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Journal of the Optical Society of America

Single-interval statistics of non-Gaussian light in the presence of number fluctuations

Takeaki Yoshimura, Hirohisa Fukumaru, Nobuo Wakabayashi

Published Jun 1, 1982• 4 citations
Publisher

Abstract

By using the basic particle-scattering theory, the high-order moments of non-Gaussian light, including number fluctuations that are due to independent particles, have been deduced for a sampling interval that is much smaller than the characteristic time of the number fluctuations but comparable with that of the interference fluctuations. The results have been compared with experiment by measuring the second- and third-factorial moments.

DOI
10.1364/josa.72.000780

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By using the basic particle-scattering theory, the high-order moments of non-Gaussian light, including number fluctuations that are due to independent particles, have been deduced for a sampling interval that is much smaller than the characteristic time of the number fluctuations but comparable with that of the interference fluctuations. The results have been compared with experiment by measuring the second- and third-factorial moments.
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Microscopic scattering processes are discussed for two structures of light incident on thermal particles. One is composed of two collinear light beams originating from different oscillating modes of a laser, and another is composed of two counter propagating beams originating from the same oscillating mode. A comparison of the cumulant expansions for the above two cases has allowed discerning which terms in the scattering structures led to the same statistical properties of the scattered photons. It is shown that, for the scattering of multimode-laser light, the statistical properties of scattered photons are not affected by the noncorrelating random phases of the incident laser fields but are the same as those in the case of single-mode laser light under practical scattering experiments. The factorial moments ${F}_{k}[=〈n(n\ensuremath{-}1)\ensuremath{\cdots}(n\ensuremath{-}k+1)〉]$ up to sixth order of the scattered photons were measured for various scattering situations including the above two cases, and they were found to support the theoretical results.
The photocount autocorrelation of non-Gaussian scattered laser light is discussed as a tool for the study of both very dilute or highly correlated scattering systems. A scaled photocount correlation technique is introduced and shown to produce a function directly proportional to the correlation function of the integrated scattered intensity, independent of the field statistics. This technique overcomes the serious problems of interpretation that can arise when the commonly used clipped correlation technique is applied to non-Gaussian fields. The scaled correlation technique is demonstrated experimentally with a simple scattering system, a small number of particles under uniform translational motion.