The bidirectional reflectance distribution function (BRDF; $\{f\_r(\backslash mathbf\{\backslash Omega\_e\}\; ,\; \backslash mathbf\{\backslash Omega\_i\})\}$) describes the ratio of reflected radiance exiting from a surface in a particular direction (defined by the vector $\backslash mathbf\{\backslash Omega\_e\}$) to the irradiance incident on the surface from direction $\backslash mathbf\{\backslash Omega\_i\}$ 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 $\{f\_r(\backslash lambda\; ,\; \backslash mathbf\{\backslash Omega\_e\}\; ,\; \backslash mathbf\{\backslash Omega\_i\})\}$ (units of sr^-1nm^-1) describes the BRDF as a function of wavelength, $\backslash lambda$.

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.

BDRF is an intrinsic optical property of the viewed surface material, however it is not a quantity that can be physically measured, beause 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 BDRF has some well-defined properties, in particular, it is symmetric (reciprocal), i.e., its value is the same, when the directons to source and observer are switched. This is not so for structured surfaces. Therefore much research have been caried out for derivation of good models for various natural surfaces, such as sea surface (clean and with various pollutions), forest canopy, various types of soil, etc., required for object classification in remote sensing, as well as for various flat but textured surfaces, to simulate, e.g., textures of construction materials (brick, concrete, wood, etc.), for realistical rendering in a wide range of applications, from architectural design or video games.

Various mathematical models have been defined to describe the BRDF of various surfaces. One model, developed quasi-experimentally by astronomer Bruce Hapke at the University of Pittsburgh, introduces five such quantities:

1. w - Single scattering albedo
2. h - Width of the opposition spike
3. S(0) - Amplitude of the opposition spike
4. g - asymmetry factor
5. $\backslash theta$ - Effective surface tilt

See also

• BSDF
• Radiometry
• Photometry (astronomy)
• Reflectance
• Albedo
• Opposition spike
• Gonioreflectometer

References

• Nicodemus, F., "Reflectance nomenclature and directional reflectance and emissivity," Appl. Opt., vol. 9, pp. 1474–1475, 1970.

Radiometry Astrophysics | Computer graphics

Bidirectional Reflectance Distribution Function | BRDF