## Experimental observation of truncated fractional Fourier transform for a partially coherent Gaussian Schell-model beam

JOSA A, Vol. 25, Issue 8, pp. 2001-2010 (2008)

http://dx.doi.org/10.1364/JOSAA.25.002001

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### Abstract

The truncated fractional Fourier transform (FRT) is applied to a partially coherent Gaussian Schell-model (GSM) beam. The analytical propagation formula for a partially coherent GSM beam propagating through a truncated FRT optical system is derived by using a tensor method. Furthermore, we report the experimental observation of the truncated FRT for a partially coherent GSM beam. The experimental results are consistent with the theoretical results. Our results show that initial source coherence, fractional order, and aperture width (i.e., truncation parameter) have strong influences on the intensity and coherence properties of the partially coherent beam in the FRT plane. When the aperture width is large, both the intensity and the spectral degree of coherence in the FRT plane are of Gaussian distribution. As the aperture width decreases, the diffraction pattern gradually appears in the FRT plane, and the spectral degree of coherence becomes of non-Gaussian distribution. As the coherence of the initial GSM beam decreases, the diffraction pattern for the case of small aperture widths gradually disappears.

© 2008 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(070.2590) Fourier optics and signal processing : ABCD transforms

(350.5500) Other areas of optics : Propagation

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

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: March 7, 2008

Revised Manuscript: May 28, 2008

Manuscript Accepted: June 3, 2008

Published: July 11, 2008

**Citation**

Fei Wang, Yangjian Cai, and Qiang Lin, "Experimental observation of truncated fractional Fourier transform for a partially coherent Gaussian Schell-model beam," J. Opt. Soc. Am. A **25**, 2001-2010 (2008)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-8-2001

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