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

JOSA A, Vol. 30, Issue 4, pp. 682-690 (2013)

http://dx.doi.org/10.1364/JOSAA.30.000682

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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.

© 2013 Optical Society of America

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(070.2590) Fourier optics and signal processing : ABCD transforms

(080.2730) Geometric optics : Matrix methods in paraxial optics

(110.1220) Imaging systems : Apertures

(070.2575) Fourier optics and signal processing : Fractional Fourier transforms

(050.5082) Diffraction and gratings : Phase space in wave options

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: October 26, 2012

Revised Manuscript: February 21, 2013

Manuscript Accepted: February 22, 2013

Published: March 21, 2013

**Citation**

Haldun M. Ozaktas and Figen S. Oktem, "Phase-space window and degrees of freedom of optical systems with multiple apertures," J. Opt. Soc. Am. A **30**, 682-690 (2013)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-4-682

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