中国物理B ›› 2009, Vol. 18 ›› Issue (2): 611-615.doi: 10.1088/1674-1056/18/2/037

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Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field

范洪义, 胡利云   

  1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
  • 收稿日期:2008-08-21 修回日期:2008-09-11 出版日期:2009-02-20 发布日期:2009-02-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174).

Relation between Fresnel transform of input light field and the two-parameter Radon transform of Wigner function of the field

Fan Hong-Yi(范洪义) and Hu Li-Yun(胡利云)†   

  1. Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, China
  • Received:2008-08-21 Revised:2008-09-11 Online:2009-02-20 Published:2009-02-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174).

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摘要： This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ( x') propagates through an optical [ D( -B) ( -C) A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D,B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A,C.

关键词: Fresnel transform, two-parameter Radon transform, Wigner function

Abstract: This paper proves a new theorem on the relationship between optical field Wigner function's two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field $\psi\left( x^{\prime }\right) $ propagates through an optical $\left[ D\left( -B\right) \left( -C\right) A\right] $ system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are $D,B.$ It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are $A,C.$

Key words: Fresnel transform, two-parameter Radon transform, Wigner function

中图分类号:  (Quantum optics)

  • 42.50.-p
02.30.Uu (Integral transforms) 42.30.Kq (Fourier optics) 42.79.Sz (Optical communication systems, multiplexers, and demultiplexers?)