Li Dayan, Kelly Damien P, Kirner Raoul, Sheridan John T
Communications and Optoelectronic Research Centre, Science Foundation Ireland-Strategic Research Cluster in Solar Energy Conversion, School of Electrical, Electronic and Communications Engineering, College of Engineering and Architecture, University College Dublin, Belfield, Dublin 4, Ireland.
Appl Opt. 2012 Feb 1;51(4):A1-10. doi: 10.1364/AO.51.0000A1.
The statistical properties of speckles in paraxial optical systems depend on the system parameters. In particular, the speckle orientation and the lateral dependence (x and y) of the longitudinal speckle size can vary significantly. For example, the off-axis longitudinal correlation length remains equal to the on-axis size for speckles in a Fourier transform system, while it decreases dramatically as the observation position moves off axis in a Fresnel system. In this paper, we review the speckle correlation function in general linear canonical transform (LCT) systems, clearly demonstrating that speckle properties can be controlled by introducing different optical components, i.e., lenses and sections of free space. Using a series of numerical simulations, we examine how the correlation function changes for some typical LCT systems. The integrating effect of the camera pixel and the impact this has on the measured first- and second-order statistics of the speckle intensities is also examined theoretically. A series of experimental results are then presented to confirm several of these predictions. First, the effect the pixel size has on the measured first-order speckle statistics is demonstrated, and second, the orientation of speckles in a Fourier transform system is measured, showing that the speckles lie parallel to the optical axis.
傍轴光学系统中散斑的统计特性取决于系统参数。特别是，散斑取向以及纵向散斑尺寸的横向依赖性（x和y）可能会有显著变化。例如，对于傅里叶变换系统中的散斑，离轴纵向相关长度与轴上尺寸相等，而在菲涅耳系统中，随着观测位置离轴移动，该相关长度会急剧减小。在本文中，我们回顾了一般线性规范变换（LCT）系统中的散斑相关函数，清楚地表明可以通过引入不同的光学元件（即透镜和自由空间段）来控制散斑特性。通过一系列数值模拟，我们研究了一些典型LCT系统中相关函数是如何变化的。理论上还研究了相机像素的积分效应及其对测量的散斑强度一阶和二阶统计量的影响。然后给出了一系列实验结果以证实其中的一些预测。首先，展示了像素大小对测量的一阶散斑统计量的影响，其次，测量了傅里叶变换系统中散斑的取向，结果表明散斑与光轴平行。
