18 October 2004 Analysis of wave propagation and wavefront sensing in target-in-the-loop beam control systems
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Target-in-the-loop (TIL) wave propagation geometry represents perhaps the most challenging case for adaptive optics applications that are related with maximization of irradiance power density on extended remotely located surfaces in the presence of dynamically changing refractive index inhomogeneities in the propagation medium. We introduce a TIL propagation model that uses a combination of the parabolic equation describing outgoing wave propagation, and the equation describing evolution of the mutual intensity function (MIF) for the backscattered (returned) wave. The resulting evolution equation for the MIF is further simplified by the use of the smooth refractive index approximation. This approximation enables derivation of the transport equation for the returned wave brightness function, analyzed here using method characteristics (brightness function trajectories). The equations for the brightness function trajectories (ray equations) can be efficiently integrated numerically. We also consider wavefront sensors that perform sensing of speckle-averaged characteristics of the wavefront phase (TIL sensors). Analysis of the wavefront phase reconstructed from Shack-Hartmann TIL sensor measurements shows that an extended target introduces a phase modulation (target-induced phase) that cannot be easily separated from the atmospheric turbulence-related phase aberrations. We also show that wavefront sensing results depend on the extended target shape, surface roughness, and the outgoing beam intensity distribution on the target surface.
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Mikhail A. Vorontsov, Mikhail A. Vorontsov, Valeri V. Kolosov, Valeri V. Kolosov, } "Analysis of wave propagation and wavefront sensing in target-in-the-loop beam control systems", Proc. SPIE 5552, Target-in-the-Loop: Atmospheric Tracking, Imaging, and Compensation, (18 October 2004); doi: 10.1117/12.561447; https://doi.org/10.1117/12.561447

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