## Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions |

Applied Optics, Vol. 51, Issue 10, pp. C77-C83 (2012)

http://dx.doi.org/10.1364/AO.51.000C77

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### Abstract

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach. Several illustrative examples with relevance for optics are given.

© 2012 Optical Society of America

**OCIS Codes**

(030.1640) Coherence and statistical optics : Coherence

(030.1670) Coherence and statistical optics : Coherent optical effects

(030.6140) Coherence and statistical optics : Speckle

(030.6600) Coherence and statistical optics : Statistical optics

(120.7250) Instrumentation, measurement, and metrology : Velocimetry

**History**

Original Manuscript: December 19, 2011

Manuscript Accepted: February 2, 2012

Published: March 23, 2012

**Citation**

Harold T. Yura and Steen G. Hanson, "Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions," Appl. Opt. **51**, C77-C83 (2012)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-10-C77

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### References

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- For this case we obtain that the non linear least squares fit parameters are given by n=−0.441, a=1.24, a1=0.460, a3=−0.516, a5=0.634, and b=−0.216.

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