TY - JOUR

T1 - Irradiance-variance behavior by numerical simulation for plane-wave and spherical-wave optical propagation through strong turbulence

AU - Flatté, Stanley M.

AU - Gerber, James S.

PY - 2000/6

Y1 - 2000/6

N2 - We have simulated optical propagation through atmospheric turbulence in which the spectrum near the inner scale follows that of Hill and Clifford [J. Opt. Soc. Am. 68, 892 (1978)] and the turbulence strength puts the propagation into the asymptotic strong-fluctuation regime. Analytic predictions for this regime have the form of power laws as a function of β02, the irradiance variance predicted by weak-fluctuation (Rytov) theory, and l0, the inner scale. The simulations indeed show power laws for both spherical-wave and plane-wave initial conditions, but the power-law indices are dramatically different from the analytic predictions. Let σI2− 1 = a(β02/βc2)−b(l0/Rf)c, where we take the reference value of β02to be βc2, = 60.6, because this is the center of our simulation region. For zero inner scale (for which c = 0), the analytic prediction is b = 0.4 and a = 0.17 (0.37) for a plane (spherical) wave. Our simulations for a plane wave give a = 0.234 ± 0.007 and b = 0.50 ± 0.07, and for a spherical wave they give a = 0.58 ± 0.01 and b = 0.65 ± 0.05. For finite inner scale the analytic prediction is b = 1/6, c = 7/18 and a = 0.76 (2.07) for a plane (spherical) wave. We find that to a reasonable approximation the behavior with β02and l0indeed factorizes as predicted, and each part behaves like a power law. However, our simulations for a plane wave give a = 0.57 ± 0.03, b = 0.33 ± 0.03, and c = 0.45 ± 0.06. For spherical waves we find a = 3.3 ± 0.3, b = 0.45 ± 0.05, and c = 0.8 ± 0.1.

AB - We have simulated optical propagation through atmospheric turbulence in which the spectrum near the inner scale follows that of Hill and Clifford [J. Opt. Soc. Am. 68, 892 (1978)] and the turbulence strength puts the propagation into the asymptotic strong-fluctuation regime. Analytic predictions for this regime have the form of power laws as a function of β02, the irradiance variance predicted by weak-fluctuation (Rytov) theory, and l0, the inner scale. The simulations indeed show power laws for both spherical-wave and plane-wave initial conditions, but the power-law indices are dramatically different from the analytic predictions. Let σI2− 1 = a(β02/βc2)−b(l0/Rf)c, where we take the reference value of β02to be βc2, = 60.6, because this is the center of our simulation region. For zero inner scale (for which c = 0), the analytic prediction is b = 0.4 and a = 0.17 (0.37) for a plane (spherical) wave. Our simulations for a plane wave give a = 0.234 ± 0.007 and b = 0.50 ± 0.07, and for a spherical wave they give a = 0.58 ± 0.01 and b = 0.65 ± 0.05. For finite inner scale the analytic prediction is b = 1/6, c = 7/18 and a = 0.76 (2.07) for a plane (spherical) wave. We find that to a reasonable approximation the behavior with β02and l0indeed factorizes as predicted, and each part behaves like a power law. However, our simulations for a plane wave give a = 0.57 ± 0.03, b = 0.33 ± 0.03, and c = 0.45 ± 0.06. For spherical waves we find a = 3.3 ± 0.3, b = 0.45 ± 0.05, and c = 0.8 ± 0.1.

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U2 - 10.1364/JOSAA.17.001092

DO - 10.1364/JOSAA.17.001092

M3 - Article

AN - SCOPUS:0000261724

VL - 17

SP - 1092

EP - 1097

JO - Journal of the Optical Society of America A: Optics and Image Science, and Vision

JF - Journal of the Optical Society of America A: Optics and Image Science, and Vision

SN - 1084-7529

IS - 6

ER -