中国物理B ›› 2004, Vol. 13 ›› Issue (7): 1025-1032.doi: 10.1088/1009-1963/13/7/010

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇    下一篇

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

蔡阳健, 林强   

  1. Optics Institute, Department of Physics, Zhejiang University, Hangzhou 310027, China
  • 收稿日期:2003-10-16 修回日期:2003-12-19 出版日期:2005-07-05 发布日期:2005-07-05
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10334050).

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

Cai Yang-Jian (蔡阳健), Lin Qiang (林强)   

  1. Optics Institute, Department of Physics, Zhejiang University, Hangzhou 310027, China
  • Received:2003-10-16 Revised:2003-12-19 Online:2005-07-05 Published:2005-07-05
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10334050).

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摘要： 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.

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.

Key words: fractional Fourier transform, partially coherent beam, spatial-frequency domain

中图分类号:  (Fourier optics)

  • 42.30.Kq
42.25.Kb (Coherence) 02.10.Ud (Linear algebra)