Reflectance
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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.
Mathematical definitions
Hemispherical reflectance
Hemispherical reflectance of a surface, denoted R, is defined as[1]
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[1]
where
- Φre,ν is the spectral radiant flux in frequency reflected by that surface;
- Φie,ν is the spectral radiant flux in frequency received by that surface;
- Φre,λ is the spectral radiant flux in wavelength reflected by that surface;
- Φie,λ is the spectral radiant flux in wavelength received by that surface.
Directional reflectance
Directional reflectance of a surface, denoted RΩ, is defined as[1]
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 Rν,Ω and Rλ,Ω respectively, are defined as[1]
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
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Fresnel_equations_-_reflectance.svg/400px-Fresnel_equations_-_reflectance.svg.png)
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,[2] which is the ratio of the reflected to incident electric field;[3] 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,[citation needed] reflectivity is distinguished from reflectance by the fact that reflectivity is a value that applies to thick reflecting objects.[4] 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.[5]
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
![](http://upload.wikimedia.org/wikipedia/en/thumb/7/7f/Water_reflectivity.jpg/400px-Water_reflectivity.jpg)
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.[6] 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.
SI radiometry units
Quantity | Unit | Dimension | Notes | ||
---|---|---|---|---|---|
Name | Symbol[nb 1] | Name | Symbol | ||
Radiant energy | Qe[nb 2] | joule | J | M⋅L2⋅T−2 | Energy of electromagnetic radiation. |
Radiant energy density | we | joule per cubic metre | J/m3 | M⋅L−1⋅T−2 | Radiant energy per unit volume. |
Radiant flux | Φe[nb 2] | watt | W = J/s | M⋅L2⋅T−3 | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power", and called luminosity in Astronomy. |
Spectral flux | Φe,ν[nb 3] | watt per hertz | W/Hz | M⋅L2⋅T −2 | Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1. |
Φe,λ[nb 4] | watt per metre | W/m | M⋅L⋅T−3 | ||
Radiant intensity | Ie,Ω[nb 5] | watt per steradian | W/sr | M⋅L2⋅T−3 | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. |
Spectral intensity | Ie,Ω,ν[nb 3] | watt per steradian per hertz | W⋅sr−1⋅Hz−1 | M⋅L2⋅T−2 | Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is a directional quantity. |
Ie,Ω,λ[nb 4] | watt per steradian per metre | W⋅sr−1⋅m−1 | M⋅L⋅T−3 | ||
Radiance | Le,Ω[nb 5] | watt per steradian per square metre | W⋅sr−1⋅m−2 | M⋅T−3 | Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity". |
Spectral radiance Specific intensity |
Le,Ω,ν[nb 3] | watt per steradian per square metre per hertz | W⋅sr−1⋅m−2⋅Hz−1 | M⋅T−2 | Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅m−2⋅nm−1. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". |
Le,Ω,λ[nb 4] | watt per steradian per square metre, per metre | W⋅sr−1⋅m−3 | M⋅L−1⋅T−3 | ||
Irradiance Flux density |
Ee[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". |
Spectral irradiance Spectral flux density |
Ee,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Irradiance of a surface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (1 Jy = 10−26 W⋅m−2⋅Hz−1) and solar flux unit (1 sfu = 10−22 W⋅m−2⋅Hz−1 = 104 Jy). |
Ee,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiosity | Je[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". |
Spectral radiosity | Je,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. This is sometimes also confusingly called "spectral intensity". |
Je,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiant exitance | Me[nb 2] | watt per square metre | W/m2 | M⋅T−3 | Radiant flux emitted by a surface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity". |
Spectral exitance | Me,ν[nb 3] | watt per square metre per hertz | W⋅m−2⋅Hz−1 | M⋅T−2 | Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m−2⋅nm−1. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity". |
Me,λ[nb 4] | watt per square metre, per metre | W/m3 | M⋅L−1⋅T−3 | ||
Radiant exposure | He | joule per square metre | J/m2 | M⋅T−2 | Radiant energy received by a surface per unit area, or equivalently irradiance of a surface integrated over time of irradiation. This is sometimes also called "radiant fluence". |
Spectral exposure | He,ν[nb 3] | joule per square metre per hertz | J⋅m−2⋅Hz−1 | M⋅T−1 | Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m−2⋅nm−1. This is sometimes also called "spectral fluence". |
He,λ[nb 4] | joule per square metre, per metre | J/m3 | M⋅L−1⋅T−2 | ||
See also: |
- ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- ^ a b c d e Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- ^ a b c d e f g Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek letter nu, not to be confused with a letter "v", indicating a photometric quantity.)
- ^ a b c d e f g Spectral quantities given per unit wavelength are denoted with suffix "λ".
- ^ a b Directional quantities are denoted with suffix "Ω".
See also
- Bidirectional reflectance distribution function
- Emissivity
- Lambert's cosine law
- Transmittance
- Sun path
- Light Reflectance Value
- Albedo
References
- ^ a b c d "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.
- ^ E. Hecht (2001). Optics (4th ed.). Pearson Education. ISBN 0-8053-8566-5.
- ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Reflectance". doi:10.1351/goldbook.R05235
- ^ CIE International Lighting Vocabulary
- ^ Palmer and Grant, The Art of Radiometry
- ^ Ottaviani, M. and Stamnes, K. and Koskulics, J. and Eide, H. and Long, S.R. and Su, W. and Wiscombe, W., 2008: 'Light Reflection from Water Waves: Suitable Setup for a Polarimetric Investigation under Controlled Laboratory Conditions. Journal of Atmospheric and Oceanic Technology, 25 (5), 715--728.
External links
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