Simplified BRDF of a Non-Lambertian Diffuse Surface

Abstract

For real diffuse surfaces, the bi-directional reflectance distribution function (BRDF) is non-Lambertian, and may require a more complex model in ray tracing simulations. The BRDF of a diffuse white surface is studied at multiple angles of incidence, and an additional reflectance component is observed, which becomes more specular as the angle of incidence increases. For angles of incidence >85°, the BRDF may be regarded as specular. In this article, a two-part model is proposed in which the BRDF of a diffuse surface consists of a Lambertian diffuse component and a Lorentzian pseudo-specular component — both of which vary with angle of incidence. This model may be used to reduce computation times for ray tracing simulations, as an alternative to large three-dimensional BRDF datasets.

Keywords

BRDF models Lambertian Diffuse reflectance Specular reflectance

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References

Luque A. , Lorenzo E. , Sala G. , Lopez-Romero S. Diffusing reflectors for bifacial photovoltaic panels. Solar Cells 1985; 13: 277—92.

Earp AA , Smith GB , Swift PD , Franklin J.

Optimisation of a three-colour luminescent solar concentrator daylighting system. Solar Energy Materials and

Solar Cells 2004; 84: 411—26.

Roncali J. , Garnier F. New luminescent back reflectors for the improvement of the spectral response and efficiency of luminescent solar concentrators. Solar Cells 1984; 13: 133—43.

Canziani R. , Peron F. , Rossi G. Daylight and energy performances of a new type of light pipe. Energy and Buildings 2004; 36: 1163—76.

Zook JD A simple model for diffuse reflection. Optics Communications 1976; 17: 77—82.

Shen YJ , Zhu QZ , Zhang ZM A scatterometer for measuring the bidirectional reflectance and transmittance of semiconductor wafers with rough surfaces. Review of Scientific Instruments 2003; 74: 4885—92.

Susaki J. , Hara K. , Kajiwara K. , Honda Y. Robust estimation of BRDF model parameters. Remote Sensing of Environment 2004; 89: 63—71.

Bryant R. , Qi J. , Moran MS , Ni W. Comparison of BRDF models with a fuzzy inference system for correction of bidirectional effects. Remote Sensing of Environment 2003; 88: 221—32.

Pokrovsky I. , Pokrovsky O. , Roujean J-L. Development of an operational procedure to estimate surface albedo from the SEVIRI/ MSG observing system by using POLDER BRDF measurements: II. Comparison of several inversion techniques and uncertainty in albedo estimates. Remote Sensing of Environment 2003; 87: 215—42.

10.

Granier X. , Heidrich W. A simple layered RGB BRDF model. Graphical Models 2003; 65: 171—84.

11.

Pont SC , Koenderink JJ Reflectance from locally glossy thoroughly pitted surfaces. Computer Vision and Image Understanding 2005; 98: 211—22.

12.

Prokhorov AV , Hanssen LM Algorithmic model of microfacet BRDF for Monte Carlo calculation of optical radiation transfer. SPIE Optical Diagnostic Methods for Inorganic Materials III. 2003: SPIE.

13.

Becker ME Evaluation and characterization of display reflectance. Displays 1998; 19: 35—54.

14.

Kelley EF , Jones GR , Germer TA Display reflectance model based on the BRDF. Displays 1998; 19: 27—34.

15.

Thomas ME , Blodgett DW and Hahn DV Analysis and representation of BSDF and BRDF measurements. SPIE Optical Diagnostic Methods for Inorganic Materials III. 2003: SPIE Int. Soc. Opt. Eng

16.

Culpepper MA Empirical bidirectional reflectivity model. SPIE Targets and Backgrounds: Characterisation and Representation. 1995: SPIE.

17.

Apian-Bennewitz P. Designing an apparatus for measuring bi-directional reflection/transmission. SPIE - Optical Materials Technology XIII, 1994, Freiburg: SPIE.

18.

Sarotto M. , Rossi G. Characterisation of redirecting daylighting systems by goniophotometric measurements . EUROSUN 2000, Copenhagen, Denmark.

19.

Breitenbach J. , Rosenfeld Jlj. Goniospectrometer measurements of the optical performance of a holographic optical element. Solar Energy 2000; 68: 427—37.

20.

Andersen M. , Michel L. , Roecker C. , Scartezzini J-L. Experimental assessment of bi-directional transmission distribution functions using digital imaging techniques. Energy and Buildings 2001; 33: 417—31.

21.

Andersen M. , Rubin M. , Powles R. , Scartezzini J-L. Bi-directional transmission properties of Venetian blinds: experimental assessment compared to ray-tracing calculations. Solar Energy 2005; 78: 187—98.

22.

Andersen M. , Rubin M. , Scartezzini J-L. Comparison between ray-tracing simulations and bi-directional transmission measurements on prismatic glazing. Solar Energy 2003; 74: 157—73.

23.

Woan G. The Cambridge Handbook of Physics Formulas. Cambridge, UK: Cambridge University Press, 58, 2000.