bidirectional reflectance distribution function について

, 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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