Partially compensated Knox-Thompson speckle imaging

Knox-Thompson Speckle Imaging is studied when partial adaptive optic compensation is employed. A generalization of previous analysis allows treatment of the compensation, finite exposure time, anisoplanatism and non-zero spectral bandwidth within the extended Huygens-Fresnel framework. The compensation process is assumed statistically stationary and accounts for wavefront sensor photon noise. The effect of finite exposure time is treated assuming Taylor's hypothesis and the Bufton wind model. An innovation is a perturbation treatment of fmite spectral bandwidth effects accurate to Significant improvement results from partial compensation when 10 degrees of freedom can be corrected with < lrad2of phase error due to shot noise. The compensation also allows significantly greater spectral bandwidth for the speckle images relative to the uncompensated case. Strategies optimizing over compensation scale, spectral bandwidth, and exposure time are chosen to optimize the SNR for a fixed observation time. The results of the analysis are compared to a computer simulation with a wave-optics propagation code.