## Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam

JOSA A, Vol. 23, Issue 9, pp. 2161-2165 (2006)

http://dx.doi.org/10.1364/JOSAA.23.002161

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### Abstract

The fractional Fourier transform (FRT) is applied to a partially coherent off-axis Gaussian Schell-model (GSM) beam, and an analytical formula is derived for the FRT of a partially coherent off-axis GSM beam. The corresponding tensor *ABCD* law for performing the FRT of a partially coherent off-axis GSM beam is also obtained. As an application example, the FRT of a partially coherent linear laser array that is expanded as a sum of off-axis GSM beams is studied. The derived formulas are used to provide numerical examples. The formulas provide a convenient way to analyze and calculate the FRT of a partially coherent off-axis GSM beam.

© 2006 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(070.2580) Fourier optics and signal processing : Paraxial wave optics

(070.2590) Fourier optics and signal processing : ABCD transforms

**ToC Category:**

Fourier Optics and Optical Signal Processing

**History**

Original Manuscript: January 3, 2006

Revised Manuscript: March 9, 2006

Manuscript Accepted: March 10, 2006

**Citation**

Chongwei Zheng, "Fractional Fourier transform for partially coherent off-axis Gaussian Schell-model beam," J. Opt. Soc. Am. A **23**, 2161-2165 (2006)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-23-9-2161

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