Abstract

In weak scattering regimes the I-K distribution^1,2 is consistent wth the assumptions of the Born approximation coupled with the further assumption of a compound or doubly stochastic field of the electromagnetic wave. Based on a pure power-law Kolmogorov spectrum and well-known results from the Born approximation for plane waves propagating through a turbulent medium, a relationship is established between the two parameters α and ρ of the I-K distribution and the strength of turbulence parameter ${\sigma }_{\text{1}}^{\text{2}}=1.23$ $C_n^{\text{2}}{k}^{7/6}{L}^{11/6}$, where $C_n^{\text{2}}$ is the refractive-index structure parameter, k is the wavenumber of the electromagnetic wave, and L is the propagation path length. A second independent relation for α in terms of ${\sigma }_{\text{1}}^{\text{2}}$ is developed by using relations from the asymptotic theory for strong turbulence regimes. Combining these results, we obtain expressions for α and ρ that appear to be valid for all conditions of turbulence. By generalizing the power spectral density of the refractive index to include the effects of the inner scale of turbulence I₀, we then develop new expressions for α and ρ that also depend on I₀. The normalized variance of the irradiance ${\sigma }_I^{\text{2}}$ as predicted by the I-K distribution is calculated as a function of ${\sigma }_1^{\text{2}}$ and I₀. Comparisons of ${\sigma }_I^{\text{2}}$ with that of plane wave data show a very good fit when inner scale corrections are introduced. Further comparisons of the normalized irradiance moments of the I-K distribution with experimental data obtained by propagating a collimated laser beam through a phase screen also show a remarkably good fit.

© 1986 Optical Society of America