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Chinese Physics, 2004, Vol. 13(7): 1025-1032    DOI: 10.1088/1009-1963/13/7/010
CLASSICAL AREAS OF PHENOMENOLOGY Prev   Next  

Fractional Fourier transform for partially coherent beam in spatial-frequency domain

Cai Yang-Jian (蔡阳健), Lin Qiang (林强)
Optics Institute, Department of Physics, Zhejiang University, Hangzhou 310027, China
Abstract  By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatial-frequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian-Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatial-frequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.
Keywords:  fractional Fourier transform      partially coherent beam      spatial-frequency domain  
Received:  16 October 2003      Revised:  19 December 2003      Accepted manuscript online: 
PACS:  42.30.Kq (Fourier optics)  
  42.25.Kb (Coherence)  
  02.10.Ud (Linear algebra)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No 10334050).

Cite this article: 

Cai Yang-Jian (蔡阳健), Lin Qiang (林强) Fractional Fourier transform for partially coherent beam in spatial-frequency domain 2004 Chinese Physics 13 1025

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