Abstract

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 the 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.

© 1998 Optical Society of America

Critical-point level-crossing geometry in random wave fields

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Critical-point screening in random wave fields

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Optical vortices in Gaussian random wave fields: statistical probability densities

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Wave-field phase singularities: near-neighbor correlations and anticorrelations

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Phase correlations at neighboring intensity critical points in Gaussian random wave fields

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