Reflectance

The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic structure of the material to the electromagnetic field of light, and is in general a function of the frequency, or wavelength, of the light, its polarization, and the angle of incidence. The dependence of reflectance on the wavelength is called a reflectance spectrum or spectral reflectance curve.

Mathematical definitions

Hemispherical reflectance

The hemispherical reflectance of a surface, denoted R, is defined as

R

=

Φ

e

r

Φ

e

i

,

{\displaystyle R={\frac {\Phi _{\mathrm {e} }^{\mathrm {r} }}{\Phi _{\mathrm {e} }^{\mathrm {i} }}},}

where Φer is the radiant flux reflected by that surface and Φei is the radiant flux received by that surface.

Spectral hemispherical reflectance

The spectral hemispherical reflectance in frequency and spectral hemispherical reflectance in wavelength of a surface, denoted Rν and Rλ respectively, are defined as

R

ν

=

Φ

e

,

ν

r

Φ

e

,

ν

i

,

{\displaystyle R_{\nu }={\frac {\Phi _{\mathrm {e} ,\nu }^{\mathrm {r} }}{\Phi _{\mathrm {e} ,\nu }^{\mathrm {i} }}},}

R

λ

=

Φ

e

,

λ

r

Φ

e

,

λ

i

,

{\displaystyle R_{\lambda }={\frac {\Phi _{\mathrm {e} ,\lambda }^{\mathrm {r} }}{\Phi _{\mathrm {e} ,\lambda }^{\mathrm {i} }}},}

where

Φe,νr is the spectral radiant flux in frequency reflected by that surface;

Φe,νi is the spectral radiant flux in frequency received by that surface;

Φe,λr is the spectral radiant flux in wavelength reflected by that surface;

Φe,λi is the spectral radiant flux in wavelength received by that surface.

Directional reflectance

The directional reflectance of a surface, denoted RΩ, is defined as

R

Ω

=

L

e

,

Ω

r

L

e

,

Ω

i

,

{\displaystyle R_{\Omega }={\frac {L_{\mathrm {e} ,\Omega }^{\mathrm {r} }}{L_{\mathrm {e} ,\Omega }^{\mathrm {i} }}},}

where

Le,Ωr is the radiance reflected by that surface;

Le,Ωi is the radiance received by that surface.

This depends on both the reflected direction and the incoming direction. In other words, it has a value for every combination of incoming and outgoing directions. It is related to the bidirectional reflectance distribution function and its upper limit is 1.