Chapter

Fourier Analysis

B. D. Guenther

in Modern Optics

Second edition

Published in print October 2015 | ISBN: 9780198738770
Published online January 2016 | e-ISBN: 9780191801983 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780198738770.003.0006
Fourier Analysis

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The techniques developed by Fourier and Dirichlet state that a Fourier series, a sum of sinusoidal functions, can be used to describe any periodic functions and that the Fourier transform, an integral transform, can be used to describe aperiodic functions. The measurement process used to obtain information about continuous functions found in nature is accomplished by making discrete measurements (called samples) of the functions. The development of the Fourier theory presents the opportunity to justify the experimental approach, by examining the processes of replication and sampling. The concepts, developed for electrical communication systems, that depend upon the use of the Fourier method are used for analysis of optical imaging systems and will be needed in the Fresnel formulation of diffraction in Chapters 9 and 10.

Keywords: Fourier series; Fourier transform; periodic function; aperiodic function; replication; sampling

Chapter.  15718 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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