Editing Reflectance (section)

==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>