Ersoy O.K. Diffraction, Fourier optics, and imaging (Wiley, 2006)(ISBN 0471238163)(427s) PEo

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Index

1-D FZP, 372

2-D BPM, 193

2-D convolution, 9, 65, 141

2-D DFT, 172

2-D FFT, 396

2-D Fourier transform, 10

2-D paraxial equation, 362

2-D sampling theorem, 333

2-D spatial filter, 45

3-D displays, 244

3-D Fourier transform, 29

3-D geometry, 344, 346

3-D plane wave solution, 35 a crystal dislocation, 178

a priori information, 218 a priori knowledge, 221

aberration wave function, 210 aberrations, 154, 163, 173, 198, 207, 210

absorbing boundary conditions (ABCs), 372 acetate, 178

acoustical holography, 284 acoustical waves, 275 agriculture, 307

airborne SAR, 307 Airy pattern, 75 ambiguity, 308

amplitude (magnitude) spectrum, 20 amplitude modulation, 245, 258, 267 amplitude spectrum, 159

amplitude transfer function, 164, 173 amplitude transmittance, 180

analog holography, 1, 198 analysis equation, 10, 20 analytic continuation, 218 analytic function, 218

analytic signal, 18, 153, 157, 161 angle, 388

angular frequency, 27

angular spectrum, 44, 47, 54, 59, 70, 71, 72, 137, 138

angular spectrum method (ASM), 90, 148, 190

antenna, 25, 316 antenna array, 307 antenna power gain, 317 aperiodic structures, 374 apodization, 212, 213

apodized phase contrast, 144 arrayed waveguide grating (AWG),

3, 338 ASM, 90

Astigmatism, 174, 187, 210 atmospheric effects, 308 AutoCAD, 250 autocorrelation, 201, 310 autocorrelation function, 169 automatic zero-crossings, 344 Azimuth (or cross-range), 307

back-projection, 331 backprojection algorithm, 321 bandpass filter, 183

bandpass signal, 323

Bartlet triangular window, 215 basis, 385

basis signals, 10

beam propagation method (BPM), 188, 190

BeamPROP, 366 BeamPROP software, 341

Bessel function, 22, 53, 81, 259 bilinear interpolation, 334

binary Fourier transform DOE, 254 binary FZP, 272

Diffraction, Fourier Optics and Imaging, by Okan K. Ersoy Copyright # 2007 John Wiley & Sons, Inc.

403

404

binary hologram, 245 binary optics, 198 binary phase DOE, 185 Blackman window, 215 blazed grating, 184 Bleaching, 177, 183 blurred image, 225 bounded signal, 332 boundedness, 240 BPM simulation, 195

CAD, 187

CAD layout, 250

Cauchy sequence, 221, 389 Cauchy-Schwarz inequality, 227, 388 causal signal, 157

central slice, 328 central-difference equations, 368 CGH transmittance, 294 characteristic impedance, 38 charge density, 31

chemical diffusion, 182 chirp pulse, 314

chirp signal, 310

circular aperture, 46, 47, 66, 75, 216 circular polarization, 39

circularly symmetric, 22, 145 clock, 2

closed convex set, 227 coarse film, 183 coherence, 162 coherent Imaging, 165

coherent imaging system, 167 coherent imaging technique, 307 coherent light, 180

coherent optical processing, 306 coherent transfer function, 167, 168 coherent wavefront recording, 198 coherent waves, 162

color film, 178 coma, 174, 210 communications, 325 compact disk, 205

complete metric space, 389

complete normed linear vector space, 219 complete power exchange, 195, 197 complex amplitude, 42, 137, 189 complex envelope, 158, 162, 164 complex Fourier transform, 18

INDEX

complex geometries, 361 complex imaging systems, 153 complex space, 219

complex wave function, 162 compression ratio, 315 Computed tomography (CT), 326

computer-generated hologram (CGH), 1, 2, 244

computer-generated holography, 198 computerized imaging, 5 computerized tomography, 306, 328 condition number, 241

conduction band, 178 confocal microscopy, 2, 145

confocal scanning microscopy, 5 conjugate gradient method, 213, 242 conjugate planes, 128, 132

constant amplitude Lohmann’s method, 248

constraint operator, 224 contraction mapping theorem, 220 contractions, 212, 219

contrast, 144 contrast reversal, 80 convex set, 225, 229 convex subspace, 384

convolution, 6, 12, 72, 147, 223, 332 convolution theorem, 9, 47, 58 correlation, 12

cosine part, 20

coupled mode theory, 193, 197 coupling coefficients, 193 Crank-Nicholson method, 361, 363, 369 cross-range (azimuth) resolution, 316 CT image, 326

cubical mesh, 371 curl, 31, 368

cutoff frequency, 165 cylinder function, 23, 146 cylindrical coordinates, 44, 52 cylindrical symmetry, 52 cylindrical wave, 44

data rate, 4

Debye approximation, 56 decimation-in-frequency (DIF), 395 decimation-in-frequency property, 275 decimation-in-time (DIT), 395 deconvolution, 212, 223

INDEX

delta function, 8, 139 demodulation, 244

dense wavelength division multiplexing (DWDM), 3, 246, 338

detection by SNR optimization, 309 detector systems, 164

detour phase method, 246, 300 DFT, 73, 224, 232

dielectric waveguides, 193 differentiation, 13 diffraction, 1, 2

diffraction grating, 3, 63, 76, 77, 82 diffraction integral, 79

diffraction limited, 142, 163 diffraction order, 77, 340 diffraction-limited imaging system, 153 diffraction-limited system, 173 diffractive apertures, 361

diffractive optical element (DOE), 1, 2, 177, 244

diffractive optical elements (DOE’s), 93, 184, 198

diffractive optics, 198, 244, 275 diffuser, 245, 257

digital holography, 93, 198 digital signal processing, 306, 325 digital volume hologram, 284 dimension, 385

dipole moment density, 32 direct sum, 384

direction cosines, 46 directional coupler, 2, 193

discrete Fourier transform (DFT), 47, 394 discrete Fourier-related transforms, 382 discrete-space system, 8

discrete-time Fourier transform (DTFT), 391

discretized OTF, 171

dispersion relationship, 348, 350 dispersive wave, 28

dispersive wave equation, 28 distance measure (metric), 386 distortion, 174, 210, 218 distortion operator, 221 distribution, 377

divergence, 31

diverging spherical waves, 58 divide-and-conquer approach, 395 Dolph-Chebyshev Window, 215

405

double slit, 41 double-concave lens, 135 double-convex lens, 135 dry etching system, 186 DTFT, 214, 224

DVD, 205

E-3 AWACS (Airborne Warning and Control System), 308

E-8C Joint STARS (Surveillance Target Attack Radar System), 308

e-beam lithography, 177, 186 echo signal, 316

effective physical aperture, 132 effective virtual reference wave, 285 eigenvalue analysis, 190

Eikonal (function), 118 Eikonal equation, 112, 119 electric (vector) field, 31 electric dipole, 25

electric displacement (flux) (vector) field, 31 electric susceptibility, 32

electromagnetic (EM) waves, 25, 31 electron source, 185

electron-beam (e-beam) lithography, 185 elliptic polarization, 39

EM pulse, 307 EM waves, 2

embossed hologram, 205 embossing, 205 entrance pupil, 133, 163

environmental sciences, 307

Envisat’s Medium Resolution Imaging Spectrometer (MERIS), 308

equivalent exit pupil, 141 Euclidian distance, 387 Euclidian norm, 219, 387 evanescent waves, 45, 48, 86, 191 even (symmetric) signal, 12

exit pupil, 133, 163, 218 exit pupil function, 173, 213 exposure, 178

extreme ultraviolet (EUVL) lithography, 185

fan-beam projection, 328 far field, 63

far field approximation (FFA), 94

fast Fourier transform (FFT), 47, 293, 395 fast Fourier transform, 90, 93

406

fast weighted zero-crossing algorithm (FWZC), 260

FD-BPM, 363 FDTD, 90

FDTD method, 368

Fejer’s arithmetic mean method, 215 femtosecond laser pulses, 185 Fermat’s principle, 113, 117

FFT, 73, 95, 96, 188 fiber optics, 2

field, 382

field amplitude, 6

field curvature, 174, 210

filtered backprojection algorithm, 326 filtered projection, 331

fine film, 183

finite aperture, 218

finite aperture size, 212 finite chirp function, 122

finite difference approximations, 367 finite difference method, 188

finite difference time domain (FDTD), 90 finite difference time domain (FDTD)

method, 361

finite differences, 361

finite element method, 90, 188 finite elements, 361

finite extent, 218

finite lens aperture, 138 finite pulse, 377 finite-difference method, 363

finite-dimensional vector space, 219, 385 finite-sized apertures, 350, 355

first focal point, 129 first principal plane, 131 fixed point, 220, 227 fixing, 178

flat lens, 272

focal length, 116, 135 focal plane, 137 forestry, 307

forward NFFA propagation, 205 four-fold symmetry, 12

Fourier analysis, 1 Fourier hologram, 203 Fourier integral, 93

Fourier modal analysis, 361 Fourier modal method, 361, 376

Fourier modal methods (FMMs), 374

INDEX

Fourier optics, 1

Fourier reconstruction algorithm, 326 Fourier reconstruction method, 333 Fourier representation, 161

Fourier series, 361 Fourier synthesis, 1

Fourier Transform, 1, 10, 134, 138, 148 Fourier transform hologram, 245 Fourier-Bessel transform, 23

Fraunhofer approximation, 90, 93, 96, 111, 258, 283

Fraunhofer diffraction, 75, 78, 81, 85, 133 Fraunhofer diffraction pattern, 137 Fraunhofer hologram, 203

Fraunhofer region, 63, 75, 82, 136 free spectral range, 341 Free-space propagation, 148 frequency analysis, 6

frequency shift, 13

Fresnel approximation, 65, 67, 71, 73, 74, 90, 92, 96, 105, 111, 138, 261, 306, 320

Fresnel cosine integral, 123

Fresnel diffraction, 66, 71, 72, 79, 84, 147 Fresnel diffraction formula, 140

Fresnel diffraction pattern, 67 Fresnel hologram, 203 Fresnel integrals, 68

Fresnel number, 69

Fresnel region, 63, 64, 65, 70, 148 Fresnel sine integral, 123

Fresnel zone plate (FZP), 246, 272 Fresnel-Kirchoff Diffraction Formula, 56, 57 front focal point, 129

gamma, 179 Gaussian field, 350

Gaussian blurring impulse response sequence, 225

Gaussian function, 310 Gaussian pulse, 314 Gaussian spectrum, 316 Gaussian window, 215

Generalized cosine windows, 215 generalized Fourier transform, 11 generalized function, 377 generalized inverse, 213, 238 generalized projections, 213, 234 geography, 307

Geometrical optics, 112, 134, 138, 147

INDEX

geophysical signal processing, 328 Gerchberg-Papoulis algorithm, 213 Gerchberg-Saxton algorithm, 236

Gibbs phenomenon, 213 GP algorithm, 229

graded-index (GRIN) material, 117 gradient method, 240

grating, 2, 78

Green’s function, 54, 55, 58, 59 Green’s theorem, 41

grid of zero-crossings, 261 grid spacing, 363

guided media, 25

Hamming window, 215, 325 Hankel transform, 7, 21, 146 Hanning window, 215 hard-clipping, 245, 255 heat, 29

Helmholtz equation, 41, 42, 55, 74, 90, 112, 119, 189, 362

He-Ne laser, 260, 270, 292 Heron’s expression, 261 high resolution printer, 244 high-contrast film, 179

higher order harmonic images, 347 higher order images, 270

Hilbert spaces, 382, 389

Hilbert transform, 153, 154, 161, 331

hologram, 198

hologram magnification, 208 Holographic imaging, 198 holographic microscopy, 284 holography, 4, 198

homogeneous medium, 11, 25, 118 homogeneous wave equation, 34, 36 homogeneous waves, 45 Hurter-Diffield (H & D) Curve, 179 Huygens-Fresnel principle, 58, 258

ideal target function, 320 IIT, 275

IIT technique, 289

image formation, 154, 279 image hologram, 203 image intensity, 212 image processing, 144 image reconstruction, 311

407

image reconstruction from projections, 306, 326

imaging, 1

imaging equation, 127 implementational issues, 359 improper integral, 155

impulse (delta or Dirac delta) function, 377 impulse function, 377

impulse response (function), 8

impulse response, 46, 65, 139, 141, 313, 336 impulse response function, 51, 144, 146 impulse response, 58

incoherent imaging systems, 166, 167 incoherent impulse response function, 169 index of refraction, 134 infinite-dimensional vector space, 385 inhomogenenous medium, 25 inhomogeneous index of refraction, 362 inhomogeneous media, 188, 189, 362 initial value problem, 190

inner-product, 386 inner-product vector spaces, 386 input pulse duration, 315

integrated optics, 2, 3, 25, 177, 193 intensity, 40, 140, 145

Intensity Transmittance, 178 interferometric control, 187 interpolation, 323, 336 inverse diffraction, 96 inverse DFT, 232

Inverse diffraction, 84 inverse DTFT, 391 inverse filter, 223

inverse Fourier transform, 10, 51 inverse Hilbert transform, 155 inverse NFFA, 205

inverse problem, 218

Inverse Radon Transform (IRT), 326, 331, 335

inverse real Fourier transform, 18 irradiance, 40

irregular sampling, 344, 347

iterative interlacing technique, 275, 290 iterative optimization, 97, 237, 245, 252

Jacobian, 23, 324

Kaiser window, 216

Kelley model, 182