Uozumi J, Asakura T
Appl Opt. 1981 Apr 15;20(8):1454-66. doi: 10.1364/AO.20.001454.
General expressions for first-order statistics of Gaussian speckle produced in the diffraction region are derived for an arbitrary profile of the illuminating beam with a plane wave front. The statistical properties of the complex amplitude, the intensity, and the phase of speckles are studied under illumination of a Gaussian beam. The joint probability density function of the speckle field characterized by an equiprobability density ellipse is investigated in some detail with an intimate relation to the correlation coefficient between the real and imaginary parts of the complex speckle amplitude. This correlation coefficient is found to affect appreciably the statistics of speckles produced especially in the near-field diffraction region when a standard deviation of the random phase variation produced by a diffuse object under illumination is relatively small and the number of independent scatterers contributing to the formation of speckles is small.
对于具有平面波前的照明光束的任意轮廓，推导了在衍射区域产生的高斯散斑一阶统计量的一般表达式。研究了高斯光束照明下散斑复振幅、强度和相位的统计特性。以等概率密度椭圆为特征的散斑场的联合概率密度函数得到了较为详细的研究，它与复散斑振幅实部和虚部之间的相关系数密切相关。当漫射物体在照明下产生的随机相位变化的标准差相对较小时，以及对散斑形成有贡献的独立散射体数量较少时，发现该相关系数对特别是在近场衍射区域产生的散斑统计有明显影响。
