Effect of optical aberration on Gaussian laser speckle

Optical aberration effects up to the second moment of Gaussian laser speckle are theoretically investigated for both partially and fully developed speckle. In the development, a plane-wave illuminated diffuser generates a phase-perturbed random field in the object plane that creates speckle in the image plane. Theoretical derivations show that image field statistics are generally non-circular Gaussian due to aberrations. Speckle statistics are not affected by odd-functional aberrations, such as coma, and dependency of aberrations is asymptotically ignorable for very weak or strong diffusers. Furthermore, Gaussian speckle contrast as a functional of optical aberrations exhibits a stationary point for the aberration free condition, where apparently contrast does not achieve a local maximum. Calculations of speckle contrast for several aberration conditions are also presented.