (Mozurkewich 1994) can be envisaged, where more than two but fewer than M beams go into each separate
fringe pattern.
µ= In the case where all M ´M 1 2 baselines are measured simultaneously, Buscher (1988) showed that, with a noiseless detector, the all-on-one scheme gives the best signal-to-noise for visibility amplitude measurement at all light levels. Is this also true with a noisy detector? The signal-to- noise ratio for visibility measurement from a generic fringe pattern is given by
V 2N2
Ô ; SNR = (3.1)
2 3 2 2 4
· σ N · 2N V 2n where V is the fringe visibility, N is the number of photons detected in the pattern, n is the number of detector reads made and σ is the noise for each read (Nightingale 1991). If M beams are
combined to form a single pattern, the visibility measured on one of the baselines is inversely = proportional to the number of beams, so V = V0 M, and the number of photons in the pattern is
proportional to the number of beams i.e. N = MN0. If the beams are combined pair-wise to form
µ= =
M ´M 1 2 fringe patterns, each made up of two beams, the visibility in each pattern will be V0 2.
= =´ µ
Each beam must be split M 1 ways, so N 2N0 M 1 . At high light levels, Equation 3.1
Ô = simplifies to SNR = V N 2. Substituting the above expressions for N and V we find that the
SNR for all-on-one beam combination is Ô
V0 N0
Ô ; SNRa = (3.2) 2M 18 CHAPTER 3. OPTICAL SYSTEMS
whereas that for pair-wise combination is Ô
V0 N0
Ô : SNRp = (3.3)
2 M 1 In the low light-level extreme, when Equation 3.1 simplifies to
V 2N2
Ô ; SNR = (3.4) 2nσ2 the results for all-on-one and pair-wise beam combination are
2 2
V0 N0
Ô ; SNR = (3.5) a 2 2naσ and 2 2
V0 N0
Ô : SNR = (3.6)
p 2 2
µ σ ´M 1 2np
If we assume that the highest frequency fringes in each pattern have four samples per fringe,
´ µ =
na = 2M M 1 and np 4. Hence in the low light-level limit,
= ´ µ= : SNRa =SNRp 2 M 1 M (3.7)
So the all-one-one scheme is better for visibility amplitude measurement with a noisy detector at all light levels. The advantage of the all-on-one scheme is greatest at low photon rates. In this limit the read noise imposes a large penalty for splitting each beam.
As pointed out by Buscher, and by Mozurkewich, the all-on-one scheme also avoids the two principal disadvantages of the pair-wise scheme. Firstly, a pair-wise beam combiner is inevitably very large, with many optical components. Secondly, a small change in the optical path in one sub-combiner (which combines one pair of beams) of the pair-wise design will add a systematic error to the closure phases involving that baseline. Calibration observations or laser metrology are needed to remove the bias. On the other hand, the all-on-one design is prone to cross-talk between the baselines, which can limit the accuracy of the closure phases. Also, if fringes are encoded temporally (see next section), the detector must be read out very fast to measure more than a few baselines at once.
COAST was designed to measure a maximum of six baselines simultaneously (from four tele- scopes). An all-on-one design is clearly better for this application.
3.2.2 Image plane v. pupil plane combination
A beam combiner may produce a fringe pattern in the image plane, or in the pupil plane. These terms can be explained as follows:
Image plane
The beams are simply imaged together e.g. by a lens, to form a spatial fringe pattern on an array detector (Figure 3.1). The resulting image will be an Airy pattern crossed by fringes. A unique 3.2. POSSIBLE CORRELATOR DESIGNS 19