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Full-Text Articles in Physics
Multi-Gaussian Random Variables For Modeling Optical Phenomena, Olga Korotkova, Milo W. Hyde Iv
Multi-Gaussian Random Variables For Modeling Optical Phenomena, Olga Korotkova, Milo W. Hyde Iv
Faculty Publications
A generalization of the classic Gaussian random variable to the family of multi-Gaussian (MG) random variables characterized by shape parameter M > 0, in addition to the mean and the standard deviation, is introduced. The probability density function (PDF) of the MG family members is an alternating series of Gaussian functions with suitably chosen heights and widths. In particular, for integer values of M, the series has a finite number of terms and leads to flattened profiles, while reducing to the classic Gaussian PDF for M = 1. For non-integer, positive values of M, a convergent infinite series of …
Independently Controlling Stochastic Field Realization Magnitude And Phase Statistics For The Construction Of Novel Partially Coherent Sources, Milo W. Hyde Iv
Independently Controlling Stochastic Field Realization Magnitude And Phase Statistics For The Construction Of Novel Partially Coherent Sources, Milo W. Hyde Iv
Faculty Publications
In this paper, we present a method to independently control the field and irradiance statistics of a partially coherent beam. Prior techniques focus on generating optical field realizations whose ensemble-averaged autocorrelation matches a specified second-order field moment known as the cross-spectral density (CSD) function. Since optical field realizations are assumed to obey Gaussian statistics, these methods do not consider the irradiance moments, as they, by the Gaussian moment theorem, are completely determined by the field’s first and second moments. Our work, by including control over the irradiance statistics (in addition to the CSD function), expands existing synthesis approaches and allows …