Abstract

A method is described for the investigation of the statistics of the sum of N independent complex variables. This method allows one to obtain the exact mean value of the squared modulus of the sum and its moments, for any value of the number N of variables. In particular, the case has been examined where the variables are lognormally distributed in amplitude and normally distributed in phase. This case is of interest in the field of atmospheric optics for the investigation of the effect of the diameter of the receiving aperture.

© 1977 Optical Society of America

Sums of independent lognormally distributed random variables

Richard Barakat
J. Opt. Soc. Am. 66(3) 211-216 (1976)

Propagation of pulsed beam waves through turbulence, cloud, rain, or fog

C. H. Liu and K. C. Yeh
J. Opt. Soc. Am. 67(9) 1261-1266 (1977)

On the theory of spatially limited light beam displacements in a randomly inhomogeneous medium

V. L. Mironov and V. V. Nosov
J. Opt. Soc. Am. 67(8) 1073-1080 (1977)

Probability distribution of optical amplitudes scattered from a rough object containing multiple glints*

Jen King Jao and Marek Elbaum
J. Opt. Soc. Am. 67(9) 1266-1269 (1977)

Optical resolution through a turbulent medium with adaptive phase compensations*

J. Y. Wang
J. Opt. Soc. Am. 67(3) 383-390 (1977)