## Electromagnetic degrees of freedom of an optical system

JOSA A, Vol. 17, Issue 5, pp. 892-902 (2000)

http://dx.doi.org/10.1364/JOSAA.17.000892

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### Abstract

We present a rigorous electromagnetic formalism for defining, evaluating, and optimizing the degrees of freedom of an optical system. The analysis is valid for the delivery of information with electromagnetic waves under arbitrary boundary conditions communicating between domains in three-dimensional space. We show that, although in principle there is an infinity of degrees of freedom, the effective number is finite owing to the presence of noise. This is in agreement with the restricted classical theories that showed this property for specific optical systems and within the scalar and paraxial approximations. We further show that the best transmitting and receiving functions are the solutions of well-defined eigenvalue equations. The present approach is useful for understanding and designing modern optical systems for which the previous approaches are not applicable, as well as for application in inverse and synthesis problems.

© 2000 Optical Society of America

**OCIS Codes**

(030.4070) Coherence and statistical optics : Modes

(100.3190) Image processing : Inverse problems

(110.6880) Imaging systems : Three-dimensional image acquisition

(180.0180) Microscopy : Microscopy

(260.1960) Physical optics : Diffraction theory

(260.2110) Physical optics : Electromagnetic optics

(350.5730) Other areas of optics : Resolution

(350.7420) Other areas of optics : Waves

**History**

Original Manuscript: June 17, 1999

Revised Manuscript: December 14, 1999

Manuscript Accepted: February 9, 2000

Published: May 1, 2000

**Citation**

Rafael Piestun and David A. B. Miller, "Electromagnetic degrees of freedom of an optical system," J. Opt. Soc. Am. A **17**, 892-902 (2000)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-5-892

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