Authors |
|
xxi | |
Acknowledgments |
|
xxiii | |
Preface |
|
xxv | |
How This Book Came to Be |
|
xxix | |
Suggested Curricula |
|
xxxi | |
Guided Tour of the Chapters |
|
xxxiii | |
Learning Features |
|
xlvii | |
List of Abbreviations |
|
xlix | |
Chapter 1 Introduction and Overview |
|
1 | (30) |
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2 | (1) |
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1.2 Polarization States and the Poincare Sphere |
|
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2 | (3) |
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1.3 Polarization Elements and Polarization Properties |
|
|
5 | (3) |
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1.4 Polarimetry and Ellipsometry |
|
|
8 | (3) |
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1.5 Anisotropic Materials |
|
|
11 | (1) |
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1.6 Typical Polarization Problems in Optical Systems |
|
|
12 | (5) |
|
1.6.1 Angle Dependence of Polarizers |
|
|
12 | (1) |
|
1.6.2 Wavelength and Angle Dependence of Retarders |
|
|
13 | (1) |
|
1.6.3 Stress Birefringence in Lenses |
|
|
14 | (2) |
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1.6.4 Liquid Crystal Displays and Projectors |
|
|
16 | (1) |
|
|
17 | (9) |
|
1.7.1 Polarization Ray Tracing |
|
|
20 | (2) |
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1.7.2 Polarization Aberrations of Lenses |
|
|
22 | (3) |
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1.7.3 High Numerical Aperture Wavefronts |
|
|
25 | (1) |
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1.8 Comment on Historical Treatments |
|
|
26 | (1) |
|
1.9 Reference Books on Polarized Light |
|
|
27 | (1) |
|
|
27 | (2) |
|
|
29 | (2) |
Chapter 2 Polarized Light |
|
31 | (32) |
|
2.1 The Description of Polarized Light |
|
|
31 | (1) |
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2.2 The Polarization Vector |
|
|
32 | (2) |
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2.3 Properties of the Polarization Vector |
|
|
34 | (2) |
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2.4 Propagation in Isotropic Media |
|
|
36 | (1) |
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2.5 Magnetic Field, Flux, and Polarized Flux |
|
|
36 | (1) |
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37 | (4) |
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2.7 Evolution of Overall Phase |
|
|
41 | (1) |
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2.8 Rotation of Jones Vectors |
|
|
42 | (1) |
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2.9 Linearly Polarized Light |
|
|
42 | (1) |
|
2.10 Circularly Polarized Light |
|
|
43 | (2) |
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2.11 Elliptically Polarized Light |
|
|
45 | (3) |
|
2.12 Orthogonal Jones Vectors |
|
|
48 | (1) |
|
|
49 | (1) |
|
2.14 Addition of Jones Vectors |
|
|
49 | (1) |
|
2.15 Polarized Flux Components |
|
|
50 | (1) |
|
2.16 Converting Polarization Vectors into Jones Vectors |
|
|
51 | (3) |
|
2.17 Decreasing Phase Sign Convention |
|
|
54 | (1) |
|
2.18 Increasing Phase Sign Convention |
|
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55 | (1) |
|
2.19 Polarization State of Sources |
|
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56 | (3) |
|
|
59 | (2) |
|
|
61 | (2) |
Chapter 3 Stokes Parameters and the Poincare Sphere |
|
63 | (28) |
|
3.1 The Description of Polychromatic Light |
|
|
63 | (1) |
|
3.2 Phenomenological Definition of the Stokes Parameters |
|
|
64 | (1) |
|
|
65 | (1) |
|
3.4 Partially Polarized Light and the Degree of Polarization |
|
|
66 | (4) |
|
|
70 | (2) |
|
3.6 Rotation of the Polarization Ellipse |
|
|
72 | (1) |
|
3.7 Linearly Polarized Stokes Parameters |
|
|
73 | (1) |
|
3.8 Elliptical Polarization Parameters |
|
|
73 | (1) |
|
3.9 Orthogonal Polarization States |
|
|
74 | (1) |
|
3.10 Stokes Parameter and Jones Vector Sign Conventions |
|
|
75 | (1) |
|
3.11 Polarized Fluxes and Conversions between Stokes Parameters and Jones Vectors |
|
|
75 | (3) |
|
3.12 The Stokes Parameters' Non-Orthogonal Coordinate System |
|
|
78 | (2) |
|
|
80 | (3) |
|
3.14 Flat Mappings of the Poincare Sphere |
|
|
83 | (2) |
|
3.15 Summary and Conclusion |
|
|
85 | (1) |
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86 | (2) |
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|
88 | (3) |
Chapter 4 Interference of Polarized Light |
|
91 | (26) |
|
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91 | (1) |
|
4.2 Combining Light Waves |
|
|
92 | (1) |
|
|
93 | (2) |
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4.4 Interference of Nearly Parallel Monochromatic Plane Waves |
|
|
95 | (5) |
|
4.5 Interference of Plane Waves at Large Angles |
|
|
100 | (2) |
|
4.6 Polarization Considerations in Holography |
|
|
102 | (1) |
|
4.7 The Addition of Polarized Beams |
|
|
103 | (10) |
|
4.7.1 Addition of Polarized Light of Two Different Frequencies |
|
|
103 | (2) |
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4.7.2 Addition of Polychromatic Beams |
|
|
105 | (4) |
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4.7.3 A Gaussian Wave Packet Example |
|
|
109 | (4) |
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113 | (1) |
|
|
113 | (3) |
|
|
116 | (1) |
Chapter 5 Jones Matrices and Polarization Properties |
|
117 | (46) |
|
|
117 | (1) |
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5.2 Dichroic and Birefringent Materials |
|
|
118 | (1) |
|
5.3 Diattenuation and Retardance |
|
|
118 | (5) |
|
|
119 | (1) |
|
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120 | (3) |
|
|
123 | (5) |
|
|
124 | (3) |
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5.4.2 Jones Matrix Notation |
|
|
127 | (1) |
|
5.4.3 Rotation of Jones Matrices |
|
|
127 | (1) |
|
5.5 Polarizer and Diattenuator Jones Matrices |
|
|
128 | (5) |
|
5.5.1 Polarizer Jones Matrices |
|
|
128 | (2) |
|
5.5.2 Linear Diattenuator Jones Matrices |
|
|
130 | (3) |
|
5.6 Retarder Jones Matrices |
|
|
133 | (5) |
|
5.6.1 Linear Retarder Jones Matrices |
|
|
133 | (4) |
|
5.6.2 Circular Retarder Jones Matrices |
|
|
137 | (1) |
|
|
137 | (1) |
|
5.7 General Diattenuators and Retarders |
|
|
138 | (5) |
|
5.7.1 Linear Diattenuators |
|
|
139 | (1) |
|
5.7.2 Elliptical Diattenuators |
|
|
140 | (1) |
|
5.7.3 Elliptical Retarders |
|
|
141 | (2) |
|
5.8 Non-Polarizing Jones Matrices for Amplitude and Phase Change |
|
|
143 | (1) |
|
5.9 Matrix Properties of Jones Matrices |
|
|
144 | (9) |
|
5.9.1 Hermitian Matrices: Diattenuation |
|
|
144 | (1) |
|
5.9.2 Unitary Matrices and Unitary Transformations: Retarder |
|
|
145 | (4) |
|
5.9.3 Polar Decomposition: Separating Retardance from Diattenuation |
|
|
149 | (4) |
|
5.10 Increasing Phase Sign Convention |
|
|
153 | (1) |
|
|
153 | (2) |
|
|
155 | (6) |
|
|
161 | (2) |
Chapter 6 Mueller Matrices |
|
163 | (56) |
|
|
163 | (1) |
|
|
164 | (1) |
|
6.3 Sequences of Polarization Elements |
|
|
165 | (1) |
|
6.4 Non-Polarizing Mueller Matrices |
|
|
165 | (1) |
|
6.5 Rotating Polarization Elements about the Light Direction |
|
|
166 | (2) |
|
6.6 Retarder Mueller Matrices |
|
|
168 | (6) |
|
6.7 Polarizer and Diattenuator Mueller Matrices |
|
|
174 | (8) |
|
|
174 | (3) |
|
6.7.2 Transmittance and Diattenuation |
|
|
177 | (3) |
|
|
180 | (1) |
|
|
180 | (2) |
|
6.8 Poincare Sphere Operations |
|
|
182 | (8) |
|
6.8.1 The Operation of Retarders on the Poincare Sphere |
|
|
182 | (4) |
|
6.8.2 The Operation of a Rotating Linear Retarder |
|
|
186 | (1) |
|
6.8.3 The Operation of Polarizers and Diattenuators |
|
|
187 | (1) |
|
6.8.4 Indicating Polarization Properties |
|
|
188 | (2) |
|
6.9 Weak Polarization Elements |
|
|
190 | (2) |
|
6.10 Non-Depolarizing Mueller Matrices |
|
|
192 | (1) |
|
|
193 | (9) |
|
6.11.1 The Depolarization Index and the Average Degree of Polarization |
|
|
195 | (1) |
|
6.11.2 Degree of Polarization Surfaces and Maps |
|
|
196 | (2) |
|
6.11.3 Testing for Physically Realizable Mueller Matrices |
|
|
198 | (2) |
|
6.11.4 Weak Depolarizing Elements |
|
|
200 | (1) |
|
6.11.5 The Addition of Mueller Matrices |
|
|
201 | (1) |
|
6.12 Relating Jones and Mueller Matrices |
|
|
202 | (9) |
|
6.12.1 Transforming Jones Matrices into Mueller Matrices Using Tensor Product |
|
|
202 | (5) |
|
6.12.2 Conversion of Jones Matrices to Mueller Matrices Using Pauli Matrices |
|
|
207 | (1) |
|
6.12.3 Transforming Mueller Matrices into Jones Matrices |
|
|
207 | (4) |
|
6.13 Ray Tracing with Mueller Matrices |
|
|
211 | (2) |
|
6.13.1 Mueller Matrices for Refraction |
|
|
212 | (1) |
|
6.13.2 Mueller Matrices for Reflection |
|
|
212 | (1) |
|
6.14 The Origins of the Mueller Matrix |
|
|
213 | (1) |
|
|
214 | (4) |
|
|
218 | (1) |
Chapter 7 Polarimetry |
|
219 | (76) |
|
|
219 | (1) |
|
7.2 What Does the Polarimeter See? |
|
|
220 | (1) |
|
|
221 | (1) |
|
7.3.1 Light-Measuring Polarimeters |
|
|
221 | (1) |
|
7.3.2 Sample-Measuring Polarimeters |
|
|
221 | (1) |
|
7.3.3 Complete and Incomplete Polarimeters |
|
|
222 | (1) |
|
7.3.4 Polarization Generators and Analyzers |
|
|
222 | (1) |
|
7.4 Mathematics of Polarimetric Measurement and Data Reduction |
|
|
222 | (18) |
|
|
222 | (3) |
|
7.4.2 Measuring Mueller Matrix Elements |
|
|
225 | (1) |
|
7.4.3 Mueller Data Reduction Matrix |
|
|
226 | (4) |
|
7.4.4 Null Space and the Pseudoinverse |
|
|
230 | (10) |
|
7.5 Classes of Polarimeters |
|
|
240 | (2) |
|
7.5.1 Time-Sequential Polarimeters |
|
|
240 | (1) |
|
7.5.2 Modulated Polarimeters |
|
|
240 | (1) |
|
7.5.3 Division of Amplitude |
|
|
241 | (1) |
|
7.5.4 Division of Aperture |
|
|
241 | (1) |
|
7.5.5 Imaging Polarimeters |
|
|
241 | (1) |
|
7.6 Stokes Polarimeter Configurations |
|
|
242 | (20) |
|
7.6.1 Simultaneous Polarimetric Measurement |
|
|
242 | (7) |
|
7.6.1.1 Division-of-Aperture Polarimetry |
|
|
242 | (1) |
|
7.6.1.2 Division-of-Focal-Plane Polarimetry |
|
|
242 | (4) |
|
7.6.1.3 Division-of-Amplitude Polarimetry |
|
|
246 | (3) |
|
7.6.2 Rotating Element Polarimetry |
|
|
249 | (5) |
|
7.6.2.1 Rotating Analyzer Polarimeters |
|
|
249 | (1) |
|
7.6.2.2 Rotating Analyzer Plus Fixed Analyzer Polarimeter |
|
|
250 | (1) |
|
7.6.2.3 Rotating Retarder and Fixed Analyzer Polarimeters |
|
|
251 | (3) |
|
7.6.3 Variable Retarder and Fixed Polarizer Polarimeter |
|
|
254 | (1) |
|
7.6.4 Photoelastic Modulator Polarimeters |
|
|
255 | (3) |
|
7.6.5 The MSPI and MAIA Imaging Polarimeters |
|
|
258 | (1) |
|
7.6.6 Example Atmospheric Polarization Images |
|
|
259 | (3) |
|
7.7 Sample-Measuring Polarimeters |
|
|
262 | (14) |
|
|
263 | (9) |
|
7.7.1.1 Linear Polariscope |
|
|
263 | (3) |
|
7.7.1.2 Circular Polariscope |
|
|
266 | (1) |
|
7.7.1.3 Interference Colors |
|
|
267 | (2) |
|
7.7.1.4 Polariscope with Tint Plate |
|
|
269 | (1) |
|
|
270 | (2) |
|
7.7.2 Mueller Polarimetry Configurations |
|
|
272 | (8) |
|
7.7.2.1 Dual Rotating Retarder Polarimeter |
|
|
274 | (1) |
|
7.7.2.2 Polarimetry Near Retroreflection |
|
|
275 | (1) |
|
7.8 Interpreting Mueller Matrix Images |
|
|
276 | (3) |
|
7.9 Calibrating Polarimeters |
|
|
279 | (1) |
|
7.10 Artifacts in Polarimetric Images |
|
|
280 | (2) |
|
7.10.1 Pixel Misalignment |
|
|
281 | (1) |
|
7.11 Optimizing Polarimeters |
|
|
282 | (4) |
|
|
286 | (5) |
|
|
291 | (1) |
|
|
291 | (4) |
Chapter 8 Fresnel Equations |
|
295 | (28) |
|
|
295 | (1) |
|
|
296 | (2) |
|
8.2.1 Plane Waves and Rays |
|
|
296 | (1) |
|
|
296 | (1) |
|
8.2.3 Homogeneous and Isotropic Interfaces |
|
|
297 | (1) |
|
8.2.4 Light Propagation in Media |
|
|
297 | (1) |
|
|
298 | (10) |
|
8.3.1 s-and p-Polarization Components |
|
|
298 | (1) |
|
8.3.2 Amplitude Coefficients |
|
|
299 | (1) |
|
8.3.3 The Fresnel Equations |
|
|
300 | (1) |
|
8.3.4 Intensity Coefficients |
|
|
301 | (3) |
|
|
304 | (1) |
|
|
305 | (1) |
|
|
306 | (1) |
|
8.3.8 Intensity and Phase Change with Incident Angle |
|
|
307 | (1) |
|
8.3.9 Jones Matrices with Fresnel Coefficients |
|
|
308 | (1) |
|
8.4 Fresnel Refraction and Reflection |
|
|
308 | (8) |
|
8.4.1 Dielectric Refraction |
|
|
308 | (1) |
|
8.4.2 External Reflection |
|
|
309 | (2) |
|
8.4.3 Internal Reflection |
|
|
311 | (2) |
|
|
313 | (3) |
|
8.4.4.1 Normal Incidence Reflectance |
|
|
315 | (1) |
|
8.4.4.2 Retardance and Diattenuation of Metal at Non-Normal Incidence |
|
|
315 | (1) |
|
8.5 Approximate Representations of Fresnel Coefficients |
|
|
316 | (2) |
|
8.5.1 Taylor Series for the Fresnel Coefficients |
|
|
317 | (1) |
|
|
318 | (1) |
|
|
318 | (2) |
|
|
320 | (3) |
Chapter 9 Polarization Ray Tracing Calculus |
|
323 | (36) |
|
9.1 Definition of Polarization Ray Tracing Matrix, P |
|
|
324 | (1) |
|
9.2 Formalism of Polarization Ray Tracing Matrix Using Orthogonal Transformation |
|
|
325 | (6) |
|
9.3 Retarder Polarization Ray Tracing Matrix Examples |
|
|
331 | (3) |
|
9.4 Diattenuation Calculation Using Singular Value Decomposition |
|
|
334 | (3) |
|
9.5 Example-Interferometer with a Polarizing Beam Splitter |
|
|
337 | (7) |
|
9.5.1 Ray Tracing the Reference Path |
|
|
338 | (2) |
|
9.5.2 Ray Tracing through the Test Path |
|
|
340 | (1) |
|
9.5.3 Ray Tracing through the Analyzer |
|
|
341 | (1) |
|
9.5.4 Cumulative P Matrix for Both Paths |
|
|
342 | (2) |
|
9.6 The Addition Form of Polarization Ray Tracing Matrices |
|
|
344 | (3) |
|
9.6.1 Combining P Matrices for the Interferometer Example |
|
|
346 | (1) |
|
9.7 Example-A Hollow Corner Cube |
|
|
347 | (4) |
|
|
351 | (1) |
|
|
352 | (5) |
|
|
357 | (2) |
Chapter 10 Optical Ray Tracing |
|
359 | (64) |
|
|
359 | (1) |
|
10.2 Goals for Ray Tracing |
|
|
360 | (4) |
|
10.3 Specification of Optical Systems |
|
|
364 | (4) |
|
|
366 | (1) |
|
|
366 | (1) |
|
10.3.3 Optical Interfaces |
|
|
367 | (1) |
|
|
367 | (1) |
|
10.4 Specifications of Light Beams |
|
|
368 | (1) |
|
|
369 | (7) |
|
|
369 | (1) |
|
|
369 | (1) |
|
10.5.3 Entrance and Exit Pupils |
|
|
370 | (1) |
|
10.5.4 Importance of the Exit Pupil |
|
|
370 | (2) |
|
10.5.5 Marginal and Chief Rays |
|
|
372 | (1) |
|
10.5.6 Numerical Aperture and Lagrange Invariant |
|
|
373 | (1) |
|
|
374 | (1) |
|
|
375 | (1) |
|
|
376 | (17) |
|
|
377 | (1) |
|
10.6.2 Multiplicity of Ray Intercepts with a Surface |
|
|
378 | (1) |
|
10.6.3 Optical Path Length |
|
|
378 | (2) |
|
10.6.4 Reflection and Refraction |
|
|
380 | (1) |
|
10.6.5 Polarization Ray Tracing |
|
|
381 | (1) |
|
10.6.6 s-and p-Components |
|
|
382 | (1) |
|
10.6.7 Amplitude Coefficients and Interface Jones Matrix |
|
|
383 | (2) |
|
10.6.8 Polarization Ray Tracing Matrix |
|
|
385 | (8) |
|
|
393 | (14) |
|
10.7.1 Normalized Coordinates |
|
|
393 | (1) |
|
10.7.2 Wavefront Aberration Function |
|
|
393 | (1) |
|
10.7.3 Polarization Aberration Function |
|
|
394 | (1) |
|
10.7.4 Evaluation of the Aberration Function |
|
|
395 | (3) |
|
10.7.5 Seidel Wavefront Aberration Expansion |
|
|
398 | (3) |
|
10.7.6 Zernike Polynomials |
|
|
401 | (4) |
|
|
405 | (1) |
|
10.7.8 Polarization Quality |
|
|
406 | (1) |
|
10.8 Non-Sequential Ray Trace |
|
|
407 | (1) |
|
10.9 Coherent and Incoherent Ray Tracing |
|
|
407 | (3) |
|
10.9.1 Polarization Ray Tracing with Mueller Matrices |
|
|
409 | (1) |
|
10.10 The Use of Polarization Ray Tracing |
|
|
410 | (1) |
|
10.11 Brief History of Polarization Ray Tracing |
|
|
411 | (1) |
|
10.12 Summary and Conclusion |
|
|
412 | (1) |
|
|
413 | (3) |
|
10.14 Appendix: Cell Phone Lens Prescription |
|
|
416 | (4) |
|
|
420 | (3) |
Chapter 11 The Jones Pupil and Local Coordinate Systems |
|
423 | (24) |
|
11.1 Introduction: Local Coordinates for Entrance and Exit Pupils |
|
|
423 | (1) |
|
|
424 | (2) |
|
|
426 | (4) |
|
11.4 Double Pole Coordinates |
|
|
430 | (6) |
|
11.5 High Numerical Aperture Wavefronts |
|
|
436 | (1) |
|
11.6 Converting P Pupils to Jones Pupils |
|
|
437 | (2) |
|
11.7 Example: Cell Phone Lens Aberrations |
|
|
439 | (1) |
|
11.8 Wavefront Aberration Function Difference between Dipole and Double Pole Coordinates |
|
|
440 | (1) |
|
|
441 | (1) |
|
|
442 | (2) |
|
|
444 | (3) |
Chapter 12 Fresnel Aberrations |
|
447 | (32) |
|
|
447 | (1) |
|
12.2 Uncoated Single-Element Lens |
|
|
448 | (7) |
|
|
455 | (6) |
|
12.4 Combination of Fold Mirror Systems |
|
|
461 | (8) |
|
12.5 Cassegrain Telescope |
|
|
469 | (5) |
|
|
474 | (1) |
|
|
475 | (1) |
|
|
475 | (2) |
|
|
477 | (2) |
Chapter 13 Thin Films |
|
479 | (28) |
|
|
479 | (1) |
|
13.2 Single-Layer Thin Films |
|
|
480 | (6) |
|
13.2.1 Antireflection Coatings |
|
|
482 | (3) |
|
13.2.2 Ideal Single-Layer Antireflection Coating |
|
|
485 | (1) |
|
13.2.3 Metal Beam Splitters |
|
|
485 | (1) |
|
13.3 Multilayer Thin Films |
|
|
486 | (11) |
|
|
487 | (1) |
|
13.3.2 Quarter and Half Wave Films |
|
|
488 | (1) |
|
13.3.3 Reflection-Enhancing Coatings |
|
|
489 | (3) |
|
13.3.4 Polarizing Beam Splitters |
|
|
492 | (5) |
|
13.4 Contributions to Wavefront Aberrations |
|
|
497 | (2) |
|
13.5 Phase Discontinuities |
|
|
499 | (2) |
|
|
501 | (1) |
|
13.7 Appendix: Derivation of Single-Layer Equations |
|
|
502 | (2) |
|
|
504 | (1) |
|
|
505 | (2) |
Chapter 14 Jones Matrix Data Reduction with Pauli Matrices |
|
507 | (36) |
|
|
507 | (2) |
|
14.2 Pauli Matrices and Jones Matrices |
|
|
509 | (6) |
|
14.2.1 Pauli Matrix Identities |
|
|
509 | (1) |
|
14.2.2 Expansion in a Sum of Pauli Matrices |
|
|
510 | (1) |
|
14.2.3 Pauli Sign Convention |
|
|
511 | (1) |
|
14.2.4 Pauli Coefficients of a Polarization Element Rotated about the Optical Axis |
|
|
511 | (2) |
|
14.2.5 Eigenvalues and Eigenvectors and Matrix Functions for the Pauli Sum Form |
|
|
513 | (1) |
|
14.2.6 Canonical Summation Form |
|
|
514 | (1) |
|
14.3 Sequences of Polarization Elements |
|
|
515 | (3) |
|
14.4 Exponentiation and Logarithms of Matrices |
|
|
518 | (11) |
|
14.4.1 Exponentiation of Matrices |
|
|
518 | (1) |
|
14.4.2 Logarithms of Matrices |
|
|
519 | (1) |
|
|
520 | (1) |
|
14.4.4 Diattenuator Matrices |
|
|
521 | (2) |
|
14.4.5 Polarization Properties of Homogeneous Jones Matrices |
|
|
523 | (6) |
|
14.5 Elliptical Retarders and the Retarder Space |
|
|
529 | (2) |
|
14.6 Polarization Properties of Inhomogeneous Jones Matrices |
|
|
531 | (2) |
|
14.7 Diattenuation Space and Inhomogeneous Polarization Elements |
|
|
533 | (2) |
|
14.7.1 Superposing the Diattenuation and Retardance Spaces |
|
|
534 | (1) |
|
14.8 Weak Polarization Elements |
|
|
535 | (1) |
|
14.9 Summary and Conclusion |
|
|
536 | (1) |
|
|
537 | (3) |
|
|
540 | (3) |
Chapter 15 Paraxial Polarization Aberrations |
|
543 | (50) |
|
|
543 | (2) |
|
15.2 Polarization Aberrations |
|
|
545 | (5) |
|
15.2.1 Interaction of Weakly Polarizing Jones Matrices |
|
|
546 | (2) |
|
15.2.2 Polarization of a Sequence of Weakly Polarizing Ray Intercepts |
|
|
548 | (2) |
|
15.3 Paraxial Polarization Aberrations |
|
|
550 | (10) |
|
15.3.1 Paraxial Angle and Plane of Incidence |
|
|
550 | (3) |
|
15.3.2 Paraxial Diattenuation and Retardance |
|
|
553 | (1) |
|
15.3.3 Diattenuation Defocus |
|
|
553 | (2) |
|
15.3.4 Diattenuation Defocus and Retardance Defocus |
|
|
555 | (1) |
|
15.3.5 Diattenuation and Retardance across the Field of View |
|
|
556 | (1) |
|
15.3.6 Polarization Tilt and Piston |
|
|
557 | (1) |
|
15.3.7 Binodal Polarization |
|
|
558 | (1) |
|
15.3.8 Summation of Paraxial Polarization Aberrations over Surfaces |
|
|
558 | (2) |
|
15.4 Paraxial Polarization Analysis of a Seven-Element Lens System |
|
|
560 | (7) |
|
15.5 Higher-Order Polarization Aberrations |
|
|
567 | (13) |
|
15.5.1 Electric Field Aberrations |
|
|
568 | (4) |
|
|
572 | (6) |
|
15.5.3 Diattenuation and Retardance |
|
|
578 | (2) |
|
15.6 Polarization Aberration Measurements |
|
|
580 | (3) |
|
15.7 Summary and Conclusion |
|
|
583 | (1) |
|
|
583 | (6) |
|
|
583 | (2) |
|
15.8.2 Setting Up the Optical System |
|
|
585 | (1) |
|
15.8.3 The Paraxial Ray Trace |
|
|
586 | (1) |
|
15.8.4 Reduced Thicknesses and Angles |
|
|
587 | (1) |
|
15.8.5 Paraxial Skew Rays |
|
|
588 | (1) |
|
|
589 | (3) |
|
|
592 | (1) |
Chapter 16 Image Formation with Polarization Aberration |
|
593 | (36) |
|
|
593 | (1) |
|
16.2 Discrete Fourier Transformation |
|
|
594 | (4) |
|
16.3 Jones Exit Pupil and Jones Pupil Function |
|
|
598 | (3) |
|
16.4 Amplitude Response Matrix (ARM) |
|
|
601 | (2) |
|
16.5 Mueller Point Spread Matrix (MPSM) |
|
|
603 | (2) |
|
16.6 The Scale of the ARM and MPSM |
|
|
605 | (2) |
|
16.7 Polarization Structure of Images |
|
|
607 | (1) |
|
16.8 Optical Transfer Matrix (OTM) |
|
|
608 | (2) |
|
16.9 Example-Polarized Pupil with Unpolarized Object |
|
|
610 | (4) |
|
16.10 Example-Solid Corner Cube Retroreflector |
|
|
614 | (4) |
|
16.11 Example-Critical Angle Corner Cube Retroreflector |
|
|
618 | (4) |
|
16.12 Discussion and Conclusion |
|
|
622 | (1) |
|
|
623 | (4) |
|
|
627 | (2) |
Chapter 17 Parallel Transport and the Calculation of Retardance |
|
629 | (24) |
|
|
629 | (2) |
|
17.1.1 Purpose of the Proper Retardance Calculation |
|
|
631 | (1) |
|
17.2 Geometrical Transformations |
|
|
631 | (9) |
|
17.2.1 Rotation of Local Coordinates: Polarimeter Viewpoint |
|
|
631 | (2) |
|
17.2.2 Non-Polarizing Optical Systems |
|
|
633 | (1) |
|
17.2.3 Parallel Transport of Vectors |
|
|
634 | (2) |
|
17.2.4 Parallel Transport of Vectors with Reflection |
|
|
636 | (1) |
|
17.2.5 Parallel Transport Matrix, Q |
|
|
636 | (4) |
|
17.3 Canonical Local Coordinates |
|
|
640 | (2) |
|
17.4 Proper Retardance Calculations |
|
|
642 | (1) |
|
17.4.1 Definition of the Proper Retardance |
|
|
642 | (1) |
|
17.5 Separating Geometric Transformations from P |
|
|
642 | (3) |
|
17.5.1 The Proper Retardance Algorithm for P, Method 1 |
|
|
643 | (1) |
|
17.5.2 The Proper Retardance Algorithm for P, Method 2 |
|
|
644 | (1) |
|
|
645 | (1) |
|
|
645 | (4) |
|
17.6.1 Ideal Reflection at Normal Incidence |
|
|
646 | (1) |
|
17.6.2 An Aluminum-Coated Three-Fold Mirror System Example |
|
|
647 | (2) |
|
|
649 | (1) |
|
|
649 | (2) |
|
|
651 | (2) |
Chapter 18 A Skew Aberration |
|
653 | (16) |
|
|
653 | (1) |
|
18.2 Definition of Skew Aberration |
|
|
654 | (1) |
|
18.3 Skew Aberration Algorithm |
|
|
655 | (3) |
|
18.4 Lens Example-U.S. Patent 2,896,506 |
|
|
658 | (2) |
|
18.5 Skew Aberration in Paraxial Ray Trace |
|
|
660 | (2) |
|
18.6 Example of Paraxial Skew Aberration |
|
|
662 | (1) |
|
18.7 Skew Aberration's Effect on PSF |
|
|
663 | (2) |
|
18.8 PSM for U.S. Patent 2,896,506 |
|
|
665 | (1) |
|
18.9 Statistics-CODE V Patent Library |
|
|
666 | (1) |
|
|
667 | (1) |
|
|
667 | (1) |
|
|
668 | (1) |
Chapter 19 Birefringent Ray Trace |
|
669 | (46) |
|
19.1 Ray Tracing in Birefringent Materials |
|
|
669 | (3) |
|
19.2 Description of Electromagnetic Waves in Anisotropic Media |
|
|
672 | (1) |
|
19.3 Defining Birefringent Materials |
|
|
673 | (6) |
|
19.4 Eigenmodes of Birefringent Materials |
|
|
679 | (2) |
|
19.5 Reflections and Refractions at Birefringent Interface |
|
|
681 | (13) |
|
19.6 Data Structure for Ray Doubling |
|
|
694 | (1) |
|
19.7 Polarization Ray Tracing Matrices for Birefringent Interfaces |
|
|
695 | (11) |
|
19.7.1 Case I: Isotropic-to-Isotropic Intercept |
|
|
698 | (2) |
|
19.7.2 Case II: Isotropic-to-Birefringent Interface |
|
|
700 | (1) |
|
19.7.3 Case III: Birefringent-to-Isotropic Interface |
|
|
701 | (2) |
|
19.7.4 Case IV: Birefringent-to-Birefringent Interface |
|
|
703 | (3) |
|
19.8 Example: Ray Splitting through Three Biaxial Crystal Blocks |
|
|
706 | (1) |
|
19.9 Example: Reflections Inside a Biaxial Cube |
|
|
707 | (3) |
|
|
710 | (1) |
|
|
711 | (2) |
|
|
713 | (2) |
Chapter 20 Beam Combination with Polarization Ray Tracing Matrices |
|
715 | (26) |
|
|
715 | (1) |
|
20.2 Wavefronts and Ray Grids |
|
|
716 | (2) |
|
20.3 Co-Propagating Wavefront Combination |
|
|
718 | (10) |
|
20.4 Non-Co-Propagating Wavefront Combination |
|
|
728 | (2) |
|
20.5 Combining Irregular Ray Grids |
|
|
730 | (6) |
|
20.5.1 General Steps to Combine Misaligned Ray Data |
|
|
730 | (2) |
|
20.5.2 Inverse-Distance Weighted Interpolation |
|
|
732 | (4) |
|
|
736 | (1) |
|
|
737 | (2) |
|
|
739 | (2) |
Chapter 21 Uniaxial Materials and Components |
|
741 | (44) |
|
21.1 Optical Design Issues in Uniaxial Materials |
|
|
741 | (2) |
|
21.2 Descriptions of Uniaxial Materials |
|
|
743 | (2) |
|
21.3 Eigenmodes of Uniaxial Materials |
|
|
745 | (1) |
|
21.4 Reflections and Refractions at a Uniaxial Interface |
|
|
746 | (3) |
|
21.5 Index Ellipsoid, Optical Indicatrix, and K-and S-Surfaces |
|
|
749 | (16) |
|
21.6 Aberrations of Crystal Waveplates |
|
|
765 | (6) |
|
21.6.1 A-Plate Aberrations |
|
|
767 | (2) |
|
21.6.2 C-Plate Aberrations |
|
|
769 | (2) |
|
21.7 Image Formation through an A-Plate |
|
|
771 | (6) |
|
|
777 | (1) |
|
|
778 | (1) |
|
|
779 | (5) |
|
|
784 | (1) |
Chapter 22 Crystal Polarizers |
|
785 | (26) |
|
22.1 Introduction to Crystal Polarizers |
|
|
785 | (1) |
|
22.2 Materials for Crystal Polarizers |
|
|
786 | (1) |
|
22.3 Glan-Taylor Polarizer |
|
|
787 | (10) |
|
|
787 | (2) |
|
22.3.2 Multiple Potential Ray Paths |
|
|
789 | (4) |
|
22.3.3 Multiple Polarized Wavefronts |
|
|
793 | (3) |
|
22.3.4 Polarized Wavefronts Exiting from the Polarizer |
|
|
796 | (1) |
|
22.4 Aberrations of the Glan-Taylor Polarizer |
|
|
797 | (2) |
|
22.5 Pairs of Glan-Taylor Polarizers |
|
|
799 | (5) |
|
|
804 | (1) |
|
|
805 | (3) |
|
|
808 | (3) |
Chapter 23 Diffractive Optical Elements |
|
811 | (26) |
|
|
811 | (3) |
|
23.2 The Grating Equation |
|
|
814 | (4) |
|
|
818 | (11) |
|
23.3.1 Reflection Diffractive Gratings |
|
|
818 | (4) |
|
23.3.2 Wire Grid Polarizers |
|
|
822 | (3) |
|
23.3.3 Diffractive Retarders |
|
|
825 | (1) |
|
23.3.4 Diffractive Subwavelength Antireflection Coatings |
|
|
826 | (3) |
|
23.4 Summary of the RCWA Algorithm |
|
|
829 | (3) |
|
|
832 | (2) |
|
|
834 | (1) |
|
|
834 | (3) |
Chapter 24 Liquid Crystal Cells |
|
837 | (42) |
|
|
837 | (1) |
|
|
838 | (3) |
|
24.2.1 Dielectric Anisotropy |
|
|
840 | (1) |
|
24.3 Liquid Crystal Cells |
|
|
841 | (5) |
|
24.3.1 Construction of Liquid Crystal Cells |
|
|
842 | (1) |
|
|
843 | (2) |
|
24.3.3 Liquid Crystal Display: High Contrast Ratio Intensity Modulation |
|
|
845 | (1) |
|
24.4 Configurations of Liquid Crystal Cells |
|
|
846 | (10) |
|
24.4.1 The Freedericksz Cell |
|
|
846 | (1) |
|
24.4.2 90° Twisted Nematic Cell |
|
|
847 | (2) |
|
24.4.3 Super Twisted Nematic Cell |
|
|
849 | (1) |
|
24.4.4 Vertically Aligned Nematic Cell |
|
|
850 | (2) |
|
24.4.5 In-Plane Switching Cell |
|
|
852 | (2) |
|
24.4.6 Liquid Crystal on Silicon Cells |
|
|
854 | (1) |
|
24.4.7 Blue Phase LC Cells |
|
|
855 | (1) |
|
|
856 | (5) |
|
24.5.1 Extended Jones Matrix Model |
|
|
856 | (1) |
|
24.5.2 Single Pass with Polarization Ray Tracing Matrices |
|
|
857 | (2) |
|
24.5.3 Multilayer Interference Models |
|
|
859 | (1) |
|
24.5.4 Calculation for Liquid Crystal Cell ZLI-1646 |
|
|
859 | (2) |
|
24.6 Issues in the Construction of LC Cells |
|
|
861 | (3) |
|
|
861 | (1) |
|
|
861 | (1) |
|
|
862 | (1) |
|
24.6.4 Oscillating Square Wave Voltage |
|
|
863 | (1) |
|
24.7 Limitations on LC Cell Performance |
|
|
864 | (8) |
|
|
865 | (2) |
|
24.7.2 Spectral Variation of Exiting Polarization State |
|
|
867 | (1) |
|
24.7.3 Variation of Retardance with Angle of Incidence |
|
|
867 | (1) |
|
24.7.4 Compensating LC Cells' Polarization Aberrations with Biaxial Films |
|
|
868 | (2) |
|
|
870 | (1) |
|
|
871 | (1) |
|
24.8 Testing Liquid Crystal Cells |
|
|
872 | (5) |
|
24.8.1 Twisted Nematic Cell Example |
|
|
873 | (1) |
|
|
874 | (1) |
|
|
875 | (1) |
|
|
875 | (1) |
|
24.8.5 Sheet Retarder Defect |
|
|
876 | (1) |
|
24.8.6 Misalignment between Analyzer and Exiting Polarization State |
|
|
877 | (1) |
|
|
877 | (1) |
|
|
878 | (1) |
|
|
878 | (1) |
Chapter 25 Stress-Induced Birefringence |
|
879 | (30) |
|
25.1 Introduction to Stress Birefringence |
|
|
879 | (2) |
|
25.2 Stress Birefringence in Optical Systems |
|
|
881 | (1) |
|
25.3 Theory of Stress-Induced Birefringence |
|
|
881 | (2) |
|
25.4 Ray Tracing in Stress Birefringent Components |
|
|
883 | (6) |
|
25.5 Ray Tracing through Stress Birefringence Components with Spatially Varying Stress |
|
|
889 | (9) |
|
25.5.1 Storage of System Shape |
|
|
890 | (1) |
|
25.5.2 Refraction and Reflections |
|
|
891 | (1) |
|
25.5.3 Stress Data Format |
|
|
891 | (1) |
|
25.5.4 Polarization Ray Tracing Matrix for Spatially Varying Biaxial Stress |
|
|
892 | (3) |
|
25.5.5 Examples of Spatially Varying Stress Function |
|
|
895 | (3) |
|
25.6 Effects of Stress Birefringence on Optical System Performance |
|
|
898 | (7) |
|
25.6.1 Observing Stress Birefringence Using Polariscope |
|
|
898 | (3) |
|
25.6.2 Simulations of Injection-Molded Lens |
|
|
901 | (2) |
|
25.6.3 Simulation of a Plastic DVD Lens |
|
|
903 | (2) |
|
|
905 | (1) |
|
|
906 | (1) |
|
|
907 | (1) |
|
|
907 | (2) |
Chapter 26 Multi-Order Retarders and the Mystery of Discontinuities |
|
909 | (20) |
|
|
909 | (1) |
|
26.2 Mystery of Retardance Discontinuity |
|
|
910 | (2) |
|
26.3 Retardance Unwrapping for Homogeneous Retarder Systems Using a Simple Dispersion Model |
|
|
912 | (4) |
|
|
912 | (1) |
|
26.3.2 Retardance of the Homogeneous Retarder System |
|
|
912 | (2) |
|
26.3.3 Homogeneous Retarder's Trajectory and Retardance Unwrapping in Retarder Space |
|
|
914 | (2) |
|
26.4 Discontinuities in Unwrapped Retardance Values for Compound Retarder Systems with Arbitrary Alignment |
|
|
916 | (8) |
|
26.4.1 Compound Retarder Jones Matrix Decomposition |
|
|
917 | (2) |
|
26.4.2 Compound Retarder's Trajectory in Retarder Space |
|
|
919 | (1) |
|
26.4.3 Multiple Modes Exit the Compound Retarder System |
|
|
920 | (2) |
|
26.4.4 Compound Retarder Example at 45° |
|
|
922 | (2) |
|
|
924 | (1) |
|
|
925 | (1) |
|
|
925 | (2) |
|
|
927 | (2) |
Chapter 27 Summary and Conclusions |
|
929 | (32) |
|
|
929 | (1) |
|
27.2 Polarization Ray Tracing Complications |
|
|
930 | (7) |
|
27.2.1 Optical System Description Complications |
|
|
930 | (1) |
|
27.2.2 Elliptical Polarization Properties of Ray Paths |
|
|
931 | (1) |
|
27.2.3 Optical Path Length and Phase |
|
|
931 | (1) |
|
27.2.4 Definition of Retardance |
|
|
932 | (1) |
|
27.2.5 Retardance and Skew Aberration |
|
|
932 | (1) |
|
27.2.6 Multi-Order Retardance |
|
|
933 | (1) |
|
27.2.7 Birefringent Ray Tracing Complications |
|
|
934 | (1) |
|
27.2.8 Coherence Simulation |
|
|
935 | (1) |
|
|
935 | (1) |
|
|
936 | (1) |
|
27.3 Polarization Ray Tracing Concepts and Methods |
|
|
937 | (3) |
|
27.3.1 Jones Matrices and Jones Pupil |
|
|
937 | (1) |
|
27.3.2 P Matrix and Local Coordinates |
|
|
937 | (1) |
|
27.3.3 Generalization of PSF and OTF |
|
|
937 | (1) |
|
27.3.4 Ray Doubling, Ray Trees, and Data Structures |
|
|
938 | (1) |
|
|
939 | (1) |
|
27.3.6 Alternative Simulation Methods |
|
|
940 | (1) |
|
27.4 Polarization Aberration Mitigation |
|
|
940 | (2) |
|
27.4.1 Analyzing Polarization Ray Tracing Output |
|
|
941 | (1) |
|
27.5 Comparison of Polarization Ray Tracing and Polarization Aberrations |
|
|
942 | (17) |
|
27.5.1 Aluminum Coating and Polarization Aberration Expression |
|
|
943 | (2) |
|
27.5.2 Polarization Ray Trace and the Jones Pupil |
|
|
945 | (1) |
|
27.5.3 Aberration Expression for the Jones Pupil |
|
|
946 | (3) |
|
27.5.4 Diattenuation and Retardance Contributions |
|
|
949 | (1) |
|
27.5.5 Design Rules Based on Polarization Aberrations |
|
|
950 | (4) |
|
27.5.5.1 Diattenuation at the Center of the Pupil |
|
|
951 | (1) |
|
27.5.5.2 Retardance at the Center of the Pupil |
|
|
951 | (1) |
|
27.5.5.3 Linear Variation of Diattenuation |
|
|
952 | (1) |
|
27.5.5.4 Linear Variation of Retardance, the PSF Shear between the XX-and YY-Components |
|
|
952 | (1) |
|
27.5.5.5 The Polarization-Dependent Astigmatism |
|
|
952 | (1) |
|
27.5.5.6 The Fraction of Light in the Ghost PSF in XY-and YX-Components |
|
|
953 | (1) |
|
27.5.6 Amplitude Response Matrix |
|
|
954 | (1) |
|
27.5.7 Mueller Matrix Point Spread Matrices |
|
|
955 | (3) |
|
27.5.8 Location of the PSF Image Components |
|
|
958 | (1) |
|
|
959 | (2) |
Index |
|
961 | |