Of paramount importance to the optical design of solar concentrators is the accurate characterization of the specular dispersion errors of the reflecting surfaces. An alternative derivation of the distribution of the azimuthal angular dispersion error is analytically derived and shown to be equivalent to the well-known Rayleigh distribution obtained by transforming the bivariate circular Gaussian distribution into polar coordinates. The corresponding inverse cumulative distribution function applied in Monte Carlo ray-tracing simulations, which gives the dispersion angle as a function of a random number sampled from a uniform distribution on the interval (0,1), does not depend on the inverse error function, thus simplifying and expediting Monte Carlo computations. Using a Monte Carlo ray-tracing example, it is verified that the Rayleigh and bivariate circular Gaussian distribution yield the same results. In the given example, the Rayleigh method is found to be ∼40% faster than the Gaussian method.
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e-mail: tcooper@ethz.ch
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November 2011
Technical Briefs
Derivation of the Angular Dispersion Error Distribution of Mirror Surfaces for Monte Carlo Ray-Tracing Applications
T. Cooper,
T. Cooper
Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich,
e-mail: tcooper@ethz.ch
Switzerland
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A. Steinfeld
A. Steinfeld
Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich, Switzerland; Solar Technology Laboratory,
e-mail: aldo.steinfeld@ethz.ch
Paul Scherrer Institute
, 5232 Villigen PSI, Switzerland
Search for other works by this author on:
T. Cooper
Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich,
Switzerland
e-mail: tcooper@ethz.ch
A. Steinfeld
Department of Mechanical and Process Engineering, ETH Zurich, 8092 Zürich, Switzerland; Solar Technology Laboratory,
Paul Scherrer Institute
, 5232 Villigen PSI, Switzerland
e-mail: aldo.steinfeld@ethz.ch
J. Sol. Energy Eng. Nov 2011, 133(4): 044501 (4 pages)
Published Online: October 13, 2011
Article history
Received:
October 11, 2010
Revised:
March 1, 2011
Online:
October 13, 2011
Published:
October 13, 2011
Citation
Cooper, T., and Steinfeld, A. (October 13, 2011). "Derivation of the Angular Dispersion Error Distribution of Mirror Surfaces for Monte Carlo Ray-Tracing Applications." ASME. J. Sol. Energy Eng. November 2011; 133(4): 044501. https://doi.org/10.1115/1.4004035
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