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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 7 — Mar. 1, 2013
  • pp: 1472–1480

Generating random rough edges, surfaces, and volumes

Chris A. Mack  »View Author Affiliations

Applied Optics, Vol. 52, Issue 7, pp. 1472-1480 (2013)

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Numerical methods of generating rough edges, surfaces, and volumes for subsequent simulations are commonly employed, but result in data with a variance that is downward biased from the desired value. Thus, it is highly desirable to quantify and to minimize this bias. Here, the degree of bias is determined through analytical derivations and numerical simulations as a function of the correlation length and the roughness exponent of several model power spectral density functions. The bias can be minimized by proper choice of grid size for a fixed number of data points, and this optimum grid size scales as the correlation length. The common approach of using a fixed grid size for such simulations leads to varying amounts of bias, which can easily be confounded with the physical effects being investigated.

© 2013 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(000.5490) General : Probability theory, stochastic processes, and statistics
(120.6660) Instrumentation, measurement, and metrology : Surface measurements, roughness
(290.5880) Scattering : Scattering, rough surfaces

ToC Category:

Original Manuscript: January 8, 2013
Revised Manuscript: January 28, 2013
Manuscript Accepted: January 29, 2013
Published: February 28, 2013

Chris A. Mack, "Generating random rough edges, surfaces, and volumes," Appl. Opt. 52, 1472-1480 (2013)

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