View source for Reflectance

{{short description|Capacity of an object to reflect light}}
[[File:Image-Metal-reflectance.png|thumb|400px|Spectral reflectance curves for [[aluminium]] (Al), [[silver]] (Ag), and [[gold]] (Au) metal [[mirror]]s at normal incidence]]

The '''reflectance''' of the surface of a [[material]] is its effectiveness in [[Reflection (physics)|reflect]]ing [[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 (optics)|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 {{mvar|R}}, is defined as<ref name="ISO_9288-1989">{{cite web| url=http://www.iso.org/iso/home/store/catalogue_tc/catalogue_detail.htm?csnumber=16943|title=Thermal insulation — Heat transfer by radiation — Physical quantities and definitions|work=ISO 9288:1989|publisher=[[International Organization for Standardization|ISO]] catalogue|year=1989|access-date=2015-03-15}}</ref>
<math display="block">R = \frac{\Phi_\mathrm{e}^\mathrm{r}}{\Phi_\mathrm{e}^\mathrm{i}},</math>
where {{math|Φ<sub>e</sub><sup>r</sup>}} is the [[radiant flux]] ''reflected'' by that surface and {{math|Φ<sub>e</sub><sup>i</sup>}} 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 {{math|''R''<sub>''ν''</sub>}} and {{math|''R''<sub>''λ''</sub>}} respectively, are defined as<ref name="ISO_9288-1989" />
<math display="block">R_\nu = \frac{\Phi_{\mathrm{e},\nu}^\mathrm{r}}{\Phi_{\mathrm{e},\nu}^\mathrm{i}},</math>
<math display="block">R_\lambda = \frac{\Phi_{\mathrm{e},\lambda}^\mathrm{r}}{\Phi_{\mathrm{e},\lambda}^\mathrm{i}},</math>
where
*{{math|Φ<sub>e,''ν''</sub><sup>r</sup>}} is the [[Radiant flux|spectral radiant flux in frequency]] ''reflected'' by that surface;
*{{math|Φ<sub>e,''ν''</sub><sup>i</sup>}} is the spectral radiant flux in frequency received by that surface;
*{{math|Φ<sub>e,''λ''</sub><sup>r</sup>}} is the [[Radiant flux|spectral radiant flux in wavelength]] ''reflected'' by that surface;
*{{math|Φ<sub>e,''λ''</sub><sup>i</sup>}} is the spectral radiant flux in wavelength received by that surface.

===Directional reflectance===
The ''directional reflectance'' of a surface, denoted ''R''<sub>Ω</sub>, is defined as<ref name="ISO_9288-1989" />
<math display="block">R_\Omega = \frac{L_{\mathrm{e},\Omega}^\mathrm{r}}{L_{\mathrm{e},\Omega}^\mathrm{i}},</math>
where
*{{math|''L''<sub>e,Ω</sub><sup>r</sup>}} is the [[radiance]] ''reflected'' by that surface;
*{{math|''L''<sub>e,Ω</sub><sup>i</sup>}} 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. Another measure of reflectance, depending only on the outgoing direction, is ''I''/''F'', where ''I'' is the radiance reflected in a given direction and ''F'' is the incoming radiance averaged over all directions, in other words, the total flux of radiation hitting the surface per unit area, divided by π.<ref>{{cite journal |first1=Jeffrey |last1=Cuzzi |first2=Lindsey |last2=Chambers |first3=Amanda |last3=Hendrix |title=Rough Surfaces: is the dark stuff just shadow? |journal=[[Icarus (journal)|Icarus]] |date=Oct 21, 2016 |volume=289 |pages=281–294 |doi=10.1016/j.icarus.2016.10.018 |pmid=31708591 |pmc=6839776 }}</ref> This can be greater than 1 for a glossy surface illuminated by a source such as the sun, with the reflectance measured in the direction of maximum radiance (see also [[Seeliger effect]]).

===Spectral directional reflectance===
The ''spectral directional reflectance in frequency'' and ''spectral directional reflectance in wavelength'' of a surface, denoted {{math|''R''<sub>Ω,''ν''</sub>}} and {{math|''R''<sub>Ω,''λ''</sub>}} respectively, are defined as<ref name="ISO_9288-1989" />
<math display="block">R_{\Omega,\nu} = \frac{L_{\mathrm{e},\Omega,\nu}^\mathrm{r}}{L_{\mathrm{e},\Omega,\nu}^\mathrm{i}},</math>
<math display="block">R_{\Omega,\lambda} = \frac{L_{\mathrm{e},\Omega,\lambda}^\mathrm{r}}{L_{\mathrm{e},\Omega,\lambda}^\mathrm{i}},</math>
where
*{{math|''L''<sub>e,Ω,''ν''</sub><sup>r</sup>}} is the [[Radiance|spectral radiance in frequency]] ''reflected'' by that surface;
*{{math|''L''<sub>e,Ω,''ν''</sub><sup>i</sup>}} is the spectral radiance received by that surface;
*{{math|''L''<sub>e,Ω,''λ''</sub><sup>r</sup>}} is the [[Radiance|spectral radiance in wavelength]] ''reflected'' by that surface;
*{{math|''L''<sub>e,Ω,''λ''</sub><sup>i</sup>}} is the spectral radiance in wavelength received by that surface.

Again, one can also define a value of {{math|''I''/''F''}} (see above) for a given wavelength.<ref>See for example {{cite journal | display-authors=etal |last1=P.G.J Irwin |title=Hazy Blue Worlds: A Holistic Aerosol Model for Uranus and Neptune, Including Dark Spots |journal=Journal of Geophysical Research: Planets | date=Jan 12, 2022 |volume=127 |issue=6 |pages=e2022JE007189 |doi=10.1029/2022JE007189 |pmid=35865671 |pmc=9286428 |arxiv=2201.04516 |bibcode=2022JGRE..12707189I |hdl=1983/65ee78f0-1d28-4017-bbd9-1b49b24700d7 |s2cid=245877540 |bibcode-access=free |doi-access=free |hdl-access=free |s2cid-access=free }}</ref>

==Reflectivity==
[[File:Fresnel equations - reflectance.svg|thumb|400px|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]]
{{redirect|Reflectivity|the EM formulation|Fresnel power reflection}}
For homogeneous and semi-infinite (see [[Half-space (geometry)|halfspace]]) materials, reflectivity is the same as reflectance. 
Reflectivity is the square of the magnitude of the [[Fresnel reflection coefficient]],<ref>E. Hecht (2001). Optics (4th ed.). Pearson Education. {{ISBN|0-8053-8566-5}}.</ref>
which is the ratio of the reflected to incident [[electric field]];<ref name=GoldBook>{{GoldBookRef|title=Reflectance|file=R05235|accessdate=2015-03-15}}</ref> 
as such the reflection coefficient can be expressed as a [[complex number]] as determined by the [[Fresnel equation]]s for a single layer, whereas the reflectance is always a positive [[real number]].

For layered and finite media, according to the [[International Commission on Illumination|CIE]],{{citation needed|date=May 2015}} reflectivity is distinguished from ''reflectance'' by the fact that reflectivity is a value that applies to ''thick'' reflecting objects.<ref name="ILV">{{Cite web |url=http://www.cie.co.at/index.php/index.php?i_ca_id=306 |title=CIE International Lighting Vocabulary |access-date=2010-12-04 |archive-date=2016-06-16 |archive-url=https://web.archive.org/web/20160616060734/http://www.cie.co.at/index.php/index.php?i_ca_id=306 |url-status=dead }}</ref> 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.<ref name="Grant">[https://www.amazon.com/dp/081947245X Palmer and Grant, ''The Art of Radiometry'']</ref>

==Surface type==
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 is nearly zero at all angles except at the appropriate reflected angle; that is the same angle with respect to the surface normal in the [[plane of incidence]], but on the opposing side. When the radiation is incident normal to the surface, it is reflected back into the same direction.

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 reflectance|Lambertian]].

Most practical objects exhibit a combination of diffuse and specular reflective properties.

==Water reflectance==
[[File:Water reflectivity.jpg|thumb|400px|Reflectance of smooth water at 20&nbsp;°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]].<ref name="Ottav">Ottaviani, M. and Stamnes, K. and Koskulics, J. and Eide, H. and Long, S.R. and Su, W. and Wiscombe, W., 2008: '[https://journals.ametsoc.org/doi/pdf/10.1175/2007JTECHA1049.1 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.</ref> 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==
The generalization of reflectance to a [[diffraction grating]], which disperses light by [[wavelength]], is called ''[[diffraction efficiency]]''.

{{clear}}

==Other radiometric coefficients==
{{Radiometry coefficients}}

==See also==
*[[Bidirectional reflectance distribution function]]
*[[Colorimetry]]
*[[Emissivity]]
*[[Lambert's cosine law]]
*[[Transmittance]]
*[[Sun path]]
*[[Light Reflectance Value]]
*[[Albedo]]
* [[Reststrahlen effect]]
* [[Lyddane–Sachs–Teller relation]]

==References==
{{reflist}}

==External links==
{{wiktionary|reflectance}}
*Reflectivity of metals {{Webarchive|url=https://web.archive.org/web/20160304024228/http://www.tvu.com/metalreflectivityLR.jpg |date=2016-03-04 }}.
*[http://www.graphics.cornell.edu/online/measurements/reflectance/index.html Reflectance Data].

[[Category:Physical quantities]]
[[Category:Radiometry]]
[[Category:Dimensionless numbers of physics]]