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Reflectance


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Spectral reflectance curves for aluminium (Al), silver (Ag), and gold (Au) metal mirrors at normal incidence.


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





  • 1 Mathematical definitions

    • 1.1 Hemispherical reflectance


    • 1.2 Spectral hemispherical reflectance


    • 1.3 Directional reflectance


    • 1.4 Spectral directional reflectance



  • 2 Reflectivity


  • 3 Surface type


  • 4 Water reflectance


  • 5 Grating efficiency


  • 6 Applications


  • 7 SI radiometry units


  • 8 See also


  • 9 References


  • 10 External links




Mathematical definitions[edit]



Hemispherical reflectance[edit]


The hemispherical reflectance of a surface, denoted R, is defined as[1]


R=ΦerΦei,displaystyle R=frac Phi _mathrm e ^mathrm r Phi _mathrm e ^mathrm i ,R=frac Phi _mathrm e ^mathrm r Phi _mathrm e ^mathrm i ,

where


  • Φer is the radiant flux reflected by that surface;

  • Φei is the radiant flux received by that surface.


Spectral hemispherical reflectance[edit]


The spectral hemispherical reflectance in frequency and spectral hemispherical reflectance in wavelength of a surface, denoted Rν and Rλ respectively, are defined as[1]


Rν=Φe,νrΦe,νi,displaystyle R_nu =frac Phi _mathrm e ,nu ^mathrm r Phi _mathrm e ,nu ^mathrm i ,R_nu =frac Phi _mathrm e ,nu ^mathrm r Phi _mathrm e ,nu ^mathrm i ,

Rλ=Φe,λrΦe,λi,displaystyle R_lambda =frac Phi _mathrm e ,lambda ^mathrm r Phi _mathrm e ,lambda ^mathrm i ,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[edit]


The directional reflectance of a surface, denoted RΩ, is defined as[1]


RΩ=Le,ΩrLe,Ωi,displaystyle R_Omega =frac L_mathrm e ,Omega ^mathrm r L_mathrm e ,Omega ^mathrm i ,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.


Spectral directional reflectance[edit]


The spectral directional reflectance in frequency and spectral directional reflectance in wavelength of a surface, denoted RΩ,ν and RΩ,λ respectively, are defined as[1]


RΩ,ν=Le,Ω,νrLe,Ω,νi,displaystyle R_Omega ,nu =frac L_mathrm e ,Omega ,nu ^mathrm r L_mathrm e ,Omega ,nu ^mathrm i ,displaystyle R_Omega ,nu =frac L_mathrm e ,Omega ,nu ^mathrm r L_mathrm e ,Omega ,nu ^mathrm i ,

RΩ,λ=Le,Ω,λrLe,Ω,λi,displaystyle R_Omega ,lambda =frac L_mathrm e ,Omega ,lambda ^mathrm r L_mathrm e ,Omega ,lambda ^mathrm i ,displaystyle R_Omega ,lambda =frac L_mathrm e ,Omega ,lambda ^mathrm r L_mathrm e ,Omega ,lambda ^mathrm 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[edit]




Fresnel reflection coefficients for a boundary surface between air and a variable material in dependence of the complex refractive index and the angle of incidence.



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[edit]


Given 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[edit]




Reflectance of smooth water at 20°C (refractive index 1.333).


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 primarily diffuses reflection.


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



Grating efficiency[edit]


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



Applications[edit]


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



SI radiometry units[edit]









































































































































































































































SI radiometry units


Quantity
Unit
Dimension
Notes

Name

Symbol[nb 1]

Name

Symbol

Symbol

Radiant energy

Qe[nb 2]

joule

J

ML2T−2
Energy of electromagnetic radiation.

Radiant energy density

we
joule per cubic metre
J/m3
ML−1T−2
Radiant energy per unit volume.

Radiant flux
Φe[nb 2]
watt

W = J/s

ML2T−3
Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power".

Spectral flux
Φe,ν[nb 3]
 or
Φe,λ[nb 4]
watt per hertz
 or
watt per metre
W/Hz
 or
W/m

ML2T−2
 or
MLT−3
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm−1.

Radiant intensity

Ie,Ω[nb 5]
watt per steradian
W/sr

ML2T−3
Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity.

Spectral intensity

Ie,Ω,ν[nb 3]
 or
Ie,Ω,λ[nb 4]
watt per steradian per hertz
 or
watt per steradian per metre
W⋅sr−1⋅Hz−1
 or
W⋅sr−1⋅m−1

ML2T−2
 or
MLT−3
Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr−1⋅nm−1. This is a directional quantity.

Radiance

Le,Ω[nb 5]
watt per steradian per square metre
W⋅sr−1⋅m−2
MT−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

Le,Ω,ν[nb 3]
 or
Le,Ω,λ[nb 4]
watt per steradian per square metre per hertz
 or
watt per steradian per square metre, per metre
W⋅sr−1⋅m−2⋅Hz−1
 or
W⋅sr−1⋅m−3

MT−2
 or
ML−1T−3
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".

Irradiance
Flux density

Ee[nb 2]
watt per square metre
W/m2
MT−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]
 or
Ee,λ[nb 4]
watt per square metre per hertz
 or
watt per square metre, per metre
W⋅m−2⋅Hz−1
 or
W/m3

MT−2
 or
ML−1T−3
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).

Radiosity

Je[nb 2]
watt per square metre
W/m2
MT−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]
 or
Je,λ[nb 4]
watt per square metre per hertz
 or
watt per square metre, per metre
W⋅m−2⋅Hz−1
 or
W/m3

MT−2
 or
ML−1T−3
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".

Radiant exitance

Me[nb 2]
watt per square metre
W/m2
MT−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]
 or
Me,λ[nb 4]
watt per square metre per hertz
 or
watt per square metre, per metre
W⋅m−2⋅Hz−1
 or
W/m3

MT−2
 or
ML−1T−3
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".

Radiant exposure

He
joule per square metre
J/m2
MT−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]
 or
He,λ[nb 4]
joule per square metre per hertz
 or
joule per square metre, per metre
J⋅m−2⋅Hz−1
 or
J/m3

MT−1
 or
ML−1T−2
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".

Hemispherical emissivity

ε



1
Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface.

Spectral hemispherical emissivity

εν
 or
ελ



1
Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface.

Directional emissivity

εΩ



1
Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface.

Spectral directional emissivity

εΩ,ν
 or
εΩ,λ



1
Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface.

Hemispherical absorptance

A



1
Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance".

Spectral hemispherical absorptance

Aν
 or
Aλ



1
Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance".

Directional absorptance

AΩ



1
Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance".

Spectral directional absorptance

AΩ,ν
 or
AΩ,λ



1
Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance".

Hemispherical reflectance

R



1
Radiant flux reflected by a surface, divided by that received by that surface.

Spectral hemispherical reflectance

Rν
 or
Rλ



1
Spectral flux reflected by a surface, divided by that received by that surface.

Directional reflectance

RΩ



1
Radiance reflected by a surface, divided by that received by that surface.

Spectral directional reflectance

RΩ,ν
 or
RΩ,λ



1
Spectral radiance reflected by a surface, divided by that received by that surface.

Hemispherical transmittance

T



1
Radiant flux transmitted by a surface, divided by that received by that surface.

Spectral hemispherical transmittance

Tν
 or
Tλ



1
Spectral flux transmitted by a surface, divided by that received by that surface.

Directional transmittance

TΩ



1
Radiance transmitted by a surface, divided by that received by that surface.

Spectral directional transmittance

TΩ,ν
 or
TΩ,λ



1
Spectral radiance transmitted by a surface, divided by that received by that surface.

Hemispherical attenuation coefficient

μ
reciprocal metre
m−1
L−1
Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.

Spectral hemispherical attenuation coefficient

μν
 or
μλ
reciprocal metre
m−1
L−1
Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume.

Directional attenuation coefficient

μΩ
reciprocal metre
m−1
L−1
Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.

Spectral directional attenuation coefficient

μΩ,ν
 or
μΩ,λ
reciprocal metre
m−1
L−1
Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume.
See also: SI · Radiometry · Photometry


  1. ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.


  2. ^ abcde Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.


  3. ^ abcdefg Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity.


  4. ^ abcdefg Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).


  5. ^ ab Directional quantities are denoted with suffix "Ω" (Greek).




See also[edit]


  • Bidirectional reflectance distribution function

  • Emissivity

  • Lambert's cosine law

  • Transmittance

  • Sun path

  • Light Reflectance Value

  • Albedo


References[edit]




  1. ^ abcd "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15..mw-parser-output cite.citationfont-style:inherit.mw-parser-output qquotes:"""""""'""'".mw-parser-output code.cs1-codecolor:inherit;background:inherit;border:inherit;padding:inherit.mw-parser-output .cs1-lock-free abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-lock-subscription abackground:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registrationcolor:#555.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration spanborder-bottom:1px dotted;cursor:help.mw-parser-output .cs1-hidden-errordisplay:none;font-size:100%.mw-parser-output .cs1-visible-errorfont-size:100%.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-formatfont-size:95%.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-leftpadding-left:0.2em.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-rightpadding-right:0.2em


  2. ^ E. Hecht (2001). Optics (4th ed.). Pearson Education.
    ISBN 0-8053-8566-5.



  3. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Reflectance".


  4. ^ CIE International Lighting Vocabulary


  5. ^ Palmer and Grant, The Art of Radiometry


  6. ^ 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[edit]





  • Reflectivity of metals (chart).


  • Reflectance Data.



Retrieved from "https://en.wikipedia.org/w/index.php?title=Reflectance&oldid=836089966#Reflectivity"





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