Bio-Inspired Reconfigurable Elastomer-Liquid Lens: Design, Actuation And

Bio-inspired Reconfigurable Elastomer-liquid Lens: Design, Actuation and

Optimization

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Kang Wei

Graduate Program in Biomedical Engineering

The Ohio State University

2015

Dissertation Committee:

Professor Yi Zhao, Advisor

Professor Derek Hansford

Professor Thomas Raasch

Kang Wei

2015

Abstract

Mother Nature presents beautiful designs for imaging with high spatial resolution, depth cues, and/or wide field of view (FOV). With the large eye diameter and densely populated photoreceptors on the retina, the human camera-eye, for example, captures image with spatial resolution as high as 1/60º. It also enables auto-focus by accommodation mechanism (about 12 diopters at maximum), and depth sensation using binocular disparity given the inter-pupil separation of about 55 mm, two premium attributes that stand out among all advanced vision systems. Compound eye, on the other, excels in panoramic imaging (FOV up to 180º), thanks to their densely populated ommatidia (individual image sampling units) arranged on a hemispherical substrate. At a sacrifice, its spatial resolution is typically larger than 1º.

Recent decades have seen a large number of optical designs that incorporate the structural characteristics of human camera-eye or compound eye. Representative examples are elastomer-liquid lens, and artificial apposition compound eye camera. The elastomer- liquid lens is usually driven by a complex actuation mechanism, and achieves a limited dioptric range and undesirable optical performances at large refractive powers. The adoption of the compound eye camera, on the other hand, is inhibited by its poor spatial resolution, lack of auto-focusing, and sophisticated fabrication and assembly processes.

The gist of this thesis is to introduce novel optical designs to solve the abovementioned issues by leveraging smart materials and reconfigurability of optofluidics.

First, a hybrid eye that incorporates the structural characteristics of both human and insect visions is described, where an elastomer-liquid lens array with variable focusing power and optical axis is developed. Its ability to acquire image with a large FOV and depth cues is demonstrated. Secondly, a compound elastomer-liquid apparatus that reconfigures from a singlet with a large aperture to binoculars with small apertures sharing a single optical channel is developed. The stacked lens design allows for the access to both two dimensional imaging by adaptive focusing, and three-dimensional imaging by binocular depth perception at a constrained space. Thirdly, a driving mechanism based on electroactive artificial muscle materials is studied, which actuates an elastomer-liquid lens at a large dioptric range and reduced voltage. Finally, the peripheral and central resolution of an elastomer-liquid lens enveloped by a membrane with aspherical cross-section is compared to that of a lens by a planar membrane. The lens with aspherical membrane results in significantly smaller field curvature, and thus much better peripheral and central resolving powers at high diopters.

These studies provide insight into elastomer-liquid lens design and configuration, actuation, and optimization, which finds immediate use in a wide range of demanding applications where adaptive focusing with high resolution, large FOV, and/or multi-modes is at a premium.

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Dedication

This dissertation is dedicated to my loving and supportive wife, Rongli Xiang, our 7-month brilliant and considerate baby boy, Jeremy Yumo Wei, and to my always encouraging, ever thoughtful parents, Xianping Wei and Hong Liu.

Acknowledgments

I would like to thank all the people who provided me with vision, confidence, and assistance throughout the Ph.D. program. Without you, I would never been able to go this far.

This research was performed under the guidance of my advisor, Professor Yi Zhao, to whom I would like to express my gratitude, for his consistent inspiration, motivation and academic support. With his timely and incisive advice, I was able to pinpoint the “Yes” from a thousand “No’s”. I am indebted to my former and current labmates, Dr. Hansong

Zeng, Dr. Qian Wang, Xu Zhang, Nicholas Domicone, Matthew Rudy, Andrew Wang,

Hanyang Huang, Lin Qi, and Michael Bush, and to my schoolmates, Dr. Jiwei Huang and

Dr. Leilei Zhang, for their support in experiments, professional development and life.

I am grateful to Professor Thomas Raasch, who opened the door of my explorations in lens design and adaptive optics, and was willing to participate in my final defense committee at the last moment. Many thanks to Dr. Ronald Xu, who mentored me on SPIE

Student Chapter leadership. Special thanks also goes to Professor Derek Hansford for his continuing service on both my candidacy and dissertation committee.

In addition, I would like to thank Dr. Robert Batchko and his colleagues, Jei-Yin

Yiu and Sam Robinson at Holochip Corporation, for developing my skillset in optics during summer internship in 2014.

Finally, I would like to express my sincerest appreciation to my wife, Rongli Xiang, who was always there cheering me up and stood by me through the good and bad times.

Vita

2008...... B.S. Biomedical Engineering, Chongqing

University, China

2010...... M.S. Biomedical Electronics and

Information Technology, Chongqing University, China

2010 to 2011 ...... University Fellow, Department of

Biomedical Engineering, The Ohio State

University

2011 to 2012 ...... Howard Hughes Med Into Grad Scholar,

Wexner Medical Center, The Ohio State

University

2012 to 2013 ...... Graduate Research Associate, Department of

Biomedical Engineering, The Ohio State

University

2013 to present ...... Graduate Pelotonia Fellow, Comprehensive

Cancer Center - James, The Ohio State

University

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Publications

Journal Articles

Wei, K., Rudy, M. S., & Zhao, Y. (2014). Systematic investigation of the benchtop surface wrinkling process by corona discharge. RSC Advances, 4(103), 59122-59129.

Wei, K., Zeng, H., & Zhao, Y. (2014). Insect–Human Hybrid Eye (IHHE): an adaptive optofluidic lens combining the structural characteristics of insect and human eyes. Lab on a Chip, 14(18), 3594-3602.

Wei, K., Domicone, N. W., & Zhao, Y. (2014). Electroactive liquid lens driven by an annular membrane. Optics letters, 39(5), 1318-1321.

Wei, K., Zeng, H., & Zhao, Y. (2013). Substrate material affects wettability of surfaces coated and sintered with silica nanoparticles. Applied Surface Science, 273, 32-38.

Wei, K., Huang, H., & Zhao, Y. (2015). A focus-tunable liquid lens encapsulated by a membrane with aspherical cross-section for improving central and peripheral resolutions at high diopters. Light Science and Applications, submitted.

Conference Proceedings (Full paper)

Wei, K., Domicone, N., Wang, A., Rudy, M., & Zhao, Y. (2014). An on-board microfluidic pump driven by magnetic stir bars. Paper presented at the Proceeding of the 18th International Conference on Miniaturized Systems for Chemistry and Life Sciences (MicroTAS 2014), San Antonio, TX, USA, in press.

Wang, Q., Wei, K., & Zhao, Y. (2014). A microdevice to investigate the synergistic effect of passive and active mechanical stimulations on cell alignment. Paper presented at the Proceeding of the 18th International Conference on Miniaturized Systems for Chemistry and Life Sciences (MicroTAS), San Antonio, TX, USA, in press.

Wei, K., Domicone, N. W., & Zhao, Y. (2014). A tunable liquid lens driven by a concentric annular electroactive actuator. Paper presented at the Micro Electro Mechanical Systems (MEMS), 2014 IEEE 27th International Conference on, San Francisco, CA, USA.

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Wei, K., & Zhao, Y. (2014). Fabrication of anisotropic and hierarchical undulations by benchtop surface wrinkling. Paper presented at the Micro Electro Mechanical Systems (MEMS), 2014 IEEE 27th International Conference on, San Francisco, CA, USA.

Wei, K., & Zhao, Y. (2013). A three-dimensional deformable liquid lens array for directional and wide angle laparoscopic imaging. Paper presented at the Micro Electro Mechanical Systems (MEMS), 2013 IEEE 26th International Conference on, Taipei, Taiwan.

Wei, K., & Zhao, Y. (2012). Fast and versatile fabrication of PDMS nanowrinkling structures. Paper presented at the Proceeding of the 16th Internatinoal Conference on Miniaturized Systems for Chemistry and Life Sciences (MicroTAS 2012), Okinawa, Japan.

Fields of Study

Major Field: Biomedical Engineering

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Table of Contents

Abstract ...... ii

Dedication ...... iv

Acknowledgments...... v

Vita ...... vii

Publications ...... viii

Fields of Study ...... iii

Table of Contents ...... iv

List of Tables ...... ix

List of Figures ...... x

Chapter 1: Background ...... 1

1.1 Overview of Bio-inspired Dioptric Apparatus ...... 2

1.2 Geometrical and Optical Characteristics of Human Camera-eye and Compound eye

...... 4

1.2.1 Human Camera-eye ...... 4

1.2.2 Compound Eye ...... 10 iv

1.3 Inspirations from Human Eye ...... 18

1.3.1 Bulk Elastomeric Lens ...... 19

1.3.2 Elastomer-liquid Lens ...... 23

1.3.3 Application ...... 36

1.4 Inspirations from Insect Eye ...... 38

1.4.1 2D ...... 39

1.4.2 3D ...... 40

1.5 Organization of the Dissertation ...... 42

1.6 References ...... 44

Chapter 2: Insect-human Hybrid Eye (IHHE): An Adaptive Optofluidic Lens

Combining the Structural Characteristics of Insect and Human Eyes ...... 51

2.1 Introduction ...... 51

2.2 Principle and design ...... 55

2.3 Fabrication and assembly ...... 59

2.4 Results ...... 61

2.4.1 Tunable Focusing Power ...... 61

2.4.2 Tunable and Large AOV ...... 65

2.4.3 Focusing Power at Different AOVs ...... 66

2.4.4 Distinguishing Objects at Different Depths and Different Perspectives ...... 68

2.5 Discussions ...... 70

2.5.1 Reconfigurable Design with a Small Number of Single lenses ...... 70

2.5.2 Temporal Image Integration and the Acquisition Time ...... 71

2.5.3 Influence of the Big Membrane Deformation on the Focusing Power of Single

Lenses ...... 73

2.5.4 Possible Integration with Flexible Photosensors ...... 73

2.5.5 Limitations and Possible Solutions...... 74

2.6 Summary ...... 76

2.7 References ...... 76

Chapter 3: Binoculars on Singlet (BIOS): an Optofluidic Lens for Switchable 2D and

3D Imaging… ...... 81

3.1 Introduction ...... 81

3.2 Principle and Design ...... 83

3.3 Fabrication and Assembly ...... 86

3.4 Results and Discussion ...... 89

3.5 Summary ...... 94

3.6 References ...... 95

Chapter 4: An Electroactive Liquid Lens Driven by an Annular Membrane ...... 98

4.1 Introduction ...... 98

4.2 Lens Design ...... 101

4.3 Lens Fabrication ...... 105

4.4 Results and Discussion ...... 106

4.5 Summary ...... 110

4.6 References ...... 111

Chapter 5: A Focus-Tunable Liquid Lens Encapsulated by a Membrane with Aspherical

Cross-section for Field Curvature Reduction at High Diopters ...... 113

5.1 Introduction ...... 114

5.2 Materials and Methods ...... 117

5.2.1 Lens Design ...... 117

5.2.2 Fabrication of Aspherical membrane ...... 123

5.2.3 Lens Assembly and Filling ...... 124

5.3 Results and Discussion ...... 125

5.3.1 BFL ...... 125

5.3.2 Image Contrast and Peripheral Resolution ...... 126

5.3.3 Central Resolution and Modulus Transfer Function (MTF) ...... 130

5.3.4 Optimization and Future Work ...... 132

5.4 Summary ...... 133

5.5 References ...... 133

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Chapter 6: Summary and Future Perspectives ...... 137

6.1 Current Work...... 137

6.2 Future Work ...... 138

6.2.1 Dynamic depth of field using IHHE ...... 138

6.2.2 Creating Nano/micro Lens/lenticular Array by Surface Wrinkling ...... 145

6.2.3 Correcting Gravity-induced Coma ...... 152

6.3 References ...... 154

Bibliography ...... 155

Appendix A: Surface Roughness Measurement of IHHE ...... 168

A.1 Equipment ...... 168

A.2 Protocol ...... 168

A.3 Results ...... 170

Appendix B: Dioptric power calculation for IHHE ...... 172

Appendix C: Equation Derivation for the Electroactive Lens ...... 174

B.1 Circular Membrane as an Actuator ...... 174

B.2 Annular Membrane as an Actuator ...... 177

B.3 Matlab Code to Calculate Volume Exchange for Circular Membrane ...... 179

B.4 Matlab Code to Calculate Volume Exchange for Annular Membrane ...... 183

Appendix D: Code to Generate Grid Sag for Zemax Simulation...... 188

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List of Tables

Table 1.1. Paraxial Ray Tracing of Human Camera-eye ...... 7

Table 1.2. Paraxial Optical Data of the Whole Human Camera-eye and the Crystalline Lens

...... 8

Table 1.3. Angular and Spatial Resolutions of Human Camera-eye ...... 8

Table 1.4. Sensitivity of Human Camera-eye (near fovea) ...... 10

Table 1.5. Optical Data of the Diurnal Honeybee (frontal eye)...... 16

Table 1.6. Optical Data of the Nocturnal Hawk Moth (frontal eye) ...... 17

Table 1.7. Optical Data of the Bulk Elastomeric Lens ...... 22

Table 1.8. Summary of the Optical Performances of Elastomer-liquid Lenses...... 34

Table 4.1. Focal Length Evolution during Forward Actuation and Backward Actuation

...... 107

List of Figures

Figure 1.1. Optical Components of Human Camera-eye(Gross et al., 2005) ...... 6

Figure 1.2. Cones and Rods in an Area adjacent to Fovea. Big circles are rods; small clusters are cones(Yanoff & Duker, 2013)...... 9

Figure 1.3. Spatial Arrangement and Surface Contours of Ommatidia(Simpson &

Chapman, 2013) ...... 10

Figure 1.4. Structure of the Apposition Ommatidium (a) and Its Image Formation

Mechanism (b). c-corneal, lens; cc-crystalline cone; p-pigmented cells...... 11

Figure 1.5. Structure of the Superposition Ommatidium and Its Image Formation

Mechanism. c-corneal lens; cc-crystalline cone; cz-clear zone; p-pigmented cells; f-focal length; d-diameter of the rhabdom...... 13

Figure 1.6. Optical Data of the Superposition Ommatidium with Gradient Refractive Index and Its Comparison to Keplerian Telescope ...... 14

Figure 1.7. Sampling Resolution and Spatial Resolution of the Apposition Ommatidia . 15

Figure 1.8. Bulk Elastomeric Lens Driven by Shape Memory Alloy Actuator ...... 21

Figure 1.9. Bulk Elastomeric Lens Driven by Electromagnets (a) and Servo Motor (b) . 21

Figure 1.10. Bulk Elastomeric Lens Driven by Mechanical Plunger ...... 22

Figure 1.11. Syringe-based Elastomer-liquid Lens...... 25

Figure 1.12. Elastomer-liquid Lens Driven by Iris Diaphragm (a) and Servo Motor (b) . 27

Figure 1.13. Elastomer-liquid Lens Driven by Mechanical Lever (a) and Rotational Ring

(b) ...... 27

Figure 1.14. Elastomer-liquid Lens Driven by Pneumatic Valves ...... 28

Figure 1.15. Elastomer-liquid Lens Driven by Thermal Pump ...... 29

Figure 1.16 Elastomer-liquid Lens Driven by Piezoelectric Ring Bender ...... 31

Figure 1.17. Elastomer-liquid Lens Driven by Electromagnetism. (a) Permanent magnet above the membrane; (b) permanent magnet underneath the membrane ...... 32

Figure 1.18. Elastomer-liquid Lens Driven by Annular Electroactive Polymer (a) and

Circular Electroactive Polymer (b) ...... 33

Figure 1.19. Planar Artificial Apposition Compound Eye Camera ...... 40

Figure 1.20. Hemispherical Artificial Compound Eye Camera ...... 40

Figure 1.21. Cylindrical Artificial Apposition Compound Eye Camera ...... 42

Figure 2.1.Structures of Insect Apposition Compound Eye (left) and Human Eye (right)

...... 55

Figure 2.2. IHHE Combining Architectural Characteristics of the Two Vision Systems by

Distributing an Array of Membrane-Enveloped Fluidic Lenses on a Big Deformable

Membrane...... 56

Figure 2.3. Working Principle of IHHE. During operation, the big membrane forms a dome shape, which changes the AOV of the peripheral single lenses and thus increases the overall

AOV. The focusing power of each single lens is tunable, allowing depth sensation along different orientations...... 57

Figure 2.4. Geometry and Mechanical Modeling of the IHHE. (a) & (b) Schematic of

IHHE, which consists of a bi-layered microfluidic network. The top layer includes a trifurcated microchannel with each branch connecting to three circular membranes; the bottom layer has a big membrane that connects to another microfluidic channel.

Ds(diameter of the small membrane)=2 mm; Ts(thickness of the small membrane)=50mm;

Ls-s(center to center distance between adjacent small membranes)=2.5 mm; Db(diameter of the big membrane)=10 mm, Tb(thickness of the big membrane)=200mm. (c) Simulated deformation profiles of the IHHE showing variable perspectives of the peripheral lens. 58

Figure 2.5. Fabrication and Assembly of the IHHE. Left to right: master templates for the big and the small membranes fabricated by SU-8 photolithography; assembled IHHE by

PDMS replica molding; the bi-layered microfluidic network highlighted by food colors; and the top and side views of the IHHE while both the big membrane and the small membranes are deformed...... 60

Figure 2.6. Ray Tracing Schematic and its Equivalent Air Model ...... 62

Figure 2.7. Center Deflection of the Small Membrane as a Function of Fluid Addition into the Microfluidic Channel in the Top Layer ...... 62

Figure 2.8. Representative Images of Beam Convergence in the Fluorescence Medium at s

= 117mm, 172mm, 241mm and 304mm, respectively ...... 63

Figure 2.9. Back Focal Distance in the Medium as a Function of the Center Deflection of the Small Membrane (a) and the Calculated Focusing Power (b)...... 63

Figure 2.10. Demonstration of Adaptive Focusing by Viewing an Array of Pillars whose

Top Surfaces were Placed at Different Depths...... 64

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Figure 2.11. Tunable AOV. (a) Center deflection of the big membrane changes with the volume of extra fluid supplied into the microfluidic channel in the bottom layer. (b)

Orientation of the center lens and a peripheral single lens in the middle row while the big membrane was at different center defections. Red line: optical axes of the single lenses.

...... 65

Figure 2.12. Focusing Power Measurement at Big Membrane Deformation.  denotes the intersection angle between the optical axis of the peripheral lens and the vertical direction.

...... 66

Only the images in the highlighted boxes are used for assembling the final image in (d).

(d) Images acquired at different AOVs (by tilting the lens from -52.5° to -52.5°) are collaged to show the overall AOV...... 69

Figure 2.14. Adaptive Focusing at Varied Viewing Angles...... 70

Figure 2.15. Visualization of the Spherical Deviation at Different Center Deflections of the

Small Membrane ...... 75

Figure 3.1. Working Principle of the Stacked Optofluidic Lenses in 2D and 3D Modes 84

Figure 3.2. Schematics of Fabrication Process ...... 87

Figure 3.3. The Assembled Stacked Optofluidic Lenses before Fluid Filling (a), after Fluid

Filling in 2D Mode (b), and after Black Ink Filling in 3D Mode (c)...... 88

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Figure 3.4. Back Focal Length Measurement of the Big Elastomer-liquid Lens and Small

Elastomer-liquid Lenses...... 89

Figure 3.5. Comparison of Adaptive Focusing and Image Resolution between the Big

Elastomer-liquid Lens and the Small Elastomer-liquid Lenses ...... 91

Figure 3.6. Distance-dependent Binocular Disparity ...... 92

Figure 3.7. Image Capture in 2D Mode (a), 3D Mode (b), and the Calibrated Anaglyph (c)

...... 93

Figure 3.8. Comparison of Depth Estimation between Theoretical Analysis and Experiment

Result in 2D and 3D Modes for (a) Nipple and Scar Sample, (b) 3D-printed Branches

Sample, and (c) Dices Sample...... 95

Figure 4.1. Illustration of the Electroactive Fluidic Lens Driven by a Concentric Annular

Dielectric Actuator. (a) Perspective view of the system. (b) Diagram of the lens in action.

The red dotted line indicates the optical axis. Δs is the change in lens sagitta. Δf is the change in focal length...... 102

Figure 4.2. Comparison of the Volume Changes of Circular and Annular DE Actuators at

Different Initial Maximal Membrane Deflections under Electrical Activation...... 104

Figure 4.3. Fabrication and Assembly Processes. (a)~(c) The process flow, (d)&(e) The top and bottom frames printed by a 3D printer. (f) The assembled electroactive fluidic lens.

The scale bar in (d) ~ (f) denotes 5 mm ...... 106

Figure 4.4. Comparison of (a) Focal Length and (b) F/# Changes with Different Initial Lens

Sags ...... 108

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Figure 4.5. Response Time for a Lens with the Initial Sag of 273 m (a) and its Resolving

Power at f = 25 mm using a 1951 USAF Target (b) ...... 109

Figure 4.6. Demonstration of focus changing. (a) Illustration of the optical setup, and

(b)~(e) Optical images showing the focal length change at the actuation voltages of 0kV,

0.25kV, 0.5kV and 1.0kV, respectively ...... 110

Figure 5.1. Perspective view (a) of VTLL integrated with a membrane having an aspherical cross-section (b). The top and bottom mounting cells fix the membrane in between by silicone adhesives (red). The optical fluid is concealed between the membrane and the bottom cover glass, which forms liquid lens when the membrane is deflected by hydraulic pressure. VTLL, varied thickness liquid lens ...... 118

Figure 5.2. Simulated Optical Profiles (a) of CTLL and VTLLs, and Their Spherical

Deviations (b) at the Center Deflection of 0.805 mm ...... 119

(tC - tE)/tE. For both CTLL and VTLLs, tC=0.3 mm. 85% aperture is used for optical simulation. CTLL has the largest spherical deviation (0.111 mm) and RMS spot radius at

6º field angle (135.47 mm). Among VTLLs, the lens with tR=1 has the smallest RMS spot radius (26.41 mm) at 6º field angle and increase from 0º to 6º (23.3%). CTLL, constant thickness liquid lens; VTLL, varied thickness liquid lens; tC, center thickness; tE, edge thickness; dpt, diopter...... 120

Figure 5.4. Simulated optical profiles (a) of VTLL (tR =1), and their corresponding spherical deviations (b) at the center deflection of 0.136, 0.199, 0.376, 0.585, 0.676, and

0.805 mm ...... 121

Figure 5.5. The ray trace diagram of VTLL and the solid lens at +100 dpt (a) and at +40 dpt (b); RMS spot radius from 0º to 6º field angle for VTLL (c) and a spherical plano- convex N-BK7 lens (d) at +16.7, 25, 40, 80, 100, 117.6 dpts. VTLL at 40~100 dpt has a good control of RMS spot radius, yet was still outperformed by the solid lens. VTLL, varied thickness liquid lens; dpt, diopter...... 122

Figure 5.6. A two setup replica molding process (a) to fabricate the lens membrane with an aspherical cross-section (b); snapshot of an assembled VTLL (c) and the VTLL without lensing effect (d). The refraction at the aspherical interface is minimized due to the refractive index match of the membrane with the optical fluid. Leaf veins outside and inside

VTLL share the same focus. VTLL, varied thickness liquid lens...... 125

Figure 5.7. BFLs (in dpts) of CTLL and VTLL as a function of hydrostatic pressure. BFL, back focal length; CTLL, constant thickness liquid lens; VTLL, varied thickness liquid lens; dpt, diopter...... 126

Figure 5.8. Center and Peripheral resolution comparison. The lenses focus on a Siemens star target at 5.0x magnification and +100 dpt. (a) CTLL, (b) VTLL, and (c) N-BK 7 plano- convex spherical solid lens. The first two columns show the original snapshots and their inverted images for visualization purposes (scale bar: 2 mm). The rest three columns show the center and peripheral regions on the meridional and sagittal planes of the images from the second column (scale bar: 0.5 mm). Relative luminance along the top and edges

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(marked dotted colored line) of the Siemens star target is shown in (d) & (e). CTLL, constant thickness liquid lens; VTLL, varied thickness liquid lens; dpt, diopter...... 128

Figure 5.9. Center and Peripheral Resolution Comparison at +40 dpt ...... 129

Figure 5.10. Central resolution measurement by imaging positive USAF 1951 resolution target via (a) CTLL (b) VTLL, and (c) solid lens at +100 dpt. The inset is the magnified view (digital zoom: 2.5x) of the highlighted region on the left image. (d) Comparison of meridional MTF curves of CTLL and VTLL at +100 dpt. The MTFs correspond to the center of the frame. VTLL presents better contrast from 16 lp/mm to 91 lp/mm. MTF, modulus transfer function; CTLL, constant thickness liquid lens; VTLL, varied thickness liquid lens; dpt, diopter...... 131

Figure 6.1. Ray Tracing of the IHHE as a Tilt-shift Lens ...... 139

Figure 6.2. Circle of Confusion on Sagittal Plane ...... 142

Figure 6.3. Ellipse of Confusion on the Meridional Plane ...... 143

Figure 6.4. DOF on the Meridional Plane...... 144

Figure 6.5. Benchtop Wrinkling Process: (a) schematic representation of corona discharge induced surface wrinkling; (b) the electrical diagram for corona discharge generation; (c) the experimental setup (the discharge is connected to output A in (b)); (d) magnified view of the highlighted regions in (c), showing bluish glow due to partial electrical breakdown of the air near the discharge tip ...... 147

Figure 6.6. Fabrication Processes for Creating Bi-layered Wrinkled Topographies ...... 148

Figure 6.7. Characterization of Single-Layered Wrinkles Resembling Lenticular Lens

Array: (a) parametric studies of wrinkle geometries with the pre-strain and the discharge

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time at the tip-surface distance of 5 mm; and (b) the resulting nanoscale (pre-strain: 40%; discharge time: 0.5 min) and microscale (prestrain: 5%; discharge time: 8 min) wrinkled structures………………………………………………………………………………..150

Figure 6.8. Dimensionless Analytical Estimation of Superimposed Bi-layered Wrinkled

Topographies at Different Wavelength Ratios. p: wavelength of the primary wrinkles; s: wavelength of the secondary wrinkles. s = 0.5, 0.75, 1.5 and 3; p = 3...... 151

Figure 6.9. AFM micrographs of Bi-layered Wrinkled Topographies Resembling

Microlens array ...... 152

Figure 6.10. Optical Axes of a 15 mm Elastomer-liquid Lens at Different Differential

Pressures ...... 153

Figure 6.11. Centrality of the Lens subject to Low and High Hydrostatic Pressures. Gravity is from right to left...... 153

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Chapter 1: Background

Miniaturized dioptric apparatus inspired by human camera-eye and compound eye have excited widespread attention courtesy of their huge potential in applications including consumer cameras, biometrics, industrial/academic microscopes, medical endoscopes/laparoscopes, ophthalmic testing, and military/environmental surveillance. In this chapter, we present a systematic perspective on the structural and optical characteristics of the human camera-eye and insect compound eye, which are incorporated in the recent development of focus tunable liquid lens and artificial compound eye camera.

Four main categories of focal tunable liquid lens – bulk elastomeric lens, elastomer-liquid lens, liquid doublet, and droplet lens – are discussed with emphasis on the underlying physics, driving mechanisms, optical performances, and limitations from lens configuration and material to dioptric range and to resolution. Progress on the development of artificial apposition, superposition and recently emerged hybrid compound eye cameras in both 2D and 3D layouts is illustrated by representative examples. The immediate biomedical applications of both focus tunable liquid lens and artificial compound eye camera are introduced. Finally, objectives and organization of this dissertation are given.

1.1 Overview of Bio-inspired Dioptric Apparatus

The harmonious integrations of anatomical simplicities and functional indispensability enable biological systems to provide operational characteristics beyond those available with existing technologies. One truly remarkable example is the biological vision system, which bestows upon almost all living species the capacity to perceive and adapt to their surrounding environments through visuomotor responses in the most simplified and efficient formats(Erichsen & Woodhouse, 2012). Biological visions systems are diversified, with each having its intrinsic limits and uniqueness that may arise for specific purposes in the course of evolution. Two of the most prevalent and advanced observing systems are human camera-eye, and insect compound-eye(L. P. Lee & Szema,

2005). The fundamental plan for human camera-eye starts with a transparent convex surface for light refraction and ends in a layer of billions of light-sensitive receptors for image recording(Artal, 2014). In between lie a crystalline lens and an iris. By simply varying the curvature of the lens and the diameter of the pupil, one can maintain a sharp focus with correct luminance on object from infinity to as close as about 7 cm(Gross,

Dörband, & Müller, 2005). The compound eye as ubiquitously seen in diurnal and nocturnal insects, on the other hand, is particularly notable for its hemispherical arrangement of hundreds of refractive or reflective lens-capped sampling units on a millimeter sized body(M. F. Land & Nilsson, 2012). Such structural hallmark offer its excellency in motion detection and wide field imaging (160º×180º in fruit fly drosophila, for example) in a compact form(Floreano et al., 2013).

The distinct attributes of human camera-eye and insect compound eye have in recent decades inspired numerous biomimetic miniaturized optical elements and systems, which have huge potential for use in consumer cameras, biometrics, industrial/academic microscopes, medical endoscopes/laparoscopes, ophthalmic testing, military/environmental surveillance, and other demanding applications(JW Duparré &

Wippermann, 2006; Ren & Wu, 2012). The focus-tunable lens bears the closest resemblance to the accommodation functionality of human camera-eye, where the shape of the lens and thereby the focal length can be finely and rapidly tuned in a dynamic range(Nguyen, 2010). The lens reshaping eliminates the need to displace multiple lens elements/groups(Chiu et al., 2012) to achieve focus adjustment using sophisticated voice coil(Kim, Lee, & Kim, 2009) or piezoelectric motors(Ko, Jeong, & Koc, 2009), an approach typically seen in conventional solid-lens based camera system. It thus creates opportunities for size, cost, and complexity reduction of vari-focal optical systems.

Advances in material science and microfabrication enable the realization of cameras with the key features present in insect compound eye: hemispherical shape in compact and monolithic forms with scalability in size, number and configuration of light-sensing elements(Madou, 2002; Rogers, Someya, & Huang, 2010; Kang Wei, Rudy, & Zhao,

2014). It provides an elegant solution to off-axis distortion and inconsistent angular resolutions often confronted by traditional fish-eye lenses(Hiura, Mohan, & Raskar, 2009).

At the same field coverage, the compound-eye camera is also much smaller than fish-eye lenses that usually have huge and deep spherical surfaces.

In this work, we review the progress made in the development of bio-inspired focus-tunable lenses and compound-eye cameras, and their potential applications. In

Section 1.2, we review the basic geometries of human camera-eye and compound eye with emphasis on the optical data of their light-refraction organs. In Section 1.3, focus-tunable lenses in the form of all-elastomer, elastomer-liquid, liquid doublet and droplet are discussed, where we especially focus on the driving mechanisms, optical performance and their applications in ophthalmology, laparoendoscopy, optical coherence tomography, microscopy and machine vision. In Section 1.4, we show representative demonstrations of artificial compound eye in both planar and 3D layouts, and their particular uses in laparoendoscopy and machine vision. The state-of-the-art hybrid optical systems that combines structural characteristics of both human camera-eye and insect apposition compound-eye are also covered.

1.2 Geometrical and Optical Characteristics of Human Camera-eye and Compound eye

1.2.1 Human Camera-eye

Along the line of sight, the human camera eye consists of cornea, aqueous humor, iris, crystalline lens, vitreous humor and retina (Figure 1.1). The cornea is a meniscus lens

(refractive index (RI) : 1.376) that has a center thickness (Tc) of 0.5 mm, an anterior surface with radius of curvature (ROC) of 7.7 mm, and a posterior surface with ROC of 6.8 mm(Vojniković & Tamajo, 2013). The cornea stroma is steep in center and flat in periphery. Aqueous humor in the thickness of 3.04 mm sits between the posterior surface

of the cornea and the anterior surface of the crystalline lens(Vojniković & Tamajo, 2013).

The vertex of the anterior surface of the crystalline lens lies on the plane of iris, which is a diaphragm of variable diameter from 2 mm to 8 mm dependent on the environmental radiance(Gross et al., 2005). The crystalline lens has a biconvex body in the diameter of 9-

10 mm, and is made up of a kernel (nucleus lens) and a shell capsule (core lens), according to the most used full Gullstrand eye model(Navarro, 2009). The lens nucleus and core have a RI of 1.406 and 1.386, respectively(Gross et al., 2005). The encircling zonular fibers connect the circumference (equator) of the lens body to the ciliary muscle, just like the spokes on the wheel. When the eye focuses on the infinity, relaxation of the ciliary muscle increases the tension in zonular fibers, causing the lens to flatten. The anterior and posterior surfaces of the core lens have ROC of 10 mm and 6mm, and those of the nucleus lens 7.911 mm and 5.76 mm(Gross et al., 2005). When the eye focuses on the near point with maximum accommodation, the ciliary muscle contracts and the zonular fibers relax. The lens becomes globular, where the ROCs of anterior and posterior surfaces of the core lens both decrease to 5.33 mm, and those of the nucleus lens to 2.665 mm(Gross et al., 2005).

The center thickness of the crystalline lens changes from 3.6 mm to 4 mm before and after accommodation. Finally, photons passes through the vitreous humor (RI = 1.336) and is received by cone and rod photoreceptors on the retina. They form the image in a pixelated fashion.

Figure 1.1. Optical Components of Human Camera-eye(Gross et al., 2005)

In paraxial ray tracing, each surface along the line of sight can be assumed to be spherical, whose refractive power () is calculated as(Geary, 2002):

nn    (1.1) R where n’ and n denotes the RIs of the media after and before the refractive surface, and R denotes the ROC. To determine the back focal length (BFL), effective focal length

(EFL)/refractive power, and locations of principle planes for the eye and crystalline lens before and after maximum accommodation, paraxial ray trace equations (PRTE) are used(Geary, 2002):

n'' u nu y (1.2) y''' y u t where u denotes the ray angle; y denotes the ray height; t denotes the thickness between two adjacent refractive surfaces; the apostrophe denotes the subsequent surface. Table 1.1

gives an example of the image-sided ray tracing sheet of the whole human camera-eye before and after maximum accommodation.

Table 1.1. Paraxial Ray Tracing of Human Camera-eye

Surf 0 1 2 3 4 5 6 7 R 10 7.911 -5.76 -6 inf 7.7 6.8 R a 5.33 2.655 -2.655 -5.33 t 3.1 0.546 2.419 0.635 17.19d 25 0.5 ta 2.7 0.6725 2.655 0.6725 13.81e n 1 1.376 1.336 1.386 1.406 1.386 1.336  5 2.53 3.47 8.33 48.83 -5.88 a 9.38 7.53 7.53 9.38 t/n 2.320 0.394 1.720 0.458 12.86b 25 0.363 ta/n 2.021 0.485 1.888 0.485 10.34c y 0.882 0.864 0.778 0.754 1 1 0.982 ya 0.895 0.870 0.761 0.730 nu -0.0475 -0.0496 -0.0523 -0.0586 0 -0.0488 -0.0431 nua -0.0515 -0.0580 -0.0637 -0.0706

a Radius of curvature, thickness between neighboring surfaces, refractive power, ray height and ray angle at maximum accommodation. b Back focal length in the air of the relaxed whole human camera-eye . c Back focal length in the air of the fully accommodated whole human camera-eye. d Back focal length in the vitreous humor of the relaxed whole human camera-eye . e Back focal length in the vitreous humor of the fully accommodated whole human camera- eye.

The EFL and refractive power of the whole eye are given by(Geary, 2002):

11 EFL  (1.3)  nulast where ulast denotes the ray angle through the last surface. The typical optical data of the

Gullstrand eye and crystalline lens are summarized in Table 1.2.

Table 1.2. Paraxial Optical Data of the Whole Human Camera-eye and the Crystalline Lens

Whole eye Crystalline lens State Relaxed Accommodated Relaxed Accommodated BFL in the air 12.86 10.34 51.28 28.79 EFL in the air 17.05 14.17 52.33 30.24  in the air 58.64 70.58 19.11 33.07 H 1.35a 1.77a 1.56b 1.46b H ’ 1.60a 2.09a 1.04c 1.46c a Distance between front (H)/rear (H’) principle planes and anterior surface of the cornea. b Distance between front principle plane and anterior vertex of the lens capsule. c Distance between rear principle plane and posterior vertex of the lens capsule.

By ignoring aberrations, the diffraction-limited angular () and spatial resolutions

(l) of a normal relaxed/accommodated human camera-eye can be calculated using the known EFL and the iris diameter, which are given by(Yanoff & Duker, 2013):

  1.22 A (1.4)   EFL l 1.22 A where  is the wavelength and is assumed to be 560 nm (yellow-green light that is most sensitive to photoreceptors); A is the aperture and is assumed to be 2.4 mm (spherical aberration is negligible). The calculated resolutions are summarized in Table 1.3.

Table 1.3. Angular and Spatial Resolutions of Human Camera-eye

State Relaxed Accommodated a 0.979 ’ 0.979 ‘ l b 4.854 4.034 a The unit of angular resolution () is arcminute (arcmin). is calculated from Equation X. b The unit of spatial resolution (l) is m. l is calculated from Equation 1.4.

Note that the angular resolution is analogous to that of an eye with 20/20 Snellen visual acuity(Artal, 2014). The number of cones employed to image an Airy disk (radius of first intensity maxima equivalent to spatial resolution) is calculated to be about 4~6 given the diameter and spacing of cone at 2 m and 0.5 m in the foveal macular area(Yanoff & Duker, 2013) (Figure 1.2). If the cone acts as a single pixel, the human camera-eye is diffraction-limited, not pixel-limited given the much higher pixel density than the spatial frequency.

The sensitivity (S) of human camera-eye, which is defined as the number of photos caught by a photoreceptor for standard radiance, also varies between day and night. It is as a function of the diameter (d) of the photoreceptor and F number (F/#)(Archer, 1999):

2 d SP 0.62 abs  (1.5) F /# where Pabs is the probability of photons that are registered. Table 1.4 summarizes the sensitivities and their associated parameters.

Figure 1.2. Cones and Rods in an Area adjacent to Fovea. Big circles are rods; small clusters are cones(Yanoff & Duker, 2013).

Table 1.4. Sensitivity of Human Camera-eye (near fovea)

Light habitat Diurnal Nocturnal d 2 m 2 m F/# F/6.8 F/2.4 Sa 0.01b 0.4b a The unit of sensitivity (S) is m2 sr b Values are taken from (M. F. Land & Nilsson, 2012)

1.2.2 Compound Eye

Compound eye is constructed from several thousand identical optical elements called ommatidia(Chapman, 1998) (Figure 1.3a&b). From the top view, the coverings of ommatidia are typically populated to form an array of hexagonal facets (Figure 1.3c).

Figure 1.3. Spatial Arrangement and Surface Contours of Ommatidia(Simpson & Chapman, 2013)

The compound eye is grossly categorized into apposition compound eye characteristic of diurnal insects, e.g. bees and flies, and superposition compound eye as seen in nocturnal insects and deep sea crustaceans, e.g. moths and shrimp(JW Duparré &

Wippermann, 2006). In a common focal apposition compound eye, each ommatidium mainly consists of a corneal lens, a watery crystalline cone with homogeneous RI(Cronin,

Johnsen, Marshall, & Warrant, 2014), and a cylinder-like photoreceptor called rhabdom that extends to the crystalline cone (Figure 1.4a). The screening pigment encircles each dioptric apparatus (cornea and the cone) to form an optically-opaque wall(E. Warrant,

Kelber, & Kristensen, 2003). The ommatidium is thus optically isolated from its neighbors and functions as an independent camera. This prevents the cross-talk between adjacent ommatidia that deteriorates the image quality.

Figure 1.4. Structure of the Apposition Ommatidium (a) and Its Image Formation Mechanism (b). c-corneal, lens; cc-crystalline cone; p-pigmented cells.

Within its field of view (FOV), each powered corneal lens projects an inverted image on the distal tip of the rhabdom(Agi et al., 2014) (Figure 1.4b). However, since the rhabdom behaves as a single light guide within which all image details are lost, image inversion can be neglected(Simpson & Chapman, 2013). The apposition compound eye thus produces an upright mosaic of a scene constituted by all microscopic images on rhabdoms.

Superposition compound eye and apposition compound eye are almost indistinguishable from outside, but have two crucial anatomical differences behind the crystalline cone. Firstly, the screen pigment only shields the facet and crystalline cone areas, leaving an extensive clear zone between the proximal end of the crystalline cone and the rhabdom (Figure 1.5a). In other words, the ommatidium is not optically isolated, allowing for cross-talk between adjacent ommatidia(E. Warrant & Nilsson, 2006).

Secondly, individual rhabdoms form a single photoreceptor layer that lies (about 100 to

200 m) beneath the ends of crystalline cones(E. Warrant et al., 2003). Thirdly, the superposition compound eye produces a single upright image of a scene(Simpson &

Chapman, 2013) (Figure 1.5b). There exist two main types of superposition compound eye in terms of image formation mechanisms. For refractive superposition compound eye, the dioptric apparatus forms a gradient index (GRIN) lens reminiscent of an afocal

Keplerian telescope(Cronin et al., 2014) (Figure 1.6). Incoming collimated light rays from one side of the optical axis of the ommatidium are converged at around the waist region of the cone to form an intermediate inverted image, which are re-collimated into parallel rays on the same side of its optical axis after exiting the crystalline cone. The ratio between the

exit and incident angles is called angular magnification. Beyond a certain angle of incidence, the dioptric apparatus is unable to relay the oblique rays to rhabdom, which are absorbed by black screening pigments on the cone(E. Warrant et al., 2003). For reflective superposition compound eye, the facets of ommatidia are squared-shaped tubes with walls that functions as mirrors to reflect the incoming collimated light(Meyer-Rochow & Gál,

2004). In both types, parallel light rays passing through a large number of ommatidia bend within the clear zone to stimulate the same rhabdom(Cronin et al., 2014). This is equivalent to light entry through a wide “superposition aperture (As)” with all rays superimposed on a single pixel. The aperture size is determined by the largest permissible incident angle. The enhanced photon catch by recruitment of multiple facets makes species with supposition compound eye excel in dim environment.

Figure 1.5. Structure of the Superposition Ommatidium and Its Image Formation Mechanism. c-corneal lens; cc-crystalline cone; cz-clear zone; p-pigmented cells; f-focal length; d-diameter of the rhabdom.

Figure 1.6. Optical Data of the Superposition Ommatidium with Gradient Refractive Index and Its Comparison to Keplerian Telescope

The overall resolution is determined by the finesse of the mosaic or the sampling resolution of the ommatidia, and the acuity of individual microscopic image or the spatial resolution (equivalent to angular resolution defined in human camera-eye(Gonzalez-

Bellido, Wardill, & Juusola, 2011)) of each ommatidium(Simpson & Chapman, 2013). The former is described by the interommatidial angle (∆), the angular separation between the optical axes of adjacent ommatidia; the latter is represented by the rhabdom acceptance angle (∆) that results from a combinational contributions of Airy disk in wave optics (w), and the angular width in ray optics (r), the angle subtended by the diameter of the photoreceptor at the nodal point of the cornea lens(M. F. Land, 1997) (Figure 1.7). ∆and

∆are given by(M. F. Land, 1997):

 DR/ e  d (1.6)   2   2 ()() 2  2 wr Df

where D is the diameter of the corneal lens; Re is the radius of the curved surface where the ommatidia reside; f is its focal length. The sensitivity of the apposition compound eye is given by(M. F. Land & Nilsson, 2012):

22 SPD0.62 abs  (1.7)

It is equivalent to Equation 1.5 when the wavelength is much smaller than the diameter of the corneal lens.

Figure 1.7. Sampling Resolution and Spatial Resolution of the Apposition Ommatidia

Evidently, there is a tradeoff between the sampling resolution and the spatial resolution. Narrowing the interommatidial angle (decrease in D) increases the sampling resolution, yet is at the sacrifice of the spatial resolution given the shrunk diameter of the corneal lens that results in larger Airy disk and decreased sensitivity. An enlarged rhabdom increases the acceptance angle and causes overlapping of fields of view between adjacent ommatidia (∆>∆). Sensitivity is thus increased at the expense of spatial resolution. 15

When ∆<∆there would be multiple blind spots among the entire mosaic. In most diurnal insects, the typical interommatidial angle is between 1º and 3º, which approximately matches the rhabdom acceptance angle (∆≈ ∆)(Simpson & Chapman,

2013). There is a little and no overlap between neighboring FOVs. Table 1.5 gives of the typical optical data of the apposition compound eye of a diurnal honeybee (Apis)(E.

Warrant & Nilsson, 2006).

Table 1.5. Optical Data of the Diurnal Honeybee (frontal eye)

Parameter Value D 20 m d 2 m f 66 m F/# F/3.3 S 0.1 ∆ 1.9º /D 1.4º ∆ 2.6º

The resolution of the supposition compound eye is determined by the collimation of rays exiting a single dioptric apparatus, the coincidence of rays exiting the superposition aperture, and the acceptance angle(M. Land, 1984; E. J. Warrant & McIntyre, 1990).

Ideally, rays from an individual dioptric apparatus should remain parallel as they cross the clear zone till the arrival at the rhabdom. Any divergence could result in poor spatial resolution. Focalized rays could potentially improve the resolution. All rays from the supposition aperture should converge on a single rhabdom, which is often jeopardized by the misalignment of the dioptric apparatus and spherical aberration. With small F/#s (as

low as F/0.5), rays entering the peripheral regions of the superposition aperture tend to front-focus than rays incident at its center(E. J. Warrant & McIntyre, 1990). Similar to apposition compound eye, the supposition eye is diffraction-limited. Although superposition aperture is significantly larger than an individual facet, the Airy disk width still counts on the diameter of a single facet. The sensitivity of the superposition compound eye is given by:

22 SPA0.62 abs s (1.8)

Given a large superposition aperture contributed by hundreds of facets, the superposition compound eye usually has a high light sensitivity. Table 1.6 shows the optical data of a nocturnal hawk moth (Deilephila).

Table 1.6. Optical Data of the Nocturnal Hawk Moth (frontal eye)

Parameter Value D 29 m As 937 m d 10.3 m f 675 m F/# F/0.7 S 69 ∆ 1.3º /D 1.0º ∆ 3º

A shared extraordinary attribute of the apposition and superposition compound eye is the extremely wide FOV horizontally and vertically, thanks to the curved arrangement of ommatidia. The decrease in the radius of curvature of the eye surface helps radiate the optical axis of the ommatidium and increases the overall FOV. Typically, the compound 17

eye has a hemispherical surface, the majority or entire area of which are densely populated with ommatidia. The overall horizontal/vertical FOV of can even exceed 180º (e.g. fruit fly with an eye radius of 180 m(Floreano et al., 2013)).

In summary, human camera-eye enjoys optical adaptability in both focalization and aperture, and has much higher spatial/angular resolution than compound eyes. Compound eyes with smaller F/#s have vastly larger FOVs and better sensitivity than human-camera eye (FOV of 108º at relaxation(Gross et al., 2005)). The spherical arrangement of multiple dioptric apparatus results in less field aberrations than human camera-eye whose peripheral visions degrades to a large degree with the increase in field angles(Gross et al., 2005).

Their distinct yet complementary strengths thus become the inspirational sources of biomimetic engineering marvels.

1.3 Inspirations from Human Eye

As the accommodation of human camera-eye needs out of plane deformation of the crystalline lens, focus tunable liquid lens implements this feature by tuning the ROC of a refractive surface sandwiched between two media of different RIs(Ren & Wu, 2012).

Typically, the phase of media at one side is air or liquid; that at the other is liquid, an elastomeric membrane that encapsulates a fluidic chamber (referred as lens chamber), or an elastomeric body. This gives rise to four main types of focus tunable liquid lens: bulk elastomeric lens, elastomer-liquid lens, double-liquid lens, and liquid droplet lens, which are driven by pneumatic, mechanical, thermal, electric, magnetic, or acoustic means to achieve varied dioptric ranges and optical performances. Like human camera-eye, the

liquid lens has a positive power, and thus takes a convex-plano, plano-convex, or bi-convex shape. The shape of the liquid lens can be defined by the shape factor (X) as(Geary, 2002):

CC X  12 (1.9) CC12 where C1 and C2 are the respective curvatures (reciprocal of ROC) of the front and rear surfaces. Using spherical assumption, its EFL is calculated as(Geary, 2002):

t EFL   (1.10) 1212 n where 1 and 2 are the respective optical powers the front and rear surfaces, which can be calculated from Equation X; t is the lens’ center thickness; n is the RI of the elastomer or the optical fluid . BFL can be also estimated using paraxial ray tracing mentioned in Section

1.2.

1.3.1 Bulk Elastomeric Lens

The bulk elastomeric lens is usually made up of polydimethylsiloxane (PDMS,

SYLGARD 184, Dow Corning). Mechanically, PDMS when mixed at the recommended ratio of 10 parts base to 1 part curing agent displays a curing temperature dependent

Young’s modulus(Johnston, McCluskey, Tan, & Tracey, 2014). When the tensile strain is less than 40%, its Young’s modulus (E) ranges from 1.32 MPa cured at 25 ºC to 2.97 MPa cured at 200 ºC(Johnston et al., 2014). Optically, its transmittance can reach 95% within visible spectrum given a 1mm-thick membrane(Chronis, Liu, Jeong, & Lee, 2003). It has a RI of 1.4118 at 589 nm and an abbe number of 50(Lin, Chen, Huang, & Wang, 2010).

The lens typically has a convex-plano or bi-convex shape before focus adjustment. To

change focus, the edge of the lens is pulled bi-laterally or radially to decrease the ROC, or its annular part is depressed axially to increase the ROC. To implement the first concept, eight loading arms with mechanical grippers clamp and encircle the elastomer lens, in a way similar to zonular fibers(J.-M. Choi, Son, & Lee, 2009) (Figure 1.8). The distal ends of each arm are affixed to a static circular frame and a rotational outer ring. Shape memory alloy (SMA) actuator during heating rotates the outer ring in a clockwise fashion, which pulls the arms and connected lens outward with equal force and displacement. The flattening of lens shape decreases its refractive power. Alternatively, the peripheral of the lens can be adhered to four or eight mechanical/metallic anchors distributed in equal azimuth angles(Liebetraut, Petsch, Liebeskind, & Zappe, 2013; Liebetraut, Petsch, Mönch,

& Zappe, 2011) (Figure 1.9). Opposing pairs of micrometers, electromagnets, or servo motors bi-laterally or radially stretch out the lens to continuously tune the BFL.

Particularly, the latter mechanism allows for individual control of the anchor, and thus the lens asphericity and wavefront errors, e.g. astigmatism. By edge-pulling, the lens changes the BFL as well as the aperture. To implement the second concept, a convex-plano elastomeric lens is mounted on a rigid plano-convex Poly (methyl metharylate) (PMMA) lens(Beadie et al., 2008) (Figure 1.10). A mechanical plunger with its opening smaller than the diameter of the elastomeric lens pushes against its marginal part, causing the bulging of lens body. To increase deformation, the lens is made of a cross-linked gel-like elastomer core (PDMS mixed at a 40:1 w/w ratio) capped by an elastomeric membrane

(styrene-ethylene/butylenes-styrene (SEBS) block copolymer). Such configuration allows

for a much larger dioptric range (30 dpt) than previously mentioned alternatives (no more than 4 dpt).

Figure 1.8. Bulk Elastomeric Lens Driven by Shape Memory Alloy Actuator

Figure 1.9. Bulk Elastomeric Lens Driven by Electromagnets (a) and Servo Motor (b)

Table 1.7 summarizes the optical data of the recently developed bulk elastomeric lenses. Generally, they are insensitive to gravitational effect, external vibration, and temperature/pressure fluctuation. As they are usually replica molded from injection molding using glass lens as a master template, their surface profiles can be conveniently customized. However, due to a large strain requirement, the bulk elastomeric lens has a limited dioptric range and a slow response time.

Figure 1.10. Bulk Elastomeric Lens Driven by Mechanical Plunger

Table 1.7. Optical Data of the Bulk Elastomeric Lens

Xa Aa Elastomer BFLa Actuation Ta

0 16 SE 1740 27.5~30.4 Electromagnet/micrometer 0 16 SE 1740 30~33.1 Electromagnet/micrometer 0 16 SE 1740 28.7~30.7 Servo motor 0 8 Sylgard 184 55.6~59.5 SMA 3 (0,1) 10.5 Sylgard 184 30 Plunger aX is the shape factor; A is the lens diameter in mm; BFL is the back focal length in diopter; T is the response time in second.

1.3.2 Elastomer-liquid Lens

Volume change and fluid redistribution are two common approaches to achieve adaptive focusing of elastomer-liquid lens. In the first approach, the volume of the optical fluid underneath the elastomeric membrane increases/decreases to decrease/increase its

ROC and thus the BFL. In the second approach, the elastomeric lens is connected to an annular fluidic chamber that encircles the lens in close proximity or adjoins another fluidic chamber via (micro) channels(s), where both chambers (referred as actuation chamber) are sealed by another elastomeric membrane (referred as actuation membrane). Depression of the actuation membrane next to the lens causes hydraulic pressure transmission to the lens membrane that deflects upward to increase the refractive power. The elastomer-liquid lens can be made as a singlet or a doublet where the lens membrane is sandwiched between two fluidic chambers, two elastomer-liquid lenses are stacked along the optical axis (the top one being meniscus and the bottom being convex-plano), or the elastomer-liquid lens is cemented to a rigid elastomeric/plastic/glass lens(Blum, Büeler, Grätzel, & Aschwanden,

2011). Mechanical deflection (w) of the lens membrane (edge-clamped) parallel to the optical axis can be described by(Q. Yang, Kobrin, Seabury, Narayanaswamy, & Christian,

2008):

r 2 w( r ) s (1 )2 (1.11) A2 where r is the radial distance from the optical axis; s is the lens saggita (sag). Its surface profile approximates a parabolic shape, can be fitted by(S. T. Choi, Son, Seo, Park, & Lee,

2014):

2 Cr 4 6 8 w( r ) 4 r   6 r   8 r  ... (1.12) 1 1  (1  k ) C22 r

th th th where k is the conic constant and is equal to -1; 4, 6, 8 … are the 4 , 6 , 8 … order aspherical coefficients. The hydraulic pressure (P) on the lens membrane is related to the lens sag by(Q. Yang et al., 2008):

448hs2 (184 112 72 2 ) 2 P4 sh 22  AA (1.13) EA2122 (1 )  840 (1 ) where  is the Poisson’s ratio that ranges from 0.45 to 0.5;  is the pre-strain that applies to lens membrane in some commercial products; h is the membrane thickness that is controlled by spin-coating or spacers. In most elastomeric-liquid lens, h/a ≤1. Equation

1.13 is thus modified as(Q. Yang et al., 2008):

P 16 hs  0 (small deflection) EA(1) 2 (1.14) Phs (736448288)23  (large deflection) EA21(1)42

Typically, spherical assumption is applied to the lens at small membrane deflection, and does not hold at large deflection, where the marginal parts of the lens deviate significantly from a spherical contour(S. T. Choi et al., 2014; Kang Wei, Zeng, & Zhao, 2014).

1.3.2.1 Syringe-based

The easiest way to achieve adaptive focusing is to connect the elastomer-liquid lens to a syringe or a programmable syringe pump via fluidic channel(s) and/or plastic tubings(Agarwal, Gunasekaran, Coane, & Varahramyan, 2004; Jeong, Liu, Chronis, &

Lee, 2004; Sugiura & Morita, 1993; K Wei & Zhao, 2013; H. Yang, Yang, & Yeh, 2008;

D.-Y. Zhang, Lien, Berdichevsky, Choi, & Lo, 2003). The latter provides better accuracy on the control of pumping and withdrawal volume and rate. Figure 1.11 shows an example in which the lens is connected to a two-syringe setup where the big syringe is used for lens filling and optical fluid supplementation, and the small one is for lens membrane inflation and deflation(Marks, Mathine, Schwiegerling, Peyman, & Peyghambarian, 2009). To estimate the hydrostatic pressure, a pressure sensor can be embedded within the channel or connected to the tube between the pump and the inlet. The syringe-based elastomer-liquid lens normally has a large dioptric range, but the entire setup is very bulky and prone to fluid leakage given the incorporation of external pump and multiple fluid inlets/outlets.

Figure 1.11. Syringe-based Elastomer-liquid Lens

1.3.2.2 Mechanical lever/rotational ring

Alternative means to manually tune the focus of elastomer-liquid lens is to use a mechanical lever(Ren & Wu, 2005, 2007) or a rotational ring(Blum et al., 2011). Figure

1.12a shows a lens that is encircled by a 1’ iris diaphragm with variable diameter(Ren &

Wu, 2005). During actuation, the clockwise rotation of the mechanical lever pushes the blades toward the lens center, and thus deforms the elastic lens periphery. Because the optical fluid is incompressible, the lens membrane bulges to increase the refractive power.

The iris diaphragm can be replaced by a thin string that wraps around the lens periphery with one end fixed and the other tied to the arm of a servo motor(Ren, Fox, Anderson, Wu,

& Wu, 2006) (Figure 1.12b). The arm rotates to put the string in tension and squeeze the lens periphery. These methods, however, introduce limited amount fluidic volume redistribution, and thus a small dioptric range on the order of centimeters. A way to solve this problem is to position the actuation membrane with increased diameter alongside the lens membrane (Figure 1.13a). A mechanical lever suppresses the actuation membrane, causing fluid redistribution through the channel that in turn deforms the lens membrane(Sugiura & Morita, 1993). Commercially, an elastomeric membrane is placed above a circular fluidic chamber (lens chamber) and a surrounding annular fluidic chamber

(actuation chamber) aligned with an annular threaded housing (Figure 1.13b). A threaded ring attached to the annular membrane rotates inside the housing to push/collect the optical fluid toward/from the lens chamber in order to change the BFL from negative/zero to positive diopters(Holochip Corporation, 2013a; Optotune AG, 2014).

Figure 1.12. Elastomer-liquid Lens Driven by Iris Diaphragm (a) and Servo Motor (b)

Figure 1.13. Elastomer-liquid Lens Driven by Mechanical Lever (a) and Rotational Ring (b)

1.3.2.3 Pneumatic/thermo-pneumatic

The elastomer-liquid lens at microscale can be embedded into the microfluidics to form an optofluidic lens(W. Song, Vasdekis, & Psaltis, 2012). As an example, a biconvex optofluidic lens is formed by a round microfluidic chamber with the top and bottom surfaces covered by thin elastomeric membranes and in the surrounding media of lower RI than that of optical fluid inside the chamber(Fei et al., 2011) (Figure 1.14). The lens is then connected in series to several rectangular microfluidic chambers via a microchannel.

Underneath each rectangular chamber is a rectangular reservoir filled with gas and connected to a pneumatic valve. Sequential on-and-off of the valves applies the pneumatic pressure on the rectangular chamber, and consequently extrudes the liquid into the round chamber to inflate the lens membranes.

Figure 1.14. Elastomer-liquid Lens Driven by Pneumatic Valves

Platinum heater can be used for generating the pneumatic pressure to drive the elastomer-liquid lens. In one configuration, the heater is placed inside an air-filed cavity enveloped by an elastomeric membrane(W. Zhang, Aljasem, Zappe, & Seifert, 2011)

(Figure 1.15a). At an elevated temperature, gas expands to swell the membrane as a thermal pump. When it is distributed on the corner of the lens chamber, the pump compresses the optical fluid to deflect the lens membrane in the center of the chamber, resulting in a focal length change. In another configuration, the heater is placed on the margin of an air tank with its center occupied by a microstructure that defines the lens chamber connected to a microchannel(W. Zhang, Zappe, & Seifert, 2014) (Figure 1.15b).

The volume expansion by heating the air pushes the optical fluid from the microchannel to the lens chamber, causing the increase in the ROC of the polyacrylate lens membrane above the chamber. The use of microfluidic networks allows for precise fluid redistribution and focus tuning, yet at an expense of fabrication and operational complexity. The thermo- pneumatically driven lens usually has a long response time (>10s) consumed by the heating and cooling cycles.

Figure 1.15. Elastomer-liquid Lens Driven by Thermal Pump

1.3.2.4 Electrical

Electrically driven elastomer-liquid lens receives the widest attention and becomes a commercial success in recent decade. Its driving mechanism is based on piezoelectric effect(Nicolas et al., 2015; Schneider, Draheim, Kamberger, Waibel, & Wallrabe, 2009;

Yiu, Batchko, Robinson, & Szilagyi, 2012), electromagnetism(Casutt, Bueeler, Blum, &

Aschwanden, 2014; Cu-Nguyen et al., 2013; S. W. Lee & Lee, 2007; Yu, Zhou, Chau, &

Sinha, 2011), or electroactive polymer(Carpi, Frediani, Turco, & De Rossi, 2011; S. T.

Choi, Lee, Kwon, Lee, & Kim, 2011; Maffli, Rosset, Ghilardi, Carpi, & Shea, 2015;

Niklaus, Rosset, & Shea, 2010; Shian, Diebold, & Clarke, 2013; Son et al., 2012; Kang

Wei, Domicone, & Zhao, 2014). Figure 1.16 show a liquid lens configuration integrated with a piezoelectric ring bender(Schneider et al., 2009). One of the world’s most widely used piezoelectric materials is lead zirconate titanate (PZT), a ceramic with perovskite crystal structure containing aligned dipoles after electric polarization. The PZT is stacked with a metal sheet, e.g. brass, to form a unimorph, which bends in response to voltage when one of its edges is clamped. As a result, it works as a pump to push optical fluid into the lens chamber via orifices, causing focal length reduction. Holochip Corporation from

Hawthorn, USA, offers lenses in the form of singlet and doublet actuated by this technique(Holochip Corporation, 2013b). Because the piezoelectric actuator can generate a large blocking force (30~40 MPa) within milliseconds or even microseconds, the dioptric range and response time of the lens are desirable(O’Halloran, O’Malley, & McHugh,

2008).

Figure 1.16 Elastomer-liquid Lens Driven by Piezoelectric Ring Bender

Voice coil motor (VCM), typically integrated into smartphone camera to displace the lens element(s) for auto-focus, can be also used as a liquid lens driver. The electromagnetic actuator often consists of a ferrite or neodymium permanent magnet that attaches to the actuation membrane on its top or bottom surface, and a spiral coil(Cu-

Nguyen et al., 2013; Yu et al., 2011) (Figure 1.17a&b). Applying a current to the coil generates a magnetic field that attracts or repels the permanent magnet, resulting in fluid redistribution between the actuation chamber and the lens chamber. Optotune AG from

Zurich, Switzerland, introduces this type of lenses that operate with voltages below 5 V and current from 0 to 300 mA, and at a response time under 10 ms(Optotune AG, 2015).

Electroactive polymer (EAP) emerges a promising driving technique to compete against the above two. The EAP actuator is similar to a capacitor where an elastomeric membrane (silicone or acrylic) is sandwiched between two compliant electrodes(O’Halloran et al., 2008). When a high voltage on the order of kV is applied to

the electrodes, the electrostatic pressure (Maxwell’s stress) squeezes the membrane that bulges if its edge is fixed. In most recent demonstrations, the EAP actuator can be made in an annular shape that undergoes out-of-plane deflection or in-plane extension to cause fluid redistribution. The one with in-plane extension works as zonular fibers, which has a response time as fast as 175 s for about 20% focal length variation(Maffli et al., 2015)

(Figure 1.18a). To save space, the EAP actuator can be made transparent by coating single walled carbon nanotube(Shian et al., 2013) or Poly(3,4- ethylenedioxythiophene)(PEDOT)(Son et al., 2012) on top of the membrane. The actuator itself becomes an elastomer-lens (Figure 1.18b). The bottom neck of this method is the need for high driving fields.

Figure 1.17. Elastomer-liquid Lens Driven by Electromagnetism. (a) Permanent magnet above the membrane; (b) permanent magnet underneath the membrane

Figure 1.18. Elastomer-liquid Lens Driven by Annular Electroactive Polymer (a) and Circular Electroactive Polymer (b)

1.3.2.5 Summary of Optical Performances

The dioptric range, resolution, response time and power consumption are four key benchmarks of elastomer-liquid lens. The response time and power consumption are usually determined by the volume of fluid redistribution, viscosity of the optical fluid and the elastomeric membrane, dioptric range, and the driving mechanism. The dioptric range is mostly influenced by the RI of the optical fluid, compliance of the membrane, and the hydrostatic pressure introduced by the driving mechanism. Spherical, comma and field curvature are three primary sources of aberrations that affect liquid lens resolution.

Spherical aberration and field curvature are typically seen in liquid lens at large membrane deflection, as its surface profile deviates significantly from a spherical shape(S. T. Choi et

al., 2014; Ren & Wu, 2007). Coma stems from gravity when the optical axis of the lens is horizontal, and can be alleviated by lens membrane pre-tensioning(Q. Yang et al., 2008), increasing its Young’s modulus(Yiu et al., 2012), or sandwiching it between two fluids of different RIs but similar densities(Wang, Oku, & Ishikawa, 2013, 2014). Selection of an appropriate optical fluid remains one of the most challenging issues for elastomer-liquid lens. An ideal optical fluid should have a high RI, low dispersion, high boiling point, minimal evaporation, no reaction with the lens membrane, and good optical transmittance(J. N. Lee, Park, & Whitesides, 2003). Good candidates include perfluorocarbon and perfluorinated polyether oils(Batchko & Szilagyi, 2010). Table 1.8 summarizes the optical data of recently developed elastomer-liquid lenses.

Table 1.8. Summary of the Optical Performances of Elastomer-liquid Lenses

Elasto Resolution X A h OF RI vd BFL range Actuation T mer (lp/mm) Sylgard 0 4 60 DI water 1.33 55.74 13.2~322.6 × Syringe × 184 Sylgard 0 4 60 DI water 1.33 55.74 -303~-13.2 × Syringe × 184

1 4 60 Sylgard DI water 1.33 55.74 49.8~413.2 × Syringe ×

Sylgard 1 2 × DI water 1.33 55.74 100~250 × Syringe × 184 1 20 60 PDMS × × × 5.8~24.4 25.39 Syringe × Glycerol & DI Sylgard 1 2 50 water 1.41 57.3 0~275 × Syringe 1400 184 (3:2 w/w) 1 25 × × Ethanol 1.36 46.7 2~20 × Mechanical lever ×

1 5 50 PDMS Water 1.33 55.74 10.9~68.6 25 Mechanical lever 40

1 10 x x x 1.29 106.8 0~50 x Rotational ring x

Continued

Table 1.8. continued

-1/1 20 x x x 1.3 100 -14.2~20 x Rotational ring x

Sylgard 1 15 60 Water 1.33 64.21 0.4~2 25 Servo motor × 184 Sylgard 15.4~25(ef 1 25 100 Water 1.33 55.74 × SMA(thermal) × 184 l) VHB Silicone 37.5(0.2 Thermo- 1 2 50 1.4 × 71.4~232.6 10000 4905 oil contrast) pneumatic Sylgard FC-40, Thermo- 1 2 60 1.29 x 66.7~333.3 65 (0.2) >10000 186 3M pneumatic Sylgard Reliber 0 0.7 × 1.39 × 83.3~1000 × Pneumatic 1000 184 PF-6802 Norland 158.7~555. 1 0.2 40 PDMS 1.56 × × Pneumatic × 63 6 Mineral oil, Sylgard 1 2 10 330779 1.47 × 15.6~467.3 × Pneumatic × 184 Sigma- Aldrich RTV 1 2.5 50 Water 1.33 55.74 1~8 117 (0.5) Piezoelectric x 615

1 10 70 Glass x x x 1.1~5 10 Piezoelectric 16

1.45 * 10 x x x x 0.56~20 x Piezoelectric 13 1.29 Sylgard VHB49 0 7.6 30 184 1.43 50 44~59.8 x EAP x 05 (base) Nusil Sylgard 100~126.6 0 5 15 CF19- 184 1.41 50 x EAP 0.175 * 2186 (base) Fomblin 0 2.4 50 PDMS PFPE 1.29 x 50 x EAP x M03 TC- 5005 99% wt 0 5 75 1.47 57.3 9.5~39.4 28.5 EAP 650 A/B, glycerol BJB -1/1 10 50 PDMS Water 1.33 55.74 -7.7~22.2 x Electromagnetic 1300

1 10 x x x 1.3 100 8~22 x Electromagnetic <2.5

1 6 x x x 1.3 100 -2~20 x Electromagnetic 10

1 4 60 PDMS Water 1.33 55.74 0~47.2 x Photo-polymer >1

1.3.3 Application

1.3.3.1 Ophthalmology

Conventional ophthalmic testing relies on a bulky phoropter that consists of different combinations of spherical and cylindrical lenses. Mechanically switching these lenses with appropriate powers and alignments along the line of sight assists in the determination of refractive errors and eyeglass prescription in patients. As a single piece of liquid lens enables fast and precise adjustment of optical powers in a wide range without translational mechanics, the physical size and cost of the phoropter can be reduced as well as the examination time. The elastomer-liquid lens with a circular aperture is normally used for defocus correction, while that with a rectangular aperture is for astigmatism correction.

By rotating the axis meridian of the cylindrical elastomer-liquid lens and/or aligning it with another lens in an angle, astigmatism can be corrected along a specific orientation of the eye. Varioptic from Lyon, France offers a commercial electrowetting lens (up to 8 mm clear aperture) that enables variable focus from -10 dpt to +14 dpt and astigmatism from -

6 dpt to +0 dpt in all axes. A second application of focus tunable liquid lens in ophthalmology is optical coherence tomography that provides volumetric imaging of the human eye based on low coherence interferometry. Axial scanning (A-scan) of the retina, for example, allows visualization of its various functional layers and assessment of their abnormalities. The liquid lens, when placed in front of the transverse scanning mirror, can rapidly focus on regions of interest at different depths, and enables an extended axial scanning range without considerable loss of lateral resolution.

1.3.3.2 Laparoendoscopic imaging

Conventional laparoscope or endoscope has a fairly large depth of field due to a large F/# without the need of auto-focus function. At a sacrifice, it loses accommodation depth cues and requires about 20,000 lux illumination. In addition, it lacks optical zoom, a feature useful for physicians to get a close-up view of minute structures on the superficial layer of the organ as well a comprehensive view of the entire diagnostic or surgical site.

The focus tunable liquid lens with a smaller F/# can auto-focus on regions of interest without external fiber optic illumination. The variable depth of fields at different focal lengths of the lens help depth perception. Two liquid lenses stacked together can reconfigure from the telephoto lens layout into the reverse telephoto (retrofocus) lens layout, which enables more than 4× optical zoom.

1.3.3.3 Microscopic imaging

Specimen focusing and scanning in microscopy are typically achieved by axially repositioning the objective lens or the sample mounting stage using the piezoelectric actuator. The mechanical movement of the stage or the lens may restrict the image acquisition speed (typically about 10 Hz) because of its inertia, and introduce motion artifacts from the sample that jeopardizes image recoding accuracy. To address these issues, the focus tunable liquid lens can be either used as a vari-focal objective or attached at the back aperture of the infinity-corrected objective to rapidly switch the focal plane in microseconds. By recording images at incrementally stepped focal planes in a movement- free manner, the entire sample volume can be rendered. Most recent studies report the use of ETL-10-30 or ETL-6-18 from Optotune AG in combination with a plano-convex offset 37

lens to perform axial scanning of, for example, the oral mucosa in confocal microscopy, the neuronal tissue in two-photon calcium imaging, or the vasculature in light-sheet microscopy and photoacoustic microscopy.

1.3.3.4 Others

Focus tunable liquid lens also finds use in machine vision, laser processing, biometrics, lighting, consumer auto-focus cameras, etc. In machine vision, for example, the lens can be combined with fixed-focus imaging lenses to scan objects such as barcode at different working distances, or with zoom lenses (Dynamic Focus VZM Lens, Edmund

Optics) to achieve variable depth imaging while maintaining zoom capabilities for the inspection of integrated circuit and solder joints, and other quality control needs. Fast 3D laser engraving is possible by setting the liquid lens behind the F-Theta and in front of the galvo-mirrors lens to shift the z-position of a laser spot. The fast and silent re-focusing ability of the liquid lens also allows for the correction of focus and handshake blur in mobile device applications like continuous autofocus in video recording, and iris/face recognition.

1.4 Inspirations from Insect Eye

The main goal of the artificial compound eye camera is to obtain a wide FOV with less image distortion in a small volume. Early avenue to adopt this concept takes advantage of a planar configuration where a planar microlens array projects images onto a flat image sensor. Thanks to the recent advancement in flexible electronics and polymeric micro/nanofabrication, a curved configuration that truly represents the structural 38

characteristics of compound eye is made possible, where a curved (micro) lens/mirror array is fabricated on a dome-shaped substrate and interfaced with a flat image sensor or flexible photodetectors.

1.4.1 2D

Monolithic planar artificial compound-eye imaging systems feature a microlens array (MLA) in concert with a flat image sensor(Brückner et al., 2010; Jacques Duparré,

Dannberg, Schreiber, Bräuer, & Tünnermann, 2004). Typically, these systems consist of an array of thermal-reflowed microlenses (F/# = 2.2) on a glass substrate and a pinhole (2 to 8 m) array positioned on the back focal plane of MLA and immediately above the photodetectors(Jacques Duparré, Dannberg, Schreiber, Bräuer, & Tünnermann, 2005)

(Figure 1.19). The pitch of the pinhole array differs from that of the MLA so as to direct the optical axes of peripheral microlenses outward. Each microlens obtains a sub-image that corresponds to a unique field angle of the object space. The system (size comparable to a euro cent) generates a FOV of merely 20×20°. Off-axis aberrations and cross-talk between neighboring lenses also limit imaging performance.

Figure 1.19. Planar Artificial Apposition Compound Eye Camera

1.4.2 3D

Biomimetic design that incorporates the structural characteristics of natural compound eye remains to the best approach to achieve a large FOV without the loss in off- axis resolution. Three representative state-of-the-art compound-eye imaging systems are now discussed.

Figure 1.20. Hemispherical Artificial Compound Eye Camera

The first imaging system leverages flexible thin-film silicon photodiodes. An array of 256 elastomeric convex lenses (diameter: 0.8 mm; focal length: 1.37 mm) is molded on an elastomeric sheet(Y. M. Song et al., 2013) (Figure 1.20). The lenslet sheet is then bonded and optically aligned to an array of deformable silicon photodiodes (pixel size:

160×160 m) on another elastomeric sheet. The as-formed bi-layer is elastically stretched from planar geometry into a hemispherical shape (height: 6mm), allowing for spherical orientation of the individual lenslets. The apposition compound eye camera results in a

FOV of 160×160°. Unfortunately, the wide-FOV imaging necessitates the fabrication of hundreds of elastomeric lenses and flexible photodiodes, and, more importantly, stringent optical alignment of the lens and photodiode across the hemisphere. In addition, the camera can only best focus on objects within millimeter-range without significant image blur, due to the short focal length and the lack of accommodation.

The second imaging system, namely CurvACE, imitates the compound eye of the

Drosophila melanogaster and interfaces with conventional flat CMOS optoelectronics(Floreano et al., 2013) (Figure 1.21). In this approach, a MLA composed of a rectangular array (15×42) of single-aperture microlenses (diameter: 172 m; F/#: 2.4) is fastened to a planar silicon-based photodetector layer supported by an ultrathin (100 m) polyimide printed circuit board (PCB). The MLA is diced along its columns into 15 individual ommatidia, allowing for the bending of the PCB widthwise to a 6.4 mm radius of curvature. CurvACE enjoys a FOV of 180×160°. However, it inherits the visual constraints of fruit fly, i.e. near-sightedness and rather low spatial resolution.

Figure 1.21. Cylindrical Artificial Apposition Compound Eye Camera

The third imaging system, unlike the former two, relies on beam-steering/refracting optics that can steer incoming collimated light from different directions onto a flat focal plane(Li & Yi, 2010). In this method, the beam-steering elements are either an array of ultra-precision diamond-machined microprisms (maximum steering angle: 18°) or freeform prism-like microlenses (maximum steering angle: 43.5°) arranged on a curved surface. The reported FOVs are 36× 36°, and 87× 87°, respectively, for these two beam steering elements. The prism-based compound eye camera takes full advantage of planar image sensor but only focuses on objects at infinity due to the absence of a front lens element. The resulting spatial resolution (MTF) is also very low (e.g., at 50 lp/mm the contrast is below 0.4).

1.5 Organization of the Dissertation

This dissertation systematically reviews the state-of-the-art focus tunable lenses and artificial compound eye cameras inspired by human camera-eye and compound eye.

Two novel reconfigurable elastomer-liquid designs and their implementation by optofluidics are described. The principle of operation, fabrication and testing of an elastomer-liquid lens driven by dielectric elastomer actuator is presented. The approach to 42

correct the spherical deviation and field curvature of the elastomer-liquid lens at large optical powers is discussed. The whole dissertation is outlined as follows.

Chapter 2 reports a refractive optofluidic apparatus that takes the advantage of structural merits of human camera-eye and insect compound eye. An elastomer-liquid lens array is fabrication on an elastic substrate that deforms to radiate the optical axes of liquid lenses on its marginal parts so as to vary and enlarge the FOV. The lens sag as a function of the volume of infused optical fluid is measured using Sessile drop technique. The corresponding optical power of the lens is characterized by fluorescence ray tracing. The angles between the optical axes of adjacent lenses are measured at different deflections of the substrate. The picture at the maximum FOV is captured by stitching all images from the lens array. The ability of the lens to capture objects with a large FOV containing monocular depth cues is demonstrated.

Chapter 3 introduces an optofluidics-based imaging device that reconfigures from a 10 mm single elastomer-liquid lens to a pair of 3 mm elastomer-liquid lenses separated at 6.4 mm. The BFLs, F/#s and resolutions of both the big lens and the small lenses are investigated and compared. The ability of the device to take 2D image containing accommodation depth cues is demonstrated using the big lens. Its conversion into binoculars to take 3D image containing binocular disparity is demonstrated at varied working distances with the help of an additional reconfigurable optofluidic iris. Depth estimation at 2D and 3D modes are compared and discussed.

Chapter 4 focuses on the driving mechanism of the elastomer-liquid lens. Unlike the use of syringe pump to actuate the liquid lens in Chapter 2&3, an annular actuator

fabricated by artificial muscle materials, i.e. electroactive dielectric elastomer actuator is designed and prototyped. The dioptric range, response time and resolution of the liquid lens is examined.

Chapter 5 presents an approach to correct the field curvature of the elastomer-liquid lens at large diopters by modifying the geometry of the lens membrane. Finite element modeling of the membrane deformation and its associated RMS spot size simulated using

Zemax is elaborated. Fabrication of an aspherical lens membrane by double replica molding and that of lens housings by 3D printing are described. The peripheral and center resolutions of the lens based on aspherical membrane is measured and compared to those of the lens based on flat membrane, and the conventional solid lens at the same BFL.

Chapter 6 summarizes the dissertation and gives perspectives into future possible work.

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Chapter 2: Insect-human Hybrid Eye (IHHE): An Adaptive Optofluidic Lens

Combining the Structural Characteristics of Insect and Human Eyes

This chapter describes a reconfigurable polymeric optofluidic device that combines the architectural merits of both vision mechanisms, featuring a large AOV (up to 120°) with adaptive focusing capabilities (from 0 to 275 diopter (D)). This device consists of bi- layered microfluidics: an array of millimeter-sized fluidic lenses is integrated into the top layer and arranged on an elastomeric membrane embedded within the bottom layer. The membrane can be deformed from a planar surface into a series of dome-shaped geometries, rearranging individual fluidic lenses in desired curvilinear layouts. Meanwhile, each fluidic lens can vary its radius of curvature for a monocular depth sensation. Such a design presents a new perspective of tunable optofluidics for a broad range of applications, such as robotic vision and medical laparoendoscopy, where adaptive focalization with a large viewing angle is a clear advantage.

2.1 Introduction

A plethora of daylight insects excel in observing the surrounding environment panoramically(Borst, 2009). Investigations into their visual organs reveal a compound-eye mechanism, e.g. the eye of drosophila melanogaster contains up to 800 microscale

ommatidia packed on a hemispherical surface with each facing towards a different orientation (from 0º to 180º)(Buschbeck & Friedrich, 2008; Chapman, 1998). Individual ommatidium manages both focusing (with a fixed focusing power about 4.7×104 diopter

(D))(Gonzalez-Bellido, Wardill, & Juusola, 2011) and imaging. The panoramic vision is created by integrating discrete views from every ommatidium in a pixelated fashion(Borst,

2009). The notably wide angle of view (AOV) of the insect compound eye has precipitated many to engineer artificial counterparts owing to its potential use in consumer optics, medical endoscopy, robotic vision and other surveillance devices(Franceschini, Pichon,

Blanes, & Brady, 1992; L. P. Lee & Szema, 2005; Szema, Rastegar, & Lee, 2004). Three types of optical configurations are reported in recent demonstrations of artificial compound eye (Brückner et al., 2010; Chan, Lam, Ng, & Mak, 2007; Duparré, Dannberg, Schreiber,

Bräuer, & Tünnermann, 2005; Duparre et al., 2004; Floreano et al., 2013; He, Liu, Yang,

Dong, & Yang, 2013; Jeong, Kim, & Lee, 2006; Jung et al., 2011; Keum, Jung, & Jeong,

2012; Kitamura et al., 2004; Ko et al., 2008; Li & Yi, 2010; Park, Choi, Jo, & Lee, 2012;

Qu et al., 2012; Y. M. Song et al., 2013; T. Wang et al., 2012). In the first type, a solid microlens array is arranged on a flat substrate and forms images through a pinhole array placed in the back focal plane. A deliberate pitch offset is introduced between the lens and the pinhole in order to tilt the direction of view and thus enlarge the overall AOV(Duparre et al., 2004). The second type closely resembles the configuration of insect compound eye(Floreano et al., 2013; He et al., 2013; Jeong et al., 2006; Jung et al., 2011; Ko et al.,

2008; Y. M. Song et al., 2013). Microlenses with fixed focusing powers are arranged on a hemispherical polymer dome and connected to either UV-written waveguides or flexible

photoreceptors. The overall AOV of this configuration is determined by the number of the microlenses and their distribution. However, fabricating and assembling hundreds or thousands of microlenses with individually aligned photoreceptors on a convex substrate are not only technically challenging, but also demand substantial labor and cost. The third type is similar to the second type except for that the microlenses are replaced by diamond- machined microprisms. Each microprism steers incident light rays at different angles onto a 2D focal plane for image formation(Li & Yi, 2010).

In natural and artificial compound eyes, the use of an array of lenslets increases the overall AOV yet at the sacrifice of the imaging performance(Gonzalez-Bellido et al., 2011;

Howard & Snyder, 1983). Due to the limited size of compound eyes, the aperture of each lenslet is only a few hundred m or smaller. Such small aperture limits the amount of light that travels through the lenslet and leads to poor image quality especially in low illumination environment. Besides, each lenslet in the compound eye has a fixed focusing power and thus can best focus on objects within a certain range of distance. Although the small aperture ensures a fairly large depth of field, objects at different depths cannot be readily distinguished. Fortunately, nature offers another vision mechanism, i.e. human camera eye, which possesses a relatively large aperture and tunable focusing power.

Despite a limited AOV due to the small total eye number, a human camera eye enables a better image resolution and accommodation to detect monocular depth cues(Keating &

Geometric, 2002; Land & Nilsson, 2012) compared to the insect compound eye. Given these, it is plausible to expect that an optical component incorporating the characteristic features of both insect compound eye and human camera eye may offer a large AOV, good

image quality, as well as vari-focal capability simultaneously for practical imaging/illumination applications.

Optofluidic devices that embed reconfigurable solid(W. Song, Vasdekis, & Psaltis,

2012) or liquid(W. Song & Psaltis, 2013; Y. Yang et al., 2012) optical elements within microfluidics are well known for its robustness in manipulating light propagation at micro/millimeter scale(Psaltis, Quake, & Yang, 2006; Y. Zhao et al., 2013), and may thus be well suited for the integration of the two vision mechanisms. Of particular interest are the adaptive optofluidic lenses which have proven success in tuning the focusing power

(Nguyen, 2010). The in-plane adaptive focusing is often achieved by changing the radius of curvature of the liquid-liquid(Seow et al., 2008) or air-liquid interface(Shi, Stratton, Lin,

Huang, & Huang, 2010), tuning the refractive index (RI)(Seow, Lim, & Lee, 2012) or the

RI profile(Mao et al., 2009) of mixing fluids, or plasmonics(Zhao, Liu, Zhao, Fang, &

Huang, 2013). The out-of-plane adaptive focusing takes advantage of the adjustable surface tension within meniscus(Berge, 2005; Dong, Agarwal, Beebe, & Jiang, 2006), or the deformability of elastomeric membrane(Fei et al., 2011; Zhang, Aljasem, Zappe, & Seifert,

2011).

In this study, we introduce a bio-inspired insect-human hybrid eye (IHHE) design that is implemented on an elastomeric optofluidic chip with out-of-plane adaptive focusing capability. The device consists of a bi-layered microfluidics: the top layer mimics the adaptive focusing capability of human camera eyes and the bottom layer can be reconfigured into various curvilinear layouts to mimic the hemispherical dome-shape in insect compound eye. The IHHE prototype delivers a viewing angle up to about 120º with

the focusing power ranging from about 0D to 275D. The enhanced imaging performance, compact design and ease of operation provide a new avenue of adaptive optics for various applications.

2.2 Principle and design

The IHHE incorporates architectural merits of both insect apposition compound eye and human camera eye (Figure 2.1). A transparent polymeric big membrane that can be deformed from a planar surface into a spherical cap with varied radii of curvature is employed to mimic the dome-shape architecture of insect compound eye. An array (3×3) of single lenses is positioned on the big membrane, where the peripheral single lenses orient outwards when the big membrane deforms (Figure 2.2). Each single lens consists of a small transparent polymeric membrane and a fluid body underneath. The focusing power of a single lens can be adjusted by altering the fluid volume, so as to achieve accommodation function. A bi-layered microfluidic channel network provides fluid connections for deforming the big membrane and the small membranes of single lenses independently.

Figure 2.1.Structures of Insect Apposition Compound Eye (left) and Human Eye (right)

Figure 2.2. IHHE Combining Architectural Characteristics of the Two Vision Systems by Distributing an Array of Membrane-Enveloped Fluidic Lenses on a Big Deformable Membrane.

Simultaneous actuation of the big membrane and the small membranes yields a large overall AOV (Figure 2.3). When the big membrane remains un-deformed, the overall

AOV is primarily determined by the focusing power of individual single lenses, and can be slightly enlarged by increasing the focusing power yet at the expense of increased optical aberration in each single lens. This is owing to the parabolic surface profile of the small membrane at large deflections(Ren & Wu, 2012). To overcome this deficit, the big membrane is deformed into a spherical cap with a certain deflection, allowing the single lenses in the peripheral region to shift their optical axes outwards and capture images at a different viewing perspective. The tilted single lenses thus allow observation of the field at a different angle without inducing a large deflection in the small membranes. In the meantime each single lens can adjust its focusing power to compensate the object distance 56

change due to the deformation of the big membrane and obtain a clear image with depth information. The overall AOV is obtained by combining the temporal AOVs of the peripheral single lenses during the entire actuation process and that of the single lens in the center. The AOVs obtained at different time points are slightly overlapped so that the temporally integrated overall AOV encompasses information of the entire field. Such usage of the deformable big membrane for temporal image integration avoids the fabrication of a large number of single lenses on a curved substrate. Tunable single lenses ensure proper focusing on all the objects at different depths in the entire field.

Figure 2.3. Working Principle of IHHE. During operation, the big membrane forms a dome shape, which changes the AOV of the peripheral single lenses and thus increases the overall AOV. The focusing power of each single lens is tunable, allowing depth sensation along different orientations.

A schematic (perspective and cross-sectional side views) of the IHHE device is illustrated in Figure 2.4a&b. The device contains a bi-layered polydimethylsiloxane

(PDMS) substrate and a glass substrate. The bottom layer of the substrate is comprised of a circular big membrane (thickness: 200 m; diameter: 10 mm) and a microchannel

(height: 500 m; width: 200 m). The top layer of the substrate immediately above the 57

bottom layer consists of nine circular small membranes (thickness: 50 m; diameter: 2 mm; center-to-center distance: 2.5 mm), and three microchannels (height: 100 m; width: 100

m). The small membrane in the center of the array is concentric to the big membrane. The three microchannels connect the nine membranes to one fluidic inlet. The bottom surface of the PDMS substrate is attached to the glass substrate (thickness: 1 mm). The membrane deformation upon actuation was examined using finite element analysis (COMSOL

Multiphysics 4.3b). In this analysis, the Young’s modulus, density, and Poisson’s ratio of the PDMS substrates were set at 1.8 MPa, 965 kg/m3, and 0.49, respectively. In all cases, the small membrane of the single lens in the center had a deflection of about 0.2 mm.

Figure 2.4. Geometry and Mechanical Modeling of the IHHE. (a) & (b) Schematic of IHHE, which consists of a bi-layered microfluidic network. The top layer includes a trifurcated microchannel with each branch connecting to three circular membranes; the bottom layer has a big membrane that connects to another microfluidic channel. Ds(diameter of the small membrane)=2 mm; Ts(thickness of the small membrane)=50mm; Ls-s(center to center distance between adjacent small membranes)=2.5 mm; Db(diameter of the big membrane)=10 mm, Tb(thickness of the big membrane)=200mm. (c) Simulated deformation profiles of the IHHE showing variable perspectives of the peripheral lens.

Figure 2.4c shows that the maximal center deflection of the big membrane from 0 mm to about 3.0 mm can successfully tilt the optical axis of the peripheral lens from 0° to

45°. It also showed that the peripheral lenses maintained an essentially symmetric profile

(intact lens function) under all conditions.

2.3 Fabrication and assembly

Figure 2.5 illustrates the fabrication and assembly process. A cylindrical structure made of SU-8 2100 (Microchem, MA) (500 m in thickness and 10 mm in diameter) served as the master template of the bottom microfluidic layer. The master template of the top microfluidic layer was fabricated using a double-layered photolithography process with

SU-8 2050 (Microchem, MA), where nine cylindrical structures for molding the small membranes were 200 m thick and the structures for molding the microfluidic channels were 100 m thick. PDMS (Sylgard 184, Dow Corning, MI) was prepared by mixing the base and the curing agent at the weight ratio of 10:1 and degassed in a vacuum desiccator.

It was cast onto the master templates of the top and the bottom layers, where polyester spacers were placed between the master template and a microscopic glass slide to control the membrane thickness. The glass was spun-coated with a 1.5 m thick S1813 (Shipley) to assist peeling. After thermal curing, the bottom and top layers were aligned and plasma bonded to form the bi-layered PDMS substrate. The bottom layer was plasma treated and bonded to a glass substrate with RI of 1.5. After each bonding process, the PDMS substrate was heated on a hotplate for 30 min at 65°C to enhance the bonding. The optical medium with RI~1.41 (matching that of PDMS) was prepared by mixing 99% glycerol and

deionized (DI) water at a weight ratio of 3:2. The medium was filled into the microfluidic channels in both layers by a syringe pump (Pump 11 Elite, Harvard Apparatus, MA) at the flow rate of 20ml/hr. For visualization purpose, the microfluidic network in the top layer of an assembled device was filled with green food color; and that in the bottom with yellow food color. The top and side view images of the IHHE prototype were captured while both the big membrane and the small membranes were deformed.

Figure 2.5. Fabrication and Assembly of the IHHE. Left to right: master templates for the big and the small membranes fabricated by SU-8 photolithography; assembled IHHE by PDMS replica molding; the bi-layered microfluidic network highlighted by food colors; and the top and side views of the IHHE while both the big membrane and the small membranes are deformed.

2.4 Results

2.4.1 Tunable Focusing Power

Because the RI of the optical medium matches that of PDMS, the effective focusing power (Plens, the reciprocal of effective focal length) of each membrane-enveloped fluid lens is determined primarily by the focusing power at the air-PDMS surface. It was measured by a custom-built fluorescence ray tracing system that consisted of a laser diode (diameter: 2 mm; wavelength: 532 nm), the IHHE prototype, a glass trough (length: 120 mm) filled with the deionized water containing Rhodamine fluorescence dye (Sigma Aldrich, MO;

RI=1.33) and a charge-coupled device (CCD) camera (Casio EX-F1). During the entire measurement, the big membrane was kept planar. A collimated beam ray from a green laser was incident on one single lens in the IHHE prototype and converged. The fluorescence image showing the optical path was analyzed by ImageJ (version 1.47, NIH) to calculate the distance (v) between backside of the glass substrate and the focal point in the medium.

To determine Plens, the measuring system was simplified as an equivalent air system (as illustrated in Figure 2.6) where the light travelled through three interfaces sequentially, namely: the air-PDMS interface, the PDMS-glass interface and the glass-fluorescence interface. Plens was determined by applying the vergence equation at each interface:

1000 P  (2.1) lens v s t 0.67 1.33 1.4 where s is the center deflection of the small membrane; and t is the total thickness of the bi-layered PDMS substrate (0.95 mm in this study).

Figure 2.6. Ray Tracing Schematic and its Equivalent Air Model

The center deflection of the lens was measured by a goniometer (ramé-hart, Model

200, NJ)(Wei, Zeng, & Zhao, 2013). Extra optical medium of 10 to 130 l was supplied to the top microfluidic channels at an increment of 10 l. The results showed the center deflection of the small membrane increased with increasing fluid volume, from about 50

m at 10 l to about 550 m at 130 l (Figure 2.7).

Figure 2.7. Center Deflection of the Small Membrane as a Function of Fluid Addition into the Microfluidic Channel in the Top Layer

Figure 2.8. Representative Images of Beam Convergence in the Fluorescence Medium at s = 117mm, 172mm, 241mm and 304mm, respectively

The focal point also changed with the small membrane deflection, as evidenced by ray tracing results (Figure 2.8). The corresponding back focal distance in the medium decreased from about 25.0 mm at the center deflection of 50 m to about 2.5 mm at the center deflection of 550 m (Figure 2.9a). Calculation showed that Plens varied from 0D at the planar surface to 275D at the maximal center deflection of 550 m (Figure 2.9b).

This was well beyond the range of the focusing power of a normal human camera eye, which ranges from 16.3D to 23.0D.

Figure 2.9. Back Focal Distance in the Medium as a Function of the Center Deflection of the Small Membrane (a) and the Calculated Focusing Power (b).

To demonstrate the adaptive focusing capability, the IHHE prototype was used to examine a 3×3 array of pillars (Figure 2.10). All the pillars were 2 mm in diameter, and spaced by 2.5 mm from the neighbors. Each pillar had a different length, from 2 mm to 18 mm with an increment of 2 mm. For better visualization, a crossing cut was created on the top surface of each pillar and stained by food color. The bottom substrate of the pillar array was positioned at 40 mm from the IHHE. The pillars and the bottom substrate were fabricated using a 3D printer (Objet 24, Stratasys, MN). The images viewed through the membrane lenses array were obtained while changing the focusing power of the single lenses from 109D to 266D. At 109D, pillars #1 through #6 (where the distance from the lens to the pillar top varied from 38 mm to 28 mm) were clearly viewed through lens #1 through #6, whereas pillar #7 through #9 were somewhat defocused. When the focusing power increased to 266D, images of pillars #7 through #9 came into focus, whereas those of pillars #1 through #6 became blurry.

Figure 2.10. Demonstration of Adaptive Focusing by Viewing an Array of Pillars whose Top Surfaces were Placed at Different Depths.

2.4.2 Tunable and Large AOV

Dome-shaped geometries of the deformed big membrane at different deflections were examined (Figure 2.11a). Extra fluid from 240 to 640 l was pumped into the bottom microfluidic network at the increment of 40 l. Results showed that the center deflection of the big membrane (h) increased from about 0.76 mm at 240 l to about 3.15 mm at 640

l. While the big membrane was deformed, optical medium of about 60 l was pumped into the top microfluidic network to highlight the position of individual single lenses.

Figure 2.11b shows the optical axes of the peripheral single lenses in the middle row of the array when the center deflection of the big membrane was 0, 0.76, 1.48, 2.1, 2.6, and

3.15 mm, respectively. At h = 0 mm, all the single lenses shared the same orientation. Their optical axes were therefore parallel. As the big membrane was deformed, the intersection angle between the optical axes of the peripheral single lenses in the same low with the center lens and the vertical direction (refers to and hereafter) changed from 0° to 45°, allowing for imaging at a different angle.

Figure 2.11. Tunable AOV. (a) Center deflection of the big membrane changes with the volume of extra fluid supplied into the microfluidic channel in the bottom layer. (b) Orientation of the center lens and a peripheral single lens in the middle row while the big membrane was at different center defections. Red line: optical axes of the single lenses.

2.4.3 Focusing Power at Different AOVs

The effective focusing power of the single lenses was examined at different big membrane deformations (= 15°, 30° and 45°) using fluorescence ray tracing (Figure

2.12).

Figure 2.12. Focusing Power Measurement at Big Membrane Deformation.  denotes the intersection angle between the optical axis of the peripheral lens and the vertical direction.

As the big membrane deformed, in-plane strain was induced into the top surface of the big membrane and thus somewhat flattened the single lenses on the top. Therefore, additional fluid was needed to keep the focusing power unchanged. When , the focusing power of a peripheral lens was slightly greater than that of the center lens with the same big membrane deformation (as can be seen from Figure 2.4c). This is due to the non-uniform strain field of the big membrane. In particular, the single lens in the center of the big membrane was subject to a higher strain magnitude than those in the peripheral region, and thus requires a higher differential pressure to deform. The focusing power difference does not affect the IHHE performance though because the device acquires images by temporal image integration and does not assume identical focusing powers of all the single lenses under a certain big membrane deformation. The results also showed that the focusing power of single lenses was not significantly affected by the  value. In addition, the focusing powers of the center lens and of the peripheral lenses under the same center deflection were similar.

The capability of the IHHE prototype of capturing images with a large AOV was demonstrated by observing characters printed on a semi-circular ribbon (Figure 2.13a).

The ribbon was 180 mm in diameter and printed by the 3D printer. The angles from –75° to +75° were indicated by lines with an increment of 3° and numbers with an increment of

15°. The IHHE prototype was positioned in the center of the semi-circular ribbon. Its position was adjusted to have the number ‘0’ indicating 0° appear in the center lens. The

CCD camera was placed behind the IHHE prototype, whose optical axis was always aligned to that of the single lens to be observed (Figure 2.13b). The distance between the

single lens and the camera was kept as 110 mm. The F-number of the camera (focal length/aperture) was kept constant at 5.0 during the entire measurement. At h=0 mm, the lens above the membrane center focused on the number ‘0’ with the focusing power of about 30D. The AOV of each single lens was about 15º. The single lenses in the peripheral region and in the same row also saw the number ‘0’, while the image appeared slightly off the center of field. At h=0.76 mm, the peripheral single lenses of both sides saw the number

‘15’ (red on the left and green on the right), indicating an enlarged overall AOV (Figure

2.13c). Similarly, the big membrane was further deformed to tilt the optical axes of peripheral single lenses to +/-7.5°, +/-22.5°, +/-30°, +/-37.5°, +/-45°, and +/-52.5°. The overall AOV was obtained after temporal integration of all these images. Given the current optical configuration, the overall AOV of up to about 120º was achieved (Figure 2.13d).

2.4.4 Distinguishing Objects at Different Depths and Different Perspectives

The adaptive focusing capability combined with the reconfigurable big membrane also allows the device to view objects at different depths and at different angles (Figure

2.14). To validate this, two sets of letters were positioned spherically in front of the IHHE prototype: the letters of ‘O’, ‘M’ and ‘U’ in the first set encircled the IHHE from the left to the right at the angle of -30°, 0°, and +30° with the axis of the big membrane respectively.

Each letter was at a distance of 32 mm from the center of the IHHE. Similarly, the letters

‘B’, ‘S’ and ‘E’ in the second set were positioned at the angle of -30°, 0°, and 30° with the optical axis of the big membrane respectively. Each letter was at a distance of 92 mm from the center of the IHHE.

Figure 2.13. Acquiring Images with a Large AOV. (a) Hemispherical ribbon marked with angles from negative 75° (in red) to positive 75° (in green). (b) Illustration of image acquisition. (c) Images viewed by the IHHE when the lens is upright and titled at +/-15°. Only the images in the highlighted boxes are used for assembling the final image in (d). (d) Images acquired at different AOVs (by tilting the lens from -52.5° to -52.5°) are collaged to show the overall AOV.

The big membrane was first deflected to have the peripheral single lenses facing

30°, i.e. the left single lens oriented towards the letters of ‘O’ and ‘B’; the middle single lens oriented towards the letters of ‘M’ and ‘S’; and the right single lens oriented towards the letters of ‘U’ and ‘E’. Afterwards, the letter ‘B’ was brought into focus by tuning the focusing power of the single lenses to about 50D. The focusing power was then increased to 100D to focus on the letter ‘M’, and tuned back to 50D to focus on letter ‘E’, completing the word of ‘BME’. Similarly, the word of ‘OSU’ was viewed by tuning the focusing power

of the single lenses to focus on individual letters (inset of Figure 2.14). It is worth noting that when one letter was in focus, the other letter along the same line of sight was fairly blurred, indicating that the two letters at different depths can be well distinguished.

Figure 2.14. Adaptive Focusing at Varied Viewing Angles.

2.5 Discussions

2.5.1 Reconfigurable Design with a Small Number of Single lenses

The IHHE design arranges a fairly small number of membrane-enveloped fluidic lenses (a total of nine) with adaptive focusing powers on a flexible big membrane with a reconfigurable curvature. The aperture of each single lens is at

least one order of magnitude greater than those in previous demonstrations of compound eye vision systems that have hundreds or even thousands of microscale single lenses. Given that the typical pixel size of CCD or CMOS sensors is on the order of tens of microns, the increased aperture size allows each single lens to capture images with a relatively high resolution. Subsequent imaging processing is thus simplified. However, different from conventional compound eyes where the orientations of adjacent single lenses only differentiate by a small angle no more than a few degrees, the differential orientation of adjacent single lenses in IHHE depends on the curvature of the big membrane. With a small curvature (the big membrane is nearly planar), the adjacent single lenses have a very small difference in their orientations. Their fields of view thus overlap with each other so that the entire field can be captured simultaneously. A large curvature is needed for increasing the AOV, which causes discrete fields of view with an un-covered region in between due to the increased differential angle between the adjacent single lenses.

Therefore, the IHHE captures multiple images while the peripheral single lenses

“sweep” the field during the big membrane deformation. In the meantime, single lenses are actuated to focus on the objects along their respective lines of sight.

2.5.2 Temporal Image Integration and the Acquisition Time

In the IHHE prototype, the final image with a large overall AOV is formed by joining multiple images with slightly overlapped fields of view, similar to stitched panorama. In particular, the objects in the overlapped areas of adjacent

frames are used for correct stitching. However, since each image is acquired by a single lens with a different focusing power, individual images are not readily

“stitchable”. Proper magnification is needed to compensate the difference of focusing powers between adjacent single lenses before the images can be stitched.

Moreover, parallax error may occur because the optical center of a peripheral lens shifts during big membrane deformation. The optimal strategy of stitching images is beyond the scope of this study and will be studied in the future.

The total acquisition time depends on response time of the big membrane as well as that of single lenses, which are determined by viscoelastic properties of the membrane material and the optical medium, and the actuation mechanism. Detailed analysis of the viscoelastic behaviour including the response time of such a system can be performed following the method reported in a previous publication(Qian

Wang, Zhang, & Zhao, 2014). Using a syringe pump as the actuation mechanism and glycerol/water mixture as the optical medium, the big membrane made of PDMS can be deformed from a planar surface to a dome shape with the center deflection of

3.15 mm within 3.6 seconds. Likewise, the small membrane can be deformed from a planar surface (0D) to a dome shape with the center deflection of 550 m (275D) within 1.4 seconds. It is worth noting that the maximal flow rate of the syringe pump

(500 ml/hr in this study) and the relatively long and distensible tubes used to connect to the syringe pump limit the response performance. This response time can be reduced by integrating an actuation mechanism within the IHHE device where external pumping and tubing are abolished, e.g. using an integrated electric or

magnetic actuator(Choi, Lee, Kwon, Lee, & Kim, 2011; S. W. Lee & Lee, 2007;

Wei, Domicone, & Zhao, 2014).

2.5.3 Influence of the Big Membrane Deformation on the Focusing Power of Single Lenses

As mentioned above, the non-uniform strain field on the top surface of the big membrane upon actuation may lead to focusing power difference among single lenses. Although this does not affect the IHHE performance, the non-uniform strain field may cause asymmetric deformation of the single lenses in the peripheral region and therefore optical aberration. Finite element analysis showed that the distortion of the single lens shape can be reduced by increasing the thickness ratio between the big membrane and the small membrane. Figure 2.4b shows that with a thickness ratio of 4:1 as in the IHHE prototype, the asymmetric lens shape distortion caused by the big membrane deformation is negligible.

2.5.4 Possible Integration with Flexible Photosensors

Since the images acquired by the single lenses on the deformed big membrane fall on a curved plane, conventional CCD or CMOS sensor on a planar surface is not adequate for image acquisition. To showcase the IHHE design with a low cost configuration, images were captured by placing a camera behind the IHHE device and having its lens plane perpendicular to the optical axis of the single lens of interest. For practical imaging applications, flexible photosensitive materials that deform with the elastomer substrates(Jung et al., 2011; Ko et al., 2008; Y. M. Song et al., 2013) can be positioned on the big membrane and aligned with each single 73

lens. Such arrangement allows the use of air for big membrane actuation and may reduce the response time. Alternatively, elastomeric optical fibers/waveguides(Kim,

2013) can be used to transfer the light received by the single lenses to planar CCD or CMOS sensors. The strategies of integrating these technologies with adaptive fluidic lenses deserve future studies.

2.5.5 Limitations and Possible Solutions

The AOV of the IHHE prototype demonstrated in this study is lower than that in natural compound eye vision system, which often exceeds 150°. The AOV is determined by the distensibility of the big membrane and the bonding strength between the big membrane and the glass substrate. In this study, the big membrane did not rupture during the actuation, while the delamination from the glass substrate was observed when the actuation pressure was beyond 35 psi. This corresponded to a maximal  value of about 54° and a maximal AOV of 124° when the focusing power of single lenses was about 30D. The AOV can be further increased by increasing the bonding strength using other bonding methods, using thinner membranes and softer membrane materials, or by increasing the focusing power of individual singles lenses.

A membrane-enveloped fluidic lens often suffers from optical aberration, as evidenced by the distorted image in its peripheral areas. This is caused by the deviation of the deformed profile of the membrane(Choi, Son, Seo, Park, & Lee,

2014; Q. Yang, Kobrin, Seabury, Narayanaswamy, & Christian, 2008) from the

spherical shape. The surface contours of deformed single lenses and of an ideal spherical lens were compared with the center deflections of 117 m, 241 m, 304

m, and 550 m. The results showed that the spherical deviation increased with the center deflection (Figure 2.15) and may deteriorate the image quality at large deflections. As mentioned earlier, one solution of reducing such aberration is to have each single lens keep a small focusing power, sweep the field by actuating the big membrane, and collage the images. Alternatively, the spherical aberration of single lenses can be reduced by using a thickness-varied membrane whose deformation approximates a more spherical shape. Such membrane can be fabricated using previously reported methods(Q. Wang & Zhao, 2011). The in-depth study of using such membranes in reducing spherical aberration will be performed in the future.

Figure 2.15. Visualization of the Spherical Deviation at Different Center Deflections of the Small Membrane

2.6 Summary

This chapter presents a unique configuration of adaptive optics that combines the structural characteristics of insect compound eye and human camera eye. This optical system was implemented on a bi-layered microfluidic device, where an array of deformable membrane-enveloped fluidic lenses within the top microfluidic layer achieves a tunable focusing power from 0D to 275D to mimic human camera eye, while an underlying elastomeric membrane in the bottom microfluidic layer was reconfigurable into a surface with varied curvatures, allowing spherical distribution of the individual fluidic lenses in the top layer, similar to the arrangement in insect compound eye. The orientation of individual fluidic lens was changed from -52.5º to 52.5º to realize an overall AOV up to

120º with the focusing power of 30D. While the device described here did not present an optimum in terms of imaging quality, the IHHE design clearly opens up a new avenue for adaptive optical systems with both the vari-focal capability and the large viewing angle in a compact setting.

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Chapter 3: Binoculars on Singlet (BIOS): an Optofluidic Lens for Switchable 2D

and 3D Imaging

This chapter reports a 10 mm optofluidic system that elastically reconfigures from

3 mm binoculars to 10 mm singlet sharing the same optical channel by adjusting their surface profiles via hydrostatic pressure. The binoculars with a horizontal separation

(baseline) of 6.4 mm capture a stereo image pair with evident binocular disparity for three- dimensional depth perception. The singlet with a larger clear aperture and minimum F number of 2.3 enables two-dimensional image acquisition with better resolution (128 line pair/mm) and larger field of view. Focal length tuning of the singlet from 23.2 mm to 85.7 mm supplements the monocular depth cue from depth of defocus. With interchangeable and complementary 2D and 3D imaging capacities, the system finds applications in robotic vision, minimally invasive surgery and environment surveillance where compactness and imaging versatility are at a premium.

3.1 Introduction

The physical world around us is three-dimensional (3D) that contains numerous depth cues(Reichelt, Häussler, Fütterer, & Leister, 2010). A great asset to perceive and discriminate them for human is the binocular parallax, where the interpupillary separation

enables the projection of the same scene onto the left and right retinas with distinct perspectives(Orban, 2011). By a process called stereopsis our brain finds the matching points between the image pair and converts the retinal disparity into 3D sensation. A direct imitation of binocular vision is the stereoscopic system based on parallel-camera structure, where two separate visual inputs are utilized under the same photographic conditions(Billingsley & Connolly, 2006). The stereoscopic pair is often captured using two independent cameras arranged side-by-side(Moqqaddem, Ruichek, Touahni, & Sbihi,

2012), two static lenses connected to split channel optics(DiMaio, Hanuschik, & Kreaden,

2011; Ogawa, 2008; Zhang, 2013), dual iris diaphragm(Bae et al., 2012; Tabaee et al.,

2009), or biprism (Lee & Kweon, 2000)/mirrors(Pachidis & Lygouras, 2005) to switch the optical path. To date the stereoscopic technique is widely adopted in entertainment, military and investigative fields, whereas is less favored in medical spectrum, such as endoscope/laparoscope assisted diagnosis or surgery (Staub et al., 2009; Van Beurden,

IJsselsteijn, & Juola, 2012). The miniaturization of the overall size of stereoscope down to several millimeters is at a sacrifice of further size shrinkage of horizontally-separated optical elements. The limited light entry worsens the final image resolution and brightness

(Chan et al., 1997; Staub et al., 2009; Van Beurden et al., 2012). In addition, the scaling down of binocular lenses introduces more image blur at its periphery, leaving only its center of vision available to the observer with acceptable sharpness.

It is known that optofluidics offer good integration and reconfigurability where the deformation of elastomeric elements within microfluidics can modify the optical boundaries and yield light tunability (Song, Vasdekis, & Psaltis, 2012; Wei, Zeng, & Zhao,

2014; Zhao et al., 2013). Leveraging this technique, we report a reconfigurable optofluidic system whose structure can be swapped between a pair of 3 mm lenses and a 10 mm single lens within the same optical channel. The binoculars capture stereoscopic images in a conventional way, while the singlet acquires a two-dimensional (2D) image yet at better resolution and brightness. Meanwhile, we incorporate accommodation capability into the binoculars to assist proper focusing (focal length: 12.4 mm~86.9 mm), and into the singlet to compensate for binocular depth loss by using depth from focus/defocus given its large

F numbers (F/#, as low as F/2.3). The accommodation is carried out by the adaptive polymeric liquid lens (Beadie et al., 2008; Casutt, Bueeler, Blum, & Aschwanden, 2014;

Wei, Domicone, & Zhao, 2014; Yiu, Batchko, Robinson, & Szilagyi, 2012), whose deflection profile and thereby the optical power is adjusted by the hydrostatic pressure applied on the lens membrane. The vari-focal binoculars and the singlet thus work interchangeably and complementarily to address the downside of stereoscope miniaturization. Coupling the characteristics of accommodation and binocular vision in a compact single-camera setting, this miniature device expects applications in machine vision, stereoscopic microscopy, and 3D endoscopic surface imaging.

3.2 Principle and Design

The system consists of two elastic optofluidic components, and a fixed glass substrate sandwiched in between (Figure 3.1a). Within the bottom component, a microchannel connects a cylindrical compartment covered by an elastomeric membrane.

The membrane and the fluid underneath form a plano-convex lens (hereafter referred as

monocular lens) whose radius of curvature changes upon fluid addition or withdrawal for focus tuning. Two smaller membrane-enveloped lenses (here after referred as left/right binocular lens) in identical geometries are contained within the top component, with the optical center of each positioned at the same distance to the left/right of the optical axis of the monocular lens. This binoculars and monocular lens sharing the same optical path ensures device compactness. In 2D imaging mode, the modular lens change shape while the binoculars remain flattened. In 3D mode, the monocular returns to zero power, while the left and right binocular lenses become active to capture stereoscopic images simultaneously. The refractive index (RI) match between the fluid and all solid parts of optofluidic components cancels the interference between the two layers.

Figure 3.1. Working Principle of the Stacked Optofluidic Lenses in 2D and 3D Modes

The pinhole model of the optofluidic system that operates in tandem with an image sensor is illustrated in Figure 3.1b. In 2D layout, the optical axis of the monocular lens coincides with that of the image detector that acts as the field stop. The field of view (FOV) of it (FOVm) is expressed as:

FOVwqm  2arctan(/2) (3.1) where w is the width of the image sensor; q is the separation between the lens and the sensor. The classical Gaussian thin lens formula within FOVm relates an arbitrary object to its conjugate in the image space:

pq 1 uu1 oi ff   (3.2) hhoi pq 1 where uo and ui are the respective angles that the incident and exiting ray from the object make with the optical axis; ho and hi are the respective height of the object and image; f is the tunable effective focal length of the lens; p is the object distance. Thus p could be roughly estimated from known f and q at a close object distance and a large lens aperture since the increased depth of field as a result of the increase in object distance and the decrease in lens aperture aggravates the estimation from depth of defocus.

In 3D layout, the optical axes of binoculars are separated in the x direction by a baseline distance w/2. The image detector is divided into two halves, thus the individual

FOV of the binocular lens (FOVb) is reduced to:

FOVwqb  2arctan(/ 4 ) (3.3)

Stereo vision is generated within the overlapped FOV of the left and right lens (same value as FOVb) at a working distance greater than q. In the stereo region, consider two object points On (xn, zn) and Of (xf, zf) in a coordinate system whose origin stands midway between the optical centers of left lenslet (Ol) and right lenslet (Or). The projection of On appears on the left and right parts of the image detector as (xnl, -q) and (xnr, -q), and that of

Of as (xfl, -q) and (xfr, -q). By using the similar triangle in the shaded areas, zn and zf can be calculated as:

11        zn wqBn wq ( x nr x nl ) w / 2          z f 2211     Bf( x fr x fl ) w / 2     (3.4)

Thus the object distance and the relative distance between the two objects can be recovered by knowing the horizontal disparities (Bn) and/or Bf) of the corresponding image points. It is worth noting that the magnitude of horizontal disparity is inversely proportional to the object depth at given system parameters, and the maximum disparity equals to the width of the image detector.

3.3 Fabrication and Assembly

In this study, a 1’ (w = 11.26 mm) monochromatic complementary metal-oxide- semiconductor (CMOS) image sensor (CMOSIS, CMV4000-3E5 CMOS, PointGrey, Inc) was selected for image acquisition. The optofluidic components were fabricated by standard photolithography and softlithography (Figure 3.2). The process began with the fabrication of two small cylindrical posts (height: 200 m, diameter: 1.5 mm, center to

center distance: 3.2 mm) made of SU-8 2050 (Microchem, MA), and of a large cylindrical post (height: 500 m, diameter: 6 mm) made of SU-8 2100 (Microchem, MA) on separate silicon wafers. Each structure was connected to a microchannel (height: 100 m, width:

500 m). Then, polydimethylsiloxane (PDMS, Sylgard 184, Dow Corning) prepolymer

(weight ratio of base to curing agent=10:1) was cast onto the two molds, where polyester spacers were used to control the membrane thickness atop the small cylinder at 50 m, and that atop the big cylinder at 100 m. After curing at 65 ◦C on hotplate for 2 hours, the two substrates were plasma bonded on the opposite sides of a 75 × 25 × 1.2mm microscopic glass slide (RI=1.52). Optical fluid was prepared by mixing 99.0 wt% glycerol with deionized water at a weight ratio of 3:2, which resulted in a RI of 1.41 at 589 nm at room temperature. It was then instilled into the top and bottom PDMS substrates by syringe pump

(Pump 11 Elite, Harvard Apparatus). The index match between the fluid and PDMS could eliminate the interference of binoculars on the monocular lens when the latter was used for imaging, as the binoculars were along the optical path of the monocular lens. The assembled device is shown in Figure 3.3a.

Figure 3.2. Schematics of Fabrication Process

In 2D mode, all empty spaces are filled with index matching optical fluid (Figure

3.3b). To prevent stray light coming to the sensor in 3D mode, black ink is flushed into the iris layer, exposing only the binoculars (Figure 3.3c). During experiment, a three-way luer fitting was used to divert the extra flow of optical liquid from one syringe pump to the top or the bottom optofluidic component so as to deform the lens membrane(s). Another three- way valve was placed at the downstream of the first one to control the left and right binocular lens independently or simultaneously. The hydrostatic pressure on the membrane was monitored by a pressure sensor (BSP004L, Balluff) installed between the first valve and the syringe pump.

Figure 3.3. The Assembled Stacked Optofluidic Lenses before Fluid Filling (a), after Fluid Filling in 2D Mode (b), and after Black Ink Filling in 3D Mode (c).

3.4 Results and Discussion

The back focal lengths (BFL) of the binoculars and the monocular lens at varied hydrostatic pressures were measured using a custom-built optical setup that consisted of a green laser diode, a spatial field, a field lens, a beam expander, a variable iris to generate 3 mm or 10 mm collimated beam, and the CMOS sensor. The BFL was approximated as the distance between the lens and the CMOS sensor that displayed the minimum spot size. For the monocular lens, its BFL ranged from 23.2 mm to 85.7 mm at the pressure input from

10 mbar to 170 mbar, which corresponded to the F/# change from F/2.3 to F/8.6 (Figure

3.4a&c).

Figure 3.4. Back Focal Length Measurement of the Big Elastomer-liquid Lens and Small Elastomer-liquid Lenses

The BFL and the F/# were rather sensitive to the hydrostatic pressure change below

90 mbar. Thus BFL within 23.2 mm to 29.2 mm and F/# within F/2.3 to F/2.9 were used for image acquisition afterwards. The BFLs of left and right binocular lenses were measured from 12.4 mm to 79.7 mm (corresponding F/# from F/4.1 to F/26.6) and 12.4 mm to 86.9 mm (corresponding F/# from F/4.1 to F/29), respectively, at the pressure from

5 mbar to 30 mbar (Figure 3.4b&c). Their difference was nominal. Likewise, the BFL as well the F/# was sensitive to pressure change under 15 mbar. BFL within 12 to 24 mm and

F/# within F/4.0 to F/8.0 were used. Overall, the monocular lens had a larger focal range and smaller F/# than the binoculars, useful for estimating depth by out-of-focus image blur; the binoculars had a larger F/# that was useful for stereo image capture at an extended depth of field.

The focus tunability of each lens was further demonstrated by individually imaging two separate dices using the CMOS sensor placed 27.18 mm from the big lens. In the first test, the binoculars stayed flat and the big lens was tuned separately. One dice was placed at 122 mm object distance, the other at 222 mm. At the big lens’ BFL of 23 mm, the distant dice was in focus. (Figure 3.5a), while at 25 mm, the near dice was in focus (Figure 3.5b).

Second test was subsequently performed under the same experimental conditions, except that the big lens stayed flat while the one of the binoculars was actuated. The small lens was tuned at the BFL of 28 mm to bring the distant dice in focus, and at 24 mm to bring the near one in focus. The placement of the binoculars within the optical path of the monocular lens did not deteriorate the imaging performance of the big lens. The resolutions of both the big lens and small lenses were evaluated at BFL of 25 mm using a

USAF 1951 resolution test target. With proper adjustment of object distance, the region of

Group 4&5 were projected to the center of frame. As shown in Figure 3.5c&d, the monocular lens could resolve element 1 in group 7 (128 lp/mm) as compared to the binoculars’ element 1 in group 5 (32 lp/mm). In fact, the image captured by the big lens was sharper and less vignetted than the binoculars due to its larger aperture and less aberration.

Figure 3.5. Comparison of Adaptive Focusing and Image Resolution between the Big Elastomer-liquid Lens and the Small Elastomer-liquid Lenses

As shown in Equation 3.4, the disparity is critically object distant dependent. To demonstrate the relationship between horizontal disparity and object’s working distance, one dice was placed along the center axis of binoculars for imaging on the CMOS censor

which was still placed 27.18mm away from the monocular lens. The monocular lens was tuned flat and the binoculars were tuned respectively and simultaneously to capture images at the dice working distance linearly from 60mm to 200mm with intervals of 10mm, among which at 60, 100, 140 and 180mm were shown in Figure 3.6a. The horizontal disparities of each dice image were measured in in ImageJ (V1.48, NIH). The fitting trendline of the normalized disparity varying with the working distance at the order of ten meets expectation as compared to the theoretical curve which derives from the Equation 3.4

(Figure 3.6b). Moreover, as observed, the experimental disparity deviates more from the theoretical after working distance is larger than 140mm, which indicates the disparity becomes more sensitive thus requires more accurate measurement at the precision of 10

m corresponding to the working distant error of 1mm.

Figure 3.6. Distance-dependent Binocular Disparity

Depth estimation by accommodation in 2D mode and stereo imaging in 3D mode were demonstrated in Figure 3.7. We use pigskin with scar and nipple, plastic branches and two separate dices served as three different groups of object and try to figure out the depth information of some obvious features. The images were captured in both 2D and 3D mode. In 2D mode, as before, the monocular lens was tuned to capture an intermediately clear image with the CMOS censor placed 27.18mm behind, as shown in Figure 3.7a. In

3D mode, the objects stayed the same and images by the binoculars were projected onto the left and right parts of the CMOS sensors, respectively (Figure 3.7b). Figure 3.7c shows the flipped over red-cyan anaglyph edited by 3D software (anaglyph maker 3D).

Figure 3.7. Image Capture in 2D Mode (a), 3D Mode (b), and the Calibrated Anaglyph (c)

The BFLs of both lenses were adjusted from 22.5mm to 24.5mm. The F/# at about

F/7.5 ~ F/8.2 ensured the objects to fall within the depth of field. The experimental, curvefitting, theoretical depth of the features circled by yellow and green in each group of objects and in individual 2d mode are compared in Figure 3.8. The curvefitting depth was calculated via the horizontal disparity measured in ImageJ (V1.48, NIH) and the previous fitting trendline, which was similarly close to the theoretical and experimental depth value.

It agreed with the previous analysis that the disparity decreased with the increase in object distance. The small deviation was due to either the disparity error or the experimental measuring error. However, it is evident that the depth in 2d mode deviates the most from that of the others. The error was mainly caused by the depth of field within which the difference in the sharpness of the object on the image sensor was nominal, and could not be distinguished by naked eye during focus tuning.

3.5 Summary

In summary, an adaptive optofluidic system with reconfigurable geometries for switchable 2D/3D imaging was reported in this chapter. In 3D mode, the fluidic binoculars horizontally separated by 6.4 mm provided 69D diopter change yet with a large F/# up to

F/29, capable of generating the binocular disparity for relative depth estimation. In 2D mode, the monocular fluidic lens with a large aperture captured image with better resolution. Its 63D optical power change and F/# down to F/2.3 supplements the accommodation cue. The compact design and versatility provide a new avenue of adaptive optofluidics for various imaging applications.

Figure 3.8. Comparison of Depth Estimation between Theoretical Analysis and Experiment Result in 2D and 3D Modes for (a) Nipple and Scar Sample, (b) 3D-printed Branches Sample, and (c) Dices Sample.

3.6 References

Bae, S. Y., Korniski, R. J., Choi, J. M., Shearn, M., Bahrami, P., Manohara, H., & Shahinian, H. K. (2012). Development of a miniature single lens dual-aperture stereo imaging system towards stereo endoscopic imaging application. Optical Engineering, 51(10), 103202-103201-103202-103206.

Beadie, G., Sandrock, M., Wiggins, M., Lepkowicz, R., Shirk, J., Ponting, M., . . . Baer, E. (2008). Tunable polymer lens. Optics express, 16(16), 11847-11857.

Billingsley, J., & Connolly, C. (2006). Stereoscopic imaging. Sensor Review, 26(4), 266- 271. doi: doi:10.1108/02602280610691962

Casutt, S., Bueeler, M., Blum, M., & Aschwanden, M. (2014). Fast and precise continuous focusing with focus tunable lenses. Paper presented at the SPIE OPTO.

Chan, A., Chung, S., Yim, A., Lau, J., Ng, E., & Li, A. (1997). Comparison of two- dimensional vs three-dimensional camera systems in laparoscopic surgery. Surgical Endoscopy, 11(5), 438-440.

DiMaio, S., Hanuschik, M., & Kreaden, U. (2011). The da Vinci surgical system Surgical Robotics (pp. 199-217): Springer.

Lee, D., & Kweon, I. (2000). A novel stereo camera system by a biprism. Robotics and Automation, IEEE Transactions on, 16(5), 528-541.

Moqqaddem, S., Ruichek, Y., Touahni, R., & Sbihi, A. (2012). Objects Detection and Tracking Using Points Cloud Reconstructed from Linear Stereo Vision. CURRENT ADVANCEMENTS IN STEREO VISION, 161.

Ogawa, K. (2008). Endoscope apparatus, method of operating the endoscope apparatus, and program to be executed to implement the method: Google Patents.

Orban, G. A. (2011). The extraction of 3D shape in the visual system of human and nonhuman primates. Annual Review of Neuroscience, 34, 361-388.

Pachidis, T. P., & Lygouras, J. N. (2005). Pseudo-stereo vision system: A detailed Study. Journal of Intelligent and Robotic Systems, 42(2), 135-167.

Reichelt, S., Häussler, R., Fütterer, G., & Leister, N. (2010). Depth cues in human visual perception and their realization in 3D displays. Paper presented at the SPIE Defense, Security, and Sensing.

Song, W., Vasdekis, A. E., & Psaltis, D. (2012). Elastomer based tunable optofluidic devices. Lab Chip, 12(19), 3590-3597.

Staub, C., Mayer, H., Osa, T., Braun, E. U., Knoll, A., & Bauernschmitt, R. (2009). Setup of a Scientific Research Platform for Robot-Assisted Minimally Invasive Heart Surgery Scenarios. In O. Dössel & W. Schlegel (Eds.), World Congress on Medical Physics and Biomedical Engineering, September 7 - 12, 2009, Munich, Germany (Vol. 25/6, pp. 259-262): Springer Berlin Heidelberg.

Tabaee, A., Anand, V. K., Fraser, J. F., Brown, S. M., Singh, A., & Schwartz, T. H. (2009). Three‐Dimensional Endoscopic Pituitary Surgery. Neurosurgery, 64(5), ons288- ons295.

Van Beurden, M., IJsselsteijn, W., & Juola, J. (2012). Effectiveness of stereoscopic displays in medicine: a review. 3D Research, 3(1), 1-13.

Wei, K., Domicone, N. W., & Zhao, Y. (2014). Electroactive liquid lens driven by an annular membrane. Optics letters, 39(5), 1318-1321.

Yiu, J.-Y., Batchko, R., Robinson, S., & Szilagyi, A. (2012). A fluidic lens with reduced optical aberration. Paper presented at the IS&T/SPIE Electronic Imaging.

Zhang, S. (2013). Handbook of 3D machine vision: Optical metrology and imaging: CRC Press.

Zhao, Y., Stratton, Z. S., Guo, F., Lapsley, M. I., Chan, C. Y., Lin, S.-C. S., & Huang, T. J. (2013). Optofluidic imaging: now and beyond. Lab on a Chip, 13(1), 17-24.

Chapter 4: An Electroactive Liquid Lens Driven by an Annular Membrane

Unlike traditional focalization that recruits multiple moving lens elements to adjust focus, liquid lenses deliver adaptive focusing by simply tuning the surface profile of liquid or the elastomer that encloses liquid. Its simple and compact configuration, low cost and actuation efficiency promise wide industrial, medical and consumer applications.

Dielectric elastomers, one type of commercially available soft active material, have been a good fit for creating adaptive optics. In this chapter, we present an adaptive, membrane- sealed liquid lens hydrostatically coupled to a concentric annular dielectric elastomer actuator. Electric actuation deforms the annular dielectric elastomer, which induces fluid transmission between the lens part and the actuation part for lens actuation. The maximum measured focal range was from 25.4 to 105.2 mm within 1.0 kV, which significantly outperforms the existing dielectric elastomer actuated liquid lenses and eliminates the need for pre-straining. The lens also enables varied focal ranges by simply adjusting its initial surface sagitta, providing flexibility for practical imaging applications.

4.1 Introduction

Fast and accurate focusing power tuning is essential for a camera-lens based imaging apparatus to produce a sharp image of the subject and to capture subjects

positioned at different distances. Conventional mechanical focusing employs magnetic actuation by voice coil or ultrasonic vibration of piezoelectric stator to induce linear motion of multiple solid lenses along the optical axis (Laikin, 2007). The use of compound lens configuration and bulky mechatronics to change focus increases the overall size of the optical system, which makes it difficult to be integrated within ultraportable devices where the space is constrained (Ren & Wu, 2012). Recently, varifocal lenses that are made of fluidic materials have achieved extraordinary research interests (Graham-Rowe, 2006).

The focal length of a liquid lens changes once the fluidic element alters its radius of curvature at liquid/liquid, liquid/solid, or liquid/vapor interfaces (Nguyen, 2010). Adaptive focusing by a single lens without any moving components is thus possible. For a bare liquid or hydrogel droplet, the curvature at the interface can be altered by electrowetting (Berge

& Peseux, 2000), dielectrophoresis (Ren, Xianyu, Xu, & Wu, 2008), ferrofluidics (Xiao &

Hardt, 2010), reduction-oxidation reactions (López, Lee, & Hirsa, 2005), acoustic oscillation (López & Hirsa, 2008) or using stimuli-response hydrogels (Dong, Agarwal,

Beebe, & Jiang, 2006). Although liquid/hydrogel droplets based focusing components are simple in configuration, droplets exposing to vapor are vulnerable to evaporation and external disturbances. To address this, the liquid droplet can be encapsulated within an elastomeric envelope, where focus can be changed by deforming the envelope by mechanical (Wei & Zhao, 2013), magnetic (Lee & Lee, 2007) or electric means (Choi, Lee,

Kwon, Lee, & Kim, 2011).

Among various actuation mechanisms, the use of dielectric elastomer (DE) is a popular approach due to its simple configuration, operation efficiency, relatively fast

response and low cost (Brochu & Pei, 2010). For example, an intraocular lens-mimicking structure was demonstrated by radially deforming the circular DE actuator surrounding an elastomer-encapsulated liquid lens by electrical actuation, thereby changing the focal length (Carpi, Frediani, Turco, & De Rossi, 2011). A liquid lens array connected by microfluidic channels and driven by a single circular DE actuator was also developed

(Niklaus, Rosset, & Shea, 2010). Most recently, liquid lenses with transparent DE actuators have been reported, which allows the fabrication of DE actuators on the lens body for better miniaturization (Shian, Diebold, & Clarke, 2013; Son et al., 2012). Despite these advances, the elastomer-encapsulated liquid lenses driven by DE actuators are usually limited by the narrow tunable focal range and high voltage input. A DC voltage of a few kVs is required to generate a measurable focal length change (Carpi et al., 2011; Shian et al., 2013). In addition, DE often needs to be homogeneously pre-stained to a large extent to obtain a small membrane thickness, which inevitably leads to a high level of mechanical instability.

This causes surface wrinkling and non-concentric bulging of DE at high voltages (Shian et al., 2013), and degrades the image quality when the DE actuator is embedded along the optical path of the lens.

In this study, we developed a 5 mm circular liquid lens driven by a concentric annular DE actuator without pre-straining. The results showed that the maximum focal length change from 25.4 to 105.2 mm (corresponding to a 300% change in focal length) can be implemented with a voltage below 1.0 kV. By changing the initial lens sagitta (sag), the focusing power can be targeted at different ranges. Due to the elimination of pre- straining of the DE actuator, no surface wrinkling was observed at the maximal operational

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voltage. Such liquid lens with better performance and enhanced reliability than previous reports promises a potential solution of adaptive focusing in various portable systems.

4.2 Lens Design

This device comprises two supporting frames (top and bottom) and a thin DE membrane sandwiched in between (Figure 4.1a). The bottom frame consists of a circular reservoir and a concentric annular reservoir, which are connected by two fluidic channels.

The top and bottom surfaces of the DE membrane above the annular reservoir (refers to actuation membrane hereafter) are covered by compliant electrodes, while the DE membrane above the circular reservoir (refers to lens membrane hereafter) is uncoated and remains transparent. Both reservoirs are filled with an optical medium. The hydrostatic pressure in the reservoirs is adjusted until the lens membrane achieves certain sag. The liquid lens is thus composed by the lens membrane and the fluid underneath, whose optical power is determined by the sag of the lens membrane and the refractive index (RI) of the optical medium. Once a DC voltage is applied across electrodes, a lateral expansion of the

DE is expected (Brochu & Pei, 2010). Given that the actuation membrane is constrained by the frames at edges and has an initial upward deflection, the lateral expansion of the actuation membrane increases the upward deflection. Consequently, the fluid is drained from the lens reservoir towards the actuation reservoir, and in turn deflates the lens membrane. The sag of the lens (s), and therefore the focal length (f) thus change as a function of the actuation voltage bias (Figure 4.1b).

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Since the deflection of lens membrane is relatively smaller comparing to its aperture, its surface profile can be approximated as a spherical cap. The focal length of the liquid lens in air can be expressed as a function of the sag:

r 2 1 f  (4.1) 21ns  where n is the RI and r is the half aperture of the lens.

Figure 4.1. Illustration of the Electroactive Fluidic Lens Driven by a Concentric Annular Dielectric Actuator. (a) Perspective view of the system. (b) Diagram of the lens in action. The red dotted line indicates the optical axis. Δs is the change in lens sagitta. Δf is the change in focal length.

Because the lens reservoir deflates upon actuation the initial sag of the liquid lens contributes to its shortest focal length. The range of the focal length is determined by the extent to which the lens sag decreases. According to equation (1), for the same sag change 102

(s), lenses with smaller initial sags have larger focal ranges than those with larger initial sags. Assuming that the total fluid volume is conserved and the fluid is incompressible, volume decrease in the circular reservoir (Vc) can be calculated as:

2 V c r s  / 2 , (4.2)

According to equation (1)&(2), the change of lens sag and therefore the change of focal length can be represented by the volume of fluid that is transported between two reservoirs.

The volume increase in the annular reservoir upon electrical actuation of the DE can be approximated as:

222  rrOI  Vh U PhP  ,0,   (4.3) a 4  where rO and rI are the outer and inner radii of the annulus, and h(0, P) and h(U, P) are the maximal deflections of the DE before and after actuation, respectively.

The analytical model of a thin-walled cylindrical pressure vessel (Collins, Busby,

& Staab, 2009) was modified to approximate the annular DE membrane. The relationship between the maximal deflection (h) of the membrane, the cross-membrane pressure (P), and the Maxwell’s stress induced by the applied voltage (U) can be expressed as:

28th Eh22 U P 22 00 r 2   r r / 4  h2  3 r  r   1  t OIOI (4.4) r r t 2 t  OI0  2 2 rOI r /4 h where E and  are the Young’s modulus and Poisson’s ratio, respectively; 0 is the residual stress during fabrication; t0 and t are thicknesses of the membrane before and after pressure application; is the permittivity in the vacuum, and r the relative permittivity of the DE.

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Combining equations (3)&(4), the volume change of the annular reservoir upon electrical actuation can be found.

Figure 4.2 compares the volume change of the annular and circular DE actuators upon electrical actuation from 0 to 1.0 kV at three representative initial maximal membrane deflections of 0.15, 0.30, and 0.45 mm. For comparison, the two membranes had the same material properties, the same thickness, and the same area of occupancy. Results suggest that the voltage-induced deflection of the annular DE actuator results in a larger volume change than that of the circular one at each initial membrane deflection; and the difference increases with the voltage. In addition, comparing to a side-by-side layout of the lens membrane and the circular DE actuator, the annular actuator concentric with the lens membrane minimizes the overall occupancy area.

Figure 4.2. Comparison of the Volume Changes of Circular and Annular DE Actuators at Different Initial Maximal Membrane Deflections under Electrical Activation.

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4.3 Lens Fabrication

Figure 4.3 shows the fabrication process. The annular DE actuator and lens were on the same membrane, which was made of silicon rubber (TC-5005 A/B, BJB

Enterprises). The membrane was prepared by mixing the resin (‘A’ component) with the curing agent (‘B’ component) at a 10:1 weight ratio, and spin-coated at 2000 rpm/s on a glass wafer. After curing at room temperature the membrane was 75 m thick. The top

(25×25×1.5mm) and bottom frames (25×25×5mm) were fabricated by a 3D printer and the bottom frame was bonded to the membrane on the wafer. To prepare compliant electrodes, carbon grease (Carbon conductive grease 846, MG Chemicals) was dispensed in isopropanol at a 1:3 weight ratio. The solution was first deposited onto the liquid side of annular region (rO = 9 mm; rI =4 mm) of the membrane defined by the frames. The bottom frame with the membrane was then peeled off, followed by covering with the top frame and electrode deposition on the air side of the annulus. Afterwards, copper foil was introduced to connect to the carbon electrode. The electrode on the top surface of the actuation membrane was connected to a high voltage and that on the bottom was grounded.

The bottom frame was sealed by a 1.2 mm thick microscope slide.

The reservoirs under the lens membrane and the actuation membrane were filled with ≥ 99wt% glycerol. It has a RI of 1.47, slightly larger than the DE (RI =1.4). Its immiscibility with carbon electrodes and dielectric properties (r =42.5) ensure electrical safety. After glycerol replaced all the air in reservoirs, the fluid outlet port was closed and an extra volume of fluid was supplied through the inlet to give the lens membrane an initial sag. During fluid addition, the lens sag was examined using an upright microscope by

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focusing on the top surface of the lens membrane center. Afterwards, both inlets and outlets were sealed so that the encapsulated fluid can only redistribute between the circular reservoir and the annular reservoir. In this study an extra volume of 96l, 121l, or 150l of glycerol was added into the device, which resulted in initial lens sag of about 273m,

412m or 624m, respectively.

Figure 4.3. Fabrication and Assembly Processes. (a)~(c) The process flow, (d)&(e) The top and bottom frames printed by a 3D printer. (f) The assembled electroactive fluidic lens. The scale bar in (d) ~ (f) denotes 5 mm

4.4 Results and Discussion

The focal length of the lens in one electrical actuation cycle- forward actuation

(voltage increases) and backward actuation (voltage decreases) was examined using a custom-built optical setup that consisted of a collimated laser diode, a spatial filter, a field lens, and a detection screen. The focal length was approximated as the distance between the lens and the screen that yielded the minimum spot size. As expected, there was no

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significant difference before the focal length at the same voltage during the forward actuation and the backward actuation, demonstrating good reversibility of focal length control (Table 4.1).

Table 4.1. Focal Length Evolution during Forward Actuation and Backward Actuation

Forward actuation (voltage increases) Backward actuation (voltage decreases) U (kV) 0 0.25 0.50 0.75 1 0.75 0.50 0.25 0 s=625 12.5±1 13.6±1 15.5±1 17.7±1 20.8±1. 16.8±1 15.0±1 14.7±1 13.3±1 m .4 .5 .5 .6 8 .8 .6 .4 .2 f(m s=412 18.5±1 20.6±1 23.4±1 28.1±1 35.2±2. 27.2±2 22.2±1 18.9±1 19.0±1 m) m .5 .7 .6 .8 0 .0 .5 .5 .6 s=273 25.4±1 28.7±2 35.2±2 52.5±3 105.2±4 49.9±2 34.4±1 29.5±1 26.2±1 m .8 .2 .4 .2 .6 .7 .9 .7 .5

Results also verified that the initial lens sag determined the maximum focusing power and the focal range of the liquid lens. Specifically, given the same maximal actuation voltage, the lens with the lowest initial sag (about 273m) had the longest starting focal length (about 25.4mm) yet exhibited the largest focal range (25.4 ~ 105.2 mm in forward actuation). The lens with the highest initial sag (about 625m), on the contrary, had the shortest starting focal length (about 12.5mm) at a sacrifice of the shortest focal range (12.5

~ 20.8 mm in forward actuation). At 1.0kV, the focal length changed by 90% and 66% with the initial lens sag of 412m and 625m respectively; the number increased to 300% with the initial sag of 273m (Figure 4.4). At a given voltage, the focal length change and the

F number (F#) of the lens with a larger initial lens sag is less sensitive to the actuation voltage. This may find uses in microscopy where fine focal adjustment and small F# are needed to resolve objects that are separated by small distances. On the contrary, the focal

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length and F# change at smaller initial lens sag is more sensitive to the applied voltage.

Such conditions can achieve an extended focal range with an increased depth of field (large

F#), which is often needed in telephotography and laparoscopy. The response time of the lens increased with the actuation voltage (Figure 4.5a). At the same voltage change, the backward actuation took longer than forward actuation. The lens resolution was also examined: a representative lens with the initial sag of 273m at the focal length of 25mm was 28.5 line pairs per mm (Figure 4.5b).

Figure 4.4. Comparison of (a) Focal Length and (b) F/# Changes with Different Initial Lens Sags

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Figure 4.5. Response Time for a Lens with the Initial Sag of 273 m (a) and its Resolving Power at f = 25 mm using a 1951 USAF Target (b)

The ability of the lens to distinguish subjects positioned at different depths was demonstrated. Two transparency films printed with letters of ‘OH’ and ‘IO’ were used as subjects and positioned at the distances of 101mm and 90.5mm from the lens, respectively.

The lens was then actuated to focus on the letters. The images were acquired by a CCD camera with a fixed-focus lens (f = 25.4mm, Numerical Aperture (N.A.) = 0.10) (Figure

4.6a). The initial sag of the lens was first adjusted (about 325 m) to bring the ‘OH’ in sharp focus while ‘IO’ appeared blurred (Figure 4.6b). When the voltage increased to about 0.25kV, ‘OH’ started to lose focus, while ‘IO’ appeared less blurry (Figure 4.6c).

When the voltage reached 0.5 kV, ‘IO’ becomes acceptably focused (Figure 4.6d). On the contrary, ‘OH’ was significantly blurred. Further voltage increase blurred all the letters, while ‘OH’ was blurred at a greater extent than ‘IO’ (Figure 4.6e). The results showed that the lens successfully distinguished the letters placed at two different focal planes by

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changing the actuation voltage. During operation, no surface wrinkling of the actuation membrane or significant optical aberration was observed.

Figure 4.6. Demonstration of focus changing. (a) Illustration of the optical setup, and (b)~(e) Optical images showing the focal length change at the actuation voltages of 0kV, 0.25kV, 0.5kV and 1.0kV, respectively

4.5 Summary

In summary, an adaptive liquid lens driven by a concentric annular DE actuator was reported. Analytical and experimental results showed that the annular DE design allows a wider focal range at a relatively lower actuation voltage (up to 1.0 kV) and improved 110

mechanical stability comparing to the existing DE-driven liquid lenses. The focal length change is also greatly improved (more than 300% with the initial lens sag of 273 m). The focal range and sensitivity can also be varied by tuning the initial sag of the lens, providing flexibility for various imaging applications.

4.6 References

Berge, B., & Peseux, J. (2000). Variable focal lens controlled by an external voltage: An application of electrowetting. The European Physical Journal E, 3(2), 159-163. doi: 10.1007/s101890070029

Brochu, P., & Pei, Q. (2010). Advances in dielectric elastomers for actuators and artificial muscles. Macromolecular Rapid Communications, 31(1), 10-36.

Carpi, F., Frediani, G., Turco, S., & De Rossi, D. (2011). Bioinspired Tunable Lens with Muscle‐Like Electroactive Elastomers. Advanced Functional Materials, 21(21), 4152-4158.

Choi, S. T., Lee, J. Y., Kwon, J. O., Lee, S., & Kim, W. (2011). Varifocal liquid-filled microlens operated by an electroactive polymer actuator. Optics letters, 36(10), 1920-1922.

Collins, J. A., Busby, H. R., & Staab, G. H. (2009). Mechanical design of machine elements and machines: John Wiley & Sons.

Dong, L., Agarwal, A. K., Beebe, D. J., & Jiang, H. (2006). Adaptive liquid microlenses activated by stimuli-responsive hydrogels. Nature, 442(7102), 551-554.

Graham-Rowe, D. (2006). Liquid lenses make a splash. Nature-Photonics, 2-4.

Laikin, M. (2007). Lens design (4th ed.). Boca Raton, FL: CRC Press.

Lee, S. W., & Lee, S. S. (2007). Focal tunable liquid lens integrated with an electromagnetic actuator. Applied Physics Letters, 90(12), 121129.

López, C. A., & Hirsa, A. H. (2008). Fast focusing using a pinned-contact oscillating liquid lens. Nature Photonics, 2(10), 610-613.

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López, C. A., Lee, C.-C., & Hirsa, A. H. (2005). Electrochemically activated adaptive liquid lens. Applied Physics Letters, 87(13), 134102-134102-134103.

Nguyen, N.-T. (2010). Micro-optofluidic Lenses: A review. Biomicrofluidics, 4, 031501.

Niklaus, M., Rosset, S., & Shea, H. (2010). Array of lenses with individually tunable focal- length based on transparent ion-implanted EAPs. SPIE Smart Structures and Materials, 76422K-76422K-76412.

Ren, H., & Wu, S.-T. (2012). Introduction to adaptive lenses. Hoboken, N.J.: Wiley.

Ren, H., Xianyu, H., Xu, S., & Wu, S.-T. (2008). Adaptive dielectric liquid lens. Optics Express, 16(19), 14954-14960.

Shian, S., Diebold, R. M., & Clarke, D. R. (2013). Tunable lenses using transparent dielectric elastomer actuators. Optics Express, 21(7), 8669-8676.

Wei, K., & Zhao, Y. (2013). A three-dimensional deformable liquid lens array for directional and wide angle laparoscopic imaging. IEEE, Micro Electro Mechanical Systems (MEMS), 133-136.

Xiao, W., & Hardt, S. (2010). An adaptive liquid microlens driven by a ferrofluidic transducer. Journal of Micromechanics and Microengineering, 20(5), 055032.

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Chapter 5: A Focus-Tunable Liquid Lens Encapsulated by a Membrane with

Aspherical Cross-section for Field Curvature Reduction at High Diopters

Elastomer-liquid lens offers a simple solution to achieve tunable optical powers.

This approach, however, suffers from substantial field curvature and thus deteriorated off- axis resolution at high diopters given the undesirable lens profiles at large membrane deformations. In this chapter, a plano-convex elastomer-liquid lens is developed where the liquid is encapsulated by an elastomer membrane with an aspherical cross-section (refers to aspherical membrane). The aspherical membrane is formed by replication from the deflection profile of another liquid lens encapsulated by a planar membrane. Such configuration allows for the lens profiles at high diopters analogous to spherical shapes by alleviating the edge-clamping effects. Resolution tests of a 6mm lens with optimized asphericity exhibit improved resolutions in both center and peripheral regions at 40 and

100 diopters than the lens with a planar membrane. It is the first report showing that aspherical membranes can reduce field curvature of elastomer-liquid lenses at high diopters, thus providing a new route of optimizing the imaging performance of adaptive liquid lenses for various applications.

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5.1 Introduction

Focus-tunable liquid lenses have excited widespread attention courtesy of its additional degree of freedom to vary diopters (dpts) without sophisticated motorized cams, which often require precise and synchronous displacement of several lens elements/groups along an extended trajectory(Chiu et al., 2012; Graham-Rowe, 2006; Nguyen, 2010).

Given its compact size, low cost, and fast and accurate focusing capability in a dynamic range, liquid lens has inspired next-generation miniaturized auto-focus and zoom lens design(Blum, Büeler, Grätzel, & Aschwanden, 2011; Hao, Cheng, & Du, 2013; Miks &

Novak, 2010; Savidis, Peyman, Peyghambarian, & Schwiegerling, 2013), and offered a great potential in laser projection and processing(Blum, Büeler, Grätzel, Giger, &

Aschwanden, 2012; Casutt, Bueeler, Blum, & Aschwanden, 2014), consumer and industrial illumination(Blum et al., 2011; Lu et al., 2011), machine vision(Amin & Riza,

2014; Goren, 2012; Huang, Chen, Cho, & Javidi, 2013), ophthalmology(Marks, Mathine,

Peyman, Schwiegerling, & Peyghambarian, 2009; Marks, Mathine, Peyman,

Schwiegerling, & Peyghambarian, 2010; Riza, Amin, & Riza, 2014), microscopy(Fahrbach, Voigt, Schmid, Helmchen, & Huisken, 2013; Grewe, Voigt, van’t

Hoff, & Helmchen, 2011; Jabbour et al., 2014), etc.

The mainstream approaches to demonstrate focus-tunable liquid lenses are electrowetting(Shamai, Andelman, Berge, & Hayes, 2008) and shape-changing polymers(Ren & Wu, 2012). Electrowetting lens consists of two liquids of similar densities yet different refractive indexes (RIs) sandwiched between two glass slides. The curvature of the liquid-liquid interface, and thus the optical power can be manipulated by external

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voltage. Due to the small capillary force along the meniscus, making lens with aperture (A) exceeding 3 mm is challenging. The basic optical layout of the elastomer-liquid lens comprises a fluid cavity with one side being a thin elastomer membrane and the other being a transparent window. Pressure changes at different magnitudes in the cavity cause the membrane to deflect into varied heights, thus forming a vari-focal plano-convex lens. Such configuration is scalable in aperture, and can be readily integrated with a wide range of actuation mechanisms, such as mechanical motor(Ren, Fox, Anderson, Wu, & Wu, 2006), head load(Zhang, Aljasem, Zappe, & Seifert, 2011; Zhang, Zappe, & Seifert, 2014), electromagnetic coil(Lee & Lee, 2007), piezoelectric actuator(Yiu, Batchko, Robinson, &

Szilagyi, 2012), and dielectric elastomer(Maffli, Rosset, Ghilardi, Carpi, & Shea, 2015;

Wei, Domicone, & Zhao, 2014).

However, most elastomer-liquid lenses developed using this layout have fairly small optical powers, where the center deflection (h) of the lens membrane is much smaller than its aperture(Nguyen, 2010). Although this is a good strategy to avoid aberrations, e.g., field curvature, that associate with large membrane deflection (h comparable to A)(Wei,

Zeng, & Zhao, 2014) add ref, the lenses find limited use in the applications that require large diopters, shallow depths of field, or short optical track lengths. Studies on membrane mechanics, particularly for the membranes made of polydimethylsiloxane (PDMS)–the most widely used elastomer material, reveal that the surface profile of an edge-clamping circular membrane at deflection resembles a paraboloid(Miks, Novak, & Novak, 2013; Ren et al., 2006). Spherical assumption can be applied to the membrane when h << A (Ren et al., 2006). Due to the edge-clamping effect, some prototypes and commercial products, for

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example Optotune EL-10-30, consider only 80% of the lens profile as spherical, and use up to 80% of the lens diameter as the clear aperture at certain back focal lengths (BFL)(Yu,

Zhou, Leung, & Chau, 2010). At large deflections, the boundary constrictions aggravate as evidenced by a significant deviation of the surface profile from a spherical shape, where the change of curvature near the edge of the membrane is restricted(Choi, Son, Seo, Park,

& Lee, 2014). Although membrane pretension can alleviate the boundary effect at low deflections, it still persists at large deflections(Yang, Kobrin, Seabury, Narayanaswamy, &

Christian, 2008), leaving alone the assembling difficulty caused by the pretension. The undesirable optical profile not only degrades the lens’s image quality(Choi et al., 2014;

Wei, Zeng, et al., 2014; Zhang et al., 2014), but also reduces the available clear aperture(Choi et al., 2014), which worsens if the lens has an original small diameter.

An alternative solution is to use an elastomer membrane with spherical or conical profiles(Feng & Chou, 2009; Shaw & Sun, 2007), rather than a thin membrane with constant thickness (hereafter referred as CTLL, constant thickness liquid lens). Optical simulation shows that these profiles may help to reduce field curvature and enhance peripheral resolution. Such claim, unfortunately, remains vague without experimental validation. This is due to the difficulty in fabricating and controlling a spherical/conical elastomeric membrane with desired thickness profile(Shaw & Sun, 2007). In this study, a circular membrane with aspherical cross-section was developed, where the membrane thickness of the lens (hereafter referred as VTLL, varied thickness liquid lens) varies from edge to center following an aspherical geometry. The membrane is replicated from the lens profile of a CTLL at given center deflection. This highly controllable process allows easy

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fabrication of elastomer membranes with designed geometries. Optical measurements using the fabricated VTLL show that by alleviating the boundary effects at small and large membrane deflections, VTLL exhibits improved center and peripheral resolutions than

CTLL at high powers.

5.2 Materials and Methods

5.2.1 Lens Design

Figure 5.1 illustrates the cross-section of a 6mm VTLL. Along the optical axis, it consists of a cover glass (thickness: 1 mm) seated on the retention lip of the top mounting cell, an air gap (thickness: 2 mm), an aspherical membrane sandwiched between the top and bottom mounting cells, a liquid cavity (thickness: 4mm), and another cover glass

(thickness: 1 mm) held in place by the bottom mounting cell. The air gap accommodates the upward deflection of the lens membrane, which, according to paraxial ray trace analysis, enables the BFL (expressed in dpt hereafter) to reach more than +200 dpt. The annular notch on the bottom cell coincides with the rim of the top cell for centration and alignment of all optical elements. The optical fluid is concealed between the lens membrane and the bottom cover glass. The lens has two luer fittings for connections with external syringe pump and stopcock. During operation, extra volume of optical fluid is pumped into the liquid cavity with one inlet blocked by the stopcock, which changes the curvature of the lens membrane and consequently the optical power.

The aspherical membrane of a VTLL is replicated from a deflection profile of a

CTLL. According to geometrically non-linear plate theory, the deflection profile of an

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edge-clamped thin membrane with constant thickness can be determined and expressed by aspherical fitting as:

Cx2 6 yAxh  2n (5.1) 22  2n 11(1) kCx n2 where x is the membrane position; y is the upward membrane deflection; C is the membrane curvature; k is the conic constant which is assumed as -1 (paraboloid).

In this study, a CTLL with 500 m thick membrane was actuated to generate the aspherical membrane profile. The replicated membrane has a small thickness at the edge

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and a large thickness at the center. The aspherical profile of the replicated membrane can be expressed by the center thickness tC and the thickness ratio TR, which is defined as:

tRCEE() t t t (5.2) where tE is the edge thickness of the membrane.

In order to determine the optimal aspherical membrane geometry that leads to least field curvatures at high diopters, the spherical deviations from VTLL with various aspherical membranes (with tC=0.3mm and varied TR values) were compared at h =

0.805mm (Figure 5.2a&b). The lens profile of VTLL at h = 0.805 mm was first obtained by multiphysics finite element analysis software (COMSOL 4.3b, CA), where the Young’s modulus of the membrane material (PDMS) was set as 1.8 MPa, Poisson’s ratio as 0.49, and the density as 965 kg/m3.

Figure 5.2. Simulated Optical Profiles (a) of CTLL and VTLLs, and Their Spherical Deviations (b) at the Center Deflection of 0.805 mm

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The profile was then imported into optical design program OpticStudio 14.2

(Zemax, LLC, USA) for obtaining the RMS spot radii at different field angles from 0° to

6.0° with 532 nm incident collimated beam (Figure 5.3a&b). The RI of the lens material was set as 1.408 and the abbe number as 50.

Figure 5.3. (a) RMS spot radii from 0º to 6º field angle and (b) changes of spot radii with respect to 0º field angle at +100 dpt. The spherical profile (green dotted curve) at the same center deflection is superimposed for comparison. The ratio (tR) in the legend is defined as (tC - tE)/tE. For both CTLL and VTLLs, tC=0.3 mm. 85% aperture is used for optical simulation. CTLL has the largest spherical deviation (0.111 mm) and RMS spot radius at 6º field angle (135.47 mm). Among VTLLs, the lens with tR=1 has the smallest RMS spot radius (26.41 mm) at 6º field angle and increase from 0º to 6º (23.3%). CTLL, constant thickness liquid lens; VTLL, varied thickness liquid lens; tC, center thickness; tE, edge thickness; dpt, diopter.

The simulation results echo previous studies on the boundary constrictions and shows that the maximum spherical deviation occurs near the lens’ edge. The CTLL has the 120

largest deviation (0.111 m), which occurs at a position that is the closest to the lens center

(2.38 mm). This leads to the worst RMS spot radius (138 μm) at the field angle of 6.0° and the largest variation across the entire field. The spherical deviation of VTLL increases with decreasing TR.. However, when TR is greater than 1, the RMS spot radii exhibit substantial increases, and may exceed that of CTLL at small field angles, although the variation of

RMS spot radius over the field remains small. The VTLL with TR=1 has the least increase of RMS spot radius over the entire field (23.3%) and smaller RMS spot radii than CTLL across the entire field. It was thus selected as the design of choice due to its least field curvature without the loss of center resolution.For the aspherical membrane with TR=1, the spherical deviations at various center deflections were determined (Figure 5.4a&b). As expected, the deflected membrane approximates a spherical shape at small center deflections. The spherical deviation manifests with increasing center deflection(Choi et al.,

2014; Yang et al., 2008).

Figure 5.4. Simulated optical profiles (a) of VTLL (tR =1), and their corresponding spherical deviations (b) at the center deflection of 0.136, 0.199, 0.376, 0.585, 0.676, and 0.805 mm

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Ray tracing analysis was performed to estimate the RMS spot radii of the VTLL and a N-BK7 plano-convex lens at various focusing powers (Figure 5.5a&b). It is interesting to note that the RMS spot radius of the VTLL does not exhibit a monotonous change with the focusing power. Instead, the smallest RMS spot radius occurs at +40 dpt, and remains below 25 m for most field angles below +100 dpt (Figure 5.5c). The RMS spot radius of the VTLL, however, is still larger than corresponding solid lens with the same BFL (Figure 5.5d).

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5.2.2 Fabrication of Aspherical membrane

As aforementioned, the aspherical membrane of the VTLL was replicated from the surface profile of a CTLL, using a previously reported fabrication process. A CTLL with

6 mm in diameter was first fabricated. A SU-8 circular microstructure with 200 m in thickness and 6 mm in diameter was patterned on a silicon wafer. The wafer was placed face to face with a microscopic glass slide that was coated with 1.5 m thick S1813 photoresist (Shipley, MA), where the gap in between was determined by a metal wire that was 700 m in diameter. The gap was later filled by PDMS (Sylgard 184, Down Corning,

MI) prepolymer with the mixing ratio of 10:1 w/w. After crosslinking, the PDMS membrane above the circular microstructure had a thickness of 500m. The PDMS substrate was then peeled from the glass slide, aligned and bonded with another PDMS substrate that had pre-patterned microfluidic channels (200 m in thickness and 500 m in width) to form the CTLL with a 500m membrane. Finally, the as-fabricated CTLL was filled by 99% glycerol (Sigma-Aldrich, MO) using a syringe pump (Pump 11 Elite,

Harvard Apparatus, MA) at a flow rate of 20 ml/h.

The two-step replica molding was used to replicate the surface profile of the CTLL at deformation (Figure 5.6a). First, a 200m thick PDMS stencil with a 6 mm through hole was bonded on the top surface of the CTLL, where the hole was concentric to the lens membrane. The CTLL was actuated to reach a center deflection of 150m. A glass slide was covered on the PDMS stencil with 1 mm thick spacers. PDMS prepolymer was then filled into the gap. After crosslinking, a 200 m pillar with a 150 m concave depression atop was created on the replicated PDMS substrate. The microstructure was soaked in 0.5% 123

(hydroxypropyl)methyl cellulose (Sigma-Aldrich, MO) for 10 min, rinsed with de-ionized water and air-dried. Afterwards, the concave PDMS structure was placed face to face with a glass slide with a 350 m thick spacers. The gap was again filled with PDMS polymer.

After crosslinking, the PDMS membrane with a convex aspherical bottom surface was achieved with the center thickness of 300 m and the edge thickness of 150 m (Figure

5.6b). The optical measurements below are based on VTLL with such an aspherical membrane.

5.2.3 Lens Assembly and Filling

The top and bottom mounting cells of the VTLL were made of a 3D printed optically-opaque resin (Formlabs 1, MA). Two cover glasses were affixed to the mounting cells by UV adhesive. The lens membrane was bonded to the bottom cell using silicone sealant with the convex aspherical surface facing towards the bottom cell. An assembled

VTLL is shown in Figure 5.6c. Using the similar approach, a CTLL with a membrane thickness of 150 m was also assembled.

The lenses were filled by 59% wt. glycerol (Sigma-Aldrich, MO)-water mixture with a RI of 1.41, which closely matches with that of PDMS (RI=1.408). The refraction at the liquid-elastomer interface was minimized, and thus the lens can be approximated as a plano-convex singlet during membrane deflection. Figure 5.6d shows a VTLL without the lensing effect, where the leaf veins acquired with and without the VTLL shared the same focus when the lens membrane was not deflected.

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5.3 Results and Discussion

5.3.1 BFL

The BFLs of horizontally placed CTLL and VTLL (optical axis perpendicular to the gravitational direction) were measured at the hydrostatic pressure of 20 to 240 mbar at a 20 mbar increment using a custom-built Foucault knife edge test setup (Figure 5.7). The lens was illuminated by a 532 nm collimated laser beam after being magnified by a 3×

Keplerian beam expander (beam diameter: 10.5 mm). A razor blade mounted on a two-axis translation stage was adjusted to intercept the converging ray bundles from the left side of the optical axis, and placed upstream of the screen to visualize the ray interception pattern.

The BFL can be thus approximated as the reciprocal of the distance between the bottom 125

glass windows of the lens and the razor blade when it obscured the left and right halves of ray bundles simultaneously. For CTLL, the BFL was measured from +7.4 dpt at 20 mbar to +108 dpt at 200 mbar. Because the VTLL had a smaller edge thickness than the CTLL, it required less hydrostatic pressure to reach the same power, i.e. +15.6 dpt at 20 mbar to

+127.9 dpt at 120 mbar. The results also indicate that the lenses exhibit good reproducibility with small hysteresis between inflating and deflating processes.

Figure 5.7. BFLs (in dpts) of CTLL and VTLL as a function of hydrostatic pressure. BFL, back focal length; CTLL, constant thickness liquid lens; VTLL, varied thickness liquid lens; dpt, diopter.

5.3.2 Image Contrast and Peripheral Resolution

The off-axis resolution was examined by having the lens of interest image a

Siemens-star resolution target at +100 dpt and +40 dpt with full aperture on a 4.1 Mega- pixel CMOS sensor (CMOSIS CMV4000-3E5, Point Grey Research Inc., Canada). The

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target was centrally aligned with the optical axis of the lens using a 3-axis translation stage and illuminated by a telecentric illumination system where the warm white light incident on a diffuser (200-grit) was collimated by an aspherical condenser. At a given power, the object and image distances were adjusted to set the magnification at about 5× in order to make the target fill 90% of the frame and in best focus.

Figure 5.8a-c shows the images taken by the CTLL, the VTLL and an off-the-shelf

6 mm N-BK7 plano-convex solid lens at +100 dpt. The Michelson contrast (C) was used to calculate the overall contrast of the star image under the same lighting condition, which is defined as:

II C  maxmin (5.3) IImaxmin where Imax and Imin are the maximal and minimal luminance among all pixels. The mean contrasts in the CTLL, the VTLL and the solid lens were calculated as 0.62, 0.69 and 0.75.

As seen from the insets, CTLL displayed the most evident gradual focus softening at the edges. VTLL presented crisper edges than CTLL, yet was outperformed by the solid lens.

CTLL and VTLL showed slight astigmatism due to fabrication imperfection that caused unexpected membrane asymmetricity. The edge sharpness in the peripheral areas was qualified by examining the luminance profile along top and right edges of the wedged lines

(6 line pair/mm) on the meridional and sagittal planes using MATLAB image analysis

(Figure 5.8d). These edge areas have the corresponding field angle of 6.0°. At both distal ends, the solid lens exhibited the sharpest transition at the edges, the CTLL exhibited the smoothest transition, and the VTLL sit in between. The rise distance (D) was used as a

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numerical indicator to qualify the edge sharpness, which counts the pixel number within which the luminance magnitudes changes from 10% to 90% within the transition range, i.e. from (0.1Imax + 0.9 Imin) to (0.9Imax + 0.1Imin)(Fauver et al., 2005). The calculated mean of rising distance D (n=4) for the CTLL, the VTLL and the solid lens were 30, 23, and 21, respectively. This indicates that VTLL had a much better resolving power at the edge than the CTLL (less field curvature), but was still outperformed by the solid lens.

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The off-axis resolutions of the CTLL, the VTLL and the solid lens at +40 dpt were also examined using the same imaging setup except that the object and image distances were elongated to set the magnification at 5.1× while maintaining the focus of the target

(Figure 5.9). The contrast for CTLL, VTLL and the solid lens now increased to 0.68, 0.76, and 0.79, respectively. The overall image contrast presented by the VTLL was very close to that of the solid lens, and was again much better than the CTLL. The calculated mean of rising distance (n=8) for the CTLL, the VTLL and the solid lens decreased to 22, 17, and

16, respectively. All lenses depicted increased edge sharpness at +40 dpt than those at +100 dpt, while the ranking order of lens performances remained the same, as at +100dpt.

Figure 5.9. Center and Peripheral Resolution Comparison at +40 dpt

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The superiority of the VTLL over the CTLL at the same membrane deflection in terms of peripheral resolution agreed well with the theoretical analysis. This is believed due to the fact that the surface profile of the VTLL born more resemblance to the spherical contour than the CTLL, which was instrumental to correct the off-axis aberration. The improved contrast and edge sharpness at +40 dpt mainly resulted from the increased F/# and smaller amount of soft focus caused by spherical deviation (i.e. the lens at smaller powers had a smaller spherical deviation than that at larger powers).

5.3.3 Central Resolution and Modulus Transfer Function (MTF)

Figure 5.8&9 reveal that other than better peripheral resolution, VTLL also had better central resolution than CTLL, although both were outperformed by the solid lens.

To quantitative measure their central resolutions at +100 dpt, the star test chart was replaced by a bright field USAF 1951 resolution target(Figure 5.10a~c). With proper alignment, the region containing Groups 6&7 of the resolution target were projected to the very center of the frame. All lenses were able to resolve elements within Groups 4&5, whereas the CTLL exhibited the worst contrast of the bar pattern. The line resolving ability can be interpreted from the inset that contains elements with higher frequencies in Groups

6&7. The CTLL resolved the vertical bars from element 2 in Group 6 (frequency: 72 lp/mm) at the contrast of about 0.21, as compared to the VTLL at about 0.30, and the solid lens at 0.43. The MTF performances of the CTLL and the VTLL were illustrated in Figure

5.10d. For example, with the minimal contrast of 0.3 the VTLL could resolve 56 lp/mm, while the CTLL can only resolve 42 lp/mm.

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5.3.4 Optimization and Future Work

The membrane geometry of the VTLL presented here may not be the best optimum in terms of field curvature correction and imaging resolution. For example, since this study makes the surface profile of focus-tunable lens approximates the spherical shape at a large power, spherical aberration is expected. Fortunately, existing ways to correcting spherical aberrations of solid lenses can be readily applied to liquid lenses(Yu et al., 2010).

One beauty of this study is to provide a simple and low-cost approach to create a lens membrane with desired inhomogeneous thickness profile for improving the optical performance. The aspherical membrane shape of the VTLL was achieved by deforming a

CTLL. Different from many previously reported elastomer-liquid lenses, pre-straining is not necessary for the VTLL reported herein. Although the results confirmed that such aspherical shape is effective in improving the resolving power on-axis ad off-axis, the membrane deformation was defined by Eq. (1). Freeform deformation profile cannot be achieved. Numerical analysis showed that other geometric profiles, such as spherical or conical contours(Santiago-Alvarado et al., 2013; Zhao, Ataman, & Zappe, 2014), may also increase the resolving power to certain extents, despite of challenging fabrication of optical grade elastomer membranes with such geometries. To identify the best geometric profile of the membrane that can lead to least field curvature and most enhanced resolving power, one can backtrace a deflected membrane profile of the VTLL that results in the best set of the target optical parameters (including RMS spot radius, wavefront error, and MTF across the required field at targeted dpts) to the thickness profile of a freeform membrane before

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deformation in an iteratively manner. The final thickness profile may be determined by considering the fabrication complexity and the need for pre-straining.

5.4 Summary

We introduce a novel focus-tunable elastomer-liquid lens design that takes advantage of a microfabricated aspherical lens membrane in this chapter. The mechanical and optical analysis show that compared to the flat membrane, the aspherical membrane effectively reduces the spherical deviations at both small and large membrane deflections, and leads to smaller RMS spot radius across the field. Experiments demonstrate that the

VTLL has better off-axis edge sharpness and better center MTF performance than the

CTLL at large optical powers. Due to the reduced field curvature and enhanced resolving power, the VTLL design allows for the use of a large fraction of the total lens diameter, which promises a potential for future miniaturization of elastomer- liquid lenses without sacrifice of imaging quality.

5.5 References

Amin, M. J., & Riza, N. A. (2014). Smart imaging using laser targeting: a multiple barcodes application. Paper presented at the SPIE Photonics Europe.

Blum, M., Büeler, M., Grätzel, C., & Aschwanden, M. (2011). Compact optical design solutions using focus tunable lenses. Paper presented at the SPIE Optical Systems Design.

Blum, M., Büeler, M., Grätzel, C., Giger, J., & Aschwanden, M. (2012). Optotune focus tunable lenses and laser speckle reduction based on electroactive polymers. Paper presented at the SPIE MOEMS-MEMS.

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Casutt, S., Bueeler, M., Blum, M., & Aschwanden, M. (2014). Fast and precise continuous focusing with focus tunable lenses. Paper presented at the SPIE OPTO.

Fahrbach, F. O., Voigt, F. F., Schmid, B., Helmchen, F., & Huisken, J. (2013). Rapid 3D light-sheet microscopy with a tunable lens. Optics Express, 21(18), 21010-21026.

Feng, G. H., & Chou, Y. C. (2009). Flexible meniscus/biconvex lens system with fluidic- controlled tunable-focus applications. Appl Opt, 48(18), 3284-3290.

Goren, D. P. (2012). Method of driving focusing element in barcode imaging scanner: Google Patents.

Graham-Rowe, D. (2006). Liquid lenses make a splash. Nature-Photonics, 2-4.

Grewe, B. F., Voigt, F. F., van’t Hoff, M., & Helmchen, F. (2011). Fast two-layer two- photon imaging of neuronal cell populations using an electrically tunable lens. Biomedical optics express, 2(7), 2035-2046.

Hao, Q., Cheng, X., & Du, K. (2013). Four-group stabilized zoom lens design of two focal- length-variable elements. Optics Express, 21(6), 7758-7767.

Huang, Y.-P., Chen, C.-W., Cho, M., & Javidi, B. (2013). Liquid crystal lens for axially distributed three-dimensional sensing. Paper presented at the SPIE Defense, Security, and Sensing.

Jabbour, J. M., Malik, B. H., Olsovsky, C., Cuenca, R., Cheng, S., Jo, J. A., . . . Maitland, K. C. (2014). Optical axial scanning in confocal microscopy using an electrically tunable lens. Biomedical optics express, 5(2), 645-652.

Lee, S. W., & Lee, S. S. (2007). Focal tunable liquid lens integrated with an electromagnetic actuator. Applied Physics Letters, 90(12), 121129.

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Lu, Y.-S., Tsai, L.-Y., Huang, K.-C., Tsai, C. G., Yang, C.-C., & Yeh, J. A. (2011). Three- dimensional illumination system using dielectric liquid lenses. Optics Express, 19(104), A740-A746.

Maffli, L., Rosset, S., Ghilardi, M., Carpi, F., & Shea, H. (2015). Ultrafast All‐Polymer Electrically Tunable Silicone Lenses. Advanced Functional Materials.

Marks, R., Mathine, D. L., Peyman, G., Schwiegerling, J., & Peyghambarian, N. (2009). Adjustable fluidic lenses for ophthalmic corrections. Optics Letters, 34(4), 515- 517.

Marks, R., Mathine, D. L., Peyman, G., Schwiegerling, J., & Peyghambarian, N. (2010). Adjustable adaptive compact fluidic phoropter with no mechanical translation of lenses. Optics Letters, 35(5), 739-741.

Miks, A., & Novak, J. (2010). Analysis of two-element zoom systems based on variable power lenses. Optics Express, 18(7), 6797-6810.

Miks, A., Novak, J., & Novak, P. (2013). Algebraic and numerical analysis of imaging properties of thin tunable-focus fluidic membrane lenses with parabolic surfaces. Applied Optics, 52(10), 2136-2144.

Nguyen, N.-T. (2010). Micro-optofluidic Lenses: A review. Biomicrofluidics, 4, 031501.

Ren, H., Fox, D., Anderson, P. A., Wu, B., & Wu, S.-T. (2006). Tunable-focus liquid lens controlled using a servo motor. Optics express, 14(18), 8031-8036.

Ren, H., & Wu, S.-T. (2012). Introduction to adaptive lenses. Hoboken, N.J.: Wiley.

Riza, N. A., Amin, M. J., & Riza, M. N. (2014). Eye vision system using programmable micro-optics and micro-electronics. Paper presented at the SPIE BiOS.

Savidis, N., Peyman, G., Peyghambarian, N., & Schwiegerling, J. (2013). Nonmechanical zoom system through pressure-controlled tunable fluidic lenses. Applied Optics, 52(12), 2858-2865.

Shamai, R., Andelman, D., Berge, B., & Hayes, R. (2008). Water, electricity, and between… On electrowetting and its applications. Soft Matter, 4(1), 38-45.

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Shaw, D., & Sun, T. E. (2007). Optical properties of variable-focus liquid-filled optical lenses with different membrane shapes. Optical Engineering, 46(2). doi: Artn 024002

Doi 10.1117/1.2540323

Wei, K., Domicone, N. W., & Zhao, Y. (2014). Electroactive liquid lens driven by an annular membrane. Optics letters, 39(5), 1318-1321.

Yang, Q., Kobrin, P., Seabury, C., Narayanaswamy, S., & Christian, W. (2008). Mechanical modeling of fluid-driven polymer lenses. Applied optics, 47(20), 3658- 3668.

Yiu, J.-Y., Batchko, R., Robinson, S., & Szilagyi, A. (2012). A fluidic lens with reduced optical aberration. Paper presented at the IS&T/SPIE Electronic Imaging.

Yu, H., Zhou, G., Leung, H. M., & Chau, F. S. (2010). Tunable liquid-filled lens integrated with aspherical surface for spherical aberration compensation. Optics Express, 18(10), 9945-9954.

Zhang, W., Aljasem, K., Zappe, H., & Seifert, A. (2011). Completely integrated, thermo- pneumatically tunable microlens. Optics express, 19(3), 2347-2362.

Zhang, W., Zappe, H., & Seifert, A. (2014). Wafer-scale fabricated thermo-pneumatically tunable microlenses. Light: Science & Applications, 3(2), e145.

Zhao, P., Ataman, Ç., & Zappe, H. (2014). An endoscopic microscope with liquid-tunable aspheric lenses for continuous zoom capability. Paper presented at the SPIE Photonics Europe.

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Chapter 6: Summary and Future Perspectives

6.1 Current Work

This dissertation centers on the design and development of novel elastomer-liquid lenses based on non-conventional fabrication, optofluidics and smart electroactive materials.

First, a bi-layered optofluidics containing an elastomer-liquid lens (2 mm in diameter) array and a deformable substrate (10 mm in diameter) was fabricated by SU-8 photolithography and PDMS replica molding. Each elastomer-liquid lens was able to change the optical power from 0 to 275 D, while that on the peripheral part of the deformable substrate varied its optical axis from 0 to 52.5º. The maximum FOV reached

120º.

Second, a tri-layered optofluidics containing a 10mm elastomer-liquid lens, a pair of 3 mm elastomer-liquid lenses with 6.4 mm baseline, and a microfluidic iris diaphragm were fabricated. These three layers were overlapped and shared the same optical channel.

At a minimum F/# of 2.3, the big lens provided accommodation depth cue from depth of defocus and had a resolution of 128 lp/mm at the BFL of 25mm. At 3D mode, the optofluidics reconfigured from the big lens into the binoculars where the iris layer defined the entrance pupils of small lenses. Because of a smaller aperture, the small lens resolved

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32 lp/mm at the BFL of 25 mm. The binoculars generated a normalized disparity from 1 to

0.3 at a working distance from 60 to 200 mm.

Third, a 5 mm elastomer-liquid lens driven by an annular dielectric elastomer actuator was developed. It enabled more than 300% focal length change at an initial lens sag of 273 m at the voltage input of 1.0 kV. The response time was less than 0.5 s. It was able to resolve 28.5 lp/mm at the BLF of 25 mm.

Fourth, a 6 mm elastomer-liquid lens encapsulated by an aspherical lens membrane

(center thickness: 0.3 mm; edge thickness: 0.15 mm) was developed. Resolution tests showed that at the field angle of 6º and resolution of 6 lp/mm, lens with aspherical membrane exhibited sharp edges than that with flat membrane. MTF tests also showed that with the minimal contrast of 0.3 the VTLL could resolve 56 lp/mm, while the CTLL can only resolve 42 lp/mm.

In summary, this dissertation opens the door for a new class of adaptive optofluidics, and for the aberration reduction of elastomer-liquid lens.

6.2 Future Work

6.2.1 Dynamic depth of field using IHHE

In IHHE can be used as a tilt-shift lens for depth of field control. As shown in chapter 2, IHHE enables two image acquisition modes. In the first mode, the big membrane remains flat and underlies an array of small membrane fluidic lenses. Each small lens converges light emerging from the object onto an image sensor placed behind the IMHE.

Similar to an ordinary camera setup, all points in focus ideally line in an object plane (OP)

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parallel to the film plane. In the second mode, the big membrane is deformed, which tilts the lenses residing on the peripheral regions of the big membrane. The lens plane (LP) is no longer parallel to the FP. An OP of sharp focus still exists but becomes oblique to the

LP and FP (Figure 6.1). It is mathematically proven as below.

Figure 6.1. Ray Tracing of the IHHE as a Tilt-shift Lens

Suppose an OP of sharp focus is randomly oriented in the object space. Its conjugated FP can be derived by applying Gaussian and Newtonian thin lens formulas.

XaYc 0 (6.1)

The function of the FP is assumed as:

px qy  d  0 (6.2)

Newtonian lens equation transfers object point (X, Y) on the OP to image point (x, y):

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()()xfXff 2 (6.3) where f is the effective focal length (EFL) of the small membrane lens.

Equation 6.3 can be arranged as:

fXfY  (6.4) fxfy 

From Equation 6.1 and 6.3, the function of FP is calculated as:

afcf xy()0 (6.5) cfcf

Solving equation (1) and (5) results in the intersection of OP and FP at (0, -c/a).

Define a plane parallel to the FP and crossing the optical center of the lens as Parallel to film plane (PTF), and a plane parallel to LP and passing the primary focal point of the lens as front focal plane (FFP). The intersection of PTF, OP and FFP is (f, -(c+f)/a). The tilting angle (angle between FP and LP) is give by:

af  arctan() (6.6) cf

In practice, the placement of FP with respect to IMHE is known. The EFL is prescribed by the small lens. The tilting angle of the small lens is controlled by the deflection of the big membrane under Laplace pressure. One can thus find the conjugated

OP by simply applying the inverse transformation of Equation 6.5.

To verify this, Equation 6.5 is rewritten as:

140

x a y  c  0 af a  (6.7) cf cf c  cf

The inverse transformation function is:

f T  (6.8) cf 

The function of OP can be calculated as:

x a T  y  c T 0 (6.9)

Equation 6.9 after simplification has the same form as Equation 6.1.

The distance between the intersection of OP with the optical axis of the lens and the optical center of the lens represents the axial object distance (u):

uc (6.10)

The small lens has a depth of field within which all object points projected to the

FP appear acceptably sharp to the human vision. The depth of field has two boundaries: the near OP limit (OPn) and the far OP limit (OPf). The object points on these two boundaries produce the largest blur spots on the FP, which is indistinguishable from a point. For traditional camera setup, the blur spot is defined as the circle of confusion

(COC). For titled camera setup, the blur spot has the same horizontal dimension but different dimension along FP, thus it is defined as the ellipse of confusion (EOC). Its two components are denoted as: EOCfp and EOCz. The EOC for the titled lens in x-y plane and x-z plane is illustrated below:

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Figure 6.2. Circle of Confusion on Sagittal Plane

On sagittal plane (Figure 6.2), OPn conjugates with FPn, OP with FP, and OPf with

FPf. FPn and FPf has the same distance (g) to FP, so that their blurry disks are overlapped. g is given by:

gFEOC/# s (6.11)

Due to similar triangle, all object points on OPn and OPf have EOCz of same size.

On meridional plane (Figure 6.3), object points on either OPn or OPf produce

EOCfp of different sizes along FP. The ray diagram shows three cases where EOCfp results from three objects on OPn and exhibits three different dimensions along FP.

Case #1: EOCfp (EOCfp) > EOCz where BC > AB (lens diameter)

Case #2: EOCfp (EOCfp) < EOCz where BC > AB

Case #3: EOCfp = EOCz where BC = AB

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Figure 6.3. Ellipse of Confusion on the Meridional Plane

If EOCz is used as the largest permissible blurry spot, the depth of field for the titled lens setup can be derived. The function of FPn is given as:

xa ycg 0 (6.12)

Or:

xayc110

aa1   (6.13)

ccg1 

The function of OPn is assumed as:

XaYcnn0 (6.14)

Based on Equation 6.8, we can calculated a and c:

af 2 a  n cg fg f 2 (6.15) cf22 cgf gf c  n gc gf f 2

143

Substitute Equation 6.15 & 16 into 6.14:

af2 cf 2 cgf gf 2 XY   0 (6.16) gc gf  f22 gc  gf  f

Similarly, the function of OPf is calculated as:

afcfcgfgf222  XY 0 (6.17) cffgfcgfgf 22

An image point on FP conjugates a single point in the object space theoretically.

Applying the lens equation as derived before, one can pinpoint the exact location of that object point in the space. However, DOF allows for only a rough estimation of that object location. Figure 4 shows the near and far DOF limits that confuse with the exact object point in best focus. The DOF near and far limits are along the lines radiating from the optical center of the lens. Along the radial lines, all object points will produce EOCs of same size on the same location on the FP. Such that these object points are indistinguishable. The tilt-shift can provide an ultra DOF when the object is far from the

IHHE and a small DOF when the object is near the IHHE. The ultra DOF is useful for eye and gastrointestinal examination.

Figure 6.4. DOF on the Meridional Plane

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6.2.2 Creating Nano/micro Lens/lenticular Array by Surface Wrinkling

A conventional method to manufacture solid lens is injection molding or ultra- precision diamond turning, which requires a pre-defined template/mold(He et al., 2013; He et al., 2011; Li et al., 2011). In surface wrinkling, spontaneous formation of continuous sinusoidal topographies upon stress removal eliminates the use of pre-machined molds in lithographic methods(Kang Wei, Rudy, & Zhao, 2014; K Wei & Zhao, 2012; Kang Wei &

Zhao, 2014).

The capability of corona discharge for creating both micro/nano lens array and lenticular lenses with controlled dimensions is explored. The process can be carried out within a general wet laboratory environment and is compatible with commercial tensile test equipment. Sinusoidal wrinkled topographies with the wavelength ranging from about

500 nm to 3000 nm were created on polydimethylsiloxane (PDMS) surface within minutes.

Hierarchical wrinkled topographies with parallel or orthogonal alignment patterns were also created by coupling this method with softlithography and/or photolithography. The corona-discharge based benchtop surface wrinkling has its little reliance on expensive deposition/oxidation equipment and/or cleanroom environment. The process is described below.

PDMS (Sylgard 184, Dow Corning, MI) was prepared by mixing the base prepolymer and the curing agent at a weight ratio of 10:1. The prepolymer was degassed in vacuum for 30 min, poured into a petri-dish, and allowed to spread into a layer with a thickness of 2 mm. After cross-linking the mixture was baked on a hotplate at 65 ºC for 2 h. The PDMS substrate was cut into rectangular elastomeric

145

membranes with 55 mm in length and 10 mm in width. The membranes were cleansed by 70% ethanol before use.

The benchtop surface wrinkling process is depicted in Figure 6.5. Briefly, the rectangular PDMS membrane was mounted on a commercial tensile test apparatus

(100Q250-6, Testresources, Shakopee, MN) and stretched lengthwise at a loading rate of

100 m/s. While the PDMS membrane was held at a given pre-strain, it was approached to the discharge tip of a hand-held high frequency corona surface treater (BD-20AC,

Electro-technic Products, Chicago, IL) and was kept at a tip-to-surface distance of 5 mm.

As shown in Fig. 1b, the discharge tip was connected to the output A of the corona tester, while the output B was grounded. The power transformer T1 set up a high voltage which caused a spark gap to break down at the rate twice of the line frequency (100-120 Hz). The spark gap charged the capacitors C1 and C2 that were connected to the primary windings of the resonator coil T2 with an air core. Because of the inductance of primary windings of

T2 and capacitors, an oscillating current with high frequency was set up in the circuit. The spark gap was adjusted to reach the resonant frequency of the circuit about 3.8 MHz. High voltage was thus induced in the secondary windings of T2, causing the corona discharge at the output A (Fig. 1c). In this study, the operational power of the corona surface treater was measured by a power monitor (P4460 Kill A Watt® EZ, P3 International, NY) and was kept as 27 W throughout all experiments. After a certain discharge time, the substrate was released to the original length at an unloading r carried out at room temperature. In order to determine the dependence of the wrinkle wavelength on the key operational parameters in the benchtop wrinkling process, a

146

parametric study was performed by varying the pre-strain from 5% to 40% and the discharged time from 0.5 min to 8 min.

Hierarchical wrinkled topographies were created by combining benchtop surface wrinkling with soft lithography (Figure 6.6). The as-wrinkled PDMS substrate that underwent the prestrain of 20% and the discharge time of 4 min was soaked in 0.5% (Hydroxypropyl)methyl cellulose (Sigma-Aldrich, MO) for 10 min, rinsed with de-ionized water, and air-dried. Degassed PDMS prepolymer was poured on top of the as-wrinkled PDMS membrane, allowed to spread into a layer with the thickness of 2 mm, and cured on a hot plate at 65 ºC for 2 h. The replicated substrate with the surface topographies complementary to those on the master

PDMS substrate was then peeled off. Afterwards, the replica substrate was stretched

147

at 0° or 45° to the longitudinal axis of the existing wrinkles and was subject to the benchtop wrinkling process with the pre-strain of 20% and the discharge time of 1 min.

Figure 6.6. Fabrication Processes for Creating Bi-layered Wrinkled Topographies

During the benchtop wrinkling process, the high electric field in the gap between the tip electrode and the substrate caused partial electric breakdown that ionized the air surrounding the electrode and created a plasma zone containing reactive oxygen species. It converted the Si-CH3 bonds at the outermost surface of the PDMS into polar functional groups (mainly, Si-OH), leaving a strain-free silica-like skin atop the prestrained substrate.

Upon unloading, the substrate contracted back to its strain-free configuration at the expense of surface undulations to minimize the total elastic energy. . Results showed that the surface exhibited anisotropic wavy patterns where the longitudinal axis of the sinusoidal groove formed only perpendicular to the direction of the applied pre-strain. Such topographical anisotropy was also evidenced by distinct water contact angles measured parallel and orthogonal to the direction of the wrinkles. With the applied operational parameters (pre-

148

strain of 5% to 40% and discharge time of 0.5 min to 8 min), the wrinkle wavelength ranged from about 500 nm to 3000 nm (Figure 6.7a). As expected, at a given pre-strain, the wrinkle wavelength increased with the discharge time; while with a given discharge time, the wrinkle wavelength decreased with the increase of the pre-strain. Consequently, a short discharge time with a large magnitude of pre-strain generally led to a small wrinkle wavelength. For instance, wrinkled structures with the average wavelength of about 574 nm were obtained with the pre-strain of 40% and the discharge time of 0.5 min; the wavelength increased to 2.5 m when the pre-strain decreased to 5% and the discharge time increased to 8 min (Figure 6.7b). The amplitude-to-wavelength ratios of these two wrinkled structures were similar: 0.10 for the nanowrinkles whose average amplitude was about 62nm; and 0.12 for the microwrinkles whose average amplitude was about 295nm.

The amplitude-to-wavelength ratios of samples obtained under other operational parameters were also around 0.10. This indicated that although the thickness of the discharge-induced oxide layer changed the wavelength and the amplitude, the changes were proportional.

149

Figure 6.7. Characterization of Single-Layered Wrinkles Resembling Lenticular Lens Array: (a) parametric studies of wrinkle geometries with the pre-strain and the discharge time at the tip-surface distance of 5 mm; and (b) the resulting nanoscale (pre-strain: 40%; discharge time: 0.5 min) and microscale (prestrain: 5%; discharge time: 8 min) wrinkled structures.

Benchtop wrinkling process can successfully produce a additional layer of wrinkled structures on the pre-existing wrinkled structures of a PDMS substrate. PDMS replica of an existing wrinkle template. When the primary replicated wrinkles and the secondary additional wrinkles intersect at 90º, the bi-layered superimposed wrinkled topography can be estimated by:

22 zAxAya rrasinsin() (6.18) ra where z, A and  are the height, the amplitude and the wavelength of the wrinkles; the subscripts r and a denote the replicated and the additional wrinkles, respectively; and the subscript a+r denote the superimposed wrinkled structures. Based on the experimental results in single-layered wrinkles, the amplitude-to-wavelength ratio was set as a constant value of 0.10 for both the wrinkle template (or replica) and the additional wrinkles. The profiles of the superimposed wrinkled structures can be obtained analytically (Figure 6.8).

It is seen that the additional wrinkles cut the wrinkle replica into an alternated array of

150

protrusions and depressions. The protrusions occurred where the crests of the replicated wrinkles and of the additional wrinkles met. Likewise, the depressions occurred where the troughs of the replicated wrinkles and of the additional wrinkles met. The projection areas of the protrusions (or the crests) were diamond-shaped, whose length-to-width ratio increased with the wavelength ratio between the replicated and the additional wrinkles

(r/a). A representative pattern of the alternative protrusions/depressions were shown by superimposing the additional wrinkles with the wavelength of 730 nm on top of the replicated wrinkles with the wavelength of 1.6 m (p/s ≈ 2.2:1 at 90º) (Figure 6.9).

Figure 6.8. Dimensionless Analytical Estimation of Superimposed Bi-layered Wrinkled Topographies at Different Wavelength Ratios. p: wavelength of the primary wrinkles; s: wavelength of the secondary wrinkles. s = 0.5, 0.75, 1.5 and 3; p = 3.

151

Figure 6.9. AFM micrographs of Bi-layered Wrinkled Topographies Resembling Microlens array

6.2.3 Correcting Gravity-induced Coma

When the elastomer-liquid lens is placed vertically, the gravitational effect will introduce lens sagging and cause coma. It is evident at small lens sag (tele-end), but is negligible at large lens sag (wide-angle end) due to membrane stiffening at high differential pressure. Figure 6.10 shows the optical axis of a 15 mm elastomer-liquid lens that undergoes different differential pressure. Evidently, it is more centered at high pressure than at low pressure.

152

Figure 6.10. Optical Axes of a 15 mm Elastomer-liquid Lens at Different Differential Pressures

The centrality of the lens can be also seen from the surface stress (Figure 6.11).

Figure 6.11. Centrality of the Lens subject to Low and High Hydrostatic Pressures. Gravity is from right to left.

To combat the gravity, one can place a concave lens behind an elastomer-liquid lens. In order to achieve the same power, the lens needs to be deformed more, which alleviates the lens de-centering issue. The large deformation can cause severe spherical aberration and field curvature, but can be solved by using the technology described in

Chapter 5, where the lens membrane is made aspherical. 153

6.3 References

He, P., Li, L., Yu, J., Huang, W., Yen, Y.-C., Lee, L. J., & Yi, A. Y. (2013). Graphene- coated Si mold for precision glass optics molding. Optics letters, 38(14), 2625- 2628.

Li, L., He, P., Wang, F., Georgiadis, K., Dambon, O., Klocke, F., & Allen, Y. Y. (2011). A hybrid polymer–glass achromatic microlens array fabricated by compression molding. Journal of Optics, 13(5), 055407.

Wei, K., Rudy, M. S., & Zhao, Y. (2014). Systematic investigation of the benchtop surface wrinkling process by corona discharge. RSC Advances, 4(103), 59122-59129.

154

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Appendix A: Surface Roughness Measurement of IHHE

A.1 Equipment

1. Bruker Nanoscaope III Multimode SPM (Bruker Biosciences Corporation)

2. Nanoscope Analysis V1.4

3. AFM probe (HQ: NSC, Micromash)

4. SPM sample mounting disk (Steel, 12 mm diameter, SD-101, Bruker Biosciences

Corporation)

5. Adhesive pad (STKYDOT, Bruker Biosciences Corporation)

A.2 Protocol

1. Prepare PDMS lens membrane with diameter smaller than 15 mm.

2. Attach the sample to a steel puck with a sticky tab.

3. Mount the steel puck on top of the scanner head. Make sure the area of interest at the center.

4. Make sure the sample height is below the height of three balls.

5. Insert the AFM probe into a small grove and fix it by a gold clamp. Make sure that the probe side faces up and the cantilever is aligned with the groove and the rear end of the cantilever is situated at the half circle at the tip of the clamp. (Bright side is coated with

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reflective coating and should be put toward the laser; Dark side is where the probe is fabricated.)

6. Check the height of the sample before inserting the holder. (Up toggle=move down the sample; toggle is on the AFM base) and tighten the holder.

7. Adjust the distance between the sample and the AFM probe (gap~2mm). Adjust the distance between the sample and the cantilever, making sure it is close enough (by naked eye). A rule of thumb is to view the sample and the cantilever through microscope. To focus the sample, rotate the knob toward you; to focus the probe, rotate the knob outward.

The sample and the probe should be approximately in focus together. If the sample and probe are out of sight, use two knobs on the bottom of the AFM setup is to move them together.

8. Locate the area of the interest of the sample

9. Find the laser on the sample (turn down the light source from the microscope) and align the laser and move the laser to the tip of the probe. To check if the red laser is right at the tip of the cantilever, make sure the number on the display is about +9.85 or -9.85 and the number for the bar is larger than 7.2. If less than 7.2, adjust the angle of the mirror.

10. Use the third knob to zero the laser, making sure the reflected laser is pointing toward the center of the photodiode from -/+9.85 to less than -/+0.05. The bar stays the same.

Negative: clockwise; positive: counterclockwise.

11. Open the software to turn on channel 1 (Height) and 2 (Amplitude). In the scan control panel, set scan area (10×10 m), aspect ratio as 1:1, zero X and Y offset, and scan rate of

1 Hz. Disable the interactive mode.

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12. Tune the probe (its typical resonance frequency is around 300Hz). Normally the tuned frequency is 5% off the peak on the steepest slope.

13. Engage the probe. Notice the Z center position, making sure the bar is in the center.

Check the scope trace where white curve indicates traces and yellow curve indicates back traces. Make sure they match together. Adjust the parameters below to adjust the Z center position. Adjust the amplitude setpoint and drive amplitude. Set the data scale to present a proper height range.

14. Process the image using low-pass filter, and perform section analysis to measure the height and pitch in Nanoscope Analysis v1.40.

A.3 Results

In the IHHE, the bottom surface of the small membrane and the top/bottom surfaces of the big membrane are all in contact with the optical fluid (water-glycerol mixture) that has a refractive index (RI) of 1.41, which is fairly close to the RI of the PDMS (1.4118 at

589 nm at room temperature). We assume there is no RI mismatch at the PDMS-optical fluid interface so the roughness of these surfaces does not affect the image quality. The top surfaces of the small membranes (lens membranes) are in touch with air, whose roughness is therefore essential for the imaging quality.

According to the fabrication process, the top surfaces of the small membranes were replicated from a thin S1813 layer spun on a glass substrate. It therefore has a fairly small surface variation. AFM measurement (Figure A.1, top left) shows that the height variation of the surface is within 45 nm. Since the number is within the surface variation range of

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conventional spherical glass lens (~100 nm), the top surface of the small membranes can be regarded optically flat and does not substantially affect the optical performance.

Figure A. 1 Surface Roughness of the Elastomer-liquid Lens

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Appendix B: Dioptric power calculation for IHHE

The actual system to measure the dioptric power of the IHHE is illustrated in Figure

3. Each individual eye of the IHHE is approximated as a PDMS plano-convex lens (RI=1.4) with a sag of s, followed by a 0.95mm thick PDMS slab (top and bottom layers of the IHHE at rest, RI = 1.4), a glass slide (RI = 1.5) and a trough containing fluorescent solution (RI

= 1.33). The system consists of a PIHHE air-PDMS interface, a Pg-p PDMS-glass interface, a Pf-g glass-fluorescence interface, and a Pf-a fluorescence-air interface. To simplify the calculation, it is reduced as the equivalent air system where each interfaces is approximated as a thin lens in the air.

The reduced thicknesses of lens ( d PDMS ), glass slide ( d g ) and fluorescent trough (

d f ) are:

st d PDMS  1.4 1.0 dmmg 0.67 (7.1) 1.5 120 dmmf 90.23 1.33

When the collimated light is incident on the air-PDMS interface, the thin lens vergence equation gives:

VUPP11  IHHE  IHHE (7.2) 172

where V1 is the vergence of wavefront exiting the lens, U1 is the vergence of the planar wavefront and equals to 0.

Applying the vergence equation at the glass-fluorescence interface (Pf-g = 0) results in:

11 VP (7.3) 2 11fg ()()ddddPDMSgPDMSg VP1 IHHE

As the light converges in the fluorescent solution, the actual image distance is given by:

1 vdd2 1.33(()) PDMSg (7.4) PIHHE

Rearrange:

1 P  (7.5) IHHE v st 2 0.67 1.33 1.4

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Appendix C: Equation Derivation for the Electroactive Lens

B.1 Circular Membrane as an Actuator

When the circular electroactive membrane is submitted to a Laplace pressure, it can be related to the biaxial stress in the membrane by the thin-walled spherical pressure vessels equation:

2RtRp 2 (7.6) where p is the Laplace pressure due to fluid addition; R is the radius of curvature of the deformed membrane; t is the thickness of the deformed membrane;  is the biaxial stress in the membrane.

According to simply geometry, R is calculated as:

rh22 R  (7.7) 2h where r is the radius of the membrane, and h is the deflection of the membrane.

The biaxial stress has three components: the stress due to the membrane’s elasticity

(E), the induced in-plane stress (V) due to the applied voltage, and the residual stress (0) due to fabrication. It is expressed as:

EV 0 (7.8)

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According to Hooke’s Law, E is:

E   (7.9) E 1 where is the Young’s modulus; is the Poisson ratio; is the strain;  is a Poisson ratio dependent constant, and is equal to (1-0.24).

V is given by the Maxwell’s stress:

V 2    (7.10) Vr0 t 2 where  is the permittivity in the vacuum; r is the permittivity of the membrane; V is the applied voltage.

Substituting Equations 7.4~7.5 into Equation 7.3 results in:

EV2  (10.24)  (7.11) 1 00r t 2

Rearrange Equation 7.1 by replacing with Equation 7.5 and R with Equation

7.2:

4htEV 2 p  ((10.24 ))   (7.12) rht2221  00r

Volume conservation of the membrane leads to:

222 rtrht0 () (7.13)

It is simplified as:

r 2 tt (7.14) rh22 0

Substituting Equation 7.8 into Equation 7.6 gives:

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2 2 2 4(1 0.24 )Et0 r 4  0 r V 4 r t 0  0 p2 2 2 h  2 h  2 2 2 h (7.15) (r h ) (1  ) t0 r ( r  h )

The strain is defined as:

22Rr    (7.16) 2r where  is the half angle the arc length of the membrane subtends.

It is calculated as:

2hr   arcsin() (7.17) rh22

The Taylor expansion of the arcsin(x) is given by:

 (2)!n arcsin xx 21n (7.18)  22n n0 2(!)nn (21) 

Equation 7.12 is simplified by using the first two terms of its Taylor series:

24hr h33 r   (7.19) r2 h 23( r 2 h 2 ) 3

Substituting Equation 7.2 and 7.14 into 7.11 result in:

2h2   (7.20) 3r 2

By substituting Equation 7.15 into Equation 7.10, we get:

22 8(1 0.24 )Et03 4  0 r V 4 r t 0  0 p2 2 2 h  2 h  2 2 2 h (7.21) 3(r h ) (1  ) t0 r ( r  h )

The change in deflection after voltage application is calculated from:

h   h( V , P )   h (0, P ) (7.22)

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The resulting volume change is thus given by:

r2 Vh Vphph ((,)(0,))((,)(0,) Vphp  ) 33 (7.23) 26

B.2 Annular Membrane as an Actuator

By simply modifying the thin-walled spherical pressure vessels equation, the

Laplace pressure applied to the annular electroactive membrane is related to the biaxial stress in the membrane as:

rrrrrrrr 2()2()(()()tRtRRRpOIOIOIOI )  22 (7.24) 2222

Equation 7.19 is simplified as:

t p  (7.25) R where p is the Laplace pressure due to fluid addition; R is the radius of curvature of the annular membrane; t is the thickness of the deformed annular membrane;  is the biaxial stress in the membrane.

According to simply geometry, R is calculated as:

(()rrh / 2) 22 R  OI (7.26) 2h

The biaxial stress has three components: the stress due to the membrane’s elasticity

(E), the induced in-plane stress (V) due to the applied voltage, and the residual stress (0) due to fabrication. It is expressed as:

EV 0 (7.27)

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According to Hooke’s Law, E is:

E   (7.28) E 1 where is the Young’s modulus; is the Poisson ratio; is the strain;  is a Poisson ratio dependent constant, and is equal to (1-0.24).

V is given by the Maxwell’s stress:

V 2    (7.29) Vr0 t 2 where  is the permittivity in the vacuum; r is the permittivity of the membrane; V is the applied voltage.

Substituting Equations 7.23~7.24 into Equation 7.22 results in:

EV2  (10.24)  (7.30) 1 00r t 2

Substituting Equation 7.21 and 7.25 into Equation 7.20 leads to:

2thEV 2 p  222 ((1 0.24 ))  00r (7.31) (()rrhtOI / 2)1 

Volume conservation of the membrane results in:

[()rrh / 2]22 ()()rrtrrt222 OI (7.32) OIOI 0 2

Rearrange Equation 7.27:

()rOI r t0 2 t  22 (7.33)  [(rOI r ) / 2] h

The strain is calculated as:

178

8h2   2 (7.34) 3(rrOI )

Thus the applied pressure is calculated from given h and V in terms of Equation 7.26, 7.28 and 7.29.

The change in deflection after voltage application is calculated from:

hhVPhP (,)(0,) (7.35)

The resulting volume change is thus given by:

 222()[(,)(0,)]rrh Vphp  V OI (7.36) 4

B.3 Matlab Code to Calculate Volume Exchange for Circular Membrane

% Circular Membrane

%% Pressure vs. Height

E=208.2*10^3;

nu=0.5;

t0=76*10^-6;

er=6.39;

e0=8.85*10^-12;

r=8.06*10^-3;

sigma0=50*10^3;

h=0:5*10^-6:600*10^-6;

% When V=0 179

V=0;

p=(8.*(1-0.24.*nu).*E.*t0.*h.^3)./(3.*(r.^2+h.^2).^2.*(1-nu))-

(4.*e0.*er.*V.^2.*h)./(t0.*r.^2)+(4.*r.^2.*t0.*sigma0.*h)./(r.^2+h.^2).^2;

plot(h,p,'r');

hold on;

% When V=250

V=250;

p=(8.*(1-0.24.*nu).*E.*t0.*h.^3)./(3.*(r.^2+h.^2).^2.*(1-nu))-

(4.*e0.*er.*V.^2.*h)./(t0.*r.^2)+(4.*r.^2.*t0.*sigma0.*h)./(r.^2+h.^2).^2;

plot(h,p,'b');

% When V=500

V=500;

p=(8.*(1-0.24.*nu).*E.*t0.*h.^3)./(3.*(r.^2+h.^2).^2.*(1-nu))-

(4.*e0.*er.*V.^2.*h)./(t0.*r.^2)+(4.*r.^2.*t0.*sigma0.*h)./(r.^2+h.^2).^2;

plot(h,p,'g');

% When V=750

V=750;

p=(8.*(1-0.24.*nu).*E.*t0.*h.^3)./(3.*(r.^2+h.^2).^2.*(1-nu))-

(4.*e0.*er.*V.^2.*h)./(t0.*r.^2)+(4.*r.^2.*t0.*sigma0.*h)./(r.^2+h.^2).^2;

180

plot(h,p,'k');

% When V=1000

V=1000;

p=(8.*(1-0.24.*nu).*E.*t0.*h.^3)./(3.*(r.^2+h.^2).^2.*(1-nu))-

(4.*e0.*er.*V.^2.*h)./(t0.*r.^2)+(4.*r.^2.*t0.*sigma0.*h)./(r.^2+h.^2).^2;

plot(h,p,'y');

%p0 is 97.1210 so plot that line too

p0=97.1210;

plot(h,p0,'-');

xlabel('Height');

ylabel('Pressure');

title('Circular Membrane');

hold off;

%% Volume vs. Voltage

E=208.2*10^3;

nu=0.5;

t0=76*10^-6;

er=6.39;

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e0=8.85*10^-12; r=8.06*10^-3; sigma0=50*10^3; h=0:5*10^-6:500*10^-6; h0=0.000412; h1=0.00041699; h2=0.000432695; h3=0.000461595; h4=0.000508945;

%deltaV0=((pi*r^2)/2)*h0+(pi/6)*(h0^3-h0^3); deltaV1=((pi*r^2)/2)*(h1-h0)+(pi/6)*(h1^3-h0^3); deltaV2=((pi*r^2)/2)*(h2-h0)+(pi/6)*(h2^3-h0^3); deltaV3=((pi*r^2)/2)*(h3-h0)+(pi/6)*(h3^3-h0^3); deltaV4=((pi*r^2)/2)*(h4-h0)+(pi/6)*(h4^3-h0^3);

deltaVmat=[0,deltaV1,deltaV2,deltaV3,deltaV4];

%deltaVmat=[deltaV0,deltaV1,deltaV2,deltaV3,deltaV4];

Voltage=[0,250,500,750,1000];

figure plot(Voltage,deltaVmat);

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xlabel('Voltage');

ylabel('Change in Volume');

title('Circular Membrane');

B.4 Matlab Code to Calculate Volume Exchange for Annular Membrane

% Annular Membrane

%% Pressure vs. Height

E=208.2*10^3;

nu=0.5;

t0=76*10^-6;

er=6.39;

e0=8.85*10^-12;

rI=4*10^-3;

rO=9*10^-3;

sigma0=50*10^3;

h=0:5*10^-6:600*10^-6;

t=(((rO-rI).*t0)./pi).*(2./(((rO-rI)./2).^2+h.^2)).^(1/2);

e=(8.*h.^2)./(3.*(rO-rI).^2);

% When V=0

V=0;

183