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24 October 2012 Long- and short-term scintillation of the focused beams and point spread functions in turbulent atmosphere
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Reciprocity principle for the optical wave propagation in turbulence suggests that scintillations in the focal point of a coherent optical beam and in the center of the point spread function (PSF) of the imaging system are identical, provided that the imaging aperture and initial beam irradiance are matched. Rigorous weak and strong scintillation asymptotes of the scintillation index (SI) in the beam focus indicate that the relatively simple extended Huygens-Fresnel (HF) approximation is accurate in both asymptotic cases. This motivated us to use the HF approximation for calculation of the SI in the moderate turbulence case when SI reaches its maximum. The 8 - fold integral representing the SI was calculated using Mont-Carlo technique. We compare the HF results to the direct numeric wave optics simulation results and find some discrepancies that can be attributed to the finite grid sampling used in simulation. In practical situation the exact position of the beam focal point at the end of the long propagation path is rarely available, but instantaneous, short-term (ST) beam center can be estimated by the beam centroid position. For imaging problems, the short-exposure (SE) PSF and its scintillation are of great interest. We used the combination of the HF approximation and available SE imaging model to calculate the short-term SI for the focused beams under weak strong and intermediate turbulence conditions using the same numeric integration technique as for the Long-Term (LT) case. Calculations show up to 500% increase in the average irradiance and substantial reduction of scintillation for the SE case.
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Mikhail Charnotskii and Gary J. Baker "Long- and short-term scintillation of the focused beams and point spread functions in turbulent atmosphere", Proc. SPIE 8517, Laser Communication and Propagation through the Atmosphere and Oceans, 85170G (24 October 2012);

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