DIFFRACTION, FOURIER OPTICS AND IMAGING
CONTENTS 1 DIFFRACTION, FOURIER OPTICS AND IMAGING INTRODUCTION EXAMPLES OF EMERGING APPLICATIONS WITH GROWING SIGNI?CANCE DENSE WAVELENGTH DIVISION MULTIPLEXING/DEMULTIPLEXING (DWDM) OPTICAL AND MICROWAVE DWDM SYSTEMS DIFFRACTIVE AND SUBWAVELENGTH OPTICAL ELEMENTS NANODIFFRACTIVE DEVICES AND RIGOROUS DIFFRACTION THEORY MODERN IMAGING TECHNIQUES 2 LINEAR SYSTEMS AND TRANSFORMS LINEAR SYSTEMS AND SHIFT INVARIANCE CONTINUOUS-SPACE FOURIER TRANSFORM EXISTENCE OF FOURIER TRANSFORM PROPERTIES OF THE FOURIER TRANSFORM REAL FOURIER TRANSFORM AMPLITUDE AND PHASE SPECTRA HANKEL TRANSFORMS 3 FUNDAMENTALS OF WAVE PROPAGATION WAVES ELECTROMAGNETIC WAVES PHASOR REPRESENTATION WAVE EQUATIONS IN A CHARGE-FREE MEDIUM WAVE EQUATIONS IN PHASOR REPRESENTATION IN A CHARGE-FREE MEDIUM PLANE EM WAVES 4 SCALAR DIFFRACTION THEORY HELMHOLTZ EQUATION ANGULAR SPECTRUM OF PLANE WAVES FAST FOURIER TRANSFORM (FFT) IMPLEMENTATION OF THE ANGULAR SPECTRUM OF PLANE WAVES THE KIRCHOFF THEORY OF DIFFRACTION KIRCHOFF THEORY OF DIFFRACTION FRESNEL–KIRCHOFF DIFFRACTION FORMULA THE RAYLEIGH–SOMMERFELD THEORY OF DIFFRACTION THE KIRCHHOFF APPROXIMATION THE SECOND RAYLEIGH–SOMMERFELD DIFFRACTION FORMULA ANOTHER DERIVATION OF THE FIRST RAYLEIGH–SOMMERFELD DIFFRACTION INTEGRAL THE RAYLEIGH–SOMMERFELD DIFFRACTION INTEGRAL FOR NONMONOCHROMATIC WAVES 5 FRESNEL AND FRAUNHOFER APPROXIMATIONS DIFFRACTION IN THE FRESNEL REGION FFT IMPLEMENTATION OF FRESNEL DIFFRACTION PARAXIAL WAVE EQUATION DIFFRACTION IN THE FRAUNHOFER REGION DIFFRACTION GRATINGS FRAUNHOFER DIFFRACTION BY A SINUSOIDAL AMPLITUDE GRATING FRESNEL DIFFRACTION BY A SINUSOIDAL AMPLITUDE GRATING FRAUNHOFER DIFFRACTION WITH A SINUSOIDAL PHASE GRATING 5 10 DIFFRACTION GRATINGS MADE OF SLITS 6 INVERSE DIFFRACTION INVERSION OF THE FRESNEL AND FRAUNHOFER REPRESENTATIONS INVERSION OF THE ANGULAR SPECTRUM REPRESENTATION ANALYSIS 7 WIDE-ANGLE NEAR AND FAR FIELD APPROXIMATIONS FOR SCALAR DIFFRACTION A REVIEW OF FRESNEL AND FRAUNHOFER APPROXIMATIONS THE RADIAL SET OF APPROXIMATIONS HIGHER ORDER IMPROVEMENTS AND ANALYSIS INVERSE DIFFRACTION AND ITERATIVE OPTIMIZATION NUMERICAL EXAMPLES MORE ACCURATE APPROXIMATIONS CONCLUSIONS 8 GEOMETRICAL OPTICS PROPAGATION OF RAYS THE RAY EQUATIONS THE EIKONAL EQUATION LOCAL SPATIAL FREQUENCIES AND RAYS MATRIX REPRESENTATION OF MERIDIONAL RAYS THICK LENSES ENTRANCE AND EXIT PUPILS OF AN OPTICAL SYSTEM 9 FOURIER TRANSFORMS AND IMAGING WITH COHERENT OPTICAL SYSTEMS PHASE TRANSFORMATION WITH A THIN LENS FOURIER TRANSFORMS WITH LENSES WAVE FIELD INCIDENT ON THE LENS WAVE FIELD TO THE LEFT OF THE LENS WAVE FIELD TO THE RIGHT OF THE LENS IMAGE FORMATION AS 2-D LINEAR FILTERING THE EFFECT OF FINITE LENS APERTURE PHASE CONTRAST MICROSCOPY SCANNING CONFOCAL MICROSCOPY IMAGE FORMATION OPERATOR ALGEBRA FOR COMPLEX OPTICAL SYSTEMS 10 IMAGING WITH QUASI-MONOCHROMATIC WAVES HILBERT TRANSFORM ANALYTIC SIGNAL ANALYTIC SIGNAL REPRESENTATION OF A NONMONOCHROMATIC WAVE FIELD QUASI-MONOCHROMATIC, COHERENT, AND INCOHERENT WAVES DIFFRACTION EFFECTS IN A GENERAL IMAGING SYSTEM IMAGING WITH QUASI-MONOCHROMATIC WAVES COHERENT IMAGING INCOHERENT IMAGING FREQUENCY RESPONSE OF A DIFFRACTION-LIMITED IMAGING SYSTEM COHERENT IMAGING SYSTEM INCOHERENT IMAGING SYSTEM COMPUTER COMPUTATION OF THE OPTICAL TRANSFER FUNCTION PRACTICAL CONSIDERATIONS 10 10 ABERRATIONS 10 10 1 ZERNIKE POLYNOMIALS 11 OPTICAL DEVICES BASED ON WAVE MODULATION PHOTOGRAPHIC FILMS AND PLATES TRANSMITTANCE OF LIGHT BY FILM MODULATION TRANSFER FUNCTION BLEACHING DIFFRACTIVE OPTICS, BINARY OPTICS, AND DIGITAL OPTICS E-BEAM LITHOGRAPHY DOE IMPLEMENTATION 12 WAVE PROPAGATION IN INHOMOGENEOUS MEDIA HELMHOLTZ EQUATION FOR INHOMOGENEOUS MEDIA PARAXIAL WAVE EQUATION FOR INHOMOGENEOUS MEDIA BEAM PROPAGATION METHOD THE VIRTUAL LENS EFFECT WAVE PROPAGATION IN A DIRECTIONAL COUPLER A SUMMARY OF COUPLED MODE THEORY COMPARISON OF COUPLED MODE THEORY AND BPM COMPUTATIONS 13 HOLOGRAPHY COHERENT WAVE FRONT RECORDING LEITH–UPATNIEKS HOLOGRAM TYPES OF HOLOGRAMS FRESNEL AND FRAUNHOFER HOLOGRAMS IMAGE AND FOURIER HOLOGRAMS VOLUME HOLOGRAMS EMBOSSED HOLOGRAMS COMPUTER SIMULATION OF HOLOGRAPHIC RECONSTRUCTION ANALYSIS OF HOLOGRAPHIC IMAGING AND MAGNI?CATION ABERRATIONS 14 APODIZATION, SUPERRESOLUTION, AND RECOVERY OF MISSING INFORMATION APODIZATION DISCRETE-TIME WINDOWS TWO-POINT RESOLUTION AND RECOVERY OF SIGNALS CONTRACTIONS CONTRACTION MAPPING THEOREM AN ITERATIVE METHOD OF CONTRACTIONS FOR SIGNAL RECOVERY ITERATIVE CONSTRAINED DECONVOLUTION METHOD OF PROJECTIONS METHOD OF PROJECTIONS ONTO CONVEX SETS GERCHBERG–PAPOULIS (GP) ALGORITHM 14 10 OTHER POCS ALGORITHMS 14 11 RESTORATION FROM PHASE 14 12 RECONSTRUCTION FROM A DISCRETIZED PHASE FUNCTION BY USING THE DFT 14 13 GENERALIZED PROJECTIONS 14 14 RESTORATION FROM MAGNITUDE 14 14 1 TRAPS AND TUNNELS 14 15 IMAGE RECOVERY BY LEAST SQUARES AND THE GENERALIZED INVERSE 14 16 COMPUTATION OF HÞ BY SINGULAR VALUE DECOMPOSITION (SVD) 14 17 THE STEEPEST DESCENT ALGORITHM 14 18 THE CONJUGATE GRADIENT METHOD 15 DIFFRACTIVE OPTICS I LOHMANN METHOD APPROXIMATIONS IN THE LOHMANN METHOD CONSTANT AMPLITUDE LOHMANN METHOD QUANTIZED LOHMANN METHOD COMPUTER SIMULATIONS WITH THE LOHMANN METHOD A FOURIER METHOD BASED ON HARD-CLIPPING A SIMPLE ALGORITHM FOR CONSTRUCTION OF 3-D POINT IMAGES EXPERIMENTS THE FAST WEIGHTED ZERO-CROSSING ALGORITHM OFF-AXIS PLANE REFERENCE WAVE 15 10 ONE-IMAGE-ONLY HOLOGRAPHY 15 10 1 ANALYSIS OF IMAGE FORMATION 15 10 2 EXPERIMENTS 15 11 FRESNEL ZONE PLATES 16 DIFFRACTIVE OPTICS II VIRTUAL HOLOGRAPHY DETERMINATION OF PHASE APERTURE EFFECTS ANALYSIS OF IMAGE FORMATION INFORMATION CAPACITY, RESOLUTION, BANDWIDTH, AND REDUNDANCY VOLUME EFFECTS DISTORTIONS DUE TO CHANGE OF WAVELENGTH AND/OR HOLOGRAM SIZE BETWEEN CONSTRUCTION AND RECONSTRUCTION THE METHOD OF POCS FOR THE DESIGN OF BINARY DOE ITERATIVE INTERLACING TECHNIQUE (IIT) EXPERIMENTS WITH THE IIT OPTIMAL DECIMATION-IN-FREQUENCY ITERATIVE INTERLACING TECHNIQUE (ODIFIIT) EXPERIMENTS WITH ODIFIIT COMBINED LOHMANN-ODIFIIT METHOD COMPUTER EXPERIMENTS WITH THE LOHMANN-ODIFIIT METHOD 17 COMPUTERIZED IMAGING TECHNIQUES I: SYNTHETIC APERTURE RADAR SYNTHETIC APERTURE RADAR RANGE RESOLUTION CHOICE OF PULSE WAVEFORM THE MATCHED FILTER PULSE COMPRESSION BY MATCHED FILTERING CROSS-RANGE RESOLUTION A SIMPLI?ED THEORY OF SAR IMAGING IMAGE RECONSTRUCTION WITH FRESNEL APPROXIMATION 17 10 ALGORITHMS FOR DIGITAL IMAGE RECONSTRUCTION 17 10 1 SPATIAL FREQUENCY INTERPOLATION 18 COMPUTERIZED IMAGING II: IMAGE RECONSTRUCTION FROM PROJECTIONS THE RADON TRANSFORM THE PROJECTION SLICE THEOREM THE INVERSE RADON TRANSFORM PROPERTIES OF THE RADON TRANSFORM RECONSTRUCTION OF A SIGNAL FROM ITS PROJECTIONS THE FOURIER RECONSTRUCTION METHOD THE FILTERED-BACKPROJECTION ALGORITHM 19 DENSE WAVELENGTH DIVISION MULTIPLEXING ARRAY WAVEGUIDE GRATING METHOD OF IRREGULARLY SAMPLED ZERO-CROSSINGS (MISZC) COMPUTATIONAL METHOD FOR CALCULATING THE CORRECTION TERMS EXTENSION OF MISZC TO 3-D GEOMETRY ANALYSIS OF MISZC DISPERSION ANALYSIS FINITE-SIZED APERTURES COMPUTER EXPERIMENTS POINT-SOURCE APERTURES LARGE NUMBER OF CHANNELS THE METHOD OF CREATING THE NEGATIVE PHASE ERROR TOLERANCES 3-D SIMULATIONS PHASE QUANTIZATION IMPLEMENTATIONAL ISSUES 20 NUMERICAL METHODS FOR RIGOROUS DIFFRACTION THEORY BPM BASED ON FINITE DIFFERENCES WIDE ANGLE BPM FINITE DIFFERENCES FINITE DIFFERENCE TIME DOMAIN METHOD YEE’S ALGORITHM FOURIER MODAL METHODS