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`SELECTED TOPICS IN NOVEL OPTICAL DESIGN
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`by
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`Yufeng Yan
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`____________________________
`Copyright © Yufeng Yan 2019
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`A Dissertation Submitted to the Faculty of the
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`JAMES C. WYANT COLLEGE OF OPTICAL SCIENCES
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`In Partial Fulfillment of the Requirements
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`For the Degree of
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`DOCTOR OF PHILOSOPHY
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`In the Graduate College
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`THE UNIVERSITY OF ARIZONA
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`2019
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`APPLE V COREPHOTONICS
`IPR2020-00906
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`THE UNIVERSITY OF ARIZONA
`GRADUATT: COLLEGE
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`As members ofthe Dissertatian Committec, we certify thal we have read the dissertation
`prepared by Yufeng Yan, titled Selected Topics in Novel Optical Design and recommendthatit be
`accepted asfulfilling the dissertation requirement for the Degree of Doctor of Philosophy.
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`Pe ANAorecono Date: {1d Zot
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`Jose
`Sasian
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`\ eeg)aan Date:_2fIG/215|
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`James Schwiegerling
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`/ngpor a—
`Date: _ 17/1ff
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`a
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`— |
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`{
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`RongguangLidng
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`Final approval and acceptance ofthis dissertation is contingent upon the candidate’s submission
`of the final copies ofthe dissertation to the Graduate College,
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`| hereby certify that I have read this dissertation prepared under mydirection and recommend
`that it be accepted as fulfilling the dissertation requirement,
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`picsanaes Date: (A>3-20!'7
`
`Joye Susian
`Dissertation Committee Chair
`Optical Sciences
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`APPLE V COREPHOTONICS
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`APPLE V COREPHOTONICS
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`ACKNOWLEDGEMENTS
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`I would like to first thank my parents in China for their support that encouraged me to
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`pursue both bachelor’s, master’s and doctorate degree abroad. I would also like to thank my
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`girlfriend Jie Feng for her strong support and being the first reader of each chapter of this
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`dissertation. I am very grateful to my adviser, Dr. Jose Sasian. This project would not have been
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`possible without his constant support and mentoring. I would also like to acknowledge the
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`members of my committee, Dr. Rongguang Liang and Dr. Jim Schwiegerling, who took their time
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`to review this dissertation and gave me valuable suggestions.
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`In addition, I would like to thank Zemax for giving me permission to use their software for
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`designing and evaluating the optical systems in this project. I would also like to thank Dr. Liang
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`for his funding and support to the project “Optical performance evaluation and chromatic
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`aberration correction of a focus tunable lens used for 3D microscopy”, which is included in Chapter
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`4 of this dissertation.
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`APPLE V COREPHOTONICS
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`DEDICATION
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`To my parents Xueping and Zhiming, and to my love Jie
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`APPLE V COREPHOTONICS
`IPR2020-00906
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`TABLE OF CONTENTS
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`LIST OF FIGURES ...................................................................................................................... 7
`LIST OF TABLES ...................................................................................................................... 14
`ABSTRACT ................................................................................................................................. 15
`1
`Introduction .......................................................................................................................... 16
`2 Photographic Fisheye Lens Design for 35mm Format Cameras ..................................... 19
`2.1 Introduction to Fisheye Lenses ....................................................................................... 20
`2.1.1 The History behind Fisheye Lenses ..................................................................... 21
`2.1.2 Diagonal and Circular Fisheye Lens for Photographic Purpose .......................... 27
`2.2 Projection Methods of Fisheye Lenses ........................................................................... 30
`2.2.1 Tangential and Sagittal Magnification ................................................................. 31
`2.2.2 Equidistant Projection .......................................................................................... 33
`2.2.3 Orthographic Projection ....................................................................................... 35
`2.2.4 Stereographic Projection ...................................................................................... 36
`2.2.5 Equisolid Angle Projection .................................................................................. 38
`2.2.6 Projection Difference and their Practice Use ....................................................... 40
`2.3 Special Properties and Design Issues of Photographic Fisheye Lenses ......................... 42
`2.3.1 Negative Meniscus Lens and Pupil Shift ............................................................. 43
`2.3.2 Inverted Telephoto Structure and Minimum BFD Requirement ......................... 46
`2.3.3 Depth of Field ...................................................................................................... 48
`2.3.4 Relative Illumination and Image Space Chief Ray Angle ................................... 51
`2.4 Design of a Zoom Fisheye Lens for 35mm Format DSLR Cameras .............................. 53
`2.4.1 Motivation and Current Designs of Zoom Fisheye Lenses ................................. 54
`2.4.2 Design Specifications and Lens Construction ..................................................... 56
`2.4.3 Aberration Control ............................................................................................... 60
`2.4.4 Lens Optimization ................................................................................................ 65
`2.4.5 Performance Evaluation ....................................................................................... 66
`2.4.6 Tolerance Analysis............................................................................................... 73
`2.5 Conclusion ...................................................................................................................... 74
`3 Miniature Camera Lens Design with a Freeform Surface ............................................... 77
`3.1 Design Challenges of a Miniature Camera Lens ............................................................ 79
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`3.2 Aspherical and Freeform Surfaces .................................................................................. 84
`3.2.1 Conventional Aspherical Surfaces ....................................................................... 85
`3.2.2 Freeform Surface based on Pedal Curve to the Ellipse ........................................ 88
`3.3 First Lens Comparison .................................................................................................... 92
`3.3.1 Nominal Performance Comparison...................................................................... 93
`3.3.2 Tolerance Sensitivity ........................................................................................... 94
`3.4 Second Lens Comparison ............................................................................................... 99
`3.4.1 Performance Comparison................................................................................... 100
`3.4.2 Reversed Asphere Design .................................................................................. 107
`3.5 Conclusion .................................................................................................................... 111
`4 Applications and Optical Performance Consideration of Liquid Lenses ..................... 114
`4.1 Development and Principles of Focus Tunable Lenses ................................................ 115
`4.2 A Review of Application Utilizing Liquid Lenses ....................................................... 121
`4.2.1 Focus Sweeping ................................................................................................. 121
`4.2.2 Zoom System based on Liquid Lens .................................................................. 130
`4.2.3 Nonmechanical Beam Steering .......................................................................... 139
`4.3 Optical Performance Evaluation of Liquid Lens used for 3D microscopy ................... 142
`4.3.1 Simulation and Experiment Setup ..................................................................... 143
`4.3.2 Simulation and Experiment Results ................................................................... 147
`4.4 Correction of Chromatic Aberration ............................................................................. 154
`4.5 Conclusion .................................................................................................................... 162
`5 Conclusion .......................................................................................................................... 165
`APPENDIX A – LENS DATA I ............................................................................................... 167
`APPENDIX B – LENS DATA II ............................................................................................. 171
`REFERENCES .......................................................................................................................... 179
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`LIST OF FIGURES
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`Figure 2.1. Modern fisheye lens applications such as (a) the “Bird’s-eye” visual system [6] and (b)
`a Samsung “360-degree” camera for virtual reality displays [7]. .......................................... 21
`Figure 2.2. Refraction of a ray at critical angle ............................................................................... 23
`Figure 2.3. (a) Water camera designed by R.W.Wood, (b) photo took by Wood’s camera, (c) fisheye
`camera designed by W.N.Bond and (d) entire sky captured by Bond’s camera ................... 23
`Figure 2.4. The layout of ‘the Hill sky lens’ designed by R. Hill ................................................... 24
`Figure 2.5. The comparison between the (a) AEG fisheye lens and (b) Nikkor’s first fisheye lens26
`Figure 2.6. A sample Image taken by a diagonal fisheye lens ........................................................ 29
`Figure 2.7. A sample Image taken by a circular fisheye lens.......................................................... 29
`Figure 2.8. The object hemisphere of a fisheye lens system ........................................................... 31
`Figure 2.9. The image space of a fisheye lens system .................................................................... 32
`Figure 2.10. Image height vs. field angle for different fisheye projection system.......................... 40
`Figure 2.11. Same object under (a) stereographic projection, (b) equidistant projection, (c) equisolid
`angle projection and (d) orthographic projection .................................................................. 41
`Figure 2.12. The projection curve fitting for the Nikkor 16mm F/2.8D fisheye lens ..................... 42
`Figure 2.13. The Nikkor 6mm F/2.8 220-degree fisheye lens with 3 negative meniscus lenses .... 44
`Figure 2.14. The pupil shift effect of the Nikkor 8mm F/8 fisheye lens ......................................... 45
`Figure 2.15. A fisheye lens with ray aiming turned on (top) and off (bottom) in Zemax............... 46
`Figure 2.16. The structure of the telephoto lens and the inverted telephoto lens ............................ 47
`Figure 2.17. For a fisheye lens without sufficient BFD, (a) the folding mirror needs to be held at
`upright position and (b) an attachable viewfinder is needed to provide live view [20] ........ 48
`Figure 2.18. Illustration of depth of field L..................................................................................... 49
`Figure 2.19. Coma aberration of the entrance pupil. Black solid lines indicate the paraxial entrance
`pupil with grid. The red dashed lines indicate the off-axis entrance pupil with corresponding
`grid. ........................................................................................................................................ 53
`Figure 2.20. A monochromatic fisheye lens design with 104% edge relative illumination (compare
`to center illumination) ............................................................................................................ 53
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`LIST OF FIGURES - Continued
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`Figure 2.21. (a) Size comparison between a 35mm sensor and an APS-C sensor, (b) zoom fisheye
`lens at its shortest focal length, (c) zoom fisheye lens providing diagonal fisheye image for
`APS-C sensor, (d) zoom fisheye lens at its longest focal length. .......................................... 54
`Figure 2.22. Lens structure at extreme zoom positions ................................................................... 58
`Figure 2.23. Cam curve of the zoom lens ....................................................................................... 58
`Figure 2.24. Image space CRA vs. HFOV at (a) wide-angle position, (b) intermediate zoom position,
`and (c) telephoto zoom position............................................................................................. 66
`Figure 2.25. Optical path difference for 0 deg, 30 deg, 60 deg, and 90 deg half field at (a) wide angle
`zoom position, (b) intermediate zoom position, and (c) telephoto zoom position. Scale is (cid:114) 2
`waves ..................................................................................................................................... 67
`Figure 2.26. Astigmatic field curves at (a) wide angle zoom position, (b) intermediate zoom position,
`and (c) telephoto zoom position............................................................................................. 67
`Figure 2.27. Longitudinal aberration at (a) wide angle zoom position, (b) intermediate zoom position,
`and (c) telephoto zoom position............................................................................................. 68
`Figure 2.28. Longitudinal aberration at (a) wide angle zoom position, (b) intermediate zoom position,
`and (c) telephoto zoom position............................................................................................. 68
`Figure 2.29. Lateral color at (a) wide angle zoom position, (b) intermediate zoom position, and (c)
`telephoto zoom position. ........................................................................................................ 69
`Figure 2.30. MTF versus spatial frequency at (a) wide angle zoom position, (b) intermediate zoom
`position, and (c) telephoto zoom position. ............................................................................. 71
`Figure 2.31. MTF versus field at (a) wide angle zoom position, (b) intermediate zoom position, and
`(c) telephoto zoom position. .................................................................................................. 71
`Figure 2.32. Entrance pupil shape at its maximum at (a) wide angle zoom position, (b) intermediate
`zoom position, and (c) telephoto zoom position. ................................................................... 72
`Figure 2.33. Relative illumination at (a) wide angle zoom position, (b) intermediate zoom position,
`and (c) telephoto zoom position............................................................................................. 73
`Figure 2.34. Effect of 1-arc min surface/element tilt, and 10-(cid:80)m surface/element decenter, at all
`three critical zoom positions, based upon the root-sum-square method ................................ 74
`Figure 3.1. Global digital still camera shipments in pieces from 2010 to 2018 .............................. 77
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`LIST OF FIGURES - Continued
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`Figure 3.2. Layout comparison between the Nikon 28mm conventional camera lens and Apple 4mm
`miniature camera lens ............................................................................................................ 80
`Figure 3.3. Sideview of a typical CMOS sensor, large angle off-axis ray bundle may cause light
`leakage into the neighboring pixels and results in color crosstalk ........................................ 81
`Figure 3.4. Comparison of relative illumination between Nikon 28mm camera lens and Apple 4mm
`miniature lens ......................................................................................................................... 82
`Figure 3.5. An example pedal curve to the ellipse, a = 2, b = 1 ...................................................... 89
`Figure 3.6. An elliptical-like curve on the x-y plane for sag equation derivation .......................... 90
`Figure 3.7. Layout and OPD plots of the benchmark lens. The maximum scales of OPD plots are (cid:114)1
`wave ....................................................................................................................................... 93
`Figure 3.8. Layout and OPD plots of the evaluation lens. The maximum scales of OPD plots are (cid:114)1
`wave ....................................................................................................................................... 94
`Figure 3.9. Nominal MTF plots of benchmark lens (left) and evaluation lens (right) .................... 94
`Figure 3.10. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 7 in Y direction .......................................................................................................... 95
`Figure 3.11. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 8 in Y direction .......................................................................................................... 95
`Figure 3.12. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 9 in Y direction .......................................................................................................... 96
`Figure 3.13. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 10 in Y direction ........................................................................................................ 96
`Figure 3.14. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`element 4 in Y direction......................................................................................................... 96
`Figure 3.15. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`element 5 in Y direction......................................................................................................... 97
`Figure 3.16. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 7 in X direction .......................................................................................................... 97
`Figure 3.17. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 8 in X direction .......................................................................................................... 97
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`LIST OF FIGURES - Continued
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`Figure 3.18. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 9 in X direction .......................................................................................................... 98
`Figure 3.19. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`surface 10 in X direction ........................................................................................................ 98
`Figure 3.20. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`element 4 in X direction......................................................................................................... 98
`Figure 3.21. MTF plots of benchmark lens (left) and evaluation lens (right) under 5 (cid:80)m decenter of
`element 5 in X direction......................................................................................................... 99
`Figure 3.22. Lens layout of the even aspere lens, the Q-type polynomial lens and the pedal freeform
`lens ....................................................................................................................................... 101
`Figure 3.23. Nominal OPD plots of the even sphere lens ............................................................. 101
`Figure 3.24. Nominal OPD plots of the Q-type polynomial lens .................................................. 102
`Figure 3.25. Nominal OPD plots of the pedal freeform lens ........................................................ 102
`Figure 3.26. Nominal MTF plots of the even asphere lens, the Q- type polymonial lens and the pedal
`freeform lens ........................................................................................................................ 103
`Figure 3.27. MTF plots under 5 (cid:80)m decenter of surface 7 in Y direction for the even asphere lens,
`the Q- type polymonial lens and the pedal freeform lens .................................................... 104
`Figure 3.28. MTF plots under 5 (cid:80)m decenter of surface 8 in Y direction for the even asphere lens,
`the Q- type polymonial lens and the pedal freeform lens .................................................... 104
`Figure 3.29. MTF plots under 5 (cid:80)m decenter of surface 9 in Y direction of the even asphere lens,
`the Q- type polymonial lens and the pedal freeform lens .................................................... 105
`Figure 3.30. MTF plots under 5 (cid:80)m decenter of surface 10 in Y direction of the even asphere lens,
`the Q- type polymonial lens and the pedal freeform lens .................................................... 105
`Figure 3.31. MTF plots under 5 (cid:80)m decenter of element 4 in Y direction of the even asphere lens,
`the Q- type polymonial lens and the pedal freeform lens .................................................... 106
`Figure 3.32. MTF plots under 5 (cid:80)m decenter of element 5 in Y direction of the even asphere lens,
`the Q- type polymonial lens and the pedal freeform lens .................................................... 106
`Figure 3.33. Layout of the pedal freeform lens (left) and the reversed asphere lens (right) ......... 108
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`LIST OF FIGURES - Continued
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`Figure 3.34. Nominal MTF plots of the pedal freeform lens (left) and the reversed asphere lens (right)
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`Figure 3.35. MTF plots of the pedal freeform lens (left) and the reversed asphere lens (right) under
`5 (cid:80)m decenter of surface 7 in Y direction ........................................................................... 109
`Figure 3.36. MTF plots of the pedal freeform lens (left) and the reversed asphere lens (right) under
`5 (cid:80)m decenter of surface 8 in Y direction ........................................................................... 109
`Figure 3.37. MTF plots of the pedal freeform lens (left) and the reversed asphere lens (right) under
`5 (cid:80)m decenter of surface 9 in Y direction ........................................................................... 110
`Figure 3.38. MTF plots of the pedal freeform lens (left) and the reversed asphere lens (right) under
`5 (cid:80)m decenter of surface 10 in Y direction ......................................................................... 110
`Figure 3.39. MTF plots of the pedal freeform lens (left) and the reversed asphere lens (right) under
`5 (cid:80)m decenter of element 4 in Y direction .......................................................................... 110
`Figure 3.40. MTF plots of the pedal freeform lens (left) and the reversed asphere lens (right) under
`5 (cid:80)m decenter of element 10 in Y direction ........................................................................ 111
`Figure 4.1. Working principle of the “butterfly cup” from Song dynasty. ................................... 116
`Figure 4.2. Working principle of LC tunable lens with inhomogeneous cell cap ......................... 117
`Figure 4.3. Electrode designs for LC lenses with homogeneous cell gap, including (a) hole-patterned
`electrode, (b) curved electrode and (c) planar electrodes. ................................................... 118
`Figure 4.4. Working principle of a liquid lens based on electrowetting. ...................................... 119
`Figure 4.5. Working principle of a liquid lens with polymer membrane, lens shape is changed by
`applying pressure on membrane. ......................................................................................... 120
`Figure 4.6. Figure of an example patented variable focus liquid ophthalmic lens. Optical power of
`liquid lens is tunable by adjusting the rotatable impeller .................................................... 122
`Figure 4.7. Example of presbyopia correction using liquid lens. (a) A relaxed eye looking at infinity
`through liquid lens, (b) a relaxed eye looking at a near object through liquid lens, (c) a relaxed
`eye looking at infinity without liquid lens, (d) an eye looking at a near object with eye lens
`accommodation. ................................................................................................................... 123
`Figure 4.8. Demonstration of VAC in HMDs. .............................................................................. 125
`Figure 4.9. A “bird bath” type HMD with a tunable lens to reduce VAC .................................... 126
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`LIST OF FIGURES - Continued
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`Figure 4.10. A wide FOV HMD with commercial off-the-shelf liquid lens ................................. 127
`Figure 4.11. A focus-tunable near-eye HMD based on commercially off-the-shelf components [71]
` ............................................................................................................................................. 128
`Figure 4.12. Light propagation through (a) a conventional infinite conjugate objective with a fixed
`focus plane and (b) an infinite conjugate objective pairs with a liquid lens ........................ 129
`Figure 4.13. System comparison between putting liquid lens at conjugated pupil of aperture stop
`(top) and putting liquid lens directly above microscope objective close to the aperture stop
`(bottom). .............................................................................................................................. 129
`Figure 4.14. An afocal zoom system. Both objective and eye piece are liquid lenses introduced by
`Nickolaos Savidis ................................................................................................................ 132
`Figure 4.15. A 4x zoom laparoscope presented by Lee. ............................................................... 134
`Figure 4.16. A 1.7x zoom camera lens presented by Kuiper [78]................................................. 134
`Figure 4.17. A 2x zoom camera lens presented by Zhao [79]. ..................................................... 135
`Figure 4.18. A 2x zoom camera lens with chromatic aberration correction. ................................ 137
`Figure 4.19. Optical performance of the 2x zoom lens based on liquid lenses ............................. 138
`Figure 4.20. 2.5x hybrid zoom lens presented by Wippermann (left) and 2.6x hybrid zoom lens
`presented by Sun [82, 83] .................................................................................................... 139
`Figure 4.21. A 9.8x hybrid zoom lens patented by Canon [84] .................................................... 139
`Figure 4.22. A non-mechanical beam steering system using liquid lenses ................................... 140
`Figure 4.23. An ultra-wide angle non-mechanical beam steering system using liquid lenses
`presented by Zohrabi [87] .................................................................................................... 141
`Figure 4.24. A camera lens with liquid lens optical image stabilizer [88] .................................... 142
`Figure 4.25. Simulation setup in Zemax ....................................................................................... 144
`Figure 4.26. A Twyman-Green interferometer to measure the spherical aberration and chromatic
`focal shift of the 3D microscopy setup in vertical direction. ............................................... 145
`Figure 4.27. Setup to measure the image contrast with a USAF 1951 target to evaluate system
`resolution. ............................................................................................................................ 146
`Figure 4.28. Setup to measure aberration and contrast of the 3D microscopy in horizontal direction
`to exam gravity effect. ......................................................................................................... 147
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`Figure 4.29. On-axis MTF of the liquid lens and OL paired with Thorlabs 2X refractive objective.
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`Figure 4.30. On-axis MTF of the liquid lens and OL paired with Thorlabs 4X refractive objective.
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`Figure 4.31. On-axis MTF of the liquid lens and OL paired with Thorlabs 15X reflective objective.
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`Figure 4.32. On-axis MTF of the liquid lens and OL paired with Thorlabs 40X reflective objective.
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`Figure 4.33. Chromatic focal shifts between F-line and C-line (blue bar) and between F-line and d-
`line (orange bar) for 4 chosen objectives with liquid lens and OL. ..................................... 150
`Figure 4.34. Chromatic focal shift plots for the objectives with and without liquid lens. ............ 151
`Figure 4.35. Optical performance evaluation of 3D microscopy setup in vertical direction ........ 152
`Figure 4.36. Optical performance evaluation of 3D microscopy setup in horizontal direction .... 154
`Figure 4.37. Optical setup for equation derivation........................................................................ 155
`Figure 4.38. An achromatic liquid lens system with 2 thin doublets ............................................ 161
`Figure 4.39. An apochromatic 3D microscopy system. ................................................................ 162
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`Table 2.1. Design specification of the zoom fisheye lens at different zoom positions ................. 57
`Table 2.2. Lens data with aspherical coefficients ......................................................................... 59
`Table 2.3. Aberration coefficients upon object shift according to the object shift parameter S ... 60
`Table 2.4. Zoom lens aberration coefficients in waves for a semi-field of 30 degrees ................ 62
`Table 3.1. Lens data for the Nikon lens, Apple lens and Nikon lens scaled to same focal length
`with the Apple lens ................................................................................................................ 80
`Table 3.2. Some example patent lenses with strongly aspherical rear elements. ......................... 85
`Table 3.3. Design specification of the first benchmark lens and evaluation lens ........