Phase-space window and degrees of freedom of optical systems with multiple apertures

Date
2013
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Source Title
Journal of the Optical Society of America A: Optics and Image Science, and Vision
Print ISSN
1084-7529
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Publisher
Optical Society of America.
Volume
30
Issue
4
Pages
682 - 690
Language
English
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Abstract

We show how to explicitly determine the space-frequency window (phase-space window) for optical systems consisting of an arbitrary sequence of lenses and apertures separated by arbitrary lengths of free space. If the space-frequency support of a signal lies completely within this window, the signal passes without information loss. When it does not, the parts that lie within the window pass and the parts that lie outside of the window are blocked, a result that is valid to a good degree of approximation for many systems of practical interest. Also, the maximum number of degrees of freedom that can pass through the system is given by the area of its space-frequency window. These intuitive results provide insight and guidance into the behavior and design of systems involving multiple apertures and can help minimize information loss.

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