| It is known that a phase-perturbed object field from a fractal-like rough surface illuminated by a partially coherent beam generates speckle on the image plane. In this works, aberration effects on Gaussian speckle on the image plane in both perfectly and partially coherent systems are theoretically and experimentally investigated. Theory shows that the second order statistics of Gaussian laser speckle are independent of odd-functional aberrations, but they do affect Gaussian speckle contrast in a partially coherent system. Furthermore, it is theoretically derived that field statistics of Gaussian laser speckle generally become non-circular Gaussian due to aberrations, and an aberration effect is asymptotically ignorable for very weak or strong roughness. A brute force simulation method is introduced for non-Gaussian speckle in a partially coherent imaging system, where speckle irradiance is calculated from a quasi-monochromatic extended incoherent source. The source is modeled as a collection of independent point sources distributed on a regular grid. The partially coherent speckle pattern is calculated from the incoherent sum of coherent speckle patterns in the image plane generated from each point source. Speckle contrasts from a brute force model show good agreement with theoretical and experimental results. It is determined that non-Gaussian speckle contrast is strongly dependent on Hurst exponent of fractal rough surfaces using brute force simulations. The concept of a contributing object area at a fixed image point effectively explains the speckle contrast dependency. Measuring spherical aberrations using Gaussian laser speckle is discussed as one of applications and future works of the present study. |
