Inradiometry,photometry, andcolor science, aspectral power distribution (SPD) measurement describes thepower per unitarea per unitwavelength of anillumination (radiant exitance). More generally, the termspectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity (e.g.radiant energy,radiant flux,radiant intensity,radiance,irradiance,radiant exitance,radiosity,luminance,luminous flux,luminous intensity,illuminance,luminous emittance).^[1][2][3][4]

Knowledge of the SPD is crucial for optical-sensor system applications.Optical properties such astransmittance,reflectivity, andabsorbance as well as the sensor response are typically dependent on the incident wavelength.^[3]

Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write:

${\displaystyle M(\lambda )=\frac{{\mathrm{\partial }}^2\mathrm{\Phi }}{\mathrm{\partial }A\mathrm{\partial }\lambda }\approx \frac{\mathrm{\Phi }}{A\mathrm{\Delta }\lambda }}$

whereM(λ) is thespectral irradiance (or exitance) of the light (SI units:W/m² =kg·m⁻¹·s⁻³);Φ is the radiant flux of the source (SI unit: watt, W);A is the area over which the radiant flux is integrated (SI unit: square meter, m²); andλ is the wavelength (SI unit: meter, m). (Note that it is more convenient to express the wavelength of light in terms ofnanometers; spectral exitance would then be expressed in units of W·m⁻²·nm⁻¹.) The approximation is valid when the area and wavelength interval are small.^[5]

The ratio of spectral concentration (irradiance or exitance) at a given wavelength to the concentration of a reference wavelength provides the relative SPD.^[4] This can be written as:

${\displaystyle M_{\mathrm{r}\mathrm{e}\mathrm{l}}(\lambda )=\frac{M(\lambda )}{M\left({\lambda }_0\right)}}$

For instance, theluminance 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'sluminosity function.^[2][6]

The SPD can be used to determine the response of asensor at a specified wavelength. This compares the output power of the sensor to the input power as a function of wavelength.^[7] This can be generalized in the following formula:

${\displaystyle R(\lambda )=\frac{S(\lambda )}{M(\lambda )}}$

Knowing the responsitivity is beneficial for determination of illumination, interactive material components, and optical components to optimize performance of a system's design.

The spectral power distribution over thevisible 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.^[8]

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 calledRayleigh scattering which produces a concentration of shorter wavelengths and hence the blue color appearance.^[3]

The human visual response relies ontrichromacy to process color appearance. While the human visual response integrates over all wavelengths, the relative spectral power distribution will providecolor appearance modeling information as the concentration of wavelength band(s) will become the primary contributors to the perceived color.^[8]

This becomes useful in photometry andcolorimetry as the perceived color changes with source illumination and spectral distribution and coincides withmetamerisms where an object's color appearance changes.^[8]

The spectral makeup of the source can also coincide withcolor temperature producing differences in color appearance due to the source's temperature.^[4]

• Spectral Power Distribution Curves, GE Lighting.

• Radiometry
• Color
• Lighting
• Physical quantities

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