## Physical optics solution for the scattering of a partially-coherent wave from a statistically rough material surface |

Optics Express, Vol. 21, Issue 6, pp. 6807-6825 (2013)

http://dx.doi.org/10.1364/OE.21.006807

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### Abstract

The scattering of a partially-coherent wave from a statistically rough material surface is investigated via derivation of the scattered field cross-spectral density function. Two forms of the cross-spectral density are derived using the physical optics approximation. The first is applicable to smooth-to-moderately rough surfaces and is a complicated expression of source and surface parameters. Physical insight is gleaned from its analytical form and presented in this work. The second form of the cross-spectral density function is applicable to very rough surfaces and is remarkably physical. Its form is discussed at length and closed-form expressions are derived for the angular spectral degree of coherence and spectral density radii. Furthermore, it is found that, under certain circumstances, the cross-spectral density function maintains a Gaussian Schell-model form. This is consistent with published results applicable only in the paraxial regime. Lastly, the closed-form cross-spectral density functions derived here are rigorously validated with scatterometer measurements and full-wave electromagnetic and physical optics simulations. Good agreement is noted between the analytical predictions and the measured and simulated results.

© 2013 OSA

**OCIS Codes**

(030.0030) Coherence and statistical optics : Coherence and statistical optics

(240.5770) Optics at surfaces : Roughness

(260.2110) Physical optics : Electromagnetic optics

(290.5880) Scattering : Scattering, rough surfaces

**ToC Category:**

Coherence and Statistical Optics

**History**

Original Manuscript: January 28, 2013

Revised Manuscript: February 13, 2013

Manuscript Accepted: February 16, 2013

Published: March 12, 2013

**Citation**

Milo W. Hyde, Santasri Basu, Mark F. Spencer, Salvatore J. Cusumano, and Steven T. Fiorino, "Physical optics solution for the scattering of a partially-coherent wave from a statistically rough material surface," Opt. Express **21**, 6807-6825 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-6-6807

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