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Aberration Fields in Tilted Anq Decentered Optical Aberration fields in tilted and decentered optical systems Item Type text; Dissertation-Reproduction (electronic) Authors Thompson, Kevin Paul Publisher The University of Arizona. Rights Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. Download date 08/10/2021 20:34:00 Link to Item http://hdl.handle.net/10150/565458 ABERRATION FIELDS IN TILTED ANQ DECENTERED OPTICAL SYSTEMS by- Kevin Paul Thompson A Dissertation Submitted to the Faculty of the COMMITTEE ON OPTICAL SCIENCES (GRADUATE) In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy ' In the Graduate College THE UNIVERSITY OF ARIZONA 1980 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Final Examination Committee r we certify that we have read the dissertation prepared by Kevin Paul Thompson _________ ________ entitled Aberration Fields in Tilted and Decentered Optical Systems and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy «■ Date YO Date 'fd Date / Date Date Final approval and acceptance of this dissertation is contingent upon the candidate's submission of the final copy of the dissertation to the Graduate College. I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement. z £ Dissertation Director Date STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to bor­ rowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or re­ production of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the in­ terests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: / Ueao. ACKNOWLEDGMENTS I would like to thank Professor Roland Shack for providing me with such a ripe topic to pursue and a very firm basis from which to begin. His restrained guidance and timely encouragement made the entire project quite enjoyable. It is he who should be credited with the development of the first and third order theory and the vector formula­ tion of the wave aberration expansion. To ThereSe, I would like to express my admiration for her un­ ending patience and support during my academic career. Thanks also go to Nancy Arora for diligently typing the manu­ script and to Kathy Seeley for editing and general assistance. Lastly, to the Perkin-Elmer Corporation for providing the funding for this research. TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS .................... vi LIST OF TABLES . .... ... xiv ABSTRACT ... ... ... ." . xvi 1. INTRODUCTION. , . .. 1 2. FIRST ORDER THEORY ............ 6 Summary of First Order Properties in Tilted and Decentered Systems .............. 19 Tilt Parameter ......... 19 Displacement of Centers of Image Fields and and Pupils . ..... 21 Optical Axis Ray . .: .............. 21 Gaussian Image Plane Tilt . ........... 21 Aberration Field Decentration . ........... 22 Aspheric Contribution.................... 22 Special Cases ......... 22 3. ABERRATION FIELDS IN PERTURBED OPTICAL SYSTEMS I THE THIRD ORDER ABERRATIONS . ............... 23 .4. THE ANALYSIS OF PERTURBED OPTICAL SYSTEMS ......... 57 5. APPLICATION: MISALIGNMENTS IN RITCHEY-CHRETIEN TELESCOPES A NEW TECHNIQUE .......... .................. 77 6. ABERRATION FIELDS IN PERTURBED OPTICAL SYSTEMS II THE INTERPRETATION OF THE FIFTH ORDER ABERRATIONS . 103 Fifth Order Spherical Aberration Wpgo ........ 108 Fifth Order Coma, . ... 109 Oblique Spherical Aberration Wg^o^, W 21+2 • • ..... 113 Focal Surface for Medial Oblique Spherical Aberration W240m • • • • • - • . • • • . 115 Oblique Spherical Aberration with respect to the Medial Focal Surface Associated with Oblique Spherical Aberration W 242 ......... ....... 117 : iv - V TABLE OF CONTENTS— Continued Page Linear and Field Cubed Coma W 1 3 1 , ^ 3 3 lM ....... 118 Elliptical Coma W 333 ................. 127 Medial Focal .Surface W2 2 0 M ^420M .......... 132 Astigmatism *2 2 2 , W422 . 136 Distortion W 31 %, V s i l ....... ......... 142 7. GRAPHICAL METHODS FOR ANALYZING PERTURBED OPTICAL SYSTEMS. 143 8 . SUMMARY AND FUTURE CONSIDERATIONS . ■» ........... 210 APPENDIX A: VECTOR RELATIONS ............... -214 Introduction to Vector Multiplication . .... 214 Summary of the Properties of Vector Multiplication, Squared and Cubic Vectors . 216 Vector Conjugates .................... 217 Vector Identities ............. ......... 218 Vector Operator for Obtaining the Gradient of the Wavefront . ...... 218 APPENDIX B: PLOTS FOR LOCATING THE NODES IN SYSTEMS WITH BINODAL ASTIGMATISM . 220 APPENDIX C: DERIVING AND SUMMARIZING THE PROPERTIES OF THE WAVE ABERRATION EXPANSION IN A PERTURBED OPTICAL SYSTEM THROUGH. FIFTH ORDER ...... 231 APPENDIX D: VECTOR GENERALIZATION OF THE ALGEBRAIC SOLUTION TO CUBIC EQUATIONS . , . .. ......... 263 APPENDIX E: DETERMINING THE ORIENTATION OF ELLIPTICAL COMA . ....... 265 APPENDIX F: EXTENDING THE EXPRESSIONS FOR ANALYZING PERTURBED SYSTEMS TO FIFTH ORDER IN THE WAVE ABERRATION EXPANSION . .... 268 LIST OF REFERENCES 272 LIST OF ILLUSTRATIONS Figure Page 2-1„ Defining the Equivalent Local Axis and Equivalent Tilt Parameter B0 f°r a Spherical Surface ...... 9 2-2. Locating Objects and Images in a Perturbed System . 10 2.3 Optical Axis Ray (OAR) . ............. 12 2-4. Finding the Displacement of the Aberration Field Contribution of a Surface; a* ............ 13 2-5. Deriving the Gaussian Tilt Invariant ........... 14 2-6. The Gaussian Tilt Invariant in a Perturbed System .... 15 2-7. First Order Tilt and Displacement of the Gaussian Image P l a n e ........... 16 2 =-8 . Locating the Center of an Aspheric Contribution to the Aberration Field .... ....... ......... 17 2-9. Summary of the First Order Parameters in Tilted and Decentered Systems ................. 20 i 3-1. Illustrating^the Field Vector H and the Aperture Vector p . .................. 26 3-2. The Effective Field Height H.. for a Surface Contribution to the Aberration Field In the Image Plane ..... 29 3-3. In a Perturbed Optical System the Center of the Total Coma Field for the System Is Displaced to the Point Located by the Vector aigi ................ 31 3-4. Properties of the Transverse Blur for Third Order Coma Wi3 ij (a) Aligned System, (b) Perturbed System . 33 3-5. The Medial Focal Surface in a Perturbed Optical System May Be Displaced Transversely and Longitudinally from the Center of the Gaussian Image Plane • . 37 3-6 . Illustrating the Special Cases for the Medial Focal Surface . ......... 40 3-7. The Relation between Linear and Squared Vectors ..... 42 " ' ■ ' - ' vi LIST OF ILLUSTRATIONS--Continued Figure Page 3-8. In a Perturbed System the Astigmatism Can Be Zero at Two Points in the Field ........... 43 3-9. Field Contours of Constant Astigmatism 44 3-10. Node Vectors for Illustrating the Properties of. Astigmatism in the Field . ........... 46 3-11. Magnitude and Orientation Plots for Binodal Astigmatism. 47 3-12. The Shape of the Two Focal Surfaces Containing Line Images in a System with Binodal A s t i g m a t i s m .......... 48 3-13. Illustrating the Special Cases for Astigmatism. Field curve profiles that contain the nodes . .... 51 .3-14. Illustrating Special Cases for Astigmatism. Magnitude and orientation plots on the focal surfaces con­ taining line images . 52 3-15. Illustrating the Four Types of Astigmatic Focal Surfaces in a Perturbed Optical System. ............ 54 4-1. Node Plot for Distortion .................. 65 5-1. Node Plots for the Arbitrarily Misaligned System ..... 83 5-2. On-Axis Spot Diagram in the Arbitrarily Misaligned System ............ ......... 83 5-3. Plotted Output for the Actual and the Change in the RMS Spot Size in the Arbitrarily Misaligned System (X and Y Field Profiles) . 85 5-4. Contour Plots for RMS Spot Size, in Micrometers ..... 87 5-5. Node Plots in the Coma-Compensated System ........ 89 5-6. Contour Plot for RMS Spot Size (Micrometers) in the Coma- Compensated System ............. 90 5-7. Simulation of a Through-Focus Star Plate Taken with a Coma-Compensated, Misaligned Ritchey-Chretien . 91 5-8. Illustrating the Technique for Determining Misalignments from Through-Focus Star Plates ........... 93 . vi'ii LIST OF ILLUSTRATIONS— Continued Figure Page 5-9. Determining if a Telescope is Misaligned from Through-Focus Star Plates ........... 94 5-10. Node Plots for the Coma-Compensated System with respect to the Local Axis of the Primary.......... 97 5-11. Measuring the Perturbation Vector b 222 from the Node Plot Corresponding to Fig. 5-8 ^ . 100 6-1. Transverse Blur for Third Order Coma W 131 . 109 6-2. Transverse Blur for Fifth Order Coma, ....... 110 6-3. In a Perturbed System the Center of the Aberration Field for Fifth Order Coma, 5 1 , Can Be Displaced in the Image P l a n e ......... Ill 6-4. Properties of the Transverse Blur for Fifth Order Coma, Wisi (a) Centered
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