Estimate of damage area due to a random optical wave

The light intensity of a laser beam which has propagated through the atmosphere will be irregular due to inhomogeneities in the atmosphere. Thus the intensity falling on a target is higher on some target areas and lower in others leading to damaged areas randomly distributed over the illuminated area. This study predicts the average area, A, of a single damaged area using a mathematical treatment, focusing largely on the concepts of two dimensional level crossings and excursion areas. After developing a solution for A for arbitrary probability density function (pdf), a solution for gamma distributed intensity is developed. This solution is then applied to several models for the spectral distribution of the intensity, including graphs illustrating the results. To reduce the problem to a manageable task, several assumptions and approximations are made. First, the pdf for the intensity is assumed to be the gamma distribution. This gamma distribution is applicable for the intensity of a gaussian field, a sum of gaussian fields, and therefore thermal light'. Second, the covariance function of the intensity is assumed to be isotropic. Furthermore, the intensity required to damage an area, Icrit, is assumed to be sufficiently high so that the probability of a damaged area containing an island of undamaged area is small. Although this assumption makes the calculated results approximate, these results become a better approximation for larger values of Icrit. Lastly, the variations in intensity are assumed to be spacially ergodic.