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| {{distinguish|Power spectral density}}
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| In [[radiometry]], [[photometry (optics)|photometry]] and [[color science]], a '''spectral power distribution''' ('''SPD''') measurement describes the [[Power (physics)|power]] per unit [[area]] per unit [[wavelength]] of an [[illumination (lighting)|illumination]] ([[radiant exitance]]). More specifically, the concentration as a function of wavelength to any radiometric quantity (e.g. [[radiant energy]], [[radiant flux]], [[radiant intensity]], [[radiance]], [[irradiance]], [[radiant exitance]], [[Radiosity (heat transfer)|radiosity]]) or photometric quantity (e.g. [[luminance]], [[luminous flux]], [[luminous intensity]], [[illuminance]], [[luminous emittance]]).<ref>{{cite book | title = Color Appearance Models | author = Mark D. Fairchild | isbn = 0-470-01216-1 | year = 2005 | publisher = [[John Wiley and Sons]]| url = http://books.google.com/books?id=8_TxzK2B-5MC&pg=PA56&dq=light+source+%22spectral+power+distribution%22&lr=&as_brr=3&ei=wgCJR6bHNpOMtAPpj6HQBQ&sig=dIlnEgPmXu9Sy3YpEVF6wy9m8tU#PPA57,M1 }}</ref><ref name=focal>{{cite book | title = The Focal Encyclopedia of Photography | author = Michael R. Peres | publisher = Focal Press | year = 2007 | isbn = 978-0-240-80740-9 | url = http://books.google.com/books?id=VYyldcYfq3MC&pg=RA1-PA383&dq=%22spectral+power+distribution%22+555+560+nm&lr=&as_brr=0&as_pt=ALLTYPES&ei=MdVTSaHNEJTckwSOpfQk }}</ref><ref name=intro>{{cite book | title = Introduction to Radiometry and Photometry | author = William Ross McCluney | isbn = 0890066787 | year = 1994 | publisher = Boston: Artech House }}</ref><ref name=meas>{{cite book | title = Optical Radiation Measurements (v. 1) | author = Franc C. Grum | isbn = 0123049016 | year = 1979 | publisher = New York: Academic Press }}</ref>
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| Knowledge of the SPD is crucial for optical-sensor system applications. Optical properties such as [[transmittance]], [[reflectivity]], and [[absorbance]] as well as the sensor response are typically dependent on the incident wavelength.<ref name=intro/>
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| [[File:NormSPD.png|thumb|550px|[[standard illuminant|CIE standard illuminant]] spectral power distribution comparisons.]]
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| == Physics of SPD==
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| Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write:
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| : <math>M(\lambda)=\frac{\partial^2\Phi}{\partial A\partial\lambda}\approx\frac{\Phi}{A \Delta\lambda}</math>
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| where <math>M(\lambda)</math> is the [[spectral irradiance]] (or exitance) of the light ([[SI]] units: [[watt|W]]/m<sup>3</sup> = [[kilogram|kg]]/(m·[[second|s]]<sup>3</sup>)); <math>\Phi</math> is the radiant flux of the source (SI unit: watt, W); <math>A</math> is the area over which the radiant flux is integrated (SI unit: square meter, m<sup>2</sup>); and <math>\lambda</math> is the wavelength (SI unit: meter, m). (Note that it is more convenient to express the wavelength of light in terms of [[nanometer]]s; spectral exitance would then be expressed in units of W·m<sup>-2</sup>·nm<sup>-1</sup><!--= W·m<sup>-9</sup> = W/mm<sup>3</sup> = W/µl-->.) The approximation is valid when the area and wavelength interval are small.<ref name=des>{{cite book | title = Radiometric System Design | author = Clair L. Wyatt | isbn = 0029488001 | year = 1987 | publisher = New York: Macmillan }}</ref>
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| ==Relative SPD==
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| The ratio of spectral concentration (irradiance or exitance) at a given wavelength to the concentration of a reference wavelength provides the relative SPD.<ref name=meas/> This can be written as:[[File:NormSPD with eye.png|thumb|550px|[[standard illuminant|CIE standard illuminant]] spectral power distribution comparisons referenced to the human visual system [[photopic vision|photopic response]].]] | |
| : <math>M_{rel}(\lambda)=\frac{M(\lambda)}{M({\lambda_o})}</math>
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| For instance, the [[luminance]] of lighting fixtures and other light sources are handled separately, a spectral power distribution may be normalized in some manner, often to unity at 555 or 560 nanometers, coinciding with the peak of the eye's [[luminosity function]].<ref name=focal/><ref name="WyszeckiStiles">{{cite book | first=Günter | last=Wyszecki | coauthors=Stiles, Walter Stanley | title=Color Science: Concepts and Methods; Quantitative Data and Formulae | edition=second edition | publisher=New York: Wiley | year=1982 | isbn=978-0-471-39918-6}}</ref>
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| ==Responsitivity==
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| The SPD can be used to determine the response of a [[sensor]] to a specified wavelength. This characterizes the response of signal out to the input power as a function of wavelength.<ref name=det>{{cite book | title = Radiometry and the Detection of Optical Radiation | author = Robert W. Boyd | isbn = 047186188X | year = 1983 | publisher = New York: Wiley }}</ref> This can be generalized in the following formula:
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| : <math>R(\lambda)=\frac{S(\lambda)}{M(\lambda)}</math>
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| Knowing the responsitivity is beneficial for determination of illumination, interactive material components, and optical components to optimize performance of a system's design.
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| ==Source SPD and Matter==
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| [[File:Rayleigh sunlight scattering.png|thumb|right|250px|Figure showing the greater proportion of blue light scattered by the atmosphere relative to red light.]]The spectral power distribution over the [[visible spectrum]] from a source can have varying concentrations of relative SPDs. The interactions between light and matter affect the absorption and reflectance properties of materials and subsequently produces a color that varies with source illumination.<ref name=mcol>{{cite book | title = The Measurement of Colour | author = William David Wright | year = 1969 | publisher = New York: Van Nostrand Reinhold Co. }}</ref> | |
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| For example, the relative spectral power distribution of the sun produces a white appearance if observed directly, but when the sunlight illuminates the Earth's atmosphere the sky appears blue under normal daylight conditions. This stems from the optical phenomenon called [[rayleigh scattering]] which produces a concentration of shorter wavelengths and hence the blue color appearance.<ref name=intro/>
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| ==Source SPD and Color Appearance==
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| The human visual response relies on [[trichromacy]] to process color appearance. While the human visual response integrates over all wavelengths, the relative spectral power distribution will provide color appearance modeling information as the concentration of wavelength band(s) will become the primary contributors to the perceived color.<ref name=mcol/>
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| This becomes useful in photometry and [[colorimetry]] as the perceived color changes with source illumination and spectral distribution and coincides with [[Metamerism (color)|metamerisms]] where an object's color appearance changes.<ref name=mcol/>
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| {| style="text-align:center; width: 10%; height: 200px" border="1"
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| !Change in color appearance due to SPD differences in sources.
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| |[[File:Metamerie 0358.JPG|center|thumb|200px]]
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| |[[File:Metamerie 0359.JPG|center|thumb|200px]]
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| The spectral makeup of the source can also coincide with [[color temperature]] producing differences in color appearance due to the source's temperature.<ref name=meas/>
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| [[File:Incand-3500-5500-color-temp-comparison.png|left|thumb|alt=Color temperature comparison of common electric lamps|Color temperature comparison of common electric lamps]]
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| ==See also==
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| *[[Radiometry]]
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| *[[Photometry (optics)]]
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| *[[Color]]
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| *[[Lighting]]
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| *[[Physical quantities]]
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| ==References==
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| <references/>
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| ==External links==
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| * [http://www.gelighting.com/na/business_lighting/education_resources/learn_about_light/distribution_curves.htm Spectral Power Distribution Curves], GE Lighting.
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| [[Category:Radiometry]]
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| [[Category:Color]]
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| [[Category:Lighting]]
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| [[Category:Physical quantities]]
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During the slip of 2008, Tour: Bryan & that have an amazing listing of , which includes Metropolitan. “It’s almost like you are acquiring a approval to look to luke bryan tour date another level, claims all those artists that were an element of the Concert tourmore than in a bigger level of performers.” It twisted as one of the best organized tours in the 15-season historical past.
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