Warp and blur imaging model consistent with the three constraints of imaging through refractive turbulence

Point spread function (PSF) for imaging through inhomogeneous refractive medium, such as atmospheric turbulence, is bounded by three constraints [Opt. Eng.52, 046001 (2013)OPEGAR0091-328610.1117/1.OE.52.4.046001]. PSF is non-negative, band-limited, and the third constraint, related to the energy conservation principle, warrants the absence of fluctuations in the image of a uniformly bright object. We develop a version of the common warp and blur model for the anisoplanatic image distortions by turbulence that satisfies these three constraints. In order to comply with the third constraint, our model supplements warp and blur by a random PSF power, which was found to be related to the Jacobian of the warp field. We illustrate statistics of the warp and blur using a simple example of anisoplanatic phase screen.