## Linear systems, Fourier transforms, and opticsA complete and balanced account of communication theory, providing an understanding of both Fourier analysis (and the concepts associated with linear systems) and the characterization of such systems by mathematical operators. Presents applications of the theories to the diffraction of optical wave-fields and the analysis of image-forming systems. Emphasizes a strong mathematical foundation and includes an in-depth consideration of the phenomena of diffraction. Combines all theories to describe the image-forming process in terms of a linear filtering operation for both coherent and incoherent imaging. Chapters provide carefully designed sets of problems. Also includes extensive tables of properties and pairs of Fourier transforms and Hankle Transforms. |

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### Contents

INTRODUCTION | 1 |

SPECIAL FUNCTIONS | 40 |

HARMONIC ANALYSIS | 99 |

Copyright | |

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aberrations amplitude filter aperture stop arbitrary autocorrelation axis beam waist behavior Chapter coherent comb function complex amplitude complex numbers configuration convolution cutoff frequency define delta function denote described determined diffraction pattern discussed distance effects eigenfunctions equal example exit pupil expression Figure focal length Fourier components Fourier transform Fraunhofer diffraction Fraunhofer pattern Fresnel Fresnel diffraction function f(x Gaussian beam Gaussian function given by Eq graph Hankel transform illustrated in Fig image irradiance image plane imaging system impulse response integral interval inverse lens element lenses line response located LSI system modulation negative Note object observation plane obtain one-dimensional operation periodic function phasor physical point spread function positive problem profiles propagation properties quantity real constants real-valued rect(x rectangle function region result sampling shift invariant shown in Fig simplify simply Sketch spectral spherical wave field surface tion transform pair transparency variable vector width zero