The Pennsylvania State University Schreyer Honors College

THE PENNSYLVANIA STATE UNIVERSITY SCHREYER HONORS COLLEGE

DEPARTMENT OF ENGINEERING SCIENCE AND MECHANICS

EXPLORING THE UTILITY OF MONOCENTRIC IMAGERS FOR ASTRONOMY

BRODY MCELWAIN SPRING 2021

A thesis submitted in partial fulﬁllment of the requirements for a baccalaureate degree in Engineering Science with honors in Engineering Science

Reviewed and approved∗ by the following:

Suvrath Mahadevan Professor of Astronomy and Astrophysics Thesis Supervisor

Gary L. Gray Professor of Engineering Science and Mechanics Honors Advisor

Judith A. Todd Department Head P. B. Breneman Chair and Professor of Engineering Science and Mechanics

∗Signatures are on ﬁle in the Schreyer Honors College. We approve the thesis of Brody McElwain:

Date of Signature

Suvrath Mahadevan Professor of Astronomy and Astrophysics Thesis Supervisor

Gary L. Gray Professor of Engineering Science and Mechanics Honors Advisor The thesis of Brody McElwain was reviewed and approved∗ by the following:

Suvrath Mahadevan Professor of Astronomy and Astrophysics Thesis Advisor

Gary L. Gray Professor of Engineering Science and Mechanics Honors Advisor

Juidth A. Todd Department Head P. B. Breneman Chair and Professor of Engineering Science and Mechanics

∗Signatures are on ﬁle in The Graduate School. Abstract

It is investigated whether monocentric imagers are applicable to time domain, wide-field, all-sky surveys. A simple prototype of an optical system consisting of a spherical lens and Lodestar detector is used to take on-sky observations. These images are interpreted with DS9 and MATLAB software to characterize the first-order parameters of the system. These results are then compared to the theoretically optimized parameters of the optic system built in Zemax OpticStudio sequential mode. Subsequent analysis suggests that the first-order parameters are within a reasonable margin of error. Additionally, the Zemax and on-sky point spread functions (PSFs) of the prototype suggest the need for aberration correction of the current optics. Therefore, future work on improving the prototype optical system is considered, in addition to further tests.

Non-Technical Abstract

The primary goals of this project are to understand the advantages and trade-oﬀs of monocentric imagers in astronomical contexts. A prototype monocentric imager is used to take pictures of stars in the night sky. These images are interpreted with a user-built program. The prototype optical system is also simulated using optical software. These programming and software tools are used to determine the properties of the prototype optical system. From these results, future work on improving the prototype is discussed.

i Table of Contents

List of Figures iv

List of Tables vi

Chapter 1 Introduction 1 1.1 Problem Statement ...... 1 1.2 Design Needs ...... 2 1.3 Objectives of Thesis ...... 3

Chapter 2 Literature Review 4 2.1 State of the Art in Astronomy ...... 4 2.1.1 Time Domain Astronomy ...... 4 2.1.2 Ground and Space-Based Projects ...... 5 2.1.2.1 The Large Synoptic Survey Telescope (LSST) ...... 6 2.1.2.2 Zwicky Transient Factory (ZTF) ...... 6 2.1.2.3 Transiting Exoplanet Survey Satellite (TESS) ...... 7 2.1.2.4 HATPI ...... 7 2.1.2.5 Evryscope ...... 9 2.1.2.6 Argus ...... 9 2.1.2.7 The Roman Space Telescope (Roman) ...... 9 2.1.3 Motivation for exploring other concepts ...... 10 2.2 Gigapixel Imaging ...... 10 2.3 Advantages of Monocentric Imagers ...... 11 2.4 sCMOS vs CCD ...... 12 2.4.1 Technology Overview ...... 13 2.4.2 Satellite Constellations and sCMOS Mitigation ...... 14

Chapter 3 Methodology 16 3.1 The Equatorial Coordinate System ...... 16 3.2 Optical Aberrations ...... 18

ii Chapter 4 Experimental Procedure 21 4.1 Observations on the Pleiades ...... 22 4.2 MATLAB program summary ...... 22 4.2.1 Reading FITS in DS9 and MATLAB input ...... 23 4.2.2 ICRS coordinates and MATLAB input ...... 24 4.2.3 Main script outline ...... 24 4.3 Zemax Lens Assembly ...... 25

Chapter 5 Results 27 5.1 MATLAB Program Results ...... 27 5.2 Zemax Aberration Plots ...... 28

Chapter 6 Discussion 32 6.1 Interpretation of Ray Fans and Spot Diagrams ...... 32 6.2 PSF analysis ...... 32

Chapter 7 Summary and Conclusions 35

Chapter 8 Future Work 36

Chapter 9 Acknowledgements 38

Appendix MATLAB Program 39 1 Introduction ...... 39 1.1 PixelSeparation user-defined function ...... 39 1.2 AngularSeparation user-defined function ...... 40 1.3 PlateScale user-defined function ...... 42 1.4 Main Script ...... 44 1.5 Main Script Output ...... 50

Bibliography 53

iii List of Figures

1.1 A prototype monocentric lens ...... 1

1.2 The relationship between SBP and a perfectly diﬀraction limited lens (Rd), a lens with geometric aberrations (Rg), and a lens whose f-number increases with lens size (Rf ) [1]. Rc is a lens that outperforms Rg without increasing the f-number of the optical system...... 3

2.1 The top of Figure 2.1 shows the light curve for TOI-1899. The rectangle marks a region where a single-transit event was observed for approximately 1.2 days. The data contained in the rectangle is enlarged in the bottom of Figure 2.1, to show the observed dip in brightness of TOI-1899 [2]. . . 8

2.2 The AWARE multiscale camera is capable of wide ﬁeld-of-view gigapixel photography. The microcameras are in a planar array around the monocentric objective lens, and each microcamera includes seven optical elements [3]. 11

2.3 Two conventional wide ﬁeld-of-view lenses and a monocentric lens [4]. Each design provides a 120 degree ﬁeld-of-view using a 12mm focal length, but the monocentric lens is a more simple design because it uses far fewer optical elements...... 12

2.4 Single frame of on-sky testing using the Andor Marana sCMOS camera [5]. 14

2.5 An image taken at the Cerro Tololo Inter-American Observatory displays the satellite streaks left by Starlink satellites...... 15

3.1 The equatorial coordinate system [6]...... 17

3.2 Transverse and longitudinal ray aberrations for several arbitrary rays. . . 19

3.3 An example of a ray fan. Points (a-e) correspond to the ray locations on the image plane in Figure 3.2...... 19

iv 3.4 An example of a spot diagram. The points (a-e) correspond to the ray locations on the image plane in Figure 3.2 if these locations were rotated about the optical axis...... 20

4.1 The Pleiades [7]...... 22

4.2 The experimental setup for the D-K9 spherical lens optical system. The experimental procedure involves measuring the on-sky angular separation α and the linear displacement on the image plane ` for a pair of stars in Pleiades, such as Atlas and Alcyone. These measurements can be used to determine ﬁrst-order parameters of this optical system (the plate scale p and the focal length f) using the relationships described by Equations 4.1 and 4.2...... 23

4.3 The Pleiades observations taken by the D-K9 spherical lens. This .FIT ﬁle is opened in DS9. Note that the Pleiades are ﬂipped in this visualization. 24

4.4 2D layout of the monocentric lens system...... 25

4.5 The lens editor for the monocentric lens system. The distance between the image plane the back surface of the lens is set to variable...... 26

5.1 Ray fan for the image plane located 15 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 55 mm...... 29

5.2 Spot diagram for the image plane located 15 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 55 mm. . . . . 30

5.3 Ray fan for the image plane located 19 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 59 mm ...... 30

5.4 Spot diagram for the image plane located 19 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 59 mm. . . . . 31

6.1 PSF measured on-sky for the ball lens using DS9 > Region > Shape > Projection across the Alcyone star in the Pleiades...... 34

8.1 A rough CAD assembly of a ball lens optical system. A ﬁne adjustment tuner between the detector and lens could improve future on-sky observations...... 37

v List of Tables

2.1 Comparison of Wide-ﬁeld Optical Survey Cameras. Parameters include single-image ﬁeld of view (Ωfov), pixels (arcsec), integration time (texp), wavelength range (λrange), and depth...... 5

2.2 sCMOS vs. CCD technology. The detectors listed are among the most commonly used in astronomical sky-survey applications [5]...... 13

5.1 MATLAB output truncated to 2 significant figures for program outlined in Chapter 4 and included in the Appendix. The program is also briefly summarized in Section 5.1...... 28

vi Chapter 1 | Introduction

1.1 Problem Statement

A monocentric lens consists of a hemispherical or spherical optical element that is concentric around a central point. Such a lens is capable of a wide ﬁeld-of-view, and they are often used in multi-scale optical designs for panoramic imaging. Figure 1.1 shows an example of a monocentric lens.

Figure 1.1. A prototype monocentric lens

It is of interest whether monocentric imagers are viable in exploring time domain photometric variability of bright sources. This is because of the potential for wide-ﬁeld,

1 all-sky panoptic imaging with monocentric imagers. Due to the simplicity in design and compact volume of the optical system, monocentric imagers have potential to test new detector technology as a space-based project.

1.2 Design Needs

The symmetry of a monocentric lens produces no off-axis aberrations such as coma, astigmatism, or lateral chromatic aberrations [8]. Axial aberrations such as spherical and chromatic aberrations are present, however. Another trade-off with monocentric lenses is that field-of-view is limited by vignetting from the central aperture stop, assuming one is actually present in this lens [4]. For a given lens, the space-bandwidth product (SBP) describes how many pixels are required to capture a given field-of-view at full resolution. The SBP is thus limited by spherical aberrations [1]. Because a monocentric lens has spherical aberrations, its SBP is very poor. Additional corrective optics are required to give images higher resolution. Figure 1.2 shows that for different lenses, SBP increases as the size of the lens increases. The dashed curve shows that it is possible to design a lens that outperforms an aberration limited lens without increasing the f-number as the lens is scaled up. Such a lens is desirable because it would allow more light into the system, shown by Equation 1.1. Given a system’s focal length f and aperture diameter D, an increasing f-number N implies a decreasing aperture size, which would let less light into the system.

f N = (1.1) D Typically, optical systems require more elements to account for aberrations that affect the quality of the image at its plane. As opposed to a flat image plane, a monocentric objective lens produces a spherical image plane that yields higher resolution and improved light-gathering [9]. Lens designs that place sensors along a flat image plane require more optical elements, which is common in traditional wide field-of-view lenses. Scaling the monocentric lens to have a longer focal length also produces a higher SBP compared to lenses with flat image planes [4].

2 Figure 1.2. The relationship between SBP and a perfectly diﬀraction limited lens (Rd), a lens with geometric aberrations (Rg), and a lens whose f-number increases with lens size (Rf ) [1]. Rc is a lens that outperforms Rg without increasing the f-number of the optical system.

1.3 Objectives of Thesis

The primary goals of this project are to understand the advantages and trade-oﬀs of monocentric imagers, research state-of-the art projects in all-sky astronomy surveys, and complete a literature background on computational imaging. Software tools will be used to analyze on-sky images with a spherical lens, and characterize the ﬁrst order parameters of the system. Early modeling and tests of the optical system will also be conducted.

3 Chapter 2 | Literature Review

2.1 State of the Art in Astronomy

Up until the turn of the century, the vast majority of observations in astronomy were limited to individual objects of interest. Large-scale sky surveys were not regularly implemented due to the limitations of technology - large telescopes had small fields of view, and those with larger fields of view could not detect dim sources [10]. Small detectors also made it difficult to complete large surveys. With the advancement of large format detectors, more discoveries in the observable universe have become possible within the past two decades. Existing all-sky surveys such as IRAS, WISE, and 2MASS all had very small temporal coverage. State of the art projects in time domain astronomy look to make advancements in observing and learning about the transient sky.

2.1.1 Time Domain Astronomy

Wide-ﬁeld, time-resolved observations from ground and space-based telescopes increase the chances of making discoveries in astronomy. Time domain astronomy addresses brightness variations in the observable sky to identify variables and transients. Variables are periodic, predictable occurrences such as stellar rotation, whereas transients are unpredictable, short-lived occurrences such as gamma ray bursts [11].

4 Time domain astronomy requires wide-ﬁeld coverage to increase the chances of discovering rare events. Acquiring good time-resolved data, improving the image quality, and obtaining color information in observations is important to distinguish variables from one other. Additionally, using long-term observations can help to identify evolving transients [10]. State of the art telescopes seek to address these requirements to characterize the variable sky. Note that time-resolved data can range from milliseconds to a full decade. Transients such as gamma-ray bursts may have associated optical ﬂashes within the range of a second [10]. On the other hand, stellar rotation variables with relatively long periods require longer time ranges of data to be studied.

2.1.2 Ground and Space-Based Projects

The following subsections discuss current and near-future projects in wide-ﬁeld, high- cadence, time domain astronomy. Note that this list below is not complete, but merely representative of ground and space-based eﬀorts. Projects such as Hyper Suprime-Cam (Subaru Telescope), PanStarrs, Palomar Transient Factory (PTF, precursor of ZTF) are not listed but have been mentioned in similar discussions. See Table 2.1 for a brief comparison of sky coverage per unit time, depth, and wavelength of various surveys.

Table 2.1. Comparison of Wide-ﬁeld Optical Survey Cameras. Parameters include single-image ﬁeld of view (Ωfov), pixels (arcsec), integration time (texp), wavelength range (λrange), and depth. 2 Survey Camera Ωfov (deg ) pixels (arcsec) texp (s) λrange depth LSST 9.6 0.2 30 320-1050 nm 21.7, 5σ ZTF 47 1.0 30 - 20.5, 5σ TESS 2300 1.0 120 600-1000 nm - Evryscope 8660 13.3 120 - 16.0, 3σ

5 2.1.2.1 The Large Synoptic Survey Telescope (LSST)

LSST is a ground-based project designed to accomplish four specific goals: probe dark energy and dark matter, take inventory of the solar system, explore transients, and map the Milky Way [10]. It will be one of the largest astronomical cameras ever constructed, with a 3.2-gigapixel camera and six filters covering wavelengths of 320-1050 nanometers on the electromagnetic spectrum. The telescope will have a 9.6 degree squared field of view and an 8.4 meter primary mirror. LSST is located in Chile and will begin surveying in 2022. Regarding the variable sky, the LSST will complete a 10 year sky survey. It will further investigate variable stars and celestial sources such as gamma-ray bursts, gravitational wave counterparts, and active galactic nuclei [10]. New classes of transients are expected to be discovered, in addition to rare sources such as neutron stars and black hole binaries. The LSST will be able to measure colors of transients, detect dim magnitude variables, and collect photometric histories of transient events.

2.1.2.2 Zwicky Transient Factory (ZTF)

ZTF is a ground-based telescope designed to survey fast-evolving transients. Its ﬁeld of view is very large - 47 degrees squared. It improves upon the PTF by an order of magnitude, and caught ﬁrst light in 2017 [12]. ZTF is located at the Palomar Observatory in California. ZTF surveys at a high cadence over a wide area, notably sweeping the Galactic equator to determine periods of stellar and cataclysmic variables within our galaxy [12]. ZTF also surveys for early observations of supernovae, emissions from gamma-ray burst afterglows, and tidal disruption events [12]. These aforementioned surveys have several varieties in timescales for the time-resolved observations.

6 2.1.2.3 Transiting Exoplanet Survey Satellite (TESS)

TESS is a space-based project launched in 2018 with the goal to discover transiting exoplanets [13]. The transit method for discovering exoplanets looks for dips in the observed brightness of a star. This dip indicates the possibility of a planet passing in front of the star, also known as a planetary transit [14]. It is possible to determine the mass, radius, orbital parameters, and atmospheric properties of transiting planets. TESS will survey 200,000 of the brightest nearby stars using the transit method, and is expected to find more than a thousand planets smaller than Neptune [14]. TESS is conducting a 2-year all-sky survey using four wide-field optical CCD cameras. TESS will specifically focus on main-sequence dwarfs with spectral types F5 to M5 [13]. The time sampling of the photometric observations will be based on transit duration, which usually occur in under an hour. To record partial transit phases, TESS will time sample brightness measurements every 2 minutes [13]. The James Webb Space Telescope (JWST) will conduct follow-up studies on the planetary observations made by TESS. Figure 2.1 shows TESS photometry of an M dwarf TOI-1899. The drop in observed brightness of TOI-1899 indicates the possibility of a transiting planet. This transit candidate has been confirmed to be a warm Jupiter by the Habitable-zone Planet Finder (HPF), an astronomical spectrograph [2]. It’s worth noting that the TOI-1899 is the lowest-mass star currently known that hosts a transiting warm Jupiter.

2.1.2.4 HATPI

HATPI is a ground-based project under development at the Las Campanas Observatory in Chile. Its main goal is to provide high-cadence light curves at high-precision for various transients. The time-series photometry will be for stars of m > 14 covering three quarters of the visible sky from the observatory [15]. HATPI’s capabilities allow for discovery of long-period transiting exoplanets in habit-

7 Figure 1. from A Warm Jupiter Transiting an M Dwarf: A TESS Single-transit Event Confirmed with the Habitable-zone Planet Finder null 2020 AJ 160 147 doi:10.3847/1538-3881/abac67 http://dx.doi.org/10.3847/1538-3881/abac67 © 2020. The American Astronomical Society. All rights reserved.

Figure 2.1. The top of Figure 2.1 shows the light curve for TOI-1899. The rectangle marks a region where a single-transit event was observed for approximately 1.2 days. The data contained in the rectangle is enlarged in the bottom of Figure 2.1, to show the observed dip in brightness of TOI-1899 [2]. able zones of bright stars, including those beyond the snow line. HATPI is also uniquely sensitive to short-lived events such as stellar ﬂares and rapidly evolving transients [15]. Higher precision light curves for bright and galactic supernovae is expected. Time-scales at shorter intervals of 30 seconds will also be used to discover new transient objects.

8 2.1.2.5 Evryscope

Evryscope consists of an array of 22 telescopes for a combined 8000 square degree ﬁeld of view. There are two ground-based models of Evryscope - one in CTIO in Chile and the other in California. The goal of the project is to observe bright, rare events by opting for shorter-timescales with the continuous all sky coverage [16]. The telescopes in the array are mounted onto a single hemispherical enclosure. The Evryscope system is an 800 Megapixel telescope that averages 5000 images per night with about 300000 sources per image [16].

2.1.2.6 Argus

The Argus Array is the next-generation system currently under development, which extends from the design of the Evryscope. Argus is a large telescope that consists of an array of 650 moderate-aperture telescopes. Its ability to collect light is similar to that of LSST. Argus is a 40 Gigapixel telescope that covers 7940 square degrees [17]. Argus is set to assemble a million-epoch movie of the northern sky, which will give insight into the evolution of variable sources. The development team is setting the goal for all-sky timescales to be as short as seconds [17].

2.1.2.7 The Roman Space Telescope (Roman)

Roman is a space-based project currently under development. The 2.4m telescope features a near-infrared camera with a 0.281 degrees squared ﬁeld of view, along with a visible-light coronagraph [18]. During its 5-year mission, Roman will complete time-domain surveys to discover and analyze Type Ia supernovae (∼5 day cadence) and galactic bulges (∼15 minutes cadence). Archival Researcher and General Observer programs also plan to use Roman data sets to study exoplanet transits, stellar remnants, galaxy evolution, gravitational lenses, and other objects of interest [18].

9 The Roman Coronagraphic Instrument (CGI) is equipped with a high-contrast imager and integral ﬁeld spectrograph, which improves signiﬁcantly on hardware and algorithms of current ground and space-based projects. CGI will allow for the study of exoplanets, circumstellar disks, and most importantly the debris, exozodiacal, and protoplanetary disks [18].

2.1.3 Motivation for exploring other concepts

In this project, we explore if monocentric imagers are suitable for ground and space-based large surveys of bright stars, and whether they oﬀer any advantages for space-based operations with lower weight and power. The advantages of monocentric imagers to current generation projects in terms of cost and simplicity are discussed in Section 2.3. Monocentric imagers may also serve as a testbed for new detector technology such as sCMOS (See Section 2.4). The testing would be on-sky to probe short timescale transients, in addition to mitigating impact of satellite constellations on astronomy.

2.2 Gigapixel Imaging

For multiscale designs, it is desirable to place an array of CMOS sensors around the monocentric objective lens. Introducing a secondary optic for each sensor could reduce dead-space between sensors by overlapping the ﬁeld-of-views of adjacent sensors [1]. Gigapixel photography is possible if microcameras are introduced in addition to the array of CMOS sensors. Note that the SBP increases with increasing dimensions of CMOS sensors [3]. Figure 2.2 shows a ray trace of a microcamera in the AWARE camera, a multiscale camera developed at the U.S. Naval Research Laboratory. The AWARE gigapixel camera is an example of a monocentric, multiscale camera with a wide ﬁeld-of-view (120 degrees by 50 degrees). It includes 98 microcameras, and the focus, gain, and exposure of each microcamera can be controlled independently. The

10 Figure 2.2. The AWARE multiscale camera is capable of wide field-of-view gigapixel photography. The microcameras are in a planar array around the monocentric objective lens, and each microcamera includes seven optical elements [3]. disadvantage of AWARE is that the camera requires an aperture stop for each individual microcamera as opposed to a single aperture stop in the monocentric lens [19]. This increases the f-number and volume of the optical system. AWARE is able to capture details of star fields using a 1.85 second exposure time. Stars of magnitude m < 8.2 are visible, however stars of magnitude m < 3.5 are blurry due to defects in microcamera lenses [19]. The microcameras in monocentric, multiscale design systems such as AWARE require aberration correction. This is because the simple design of the monocentric objective lens has few variables for aberration correction as it is scaled up [8]. At small scales, the chromatic and spherical aberrations are not prominent due to the curvature of the image field, but these aberrations have to be offset by microcameras at larger scales.

2.3 Advantages of Monocentric Imagers

Monocentric lenses can achieve higher performance designs with fewer elements than traditional wide field-of-view lenses. Figure 2.3 compares two traditional wide field-of- view lenses to a monocentric lens [4]. Despite each lens achieving the same field-of-view,

11 the monocentric lens uses far fewer optical elements. The complexity of the traditional lenses can also cause problems since all of the optical elements must be aligned properly to maintain good image quality. A monocentric imager is cost-eﬀective due to its compact volume and simple design.

Figure 2.3. Two conventional wide ﬁeld-of-view lenses and a monocentric lens [4]. Each design provides a 120 degree ﬁeld-of-view using a 12mm focal length, but the monocentric lens is a more simple design because it uses far fewer optical elements.

2.4 sCMOS vs CCD

Sensor technology is another factor to consider for monocentric imagers. Complementary metal oxide semiconductor (CMOS) image sensors are a new alternative to charge-coupled device (CCD) sensors in astronomy. CCDs have been the industry standard for sky survey applications, but their main drawback is the read-out speed. This drawback can become a problem when detecting transients or moving objects.

12 CMOS were previously not used for precise astronomy surveys because the read-out noise was too large for most applications (≥ 10e−), and they had less stability when compared to CCDs. However, low-noise scientiﬁc CMOS (sCMOS) chips have since been developed, bringing read-out noise down signiﬁcantly.

2.4.1 Technology Overview

The sCMOS chip first used for astronomical applications was with the Andor Neo camera, which could perform satellite tracking, fast photometry, and rapid optical transient detection [5]. A sCMOS chip with significantly improved quantum efficiency (QE) and back-illuminated options has been built with the Andor Marana camera. In Table 2.2, the parameters for the aformentioned sCMOS detectors are compared to the iKon CCD and the Electron Multiplying CCD (EMCCD) iXon models, both used in astronomical imaging systems. Note how the read noise is similar among these listed detectors.

Table 2.2. sCMOS vs. CCD technology. The detectors listed are among the most commonly used in astronomical sky-survey applications [5]. Neo sCMOS Marana sCMOS iXon Ultra EMCCD iKon-L CCD Active pixels (H x V) 2560 x 2160 2048 x 2048 512 x 512 2048 x 2048 Pixel size (µm) 6.4 11 16 13.5 Read noise (e−) 1.0 1.6 ≤ 1 2.9 Peak QE 60% 95% 90% 60% Max frame rate (fps) 30 48 56 0.95

To further discuss the advantages of sCMOS detectors for wide-ﬁeld sky surveys, a Marana sCMOS camera conducted on-sky observations shown in Figure 2.4. Note that there are no hot and dark columns or blooming from over-saturated stars, which are typical defects for CCD frames [5].

13 Figure 2.4. Single frame of on-sky testing using the Andor Marana sCMOS camera [5].

2.4.2 Satellite Constellations and sCMOS Mitigation

Satellite streaks can pose a problem for astronomers, and specifically became a topic of discussion among the community when SpaceX began its Starlink satellite launches in 2019. The Starlink constellations were extremely bright, and Figure 2.5 shows their effects on ground-based observations. Its rather difficult, and in some instances, impossible to remove these streaks from astronomical images. While SpaceX has plans to address this problem by implementing sunshades on their satellites, there is no specific regulation for satellites affecting ground-based astronomy. And with SpaceX’s future plans to launch thousands of satellites that form orbital internet constellations, it is of interest to develop technology that can eliminate streaks. In terms of long-term mitigation for addressing satellite constellation streaks, there is

14 Figure 2.5. An image taken at the Cerro Tololo Inter-American Observatory displays the satellite streaks left by Starlink satellites. promise in future-development of sCMOS technology that can remove streaks. This can be accomplished due to the active shuttering with sCMOS that is not present in CCDs. The monocentric imager proposed in this project could serve as a testbed for sCMOS technology.

15 Chapter 3 | Methodology

3.1 The Equatorial Coordinate System

It is useful to characterize the properties of a monocentric imager, such as its plate scale and focal length. These properties can be determined by comparing on-sky observations from the imager to stellar positions, which are included on the Set of Identifications, Measurements and Bibliography for Astronomical Data (SIMBAD). In other words, to get the plate scale of the system, first determine the pixel separation between a pair of stars by reading off the coordinates of the centroid of the stars. Use planar trigonometry to calculate the physical distance between the two stars in the focal plane. Next, navigate SIMBAD to get the coordinates of the pair of stars. Then, use the equatorial astronomical coordinate system and spherical trigonometry to determine angular separations between the stars. Finally, compare the angular separation and pixel separation of the pair of stars to calculate the plate scale of the monocentric imager. There are several astronomical coordinate systems, but for this project, the Inter- national Celestial Reference System (ICRS) coordinates on SIMBAD are used. This is because ICRS is the best estimate of equatorial coordinates. With ICRS coordinates, a star’s position is designated by its Right Ascension and Declination. If we consider all

16 stars to be projected onto a sphere surrounding the Earth, the line of Right Ascension is analogous to longitude as the line of Declination is analogous to latitude (See Figure 3.1). For a pair of objects in a plane, simple trigonometry can be used to determine the distance between the objects. However, since stars are in a spherical plane, spherical trigonometry must be considered.

Figure 3.1. The equatorial coordinate system [6].

The arclength of a circle which is parallel to the celestial equator changes with latitude. Thus, cosine and sine terms are introduced in expressions to determine the diﬀerence in Right Ascension between two arbitrary points. Since the arclength of a circle which is parallel to the prime meridian does not change with longitude, the diﬀerence in Declination does not need this factor. Equation 3.1 is used to calculate the arclength γ between two arbitrary stellar locations, where Dec1, Dec2, RA1, and RA2 are the Declination and Right Ascension coordinates of stars 1 and 2, respectively.

17 ◦ ◦ ◦ ◦ cos γ = cos(90 Dec1)∗cos(90 Dec2)+sin(90 Dec1)∗sin(90 Dec2)∗cos(RA1∗RA2) (3.1)

Because we conducted observations on stars within one degree of Declination, Equa- tion 3.1 can be approximated with Equation 3.2, where Decavg is the average Declination of star 1 and star 2. Note that Equation 3.2 is just a variation of the Pythagorean formula in planar geometry.

q 2 2 γ = (Dec1 − Dec2) + ((RA1 − RA2) ∗ cos Decavg) (3.2)

3.2 Optical Aberrations

In this project, the optical performance of our imaging system is quantified using aberrations, or flaws in an optical system. Aberrations can be measured using transverse ray aberrations (TRA), which is the distance on the image plane that a ray differs from the ideal image point located on the optical axis, shown in Figure 3.2. Longitudinal ray aberrations (LRA) are another quantification of optical performance. TRA is generally plotted against normalized pupil coordinates, called a ray fan, shown in Figure 3.3. For reference, the points (a-e) on the ray fan correspond to the normalized pupil coordinates and ray locations on the image plane in Figure 3.2. A spot diagram is another method of aberration analysis, shown in Figure 3.4. This type of plot shows the image of a point source after its light travels through an optical system. Ideally, a point source converges to a perfect point, which occurs when no aberrations are present.

18 Figure 3.2. Transverse and longitudinal ray aberrations for several arbitrary rays.

Figure 3.3. An example of a ray fan. Points (a-e) correspond to the ray locations on the image plane in Figure 3.2.

19 Figure 3.4. An example of a spot diagram. The points (a-e) correspond to the ray locations on the image plane in Figure 3.2 if these locations were rotated about the optical axis.

20 Chapter 4 | Experimental Procedure

As mentioned in Chapter 3, on-sky observations can be used to characterize the ﬁrst order parameters of an optical system. Plate scale p is the relationship between the angular measurement of the object α and the linear size ` of that object’s light that gets spread out on a detector. Equation 4.1 describes this relationship, where p is the plate

arcsec scale measured in mm . In this project, we determine the plate scale of our optical system by measuring the displacement ` between observed stars in terms of pixels from FITS ﬁles. We then compare this physical distance in the image plane to the on-sky angular separation α between the same pair of stars. Once the plate scale is calculated, Equation 4.2 can be used to calculate the focal length of the optical system, where f is the focal length measured in mm.

α p = (4.1) `

206265 f = (4.2) p

21 4.1 Observations on the Pleiades

For this project, the objects of interest for observations include the Pleiades - an asterism in the sky shown in Figure 4.1.

Figure 4.1. The Pleiades [7].

Observations of the Pleiades were taken at Davey Laboratory on November 22, 2019 using an 80mm focal length spherical lens, and a Lodestar detector. The experimental setup is shown in Figure 4.2. The lens is made of CDGM-K optical glass. This material is crown glass, speciﬁcally D-K9, which has a refractive index of n = 1.5163. The Lodestar detector has 2 pixel binning, with each pixel a size of 8.2 µm. The Pleiades observations were compiled into .FIT ﬁles.

4.2 MATLAB program summary

Reference the Appendix to view the MATLAB program designed for this project, which compares observations and SIMBAD coordinates to determine the plate scale of our lens system. This MATLAB program will be outlined and described in detail in the following subsections.

22 Figure 4.2. The experimental setup for the D-K9 spherical lens optical system. The experimental procedure involves measuring the on-sky angular separation α and the linear displacement on the image plane ` for a pair of stars in Pleiades, such as Atlas and Alcyone. These measurements can be used to determine ﬁrst-order parameters of this optical system (the plate scale p and the focal length f) using the relationships described by Equations 4.1 and 4.2.

4.2.1 Reading FITS in DS9 and MATLAB input

These .FIT files for the Pleiades observations can be opened in DS9, an imaging visualization software frequently used in astronomy for reading FITS files. Figure 4.3. Note that the FITS file has an x and/or y 180 degree flip relative to the Pleiades view in Figure 4.1. It is desired to measure the difference between a given pair of stars in terms of pixels (and hence microns). In DS9, the coordinates of the centroids of the 6 brightest stars in the Pleiades (Merope, Maia, Atlas, Electra, Taygeta, and Alcyone) are recorded into matrices in the MATLAB program main script. A user-defined function PixelSeparation

1 function pixels = PixelSeparation(star1coord,star2coord)

then takes as input the coordinates of a pair of stars and calculates the physical distance between the pair. This is repeated for a total of 15 pairs of stars. This is accomplished

23 Figure 4.3. The Pleiades observations taken by the D-K9 spherical lens. This .FIT ﬁle is opened in DS9. Note that the Pleiades are ﬂipped in this visualization.

by simple planar trigonometry.

4.2.2 ICRS coordinates and MATLAB input

Using SIMBAD, the ICRS coordinates for the 6 brightest stars of the Pleiades are recorded and inputted into matrices in the main script of the MATLAB program. A user-deﬁned function AngularSeparation

1 function angle = AngularSeparation(star1matrix,star2matrix)

then takes the ICRS matrices for a pair of stars as input and calculates the on-sky angular separation between the pair of stars. This is accomplished using spherical trigonometry methods and Equation 3.2.

4.2.3 Main script outline

To reiterate, the main script includes all of the pixel and ICRS coordinates of the 6 brightest stars of the Pleiades. The script then calls the user-deﬁned function PlateScale,

24 1 function [p,f] = PlateScale(star1matrix,star2matrix, star1coord,star2coord)

which itself calls the functions PixelSeparation and AngularSeparation to determine the plate scale and focal length of the D-K9 spherical lens. The inputs for PlateScale are hence the combined inputs for PixelSeparation and AngularSeparation. The values of the plate scale and focal length for each pair of stars is unique, and they are tabulated in Table 5.1. These values are averaged to approximate the plate scale and focal length of the system.

4.3 Zemax Lens Assembly

To compare these observations, the monocentric lens system can be built in Zemax OpticStudio. In addition to comparing the focal length and plate scale calculations, OpticStudio is also useful for an aberration analysis. The 2D layout for the system built in OpticStudio is shown in Figure 4.4.

Figure 4.4. 2D layout of the monocentric lens system.

25 The lens editor for this system is shown in Figure 4.5. The system is built in sequential mode, and consists of two surfaces, in addition to the object and image planes. To reiterate, the material chosen for the optical glass is D-K9, which has a refractive index of n = 1.5163. The distance between the back surface of the spherical lens and image plane is set to variable. This parameter determines the location of the focal plane, and thus the focal length of the system. The ray fans and spot diagrams for this system can be plotted for various focal lengths. Speciﬁcally, the slider is set to the distance between the back surface of the spherical lens and the focal plane as determined by two cases: the MATLAB program, and the eﬀective focal length provided in OpticStudio’s sequential mode. The ray fans and spot diagrams for these two cases are plotted and can be referenced in Chapter 5.

Figure 4.5. The lens editor for the monocentric lens system. The distance between the image plane the back surface of the lens is set to variable.

26 Chapter 5 | Results

5.1 MATLAB Program Results

Table 5.1 includes the tabulated values of the MATLAB output for the program in the Appendix. Recall that the program takes as input the pixel coordinates and ICRS coordinates for a given pair of stars. The program calculates the physical distance between the stars in the focal plane, and the on-sky angular separation between the stars. The program outputs the plate scale and focal length of the system for each pair of stars. The averages of the plate scale and focal length of the system in Table 5.1 are

arcseconds p = 3.8 µm and 55 mm, respectively.

27 Table 5.1. MATLAB output truncated to 2 significant figures for program outlined in Chapter 4 and included in the Appendix. The program is also briefly summarized in Section 5.1. arcseconds Stars plate scale ( µm ) focal length (mm) Merope and Maia 3.8 54 Merope and Atlas 3.7 55 Merope and Electra 3.7 56 Merope and Taygeta 3.8 54 Merope and Alcyone 3.9 53 Maia and Atlas 3.8 55 Maia and Electra 3.7 56 Maia and Taygeta 3.7 56 Maia and Alcyone 3.8 54 Atlas and Electra 3.7 56 Atlas and Taygeta 3.7 55 Atlas and Alcyone 3.7 56 Electra and Taygeta 3.9 53 Electra and Alcyone 3.7 55 Taygeta and Alcyone 3.8 55

5.2 Zemax Aberration Plots

As described in section 4.3, the D-K9 spherical lens system is built in OpticStudio. A slider is used in sequential mode to modify the distance between the back surface of the spherical lens and the focal plane for two cases. Ray fan and spot diagrams are plotted and included in this section for each of these cases, and discussed in further detail in Chapter 6. Recall from section 3.2 that these plots characterize the performance of the optical system in terms of how many aberrations are present. The ﬁrst case is based on the focal length determined by the MATLAB program, and from Table 5.1 the average focal length of the D-K9 spherical lens system is 55 mm. Thus, the distance between the back surface of the lens and the focal plane for an 80 mm

80 spherical lens is 55 mm − 2 mm = 15 mm. The ray fan and spot diagram for this case are shown in Figures 5.1 and 5.2, respectively. The second case is based on the focal length of the lens system as determined in

28 Figure 5.1. Ray fan for the image plane located 15 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 55 mm. sequential mode, which is reported as EFFL = 59 mm. Thus, the distance between the back surface of the lens and the focal plane for the system is 19 mm. The ray fan and spot diagram for this case are shown in Figures 5.3 and 5.4, respectively.

29 Figure 5.2. Spot diagram for the image plane located 15 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 55 mm.

Figure 5.3. Ray fan for the image plane located 19 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 59 mm

30 Figure 5.4. Spot diagram for the image plane located 19 mm from the back surface of the D-K9 spherical lens, giving a system focal length of 59 mm.

31 Chapter 6 | Discussion

6.1 Interpretation of Ray Fans and Spot Diagrams

In Figure 5.1, the ray fan for the optical system with f = 55 mm (MATLAB average f) shows a combination of defocus and spherical aberration. Considering the D-K9 spherical lens diameter of 80mm and the focal length of 55mm, this translates to an f/# of ≈ 0.68 for the optical system. The RMS radius reported in the corresponding spot diagram in Figure 5.2 is 4916 µm. Using OpticStudio’s eﬀective focal length of 59 mm to build the lens, the ray fan in Figure 5.3 shows contributions from only spherical aberrations. This optical system does not feature defocus aberrations, and the system has an f/# of ≈ 0.74. The RMS radius reported in the corresponding spot diagram in Figure 5.2 is 16000 µm.

6.2 PSF analysis

The radius of the ﬁrst minima of the PSF is given angularly (in radians) by

1.22 ∗ λ θ ≈ (6.1) D

32 where D is the aperature of the optical system and λ is the wavelength of light. The PSF is given linearly by the full width half maximum (FWHM) in microns by

FWHM ≈ 2.44 ∗ λ ∗ f/# (6.2)

Given an 80 mm aperture for the spherical lens system and using λ = 0.550 µm, the angular radius of the PSF is θ ≈ 8.4e − 6 radians ≈ 1.7 arcseconds. Then, (using FWHM) the diffraction limit on this optical system is ≈ 2 ∗ 1.7 ≈ 3.4 arcseconds. Note that this diffraction limit is greater than the natural seeing limit of 1 arcsecond. Therefore, the optical system is not limited by the atmosphere, and the spot size does not need to be less than 1 arcsecond. For this specific prototype, a spot size less than 3.4 arcseconds is the goal for the aberration limited optics. It is useful to compare these numbers to the approximated on sky PSF using the Pleiades observations shown in Figure 6.1. The radius of the first minima of the PSF is ≈ 0.9 pixels ≈ 14µm after using the 2 pixel binning and 8.2µm conversion. Using the

arcsec system’s estimated plate scale of 3.8 µm , the radial PSF is ≈ 53 arcseconds, and the FWHM is ≈ 106 arcseconds, which is larger than the diﬀraction limit of ≈ 3.4 arcseconds mentioned earlier.

33 Figure 6.1. PSF measured on-sky for the ball lens using DS9 > Region > Shape > Projection across the Alcyone star in the Pleiades.

34 Chapter 7 | Summary and Conclusions

The first-order parameters of the D-K9 spherical lens system determined from observations of the Pleiades were compared to a Zemax lens assembly. The plate-scale and focal length approximations are reasonable estimates of the optical system; the Zemax effective focal length was only a difference of 4 mm from the focal length determined by the MATLAB program. Additionally, as a disclaimer, note that the Zemax PSF numbers are preliminary and require further analysis, because the RMS radius of 4919 µm and 16000 µm are too large to be correct. Both the Zemax spot diagrams and on-sky PSF measurements are useful in the sense that they display the need to design corrective optics to reduce the aberrations in the optical system.

35 Chapter 8 | Future Work

To obtain a better estimate of the spherical aberrations from the ball lens prototype, further tests can be conducted with the optical system. The observations of the Pleiades were broadband, and therefore chromatic aberrations are likely present in the system. The observations could be redone using a narrowband filter to let in a small region of wavelengths in the electromagnetic spectrum, which would reduce chromatic aberrations. An EQ6R-Pro mount has been purchased to build upon the prototype of the D-K9 spherical lens in the future. A rough CAD assembly to improve the mechanical design of the prototype ball lens system is shown in Figure 8.1. A universal d-series dovetail plate will be used to interface with the EQ6R-Pro mount. A fine adjustment tuner will also be incorporated in the design so we can fine tune the distance between the detector and the ball surface. Additionally, a 25mm diameter filter will be included for monochromatic observations.

36 Figure 8.1. A rough CAD assembly of a ball lens optical system. A ﬁne adjustment tuner between the detector and lens could improve future on-sky observations.

37 Chapter 9 | Acknowledgements

I would like to acknowledge everyone who played a role in my academic accomplishments: My supervisors - Dr. Mahadevan and Dr. Gray - each of whom has provided advice and guidance throughout the research process. The graduate student in our research group, Shubham Kanodia, who has been an incredible mentor throughout the project. My cousin Michael McElwain who inspired and encouraged me to get involved in undergraduate research at the Penn State Department of Astronomy and Astrophysics. My parents and grandparents, who supported me with love and understanding. Thank you to all. Without your collective support (especially during the challenging circumstances of COVID-19) this project would not be possible.

38 Appendix | MATLAB Program

1 Introduction

This section outlines this MATLAB source code that is referred to in the Experimental Procedure in Chapter 4. The goal of the MATLAB program is to determine the plate-scale of the Crystal Ball system. Subsection 1.1 is a user-deﬁned function that takes inputs of pixel coordinates of a pair of stars. It then calculates the physical distance between the two stars in the focal plane. Subsection 1.2 takes the SIMBAD coordinates of a pair of stars and calculates the angular separation between the pair. Subsection 1.3 calls the aforementioned functions and calculates the plate scale of the system for the given pair of stars. Subsection 1.4 includes code for the main script of the MATLAB program which calls the user-deﬁned function in subsection 1.3. The script compiles the values of the plate-scale for 15 pairs of stars, and averages them to approximate the plate scale of the Crystal Ball. The output for this script is included in subsection 1.5.

1.1 PixelSeparation user-deﬁned function

1 function pixels = PixelSeparation(star1coord,star2coord)

39 2 %PIXELSEPARATION determines the pixel separation between two stars 3

4 %INPUTS: 5 %star1coordA matrix containing the pixel coordinates of star1[x1;y1] 6 %star2coordA matrix containing the pixel coordinates of star2[x2;y2] 7

8 %OUTPUT: 9 %pixels The separation between the two stars in[microns] 10

11 deltax = abs(star1coord(1)-star2coord(1)); 12 deltay = abs(star1coord(2)-star2coord(2)); 13 binning = 2;%the data taken is with2 pixel binning, so multiple by two 14 pixels = sqrt(deltax^2+deltay^2)*binning*8.2;% The physical distance between the two stars in the focal plane in[ microns]. Use the pythagorean theorem with nested pixel to micron unit conversion and binning. 15

16 end

1.2 AngularSeparation user-deﬁned function

1 function angle = AngularSeparation(star1matrix,star2matrix)

40 2 %ANGULARSEPARATION determines the angular separation between a pair of stars. 3

4 %INPUTS 5 %star1matrix The Right Ascension and Declination coordinates of star1 in matrix form.(i.e.[hour, min, sec; deg, arcminute, arcsecond];) 6 %star2matrix The Right Ascension and Declination coordinates of star2 in matrix form.(i.e.[hour, min, sec; deg, arcminute, arcsecond];) 7

8 %OUTPUT 9 %separation The angular separation between star1 and star2 in[arcseconds] 10

11 %Declination Calculations 12 star1Dec = star1matrix(2,1) + star1matrix(2,2)/60 + star1matrix(2,3)/3600;%[degrees] degrees arcminutes arcseconds conversion to degrees 13 star2Dec = star2matrix(2,1) + star2matrix(2,2)/60 + star2matrix(2,3)/3600; 14 deltaDec = abs(star1Dec-star2Dec);%the difference in Declinations of the two stars 15 avgDec = (star1Dec + star2Dec)/2;%the average Declination of the two stars 16

41 17 %Right Ascension Calculations 18 star1RA = (star1matrix(1,1) + star1matrix(1,2)/60 + star1matrix(1,3)/3600)*15;%[degrees] hours min seconds to hours conversion nested in degree conversion 19 star2RA = (star2matrix(1,1) + star2matrix(1,2)/60 + star2matrix(1,3)/3600)*15; 20 deltaRA = abs(star1RA - star2RA);%the difference in Right Ascension of the two stars 21

22 %Spherical Trigonometry 23 angle = (sqrt(deltaDec^2+(deltaRA*cosd(avgDec))^2))*3600;%[ arcseconds]%pythagorean theorem with the correctional cosine term for spherical trigonometry, nested insidea degrees to arcseconds unit conversion 24

25 end

1.3 PlateScale user-deﬁned function

1 function [p,f] = PlateScale(star1matrix,star2matrix, star1coord,star2coord) 2 %PlateScale calls the functions AngularSeparation and PixelSeparation to 3 %determine the plate scale and focal length of the Crystal Ball. 4

42 5 %INPUTS 6 %star1matrix The Right Ascension and Declination coordinates of star1 in matrix form.(i.e.[hour, min, sec; deg, arcminute, arcsecond];) 7 %star2matrix The Right Ascension and Declination coordinates of star2 in matrix form.(i.e.[hour, min, sec; deg, arcminute, arcsecond];) 8 %star1coordA matrix containing the pixel coordinates of star1[x1;y1] 9 %star2coordA matrix containing the pixel coordinates of star2[x2;y2] 10

11 %OUTPUTS 12 %p plate scale in[arcseconds/mm] 13 %f focal length in[mm] 14

15 angle = AngularSeparation(star1matrix,star2matrix);%The angular separation between the pair of stars in[ arcseconds] 16 pixels = PixelSeparation(star1coord,star2coord);%The physical distance between the pair of stars in the focal plane in[microns] 17

18 p = (angle/pixels)*1000;%Plate scale in[arcseconds/mm]. Plate scale is defined as the angular distance between two stars divided by the physical distance between the

43 stars in the focal plane. Conversion from microns to mm included. 19 f = (206265/p);%Focal length of Crystal Ball in[mm]. We can approximate the focal length of the lens using the plate scale equation. 20

21 end

1.4 Main Script

1 %{ 2 This script determines the plate scale of the Crystal Ball, using data from 3 .FIT files on The Pleiades. The script includesICRS astronomical coordinates(RA and Declination) 4 and pixel coordinates for several stars in The Pleiades. The script calls the function 5 PlateScale, which calculates the on-sky angular separation and pixel 6 separation on the focal plane of pairs of stars in The Pleiades. The plate 7 scale and focal length of the Crystal Ball are tabulated for each pair of 8 star, and the averages are calculated. 9 %} 10

44 11 %createa string matrix to keep track of stars 12 stars = ["Merope","Maia","Atlas","Electra","Taygeta"," Alcyone "]; 13

14 %To determine the plate scale of the Crystal Ball, the must be determined fora pair of stars in The Pleiades 15 fprintf ('The following stars in the Pleiades are each considered in individual pairs to determine the plate scale of the Crystal Ball lens:\n ') 16 disp(stars) 17

18 %Define astronomical coordinates for stars in Pleiades using SIMBADICRS 19 %for Right Ascension coordinates, enter in matrix as[hour; min; sec] 20 %for Declination coordinates, enter in matrix as[deg; arcminute; arcsecond] 21 Merope_ICRS = [3, 46, 19.5738428 22 23, 56, 54.081244]; 23

24 Maia_ICRS = [3, 45, 49.6065620 25 24, 22, 3.886360]; 26

27 Atlas_ICRS = [3, 49, 9.7425852 28 24, 3, 12.300277]; 29

45 30 Electra_ICRS = [3, 44, 52.5368818 31 24, 6, 48.011217]; 32

33 Taygeta_ICRS = [3, 45, 12.4957802 34 24, 28, 2.209730]; 35

36 Alcyone_ICRS = [3, 47, 29.0765529 37 24, 6, 18.488347]; 38

39 %Record pixel coordinates from.FIT files on ds9 in matrices 40 Merope_pcoord = [161;219]; 41 Maia_pcoord = [185;226]; 42 Atlas_pcoord = [168;181]; 43 Electra_pcoord = [170;239]; 44 Taygeta_pcoord = [190;235]; 45 Alcyone_pcoord = [170;204]; 46

47 %Call the function PlateScale to tabulate values of plate scale and focal 48 %length for each pair of stars in the Pleaides. 49 [MeropeMaia_platescale,MeropeMaia_focallength] = PlateScale( Merope_ICRS,Maia_ICRS,Merope_pcoord,Maia_pcoord); 50 [MeropeAtlas_platescale,MeropeAtlas_focallength] = PlateScale(Merope_ICRS,Atlas_ICRS,Merope_pcoord, Atlas_pcoord);

46 51 [MeropeElectra_platescale,MeropeElectra_focallength] = PlateScale(Merope_ICRS,Electra_ICRS,Merope_pcoord, Electra_pcoord); 52 [MeropeTaygeta_platescale,MeropeTaygeta_focallength] = PlateScale(Merope_ICRS,Taygeta_ICRS,Merope_pcoord, Taygeta_pcoord); 53 [MeropeAlcyone_platescale,MeropeAlcyone_focallength] = PlateScale(Merope_ICRS,Alcyone_ICRS,Merope_pcoord, Alcyone_pcoord); 54

55 [MaiaAtlas_platescale,MaiaAtlas_focallength] = PlateScale( Maia_ICRS,Atlas_ICRS,Maia_pcoord,Atlas_pcoord); 56 [MaiaElectra_platescale,MaiaElectra_focallength] = PlateScale(Maia_ICRS,Electra_ICRS,Maia_pcoord, Electra_pcoord); 57 [MaiaTaygeta_platescale,MaiaTaygeta_focallength] = PlateScale(Maia_ICRS,Taygeta_ICRS,Maia_pcoord, Taygeta_pcoord); 58 [MaiaAlcyone_platescale,MaiaAlcyone_focallength] = PlateScale(Maia_ICRS,Alcyone_ICRS,Maia_pcoord, Alcyone_pcoord); 59

60 [AtlasElectra_platescale,AtlasElectra_focallength] = PlateScale(Atlas_ICRS,Electra_ICRS,Atlas_pcoord, Electra_pcoord);

47 61 [AtlasTaygeta_platescale,AtlasTaygeta_focallength] = PlateScale(Atlas_ICRS,Taygeta_ICRS,Atlas_pcoord, Taygeta_pcoord); 62 [AtlasAlcyone_platescale,AtlasAlcyone_focallength] = PlateScale(Atlas_ICRS,Alcyone_ICRS,Atlas_pcoord, Alcyone_pcoord); 63

64 [ElectraTaygeta_platescale,ElectraTaygeta_focallength] = PlateScale(Electra_ICRS,Taygeta_ICRS,Electra_pcoord, Taygeta_pcoord); 65 [ElectraAlcyone_platescale,ElectraAlcyone_focallength] = PlateScale(Electra_ICRS,Alcyone_ICRS,Electra_pcoord, Alcyone_pcoord); 66

67 [TaygetaAlcyone_platescale,TaygetaAlcyone_focallength] = PlateScale(Taygeta_ICRS,Alcyone_ICRS,Taygeta_pcoord, Alcyone_pcoord); 68

69 %tabulate the values of the plate scale 70 platescale = [MeropeMaia_platescale; 71 MeropeAtlas_platescale; 72 MeropeElectra_platescale; 73 MeropeTaygeta_platescale; 74 MeropeAlcyone_platescale; 75 MaiaAtlas_platescale; 76 MaiaElectra_platescale;

48 77 MaiaTaygeta_platescale; 78 MaiaAlcyone_platescale; 79 AtlasElectra_platescale; 80 AtlasTaygeta_platescale; 81 AtlasAlcyone_platescale; 82 ElectraTaygeta_platescale; 83 ElectraAlcyone_platescale; 84 TaygetaAlcyone_platescale]; 85 fprintf ('The tabulated values of the plate scale of the Crystal Ball for each pair of stars are:\n\n ') 86 disp(platescale) 87

88 %tabulate the values of the focal length 89 focallength = [MeropeMaia_focallength; 90 MeropeAtlas_focallength; 91 MeropeElectra_focallength; 92 MeropeTaygeta_focallength; 93 MeropeAlcyone_focallength; 94 MaiaAtlas_focallength; 95 MaiaElectra_focallength; 96 MaiaTaygeta_focallength; 97 MaiaAlcyone_focallength; 98 AtlasElectra_focallength; 99 AtlasTaygeta_focallength; 100 AtlasAlcyone_focallength; 101 ElectraTaygeta_focallength;

49 102 ElectraAlcyone_focallength; 103 TaygetaAlcyone_focallength]; 104 fprintf ('The tabulated values of the focal length of the Crystal Ball for each pair of stars are:\n\n ') 105 disp(focallength) 106

107 %calculate the average plate scale 108 platescale_average = mean(platescale,'all '); 109 fprintf ('The average plate scale of the tabulated values is %f arcseconds/mm.\n ',platescale_average) 110

111 %calculate the average focal length 112 focallength_average = mean(focallength,'all '); 113 fprintf ('The average focal length of the tabulated values is %f mm.\n ',focallength_average)

1.5 Main Script Output

1 The following stars in the Pleiades are each considered in individual pairs to determine the plate scale of the Crystal Ball lens: 2 "Merope" "Maia" "Atlas" "Electra" "Taygeta" " Alcyone " 3

4 The tabulated values of the plate scale of the Crystal Ball for each pair of stars are:

50 5

6 1.0e+03 * 7

8 3.8159 9 3.7279 10 3.7036 11 3.8318 12 3.8584 13 3.7553 14 3.6967 15 3.6763 16 3.7940 17 3.7077 18 3.7334 19 3.6741 20 3.8957 21 3.7343 22 3.7643 23

24 The tabulated values of the focal length of the Crystal Ball for each pair of stars are: 25

26 54.0540 27 55.3302 28 55.6924 29 53.8301

51 30 53.4584 31 54.9257 32 55.7977 33 56.1066 34 54.3668 35 55.6317 36 55.2484 37 56.1399 38 52.9470 39 55.2357 40 54.7955 41

42 The average plate scale of the tabulated values is 3757.956760 arcseconds/mm. 43 The average focal length of the tabulated values is 54.904011 mm.

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54 BRODY D. MCELWAIN

EDUCATION The Pennsylvania State University University Park, PA B.S. & M.S. in Engineering Science Anticipated Graduation: May 2022 Minor in Engineering Mechanics

WORK EXPERIENCE Try Tek Machine Works Inc. June - August 2019 Electrical Engineering Intern Jacobus, PA Experimented with capacitors and magnetic fields to map out sewer systems. · Researched methods to solve issues concerning trenchless pipe repair. · Documented tire wear on pipeline robots in an environmentally simulated lab. · Coupling Corporation of America May - August 2018 Mechanical Engineering Intern Jacobus, PA Designed a dolly in Solid Edge to improve workflow in the assembly area. · Pitched replacement of old equipment to Peach Bottom Atomic Power Station staff. · Organized balance tooling, gauge plugs, and bearings to improve efficiency. · Coupling Corporation of America June 2015 - August 2017 Test Technician & Maintenance Assistant Jacobus, PA Assembled, measured, and tested couplings for nuclear and energy industries. · Implemented new industry standards to improve safety in storage areas. · Tracked inventory by location and quantity using Microsoft Excel. ·

GLOBAL EXPERIENCE Contemporary Colombia Study Abroad Program May 2019 Participant among the Schreyer Honors College Staﬀ Colombia, South America Presented a research paper on ecotourism and biodiversity in Colombia. · Participated in a cultural exchange with University of Ibagu´estudents. · Traveled to several regions to perceive the socioeconomic aspects of the culture. ·

EXTRACURRICULARS • Producer, Writer, and Lead Actor in the 80’s style detective ﬁlms Bread and Toast. • Rhythm Guitarist and Vocalist in the garage-rock band Suburban Ingenuity. • Group Workout Leader for 8k’s and half-marathons in Penn State Club Cross Country. • Medalist in the Penn State Blue & White Bouldering Competition in Spring 2020.

TECHNICAL SKILLS

Programming Languages MATLAB, Mathematica Engineering Software SolidWorks, Zemax OpticStudio, DS9 Proﬁciencies Intermediate Spanish, LATEX, Overleaf