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ADVANCED THEORY of FIELD CURVATURE by Yuhao Advanced Theory of Field Curvature Item Type text; Electronic Dissertation Authors Wang, Yuhao 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 29/09/2021 09:20:18 Link to Item http://hdl.handle.net/10150/325494 ADVANCED THEORY OF FIELD CURVATURE by Yuhao Wang ____________________________ A Dissertation Submitted to the Faculty of the COLLEGE OF OPTICAL SCIENCES In Partial Fulfillment of the Requirements For the Degree of DOCTOR OF PHILOSOPHY In the Graduate College THE UNIVERSITY OF ARIZONA 2014 THE UNIVERSITY OF ARIZONA GRADUATE COLLEGE As members of the Dissertation Committee, we certify that we have read the dissertation prepared by Yuhao Wang, titled Advanced Theory of Field Curvature and recommend that it be accepted as fulfilling the dissertation requirement for the Degree of Doctor of Philosophy. _______________________________________________________________________ Date: (Enter Date) Jose M. Sasian _______________________________________________________________________ Date: (Enter Date) Rongguang Liang _______________________________________________________________________ Date: (Enter Date) Jim Schwiegerling Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies 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. ________________________________________________ Date: (Enter Date) Dissertation Director: Jose M. Sasian 2 STATEMENT BY AUTHOR This dissertation has been submitted in partial fulfillment of the requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library. Brief quotations from this dissertation are allowable without special permission, provided that an accurate acknowledgement of the source is made. Requests for permission for extended quotation from or reproduction 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 or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author. SIGNED: Yuhao Wang 3 ACKNOWLEDGEMENTS I am deeply grateful to my advisor, Dr. José Sasián, for supporting me in the study of my dissertation work. I appreciate his patient guidance which kept me on track throughout my research studies. I am also deeply grateful to the other members of my dissertation committee, Dr. Rongguang Liang and Dr. Jim Schwiegerling, for reviewing my dissertation. Additional thanks to Dmitry Reshidko and Chia-Ling Li for their help on my research study. 4 TABLE OF CONTENTS LIST OF FIGURES………………………………………………………………………8 LIST OF TABLES……………………………………………………………………….14 ABSTRACT……………………………………………………………………………...16 CHAPTER 1 …………………………………………………………………………….17 INTRODUCTION TO FIELD CURVATURE 1.1What is field curvature……………………………………………………………….17 1.2 How field curvature affects image quality…………………………………………..17 1.3 Classical theory of field curvature (Petzval theorem)……………………………….18 CHAPTER 2……………………………………………………………………………..24 CLASSICAL METHODS TO CONTROL FIELD CURAVATURE 2.1 Meniscus lens………………………………………………………………………..24 2.2 Field flattener………………………………………………………………………..26 2.3 Separating elements…………………………………………………………………28 2.4 New glass type………………………………………………………………………30 2.5 Miscellaneous methods……………………………………………………………..31 CHAPTER 3…………………………………………………………………………….34 WAVE ABERRATION THEORY OF HIGH ORDER FIELD CURVATURE 3.1 High Order Aberrations……………………………………………………………..34 3.2 Aspheric contribution to high order field curvature………………………………...35 3.3 Theory of balancing 4th order and higher order field curvature…………………….36 CHAPTER 4 ……………………………………………………………………………40 MODELING FIELD CURVATURE CORRECTION USING AN ASPHERIC SURFACE 4.1 Model of Petzval Field Curvature…………………………………………………..40 5 4.2 Modeling results using one aspheric surface………………………………………42 4.3 Modeling results using two aspheric surfaces……………………………………..48 4.4 Induced Aberrations……………………………………………………………….50 4.5 Aspheric field flattener…………………………………………………………….52 4.6 Field curvature evaluation criteria…………………………………………………62 CHAPTER 5…………………………………………………………………………...68 BALANCING ASTIGMATISM AND PETZVAL FIELD CURVATURE 5.1 Petzval and astigmatism……………………………………………………………68 5.2 High order astigmatism…………………………………………………………….68 5.3 Examples of cellular phone lenses…………………………………………………69 5.4 Examples of wide angle lenses…………………………………………………….75 5.5 Miscellaneous examples…………………………………………………………...77 CHAPTER 6……………………………………………………………………………79 CONTROL PETZVAL FIELD CURVATURE BY OBLIQUE SPHERICAL ABERRATION 6.1 Oblique spherical aberration………………………………………………………..79 6.2 Balancing Petzval field curvature with Oblique spherical aberration………………79 6.3 Double Gauss lens example…………………………………………………………80 CHAPTER 7 …………………………………………………………………………….83 NOVEL ASPHERIC SURFACES 7.1 Review of the existing aspheric surfaces…………………………………………….83 7.2 Novel aspheric surfaces……………………………………………………………...85 7.3 Application of novel aspheric surfaces………………………………………………92 CHAPTER 8……………………………………………………………………………..97 SUMMARY & FUTURE WORK 6 8.1 Summary…………………………………………………………………………….97 8.2 Suggestion for future work………………………………………………………….99 APENDIX………………………………………………………………………………100 REFERENCES…………………………………………………………………………125 7 LIST OF FIGURES Figure 1-1 Original image compared to the image with field curvature…………………16 Figure 1-2 Schematic of field curvature of a positive singlet lens………………………18 Figure 1-3 Field curvature plot of pure Petzval curvature……………………………….19 Figure 1-4 OPD (optical path difference) of field curvature…………………………….19 Figure 1-5 Transverse ray aberration plot of field curvature……………………………20 Figure 1-6 Spot diagram of field curvature……………………………………………..21 Figure1-7 MTF (modulation transfer function) of field curvature……………………..21 Figure 1-8 MTF through field of view plot of field curvature………………………….22 Figure 2-1 Double Gauss lens layout and Seidel aberration diagram………………….24 Figure 2-2 Field curvature and distortion plot………………………………………….24 Figure 2-3 Petzval lens layout and Seidel aberration diagram…………………………26 Figure 2-4 Field curvature and distortion plot………………………………………….26 Figure 2-5 Cooke triplet lens layout and Seidel aberration diagram…………………...27 Figure 2-6 Field curvature and distortion plot………………………………………….28 Figure 3-1 Field curvature with W220 = -1λ…………………………………………….36 Figure 3-2 Field curvature with W220 = -1λ, W420 = 1λ………………………………..37 8 Figure 3-3 Field curvature with W220 = -1λ, W420 = 2.2λ, W620 = -1.2λ………………37 Figure 4-1 Layout of model and plot of field curvature………………………………40 Figure 4-2 Seidel diagram of the field curvature model………………………………41 Figure 4-3 Design layout and field curvature plot with one aspheric term A4……….42 Figure 4-4 Design layout and Field curvature plot with two aspheric terms A4 and A6.43 Figure 4-5 Theoretical calculation results of (a) W220 only, (b) W220 balanced with W420, (c) W220 balanced with W420 and W620………………………………………………..43 Figure 4-6 Software optimization results for (a) W220 only, (b) W220 balanced with W420, (c) W220 balanced with W420 and W620………………………………………………..44 Figure 4-7 Four image surfaces (T-tangential, M-medial, S-sagittal, P- petzval) when astigmatism is biased on field curvature………………………………………………45 Figure 4-8 Plots of the Generalized Petzval Surface when asphere is 10 mm away from image (a) with one aspheric term A4 (b) with two aspheric terms A4 and A6………..46 Figure 4-9 Optimization results for two aspheric surfaces model…………………….48 Figure 4-10 Model of induced aberration layout………………………………………50 Figure 4-11 Spot diagram and OPD……………………………………………………51 Figure 4-12 Schmidt telescope design layout and its field curvature………………….52 Figure 4-13 OPD and Seidel diagram………………………………………………….53 9 Figure 4-14 Aspheric flattener lens zoomed layout and field curvature plot when flattener lens applied……………………………………………………………………………..53 Figure 4-15 OPD plot when aspheric flattener lens applied…………………………...54 Figure 4-16 Positive lens zoomed layout and field curvature plot……………………..55 Figure 4-17 OPD plot when positive flattener lens applied…………………………….55 Figure 4-18 Optimized Petzval lens on its Petzval surface layout and its OPD plot…..56 Figure 4-19 Optimized Petzval lens on a flat image surface and its field curvature plot..57 Figure 4-20 OPD and Seidel diagram……………………………………………………57 Figure 4-21 Layout of (a) original (b) asphere with one term A4 (c) asphere with two terms A4 and A6………………………………………………………………………….58 Figure 4-22 Field curvature plot of (a) original (b) asphere with one term A4 (c) asphere with two terms A4 and A6……………………………………………………………….58 Figure 4-23 Generalized Petzval surface plot of (a) original (b) asphere with one term A4 (c) asphere with two terms A4 and A6………………………………………………….58 Figure 4-24 Petzval lens with a flattener lens use two aspheric surfaces……………..59 Figure 4-25 Field curvature & distortion and Generalized Petzval surface……………59 Figure 4-26 Petzval lens with an aspheric flattener lens that are away from image…..60 Figure 4-27 Field curvature
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