Optical Information Processing. Adolf W. Lohmann. Edited by Stefan Sinzinger. Ch>

Transcription

1 Optical Information Processing Adolf W. Lohmann Edited by Stefan Sinzinger Ch> Universitätsverlag Ilmenau 2006

2 Contents Preface to the 2006 edition 13 Preface to the third edition 15 Preface volume Outline 19 2 Fourier Series Introduction Some Useful Properties of Fourier Series Fourier Series for Two-Dimensional Functions 34 3 The Moire Effect Measurement of small shifts Moire of two equal, rotating gratings Moire illustrations 42 4 An Optical Analog Computer for Fourier Transformation 43 5 Some More Moire Effects Fourier series representation of quasi-periodic functions Schuster fringes 49 6 The Dirac or Delta "Function" Introduction Several forms of ö (x) 57 7 The Fourier Integral Transformation Some general properties Some specific properties Polar coordinates More about the Fourier-Integral transformation Now some examples 74 8 Some Additions About the Analog Computer 81

3 6 Contents 9 Nonlinear Transforms Graphical solution Polynomial Nonlinearity FM-Nonlinearity Hardclipping Amplitude height analysis Schwarz Inequality Sampling Theorem Properties of the SINC-Function Sampling at Shifted Points Sampling of periodic functions Sampling at the wrong interval Sampling in two dimensions Fourier transform by digital computation Large digital Fourier transform Fresnel-Transformation Definitions Shift-theorem Tilt-theorem Sampling theorem for Fresnel transform pairs The Stationary Phase Integral Fourier transform of the step-function Ill 13.2 The Fresnel integral The method of stationary phase Saddle-point method What is Light? History What is Observable? The wave equation Complex representation of the wavefield Frequency averages The envelope representation of complex signals The Uncertainty Principle The usual derivation The uncertainty of some specific fields Other definitions of x- and v spreads Gabor's information cells Fundamentals of Diffraction Theory Terminology: diffraction and interference 141

4 Contents History and classification of diffraction theories Kirchhoff-approximation The RSD theory of Fresnel diffraction Derivation of the HFK-integral from the RSD-intgral The sampling theorem for FRS-diffraction Justification of Young's Diffraction Theory (YMR) More About Evanescent Waves Boundary conditions for E and H; Fresnel coefficients A more abstract look at evanescent waves Fresnel Diffraction on Periodic Objects The Talbot-Effect (1836) HFK-theory of the Talbot effect RSD-Theory of the Talbot effect Plane wave theory of the Talbot effect What are these modulated plane waves, really? A Fourier spectrometer based on the Talbot effect The walk-off effect Yet another look at Talbot images Fresnel Diffraction on Zone Plates and Lenses About inventing Diffraction on the Fresnel Zone Plate Image formation in terms of Fresnel diffraction What is a Light Ray? Motivation of our approach The Fermat Principle as a consequence of wave optics What are Shadows or "Non-Rays"? Two examples of parageometrical optics Tilted plane wave falling onto wide screen A spherical wave falling onto a wide slit An application of parageometric optics: Application of Fresnel Diffraction to Signal Detection Fraunhofer Diffraction Observer at distance R no lens is involved Plane wave illumination single lens About the lens used for creating "infinity" The "light tube" Convergent illumination Divergent illumination Fraunhofer diffraction by an array of equal objects Babinet's principle 243

5 8 Contents 23 Application of Fraunhofer Diffraction to Optical Character Recognition Coherent Image Formation Two setups Convolution theory of image formation Spatial Filter theory of coherent image formation Some Applications of Spatial Filtering Historical remarks about Ernst Abbe ( ) Phase contrast microscopy Differential interference contrast Several image enhancement methods Incoherent Image Formation Definition of "coherent" and "incoherent" light Convolution theory of incoherent image formation Linear filter theory of incoherent image formation The Duffieux formula Measurement of the OTF Incoherent image formation with transparent objects Lens aberrations The OTF of a perfect lens Some specific OTF's Defocussing Other lens aberrations Rough lens surface Double-slit aperture Object Motion Photography TheOTF-chainofTV Quality criteria based on the OTF HOTF synthesis Apodisation Pseude-coherent image formation Synthesis of incoherent matched filters Theory of Image Formation in Partially-Coherent Light 297 Preface volume II Boundary Conditions Discontinuities of the Medium Consequences of the boundary conditions Interference Division of Wavefront and Division of Amplitude 317

6 Contents 9 30 Coherence Fundamentals of coherence theory Coherence and interference by division of amplitude Monochromatic point source Polychromatic point source Monochromatic extended source extended perpendicular to the mirror Monochromatic extended source extended parallel to mirror, observed at large z Tolerances Solution of the example #4, suggested for self-study: Coherence Division of the Wavefront Polychromatic point source Extended monochromatic source Coherence division by grating diffraction Coherence Division by a scatter plate (Jim Burch~ 1950) Partial Coherence in Case of Wavefront Division A Final Look at Coherence Theory logroup velocity Polarization Polarization and Crystal Optics Some crystal-optical elements Quater-wave plate Half-wave plate Refraction in the Wollaston prism Circular birefringence Compensators Holography Rogers' Explanation Discussion of the phase loss Generalized Rogers' Explanation Some attempts to remove the twin-image Wave Propagation and Fresnel Transformation Off-Line Fresnel Holography Recording Step Reconstruction Theory of Off-Line-Fresnel Holography Theory of the reconstruction process About the Pseudoscopic Structure of the Conjugate Image Why is it so tricky to see the pseudoscopic image? Dynamic angular velocity Classification of holographic setups Fraunhofer off-line holography 401

7 10 Contents Fourier holography (off-line) Lensless Fourier holography Image holography Talbot bands Influence of the photographic material on spatial data processing Effects in a Photographic Emulsion (3) Light Scattering During Recording (4) The photographic nonlinear effect (6) Adjacency Effect (5) Grain-Noise The influence of light scattering within the emulsion during holographic recording Image holography Fourier holography Fresnel hologram The Space-Bandwidth-Product SW Appendix publications reprinted from OSA Journals 459 Theta modulation in optics 460 Character recognition by incoherent signal filtering 465 A lateral wavefront shearing interferometry with variable shear 472 Signal detection by correlation of Fresnel diffraction patterns 476 Single-sideband holography 481 Interferograms are image holograms 486 Nonlinear effects in holography 488 Index 499