## Abstract

The irradiance fluctuations imposed on a laser beam that has propagated over horizontal terrestrial paths in the range of 2 to $24\text{\hspace{0.17em}}\mathrm{km}$ are compared to lognormal (LN) and gamma-gamma (GG) distributions. For the direct links reported here the irradiance fluctuations follow a LN distribution except in cases of weak turbulence, characterized by a scintillation index of less than 1 and a Fried parameter larger than the receiver aperture, in which case the GG distribution gives an improved fit. In very weak turbulence the difference between the two distributions is insignificant.

© 2011 Optical Society of America

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### Equations (5)

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(1)
$$p(I)=\frac{1}{I\sqrt{2\pi {\sigma}_{\mathrm{ln}I}^{2}}}\mathrm{exp}(-{\frac{(\mathrm{ln}(I)+\frac{1}{2}{\sigma}_{\mathrm{ln}I}^{2})}{2{\sigma}_{\mathrm{ln}I}^{2}}}^{2}),$$
(2)
$$p(I)=\frac{2}{\mathrm{\Gamma}(\alpha )\mathrm{\Gamma}(\beta )I}(\alpha \beta I{)}^{\frac{\alpha +\beta}{2}}{\mathrm{K}}_{\alpha -\beta}(2\sqrt{\alpha \beta I}),$$
(3)
$$\alpha =\frac{1}{{\sigma}_{x}^{2}}=\frac{1}{\mathrm{exp}({\sigma}_{\mathrm{ln}x}^{2})-1},$$
(4)
$$\beta =\frac{1}{{\sigma}_{y}^{2}}=\frac{1}{\mathrm{exp}({\sigma}_{\mathrm{ln}y}^{2})-1}\mathrm{.}$$
(5)
$${\sigma}_{I}^{2}=\mathrm{exp}({\sigma}_{\mathrm{ln}x}^{2}+{\sigma}_{\mathrm{ln}y}^{2})-1=(1+\frac{1}{\alpha})(1+\frac{1}{\beta})-1.$$