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Concept
Spectral power distribution
Summary
In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term spectral 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).
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.
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write:
where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m3 = 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); and λ is the wavelength (SI unit: meter, m). (Note that it is more convenient to express the wavelength of light in terms of nanometers; 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.
The ratio of spectral concentration (irradiance or exitance) at a given wavelength to the concentration of a reference wavelength provides the relative SPD. This can be written as:
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.
The SPD can be used to determine the response of a sensor at a specified wavelength. This compares the output power of the sensor to the input power as a function of wavelength.
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