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Bidirectional reflectance distribution function : ウィキペディア英語版
Bidirectional reflectance distribution function

The bidirectional reflectance distribution function (BRDF; f_},\, \omega_}, and outgoing direction, \omega_} to the irradiance incident on the surface from direction \omega_{\text{i}}. Each direction \omega is itself parameterized by azimuth angle \phi and zenith angle \theta, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr−1, with steradians (sr) being a unit of solid angle.
==Definition==
The BRDF was first defined by Fred Nicodemus around 1965.〔
〕 The definition is:
f_},\, \omega_}(\omega_})} \,=\, \frac})}})\cos\theta_}}
where L is radiance, or power per unit solid angleApplied Optics
| url = http://ao.osa.org/abstract.cfm?id=13818
| format = abstract
| doi = 10.1364/AO.4.000767
| year = 1965
|bibcode = 1965ApOpt...4..767N }}〕 The definition is:
f_},\, \omega_}(\omega_})} \,=\, \frac})}})\cos\theta_}}
where L is radiance, or power per unit solid-angle-in-the-direction-of-a-ray per unit projected-area-perpendicular-to-the-ray, E is irradiance, or power per unit ''surface area'', and \theta_} and the surface normal, \mathbf n. The index \text indicates incident light, whereas the index \text indicates reflected light.
The reason the function is defined as a quotient of two differentials and not directly as a quotient between the undifferentiated quantities, is because other irradiating light than \operatorname dE_}), which are of no interest for f_},\, \omega_}(\omega_}(\omega_}(\omega_{\text{i}}).

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