Bidirectional reflectance distribution function
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The bidirectional reflectance distribution function (BRDF; 
) describes the ratio of reflected radiance exiting from a surface in a particular direction (defined by the vector 
) to the irradiance incident on the surface from direction 
over a particular waveband. It was first defined by F. Nicodemus in 1970, and has units sr-1, with steradians (sr) being a unit of solid angle. The spectral BRDF 
(units of sr-1nm-1) describes the BRDF as a function of wavelength, λ.
The function is used in image processing, including pattern recognition and remote sensing, and computer graphics for rendering of realistic looking images. In plain words, the function formalizes an observation that color shades and brightness of an object depend on both the direction of illumination and the direction to observer.
BRDF is an intrinsic optical property of the viewed surface material, however it is not a quantity that can be physically measured, because it is defined over infinitesimal solid angles both towards the illumination source and the detector (observer). However it may be modelled basing on the measurements of quantities integrated over the source/observer solid angles.
For flat surfaces, BRDF has some well-defined properties, in particular, it is symmetric (reciprocal), i.e., its value is the same when the directions to source and observer are switched. This is not so for structured surfaces. Therefore, much research has been carried out for the derivation of good models for various natural surfaces. Examples include sea surface (clean or with various pollutions), forest canopy, various types of soil, etc., required for object classification in remote sensing. This has also been done for various flat but textured surfaces, for example, to simulate textures of construction materials (brick, concrete, wood, etc.). These techniques are used for realistical rendering in a wide range of applications, such as architectural design or video games.
A number of mathematical models have been defined to describe the BRDF of various surfaces. One model that is used to describe the surface reflectance properties of airless solar system bodies, developed quasi-experimentally by astronomer Bruce Hapke at the University of Pittsburgh, introduces five such quantities, the Hapke parameters:
- w - Single scattering albedo
- h - Width of the opposition spike
- S(0) - Amplitude of the opposition spike
- g - asymmetry factor
- θ - Effective surface tilt
[edit] See also
[edit] References
- Nicodemus, F., "Reflectance nomenclature and directional reflectance and emissivity," Appl. Opt., vol. 9, pp. 1474–1475, 1970.
- Schaepman-Strub, G., Schaepman, M. E., Painter, T. H., Dangel, S., Martonchik, J. V., "Reflectance quantities in optical remote sensing--definitions and case studies," Remote Sensing of Environment, vol. 103, pp. 27–42, 2006.
