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

408

kernel, 10 kinoform, 1

Kirchhoff approximation, 56, 59 Kirchoff boundary conditions, 56 Kirchoff theory, 41

Kirchoff Theory of Diffraction, 55 Kramers-Kro¨nig relations, 157

Lanczos’ s factors, 215 Laplacian, 14, 31

large number of channels, 353 laser, 198

laser film writer, 244 laser machining, 244 least-squares, 176, 237 lens, 1, 134, 136

lens law, 132

lensless Fourier arrangement, 278 lensless Fourier transform hologram, 203 light scattering, 182

line integral, 327 linear convolution, 58

linear frequency modulated (linear fm) signal, 310

linear operator, 219, 231 linear polarization, 39

linear shift invariant (LSI) system, 9 linear system, 7

linear system theory, 2, 6 linear systems, 6

linear vector spaces, 219, 382 linearity, 12, 331

linearly independent vectors, 385 liquid gate, 180

lithography, 185

LM-ODIFIIT hologram, 301, 304 LM-ODIFIIT method, 300

local direction cosines, 121 local spatial frequencies, 121 Lohmann cell, 246, 300 Lohmann method, 245, Lohmann’s method, 246

Lohmann-ODIFIIT method, 245, 300 low-contrast film, 179

lower sideband, 159 low-pass filter, 218 lowpass filtering, 88, 214 lowpass signal, 323

LTI system, 311

INDEX

magnetic (vector) field, 31 magnetic density (vector) field, 31

magnetic resonance imaging (MRI), 2, 306 magnification, 128, 198

magnification factor, 129 main lobe, 214

mass conservation, 331 master hologram, 205 matched filter, 311

matched filtering, 306, 309, 311 matrix norm, 219

maximum eigenvalue, 241 maximum SNR, 311

Maxwell’s equations, 4, 31, 33, 361, 368 mechanical waves, 28

medical imaging, 326 meridional rays, 112, 123 metallic grating, 376 metallic silver, 178, 183

method of constrained iterative signal restoration, 212, 221

method of irregularly sampled zero-crossings (MISZC), 338

method of least-squares, 213 method of POCS, 227

method of projections on to convex sets (POCS), 212

method of stationary phase, 92 method of steepest descent, 241 metric spaces, 387

micro/nano technology, 2 microelectromechanical systems (MEMs), 4 microelectronics, 2

micromachining, 185 micromirrors, 4 microscope, 143 microwave DWDM, 3 microwaves, 275 minimum eigenvalue, 241 minimum norm, 239 mirror, 114

missing information, 212, 218 mode m, 372

modulation, 13, 244 modulation property, 157

modulation transfer function (MTF), 167, 177, 183

monochromatic wave, 42, 153 MTF, 174

INDEX

multidimensional Fourier transform, 10 multidimensional signal processing, 328 multiple constraints, 235

multiple focal points, 244 mutual intensity, 164

nanodiffractive devices, 4 narrow bandwidth, 321 narrowband waveform, 158 near field, 63

near field approximation (NFA), 94 negative film, 180

negative lens, 130

NFFA, 94, 103, 104, 105, 108, 109, 111, 205 N-level quantization, 249

noise power, 311 nonconvex constraints, 234 nonconvex set, 225, 234

nondestructive materials testing, 326 nondipersive wave equation, 27, 34 nonexpansive mapping, 219 nonlinear encoding, 347

nonlinear optical element, 6 nonmonochromatic wave field, 153, 161 nonmonochromatic waves, 41, 61, 86 nonperiodic grating-assisted directional

coupler, 197 nonstationary signal, 120

nonsynchronous waveguides, 197 nontanning bleach, 183

norm of a matrix, 219 numerical integration, 99

objective and collector lenses, 146 oceanography, 307

odd (antisymmetric) signal, 12 ODIFIIT, 275

one-image only holography, 245, 258, 265, 285

one-step gradient algorithm, 241 operator algebra, 134, 147

optical communications, 2, 76, 193

optical communications and networking, 338 optical communications/networking, 244 optical fiber, 25, 188

optical Fourier techniques, 338 optical imaging, 6, 212 optical imaging system, 1 optical interconnects, 2, 244

409

optical lithography, 185 optical matched filter, 6 optical networking, 2, 76 optical path length, 113 optical pattern recognition, 244 optical phased array, 245, 258 optical pulses, 2

optical recording devices, 199 optical spatial filtering, 139

optical transfer function (OTF), 153, 167, 173

optimal decimation-in-frequency iterative interlacing technique (ODIFIIT), 293

orthogonal basis, 386 orthogonality, 389 OTF, 169, 174

Pade approximation, 361, 365 parallel projection, 328

paraxial approximation, 124, 135, 139, 147, 279, 349

paraxial BPM method, 361 paraxial Helmholtz equation, 362 paraxial optics, 113

paraxial ray equations, 118 paraxial rays, 113

paraxial wave equation, 74, 188, 189, 193 paraxiality, 190

Parseval’s theorem, 13, 154, 156, 233 perfect image, 141

perfect lens, 135 periodic grating, 376 periodic sequence, 394 periodicity, 50 permeability, 32 permittivity, 32 phasar, 245

phase contrast microscopy, 134, 142 phase error tolerance, 356

phase factor, 137

Phase modulation, 177, 180, 245 phase plate, 143, 284

phase quadrature, 143 phase quantization, 358 phase relief, 184

phase retrieval, 213, 235 phase spectrum, 20

phase transformation, 134, 135 phase velocity, 28, 34, 35, 61

410

phased arrays (PHASAR), 3 phased arrays, 2 phased-array (PHASAR), 338 phasefront, 35

phase-only filter, 314 phasor, 33, 42

phasor amplitude, 158, 165 photographic density, 178 photographic emulsion, 182 photographic film, 177, 199 photography, 164 photoreduction, 244 photorefractive media, 188 photoresist, 205 photothermoplastic, 205 planar geometry, 341

plane boundary, 125 plane wave, 25, 37

plane wave spectrum, 191 PMMA, 187

PMMA positive photoresist, 260 POCS algorithm, 213, 290 POCS method, 275, 288

point spread function (PSF), 239 point-source apertures, 351 point-spread function, 8

polar coordinates, 21, 330 polarization, 38 polynomials, 236

positive and negative phase contrast, 143 positive lens, 129

positivity, 218

power exchange, 193, 195 Poynting vector, 38, 40

prediction and evaluation of natural disasters, 307

pre-Hilbert spaces, 389 principal planes, 131 projection operator, 225, 230

projection slice theorem, 326, 328 projections, 213, 225, 231, 328 projections onto convex sets (POCS), 225 projector, 225

pseudo inverse, 238

pulse compression, 309, 311, 314 pulse duration, 314

pulse shape, 309 pulse spectrum, 314 pupil function, 172

INDEX

quadratic phase factor, 148 quadrature filter, 154 quantization, 184

quantized Lohmann method, 249 quasi-monochromatic, 153, 154, 162 quasi-monochromatic wave field, 153, 158

radar, 306

radar bandwidth, 321 radar range swath, 323 radix, 395

Radon transform, 326, 327 raidian spatial frequency, 27, 30 random phase factor, 245 Range (or slant range), 307 range resolution, 308, 313 range stacking algorithm, 321 rank, 238

ray equation, 117 ray integral, 328 ray optics, 112

Rayleigh criterion, 248, 282 Rayleigh distance, 218 Rayleigh-Sommerfeld diffraction

integral, 91

Rayleigh-Sommerfeld integral, 59, 61, 63 Rayleigh-Sommerfeld region, 63 Rayleigh-Sommerfeld theory, 41, 57, 59, 61 rays, 112

ray-sum, 328

ray-transfer matrix, 123, 126 reactive ion etching, 2, 177, 185, 346 real Fourier hologram, 203

real Fourier transform, 7, 18 real hologram, 276

real representation, 161 real space, 219

rear focal plane, 129 rear focal point, 129 reciprocity principle, 339

recovery of signals, 212, 217 rectangular aperture, 70 rectangular lattice, 334 rectangular sequence, 213 reflecting diffraction gratings, 77 reflection, 115

reflection function, 78 reflection hologram, 202, 205 reflection phase gratings, 77

INDEX

refraction, 115 refractive index, 25, 113

refractive index inhomogeneity, 191 refractive lens, 1

regular sampling, 347

removal of spherical aberration, 245 resist, 187

resolution, 185

restoration from magnitude, 213, 235 restoration from phase, 213, 231 RIE, 185

rigorous coupled-wave analysis (RCWA), 374

ringing, 213 rotation, 332 rotation of axis, 14

Rowland geometry, 344

sampled wavefront, 258 sampling (sifting) property, 377 sampling interval, 213, 391 SAR image processing, 306 SAR imaging, 318

satellite system, 307

scalar diffraction theory, 41, 361 scalar wave equation, 189 scaled Fourier transform, 149 scaled pupil function, 141 scaling, 148, 332

scanning confocal microscopy, 134, 144

scanning electron beam microscopy, 346 scanning electron beam writer, 244 scanning electron microscope, 2, 258,

260, 270

scanning electron microscope system, 258 Schrodinger’s wave equation, 29 Schwarz’ inequality, 168, 220, 312, 387 second focal plane, 129

security devices, 244 Seidel aberrations, 174

seismic image reconstruction, 86 self-images, 80

semi-irregular sampling, 91, 245 separable function, 13, 122 separable transform, 10

shift, 332

shift invariant, 8 shift-invariance, 6

411

shift-variant, 224

short-time Fourier transform, 120 Shuttle Imaging Radar (SIR) system, 307 sidelobes, 214

sifting property, 8

signal recovery, 218, 225

signal recovery by contractions and projections, 218

signal restoration, 227 signal-to-noise ratio (SNR), 308, 306 silica glass, 185

silver grains, 178

silver halide particles, 177 silver speck, 178

simple harmonic solution, 27 Simpson quadrature algorithm, 99 sinc function, 88, 300, 325

sinc oscillations, 248 sine part, 20

single sideband modulation, 153, 154 single sideband signal, 161

singular value decomposition, 213, 239 sinusodial phase grating, 81

sinusoidal amplitude grating, 63, 79 sinusoidal phase grating, 63

Snell’s law, 115

SNR optimization, 314 sombrero function, 24, 47

Sommerfeld radiation condition, 56 source deconvolution, 319

South Greenland, 308 space charge, 32 space invariant, 8 space shift, 13

space-bandwidth product, 282 spaceborne SAR, 307

span, 385

spatial coherence, 4, 6, 153, 162 spatial filtering, 1

spatial frequencies, 137 spatial frequency, 27, 30 spatial frequency interpolation

algorithm, 321

spatial light modulator, 177 spectral norm, 219 spectral width, 315 spectroscopic imaging, 76 spectroscopy, 76, 244 spherical aberration, 210

412

spherical boundary, 125 spherical mirror, 125

spherical reference wave, 245, 266, 270 spherical wave, 25, 43, 57, 60, 138, 139 spot size, 185

spotlight mode, 318 square aperture, 69, 75, 78 squint mode, 318 standard basis, 386

stationary, 2-D random field, 169 stationary phase, 67

stationary random field, 169 steepest descent, 240

steepest descent algorithm, 213 strictly nonexpansive contraction, 220 strictly nonexpansive mapping, 219 subholograms, 275, 289, 296 subspace, 219, 383

subwavelength optical elements (SOEs), 3 sufficient conditions, 11

superposition integral, 8, 139 superposition principle, 7 superresolution, 212

super relief, 183

surface relief hologram, 205 symmetry, 331

synchronous communications, 2 Synchronous Waveguides, 195 synthesis equation, 10, 20

synthetic aperture radar (SAR), 1, 306

Talbot images, 80 Talbot subimages, 81 tanning bleach, 183

Taylor series, 96, 143, 261 Taylor series expansion, 207, 367 Taylor’s series, 92

telescopic system, 278, 283 temporal coherence, 162

temporal frequency spread, 153, 162 temporally coherent, 162

the Fresnel diffraction formula, 137 thick lens, 130

thickness, 134 thickness function, 136 thin lens, 126, 135 time coherence, 153

time domain correlation algorithm, 321 time frequency, 27, 30

INDEX

time-bandwidth product, 316 time-varying electric field, 25 time-varying imagery, 29, 30 time-varying magnetic field, 25 TM polarized light, 376 tomography, 2, 326

topographic and thematic mapping, 307 transfer function, 9, 46, 51, 58, 65, 70, 79 transformation operator, 218 transmission amplitude grating, 76 transmission function, 78

Transmission holograms, 202 transmittance, 180

transparent boundary condition, 364 transparent objects, 142

transverse electric field, 350 transverse magnification, 209 trap, 237

triangular inequality, 387, 389 triangular pulse, 378 tridiagonal matrix equation, 364 tunnel, 237

twin images, 199, 200, 251, 257, 265 two-fold symmetry, 12

Two-point resolution, 212, 217

ultrasonic image reconstruction, 86 unguided media, 25

uniform plane wave, 36 upper sideband, 159 urban planning, 307

vector, 382 vector norm, 219 vector space, 382 vignetting, 138

virtual hologram, 276 virtual holography, 275 virtual image, 199, 200 virtual lens effect, 192 virtual lenses, 191 virtual object, 281 VLSI, 177

volume diffraction gratings, 188 volume hologram, 203

wave equation, 41 wave modulation, 177 wave number, 27, 36

INDEX	413
wave vector, 35	windowing, 213
wavefront, 31, 119	windowing techniques, 212
wavefront reconstruction, 198	wireless systems, 2
waveguide, 193
wavelength, 27	XFDTD, 371
wavelength demultiplexer, 3, 338	x-ray lithography, 185
wavelength dispersion, 339
wavelength multiplexer, 3, 338	Yee cell, 369
wavelength ratio, 208	Yee’s algorithm, 368
waves, 26, 84
waveshaping, 244	Zernike polynomials, 154, 174
Weak convergence, 228	zero crossings, 261
wide angle BPM, 361, 365	zero-crossings, 261, 344
wide angle propagation, 188	zeroth order or linear interpolation, 334
wide-sense stationary (WSS)	zone plates, 2
process, 311	z-transform, 236

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