Level-crossing densities in random wave fields

Level-crossing densities along two orthogonal directions in an isotropic two-dimensional Gaussian random wave field are discussed for the real and the imaginary parts of the wave function, for the intensity, for thec phase, and for all the first-and second-order spatial derivatives of these functions. Analytical expressions are given for most crossing densities and are supplemented by numerical densities obtained from multidimensional Monte Carlo evaluations in cases in which analysis proved intractable. The analytical results and the Monte Carlo evaluations are generally found to be in good agreement with densities derived from a computer simulation that yields an accurate numerical representation of the wave function.