First-order correction for the scintillation index and correlation of intensity function

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Abstract
In a previous paper [J. Opt. Soc. Am. A 2, 2133 (1985)] we calculated the scintillation index (intensity variance) for plane-wave propagation, using the zero-order approximation of the two-scale method. Here we perform a similar calculation adding the first-order correction. We also include results for the correlation of intensities by both the zero-order and the first-order corrections. Our calculations include an inner-scale effect only for the scintillation index. The effect of including the first-order correction is to raise σI by approximately 5-11% at its peak value. There is little change in the normalized form of the correlation of intensity function. The results are compared with the results of recent studies by Martin and Flatte [Appl. Opt. 27, 2111 (1988)].