List of Contents………. iii

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Acknowledgements………. i

Abstract……… ii

List of Contents………. iii

1. INTRODUCTION……….1

References……… 3

2. BIOLOGICAL OPTICAL SYSTEM……… 4

2.1. Introduction……… 4

2.2. Human Eye………. 5

2.2.1. The Structure………. 6

2.2.2. Optical Properties……….. 8

2.2.3. Visual Acuity………. 11

2.3. Eye of the Bird of Prey……….12

2.3.1. Structure and Properties………. 12

2.3.2. Visual Acuity………..14

References ……….. 16

3. TUNABLE LENSES ………. 18

3.1. Introduction……… 18

3.2. State of Art………. 19

3.3. Bionspired Tunable Lenses with Electroactive Elastomers……….. 29

3.3.1. Tunable Crystalline Lens………. 30

3.3.2. Tunable Corneal Lens ……….34

3.3.3. Features ……….36

Reference ………... 37

4. MEASURAMENT OF THE REFRACTIVE INDEX: SYLGAR 184 ®…….. 41

4.1. Introduction……… 42

4.2. Configuration………. 43

4.3. Theoretical Aspects………. 46

4.4. Practical Aspects………. 48

4.4.1. Lateral Displacement ………. 48

4.4.2. The Effects of the Thickness of the Glass Plates………..50

4.5. Data Elaboration………. 52

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4.5.1. Algorithm 1: Center of Spot Extraction……… 54

4.5.2. Algorithm 2: Evaluation of the Refractive Index ………56

4.5.3. Algorithm 3: Optimization of the Refractive Index………….58

4.6. Calibration of the System………. 62

4.7. Error Propagation………... 65

4.8. Measurement Protocol……….68

4.9. Results………68

4.9.1. Algorithm 1………69

4.9.2. Algorithm 2………71

4.9.3. Algorithm 3………73

4.9.4. Temperature Effect……….74

4.9.5. Cauchy’s Equation and Abbe Number……….. 76

References ………. 78

5. OPTICAL SYSTEM: MODELING………. 79

5.1. Introduction………... 79

5.2. Lenses Model……….. 80

5.3. Model of the Bio-Inspired Optical System………. 84

5.4. Constraints………. 87

5.5. Development……….. 88

5.6. Sizing and Comparison……… 93

References……….. 95

6. OPTICAL SYSTEM: EVALUATION………. 96

6.1. Introduction………... 97

6.2. Cardinal Points……… 97

6.2.1. Rest Condition………. 98

6.2.2. Accommodation………. 101

6.2.3. Discussion………. 108

6.3. Aberrations……… 108

6.3.1. Rest Condition ………. 109

6.3.2. Accommodation ……….. 112

6.3.3. Chromatic Aberration ……….. 116

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6.3.4. Discussion……… 117

References………. 117

7. CONCLUSIONS AND FUTURE WORKS……….. 118

References………. 120

APPENDIX A: I. GEOMETRICAL OPTICS………. 121

1. Introduction………... 122

2. Geometrical Optics………. 124

3. Image Formation ………. 126

4. Cardinal Points of an Optical System………. 128

5. Sign Convention………. 129

6. First-Order Optic for a Single Surface………... 130

7. Lenses………. 132

8. The Lagrange Invariant………. 134

9. Stops and Pupils ……….. 135

10. F-Number and Numerical Aperture……….. 137

References………138

II. ABERRATIONS……… 139

1. Introduction……… 141

2. The Third Order Theory……….. 141

3. Spherical Aberration………. 144

4. Coma……….. 144

5. Astigmatism………. 145

6. Field Curvature……… 146

7. Distortion……… 147

8. Chromatic Aberration……….. 147

9. Seidel Coefficients……… 149

10. Calculation of the Seidel Coefficients………. 151

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References……….. 153

III. BASICS OF OPTICAL SYSTEM DESIGN……….. 154

1. Introduction……… 155

2. Mathematical Model of the Lens Shape……….. 156

3. Optical Material Properties……….. 157

4. Two-Component System……….. 159

5. Aberration Corrections……… 161

6. Resolution of a Optical Imaging System………. 164

References………. 168

IV. OPTICAL COMPUTATION……… 169

1. Introduction……….. 170

2. Meridional Rays ………. 171

APPENDIX B: DATA ANALISYS:MATLAB® FUNCTIONS………..173

 Algorithm1 ……….. 175

 Algorithm2 ……… 189

 Algorithm3. ……….. 200

APPENDIX C: OPTICAL SYSTEM:MATLAB® FUNCTIONS……….. 207

 Algorithm A:MODELING……….. 207

 Algorithm B:ACCOMMODATION………. 218

 Algorithm B:ABERRATIONS…... ……….. 221