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1.5: Reflectance Functions

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    In the most general case of diffuse reflection, the reflectance of a surface will depend on both the direction of the incident radiation and that of the reflected radiation. The bidirectional reflectance distribution function, fr, links the irradiance E to the reflected radiance, such that

    \[L_{r}=f_{r}\left(\mu, \varphi ; \mu_{0}, \varphi_{0}\right) E\left(\mu_{0}, \varphi_{0}\right).\]

    For a surface irradiated with flux density F, the irradiance is simply the component of the flux density perpendicular to the surface

    \[E=\mu_{0} \mathbf{F},\]

    so that, abbreviated, we can write

    \[ L_{r}=f_{r} \mu_{0} \mathbf{F}\]

    One of the simplest examples of a reflectance rule is that of a Lambertian reflecting surface for which the radiance is isotropic, so that

    \[L_{r}=\frac{\lambda_{0}}{\pi} \mu_{0} \mathbf{F},\]

    where λ0 is sometimes referred to as the Lambertian albedo . Although it is not strictly physically correct, it is convenient (Chandrasekhar, p147) to identify λ0 with the single scattering albedo ϖ0, so for Lambert’s law the BRDF is

    \[f_{r}=\frac{\varpi_{0}}{\pi}.\]

    For the most part, we shall refer all reflectance rules used to a BRDF; alternative reflectance functions will be discussed in §8.

    This page titled 1.5: Reflectance Functions is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Max Fairbairn & Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.