An improved solution to the fourth moment equation for intensity fluctuations

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Abstract
An approximate solution is presented for the fourth moment equation that describes fluctuations of intensity in a wave propagating through a randomly fluctuating medium. The solution is valid for high frequency or relatively strong fluctuations in the medium. The solution procedure is straightforward and at zero order agrees with previously derived approximate solutions. However, the present method is much more direct and more easily extended to complicated problems. Indeed, the first order correction to this basic solution is also determined and it is found that significantly better agreement with previous numerical work is obtained. In addition, knowledge of the correction term allows approximate estimates to be made for the error involved in using the basic solution.

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