Li Dayan, Kelly Damien P, Sheridan John T
School of Electrical, Electronic and Communications Engineering, College of Engineering and Architecture, University College Dublin, Belfield, Dublin 4, Ireland.
J Opt Soc Am A Opt Image Sci Vis. 2013 May 1;30(5):969-78. doi: 10.1364/JOSAA.30.000969.
The scattering of coherent monochromatic light at an optically rough surface, such as a diffuser, produces a speckle field, which is usually described by reference to its statistical properties. For example, the real and imaginary parts of a fully developed speckle field can be modeled as a random circular Gaussian process. When such a speckle field is used to illuminate a second diffuser, the statistics of the resulting doubly scattered field are in general no longer Gaussian, but rather follow a K distribution. In this paper we determine the space-time correlation function of such a doubly scattered speckle field that has been imaged by a single lens system. A space-time correlation function is derived that contains four separate terms; similar to the Gaussian case it contains an average DC term and a fluctuating AC term. However, in addition there are two terms that are related to contributions from each of the diffusers independently. We examine how our space-time correlation function varies as the diffusers are rotated at different speeds and as the point spread function of the imaging system is changed. A series of numerical simulations are used to confirm different aspects of the theoretical analysis. We then finish with a discussion of our results and some potential applications, including controlling spatial coherence and speckle reduction.
相干单色光在诸如漫射器等光学粗糙表面上的散射会产生散斑场，通常通过其统计特性来描述该散斑场。例如，充分发展的散斑场的实部和虚部可建模为随机圆高斯过程。当用这样的散斑场照射第二个漫射器时，所产生的双散射场的统计特性通常不再是高斯分布，而是遵循K分布。在本文中，我们确定了由单透镜系统成像的这种双散射散斑场的时空相关函数。推导了一个包含四个独立项的时空相关函数；与高斯情况类似，它包含一个平均直流项和一个波动的交流项。然而，此外还有两个项分别与每个漫射器的贡献相关。我们研究了随着漫射器以不同速度旋转以及成像系统的点扩散函数发生变化时，我们的时空相关函数如何变化。使用一系列数值模拟来证实理论分析的不同方面。然后我们以对结果的讨论以及一些潜在应用作为结尾，包括控制空间相干性和散斑减少。
