Preface ........................................................ ix
Chapter 1 Foundations of Scalar Diffraction Theory .............. 1
1.1 Basics of Classical Electrodynamics ........................ 1
1.1.1 Sources of electric and magnetic fields ............. 2
1.1.2 Electric and magnetic fields ........................ 2
1.2 Simple Traveling-Wave Solutions to Maxwell's Equations ..... 5
1.2.1 Obtaining a wave equation ............................ 5
1.2.2 Simple traveling-wave fields ......................... 7
1.3 Scalar Diffraction Theory .................................. 9
1.4 Problems .................................................. 12
Chapter 2 Digital Fourier Transforms ........................... 15
2.1 Basics of Digital Fourier Transforms ...................... 15
2.1.1 Fourier transforms: from analytic to numerical ..... 15
2.1.2 Inverse Fourier transforms: from analytic to
numerical .......................................... 17
2.1.3 Performing discrete Fourier transforms in
software ........................................... 18
2.2 Sampling Pure-Frequency Functions ......................... 21
2.3 Discrete vs Continuous Fourier Transforms ................. 23
2.4 Alleviating Effects of Discretization ..................... 26
2.5 Three Case Studies in Transforming Signals ................ 30
2.5.1 Sine signals ....................................... 30
2.5.2 Gaussian signals ................................... 31
2.5.3 Gaussian signals with quadratic phase .............. 33
2.6 Two-Dimensional Discrete Fourier Transforms ............... 35
2.7 Problems .................................................. 37
Chapter 3 Simple Computations Using Fourier Transforms ........ 39
3.1 Convolution ............................................... 39
3.2 Correlation ............................................... 43
3.1 Structure Functions ....................................... 47
3.4 Derivatives ............................................... 50
3.5 Problems .................................................. 53
Chapter 4 Fraunhofer Diffraction and Lenses ................... 55
4.1 Fraunhofer Diffraction .................................... 55
4.2 Fourier-Transforming Properties of Lenses ................. 58
4.2.1 Object against the lens ............................ 59
4.2.2 Object before the lens ............................. 59
4.2.3 Object behind the lens ............................. 61
4.3 Problems .................................................. 64
Chapter 5 Imaging Systems and Aberrations ..................... 65
5.1 Aberrations ............................................... 65
5.1.1 Seidel aberrations ................................. 66
5.1.2 Zernike circle polynomials ......................... 66
5.1.2.1 Decomposition and mode removal ............. 73
5.1.2.2 RMS wavefront aberration ................... 75
5.2 Impulse Response and Transfer Function of Imaging
Systems ................................................... 77
5.2.1 Coherent imaging ................................... 77
5.2.2 Incoherent imaging ................................. 79
5.2.3 Strehl ratio ....................................... 82
5.3 Problems .................................................. 84
Chapter 6 Fresnel Diffraction in Vacuum ....................... 87
6.1 Different Forms of the Fresnel Diffraction Integral ....... 88
6.2 Operator Notation ......................................... 89
6.3 Fresnel-Integral Computation .............................. 90
6.3.1 One-step propagation ............................... 90
6.3.2 Two-step propagation ............................... 92
6.4 Angular-Spectrum Propagation .............................. 95
6.5 Simple Optical Systems ................................... 102
6.6 Point Sources ............................................ 107
6.7 Problems ................................................. 113
Chapter 7 Sampling Requirements for Fresnel Diffraction ...... 115
7.1 Imposing a Band Limit .................................... 115
7.2 Propagation Geometry ..................................... 117
7.3 Validity of Propagation Methods .......................... 120
7.3.1 Fresnel-integral propagation ...................... 120
7.3.1.1 One step, fixed observation-plane grid
spacing .................................. 120
7.3.1.2 Avoiding aliasing ........................ 121
7.3.2 Angular-spectrum propagation ...................... 124
7.3.3 General guidelines ................................ 128
7.4 Problems ................................................. 130
Chapter 8 Relaxed Sampling Constraints with Partial
Propagations .................................................. 133
8.1 Absorbing Boundaries ..................................... 134
8.2 Two Partial Propagations ................................. 135
8.3 Arbitrary Number of Partial Propagations ................. 138
8.4 Sampling for Multiple Partial Propagations ............... 139
8.5 Problems ................................................. 146
Chapter 9 Propagation through Atmospheric Turbulence .......... 149
9.1 Split-Step Beam Propagation Method ....................... 149
9.2 Refractive Properties of Atmospheric Turbulence .......... 150
9.2.1 Kolmogorov Theory of turbulence ................... 152
9.2.2 Optical propagation through turbulence ............ 156
9.2.3 Optical parameters of the atmosphere .............. 157
9.2.4 Layered atmosphere model .......................... 164
9.2.5 Theory ............................................ 164
9.3 Monte-Carlo Phase Screens ................................ 166
9.4 Sampling Constraints ..................................... 172
9.5 Executing Properly Sampled Simulation .................... 174
9.5.1 Determine propagation geometry and turbulence
conditions ........................................ 174
9.5.2 Analyze the sampling constraints .................. 176
9.5.3 Perform a vacuum simulation ....................... 178
9.5.4 Perform the turbulent simulations ................. 179
9.5.5 Verify the output ................................. 180
9.6 Conclusion ............................................... 182
9.7 Problems ................................................. 183
Appendix A Function Definitions ............................... 185
Appendix В MATLAB Code Listings ............................... 187
References .................................................... 189
Index ......................................................... 195
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