Spectral power distribution


In radiometry, photometry, and color science, a spectral power distribution measurement describes the power per unit area per unit wavelength of an illumination. More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity.
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.

Physics

Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write:
where M is the spectral irradiance of the light ; Φ is the radiant flux of the source ; A is the area over which the radiant flux is integrated ; and λ is the wavelength. The approximation is valid when the area and wavelength interval are small.

Relative SPD

The ratio of spectral concentration 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.

Responsivity

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. This can be generalized in the following formula:
Knowing the responsitivity is beneficial for determination of illumination, interactive material components, and optical components to optimize performance of a system's design.