Experimental exploration of the correlation coefficient of static speckles in Fresnel configuration

Quasi-monochromatic light reflected from an optically rough surface produces a complicated 3D speckle field. This speckle field is often described using a correlation function from which the 3D speckle properties can be examined. The derivation of the correlation function is based on a physical model where several critical assumptions about the input and output fields in the model are made. However, experimental works verifying this correlation function are rare and sometimes produce inconsistent results. In this paper, we examine some practical issues encountered when experimentally measuring this correlation function, including: The realization of the ensemble average between speckle fields at two point positions; and, The pixel integrating effect of the recording camera and the implications this has for the statistics of the measured speckle field. Following verification of the correlation function and examining the speckle decorrelation properties in 3D space, two practical applications are proposed, one is the aligning of the system optical axis with the camera center and the other is the measurement of the out-of-plane displacement of an object surface. Simulation and experimental results that support our analysis are presented