Superposition of the radiation from N independent sources and the problem of random flights

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Abstract
It is often stated that the intensity of the signal produced by superposition of N equally intense, but randomly phased, monochromatic coherent waves tends to N as N becomes large. An examination (first made by Rayleigh) of the distribution of intensities obtained by superposing N independent monochromatic waves shows that the mean intensity is N and the variance is N2−N. Exploiting the analogy of this problem to random walk in two dimensions (’’random flight’’), we have recalculated the distribution for N=2 to 6 and compared it with the results from a computer experiment.

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