Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of first-order optical systems

Date
1997-11-01
Advisor
Instructor
Source Title
Optics Communications
Print ISSN
0030-4018
Electronic ISSN
Publisher
Elsevier BV * North-Holland
Volume
143
Issue
1-3
Pages
75 - 86
Language
English
Type
Article
Journal Title
Journal ISSN
Volume Title
Abstract

Although wave optics is the standard method of analyzing systems composed of a sequence of lenses separated by arbitrary distances, it is often easier and more intuitive to ascertain the function and properties of such systems by tracing a few rays through them. Determining the location, magnification or scale factor, and field curvature associated with images and Fourier transforms by tracing only two rays is a common skill. In this paper we show how the transform order, scale factor, and field curvature can be determined in a similar manner for the fractional Fourier transform, Our purpose is to develop the understanding and skill necessary to recognize fractional Fourier transforms and their parameters by visually examining ray traces. We also determine the differential equations governing the propagation of the order, scale, and curvature, and show how these parameters are related to the parameters of a Gaussian beam.

Course
Other identifiers
Book Title
Keywords
Fourier optics, Optical information processing, Fractional Fourier transforms, Fourier transforms, Lenses, Optical filters, Optical systems, Gaussian beam, Ray optics, Wave optics
Citation
Published Version (Please cite this version)