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).[1] [2] [3] [4]
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.[3]
Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write:
| M(λ)= | \partial2\Phi | ≈ |
| \partialA\partialλ |
| \Phi | |
| A\Deltaλ |
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:
| M | ||||
|
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.[7] This can be generalized in the following formula:
| R(λ)= | S(λ) |
| M(λ) |
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.[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 called Rayleigh scattering which produces a concentration of shorter wavelengths and hence the blue color appearance.[3]
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.[8]
This becomes useful in photometry and colorimetry as the perceived color changes with source illumination and spectral distribution and coincides with metamerisms where an object's color appearance changes.[8]
The spectral makeup of the source can also coincide with color temperature producing differences in color appearance due to the source's temperature.[4]