标题： 散射体随机数量和非均匀相位分布的斑点图案的统计特性 显示英文标题

标题： Statistical properties of speckle patterns for a random number of scatterers and nonuniform phase distributions

摘要： 斑点图案的统计特性在光学、海洋学和无序系统中的传输现象中有重要应用。 在这里，我们得到了由随机数量的部分波形成的斑点图案振幅分布的闭式解析结果，这些部分波由任意相位分布表征，推广了斑点图案随机行走理论的经典结果。 我们证明了振幅分布的功能形式仅由散射体数量的分布决定，而相位分布仅影响尺度参数。 在散射体数量不是随机的情况下，我们找到了一个解析表达式，将瑞利定律扩展到非均匀随机相位的情况。 对于散射体数量的负二项分布，我们的结果揭示了在有偏随机相位的情况下，波幅的大波动变得更加显著。 我们提供了完全支持我们解析结果的数值结果。 显示英文摘要

摘要： The statistical properties of speckle patterns have important applications in optics, oceanography, and transport phenomena in disordered systems. Here we obtain closed-form analytic results for the amplitude distribution of speckle patterns formed by a random number of partial waves characterized by an arbitrary phase distribution, generalizing classical results of the random walk theory of speckle patterns. We show that the functional form of the amplitude distribution is solely determined by the distribution of the number of scatterers, while the phase distribution only influences the scale parameters. In the case of a non-random number of scatterers, we find an analytic expression for the amplitude distribution that extends the Rayleigh law to non-uniform random phases. For a negative binomial distribution of the number of scatterers, our results reveal that large fluctuations of the wave amplitudes become more pronounced in the case of biased random phases. We present numerical results that fully support our analytic findings.