A Rotating Aperture Mask for Small Telescopes
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A ROTATING APERTURE MASK FOR SMALL TELESCOPES A Thesis presented to the Faculty of California Polytechnic State University, San Luis Obispo In Partial Fulfillment of the Requirements for the Degree Master of Science in Mechanical Engineering by Edward Leo Foley November 2019 © 2019 Edward Leo Foley ALL RIGHTS RESERVED ii COMMITTEE MEMBERSHIP TITLE: A Rotating Aperture Mask for Small Telescopes AUTHOR: Edward Leo Foley DATE SUBMITTED: November 2019 COMMITTEE CHAIR: John Ridgely, Ph.D. Professor of Mechanical Engineering COMMITTEE MEMBER: Russell Genet, Ph.D. Research Scholar in Residence COMMITTEE MEMBER: William R. Murray, Ph.D. Professor of Mechanical Engineering COMMITTEE MEMBER: Jane Zhang, Ph.D. Professor of Electrical Engineering iii ABSTRACT A Rotating Aperture Mask for Small Telescopes Edward Leo Foley Observing the dynamic interaction between stars and their close stellar neighbors is key to establishing the stars’ orbits, masses, and other properties. Our ability to visually discriminate nearby stars is limited by the power of our telescopes, posing a challenge to astronomers at small observatories that contribute to binary star surveys. Masks placed at the telescope aperture promise to augment the resolving power of telescopes of all sizes, but many of these masks must be manually and repetitively reoriented about the optical axis to achieve their full benefits. This paper introduces a design concept for a mask rotation mechanism that can be adapted to telescopes of different types and proportions, focusing on an implementation for a Celestron C11 Schmidt–Cassegrain optical tube assembly. Mask concepts were first evaluated using diffraction simulation programs, later manufactured, and finally tested on close double stars using a C11. An electronic rotation mechanism was designed, produced, and evaluated. Results show that applying a properly shaped and oriented mask to a C11 enhances contrast in images of double star systems relative to images captured with the unmasked telescope, and they show that the rotation mechanism accurately and repeatably places masks at target orientations with minimal manual effort. Detail drawings of the mask rotation mechanism and code for the software interface are included. iv ACKNOWLEDGMENTS This thesis is submitted as the product of hard work from many different contributors. I would like to extend my sincere thanks to Dr. Russell Genet for reigniting my love of astronomy through his contagious mix of passion, curiosity, and geniality. He fully supported me throughout my odyssey to complete this project by offering vital direction and encouragement, not to mention connecting me with other astronomers and co-authoring an earlier paper published in the Journal of Double Star Observations. He graciously hosted me at the Orion Observatory and allowed me to use one of his telescopes for crucial optical and mechanical tests. I deeply appreciate the collaborative and positive research environment he fostered—not just for me and this project but also for others and their own scientific pursuits. I am very grateful to thesis committee chair Dr. John Ridgely for the guidance he offered me and the patience he exhibited throughout this project. I also sincerely thank my committee members, Drs. William Murray and Jane Zhang, for attending my defense and sharing constructive feedback on a draft of this paper. I am indebted to Dr. Neil Zimmerman of Princeton University for his counsel and for kindly contributing an optimized mask design for the Celestron C11 telescope. This paper and the conclusions drawn within it benefitted greatly from his efforts, just like the astronomers who might fruitfully use his bowtie mask in double star observations. I am grateful to Jimmy Ray for running the first practical tests of the Gaussian donut mask on a telescope; and to Donald Loveland, who diligently evaluated and documented the performance of two mask designs on several pairs of double stars. v I thank Kevin Jantz for his machining assistance and feedback on early drawings. I also appreciate the efforts of Nick Bonafede, Marc Goupil, and Bodin Rojanachaichanin, who lent some of their time to review my engineering documentation. I must recognize Keenan Reimer, who helped me get to and from campus in the home stretch of the project. I also thank Luke Williams, who delivered the Orion Observatory’s C11 to my house for an afternoon of important mechanical tests. I extend gratitude to David Rowe, who kindly shared with me his Atmospheric Seeing Distortion simulator and adapted it to work with arbitrary aperture shapes in support of this project. I thank the professors and administrators at Cal Poly for actively applying the University’s “Learn by Doing” mantra and for granting a mechanical engineering student the opportunity to enroll in courses within the fields of computer science, computer vision, image processing, digital control systems, and optics. The lessons from this unusual palette of subjects were fundamental in my acquiring an inside-out understanding of a unique project. I give thanks to the many housemates, coworkers, grad lab occupants, and friends who cheered me on through this endeavor. Finally, I thank my parents, Bill and Lori; my brother, Matt; and all my relatives for their love and encouragement. Hopefully their reading these sentences answers their long-standing and oft-repeated question of whether my thesis is done yet. vi TABLE OF CONTENTS Page LIST OF TABLES ......................................................................................................... XIII LIST OF FIGURES ....................................................................................................... XVI CHAPTER 1. INTRODUCTION .................................................................................................. 1 1.1 Statement of problem .................................................................................. 1 1.2 Resolution and contrast targets ................................................................... 5 1.3 Existing approaches .................................................................................... 8 1.3.1 Color filters ..................................................................................... 8 1.3.2 Occulting bars ................................................................................. 9 1.3.3 Lyot coronagraphs ......................................................................... 11 1.3.4 Apodizing masks ........................................................................... 12 1.4 Selection of method .................................................................................. 22 2. SIMULATING SHAPED APERTURES ............................................................. 23 2.1 Optics summary ........................................................................................ 23 2.2 Diffraction simulation ............................................................................... 24 2.2.1 Diffraction simulation using MATLAB ........................................ 24 2.2.2 Diffraction simulation using Maskulator ...................................... 25 2.3 Displaying power spectra .......................................................................... 27 3. APERTURE MASKS FOR THE CELESTRON C11 OPTICAL TUBE ASSEMBLY ......................................................................................................... 29 vii 3.1 The Celestron C11 optical tube assembly ................................................. 29 3.2 Effect of central obstruction on diffraction pattern................................... 30 3.3 Past attempts to mask a central obstruction .............................................. 34 3.4 New mask candidates ................................................................................ 40 3.4.1 Gaussian donut mask..................................................................... 40 3.4.2 Multi-Gaussian mask .................................................................... 46 3.4.3 Concentric ring mask .................................................................... 47 3.4.4 Bowtie mask .................................................................................. 49 3.5 Mask selection .......................................................................................... 52 3.6 Enforcing structural connectivity .............................................................. 53 3.6.1 Structural accommodations for bowtie mask ................................ 53 3.6.2 Structural accommodations for Gaussian donut mask .................. 55 4. MASK ROTATION MECHANISM FOR THE CELESTRON C11 OPTICAL TUBE ASSEMBLY ............................................................................ 58 4.1 Need for rotation mechanism .................................................................... 58 4.2 Mechanical design considerations ............................................................ 60 4.3 Early designs ............................................................................................. 62 4.3.1 Virtual axis design ......................................................................... 62 4.3.2 Lazy Susan design ......................................................................... 66 4.4 Final design ............................................................................................... 69 4.4.1 Establishing a fixed axis ................................................................ 69 4.4.2 Strategies for powering rotation ...................................................