Fractional free space, fractional lenses, and fractional imaging systems
Date
2003Source Title
Optical Society of America. Journal A: Optics, Image Science, and Vision
Print ISSN
1084-7529
Publisher
OSA - The Optical Society
Volume
20
Issue
11
Pages
2033 - 2040
Language
English
Type
ArticleItem Usage Stats
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Abstract
Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they are interpolations of their conventional counterparts. Optical realizations of these operators are possible with use of common physical components. These three operators can be interpreted as fractional lenses, fractional free space, and fractional imaging systems, respectively. Any optical system consisting of an arbitrary concatenation of sections of free space and thin lenses can be interpreted as a fractional imaging system with spherical reference surfaces. As a special case, a system departing from the classical single-lens imaging condition can be interpreted as a fractional imaging system. © 2003 Optical Society of America.
Keywords
ConvolutionFourier transforms
Interpolation
Lenses
Matrix algebra
Optical systems
Fractional imaging systems
Imaging systems