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Energy conservation: a forgotten property of the turbulent point spread function

Energy conservation is an essential feature of the optical waves propagating through refractive turbulence. It was well understood for almost 30 years, that energy conservation has a very important consequence for the fluctuations in the images of the incoherent objects observed through turbulence. Namely the image of the uniformly illuminated areas of the object does not scintillate. As a consequence the low-contrast parts of the scene exhibit weak fluctuation even for very strong turbulence, but scintillations near the sharp edges can be strong even for the weak turbulence. Energy conservation property of the turbulent Point Spread Function (PSF) is essential for modeling of the turbulent image distortions, both for the development of the image processing techniques and for simulations of the turbulent imaging. However it is completely neglected in the current literature on the turbulent imaging theory and modeling. We discuss the relations between the energy conservation and anisoplanatism for the most common turbulence imaging models. Our analysis reveals that the only isoplanatic authentic turbulent PSF that is compliant with energy conservation corresponds to the thin aperture plane phase screen model of turbulence. This implies that for the near-the-ground imaging, and even for the astronomical-type imaging under strong turbulence conditions the turbulent PSF has to be modeled as a random function of four arguments with certain constraints. We show some practical ways how the three functional constrains on the turbulent PSF: nonnegative values, finite bandwidth and energy conservation can be complied with in practical generation of turbulent PSF.