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Reflectance

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Reflectance

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 an interface. The reflectance spectrum or spectral reflectance curve is the plot of the reflectance as a function of wavelength.

Contents

Hemispherical reflectance

Hemispherical reflectance of a surface, denoted R, is defined as

R = Φ e r Φ e i ,

where

  • Φer is the radiant flux reflected by that surface;
  • Φei is the radiant flux received by that surface.

    • Spectral hemispherical reflectance

    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 , R λ = Φ e , λ r Φ e , λ 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

    Directional reflectance of a surface, denoted RΩ, is defined as

    R Ω = L e , Ω r L e , Ω i ,

    where

  • Le,Ωr is the radiance reflected by that surface;
  • Le,Ωi is the radiance received by that surface.

    • Spectral directional reflectance

    Spectral directional reflectance in frequency and spectral directional reflectance in wavelength of a surface, denoted RΩ,ν and RΩ,λ respectively, are defined as

    R Ω , ν = L e , Ω , ν r L e , Ω , ν i , R Ω , λ = L e , Ω , λ r L e , Ω , λ i ,

    where

  • Le,Ω,νr is the spectral radiance in frequency reflected by that surface;
  • Le,Ω,νi is the spectral radiance received by that surface;
  • Le,Ω,λr is the spectral radiance in wavelength reflected by that surface;
  • Le,Ω,λi is the spectral radiance in wavelength received by that surface.

    • Reflectivity

    For homogeneous and semi-infinite (see halfspace) materials, reflectivity is the same as reflectance. Reflectivity is the square of the magnitude of the Fresnel reflection coefficient, which is the ratio of the reflected to incident electric field; as such the reflection coefficient can be expressed as a complex number as determined by the Fresnel equations for a single layer, whereas the reflectance is always a positive real number.

    For layered and finite media, according to the CIE, reflectivity is distinguished from reflectance by the fact that reflectivity is a value that applies to thick reflecting objects. When reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness. Reflectivity is the limit value of reflectance as the sample becomes thick; it is the intrinsic reflectance of the surface, hence irrespective of other parameters such as the reflectance of the rear surface. Another way to interpret this is that the reflectance is the fraction of electromagnetic power reflected from a specific sample, while reflectivity is a property of the material itself, which would be measured on a perfect machine if the material filled half of all space.

    Surface type

    Going back to the fact that reflectance is a directional property, most surfaces can be divided into those that give specular reflection and those that give diffuse reflection:

  • for specular surfaces, such as glass or polished metal, reflectance will be nearly zero at all angles except at the appropriate reflected angle; that is, reflected radiation will follow a different path from incident radiation for all cases other than radiation normal to the surface;
  • for diffuse surfaces, such as matte white paint, reflectance is uniform; radiation is reflected in all angles equally or near-equally. Such surfaces are said to be Lambertian.

    • Most real objects have some mixture of diffuse and specular reflective properties.

    Water reflectance

    Reflection occurs when light moves from a medium with one index of refraction into a second medium with a different index of refraction.

    Specular reflection from a body of water is calculated by the Fresnel equations. Fresnel reflection is directional and therefore does not contribute significantly to albedo which is primarily diffuse reflection.

    A real water surface may be wavy. Reflectance assuming a flat surface as given by the Fresnel equations can be adjusted to account for waviness.

    Grating efficiency

    The generalization of reflectance to a diffraction grating, which disperses light by wavelength, is called diffraction efficiency.

    Applications

    Reflectance is an important concept in the fields of optics, solar thermal energy, telecommunication and radar.

    References

    Reflectance Wikipedia
    (Text) CC BY-SA