中国物理B ›› 2005, Vol. 14 ›› Issue (10): 1990-1995.doi: 10.1088/1009-1963/14/10/012

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The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

滕树云1, 刘曼1, 桂维玲1, 程传福2, 徐至展3   

  1. (1)Department of Physics, Shandong Normal University, Jinan 250014, China; (2)Department of Physics, Shandong Normal University, Jinan 250014, China;Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China; (3)Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
  • 收稿日期:2005-04-20 修回日期:2005-08-01 出版日期:2005-10-20 发布日期:2005-10-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 69978012), and by the National Key Basic Research Special Foundation (NKBRSF) of China (Grant No G1999075200).

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

Teng Shu-Yun (滕树云)a, Cheng Chuan-Fu (程传福)ab, Liu Man (刘曼)a, Gui Wei-Ling (桂维玲)a, Xu Zhi-Zhan (徐至展)b   

  1. a Department of Physics, Shandong Normal University, Jinan 250014, China; b Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
  • Received:2005-04-20 Revised:2005-08-01 Online:2005-10-20 Published:2005-10-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 69978012), and by the National Key Basic Research Special Foundation (NKBRSF) of China (Grant No G1999075200).

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摘要： This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e.~the roughness w, the lateral correlation length \xi and the roughness exponent \alpha , from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with \alpha = 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

关键词: speckles, deep Fresnel diffraction, random self-affine fractal surface

Abstract: This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length $\xi$ and the roughness exponent $\alpha$, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with $\alpha$ = 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

Key words: speckles, deep Fresnel diffraction, random self-affine fractal surface

中图分类号:  (Speckle and moiré patterns)

  • 42.30.Ms
42.25.Fx (Diffraction and scattering) 68.35.B- (Structure of clean surfaces (and surface reconstruction))