Measurement of Spectral Radiant Intensity

Spectral radiant Intensity in a given direction is defined by the equation :

Radiant Intensity Formula

Symbol: I

Unit: W∙sr-1∙nm-1

Radiant Intensity Diagram

Where dΦ(λ) is the spectral radiant power propagating within the solid angle, dΩ, in the given direction. The definition holds strictly only for a point source.

Spectral radiant intensity is used to characterise sources which are sufficiently distant that they can be considered as point sources. A simplistic rule of thumb suggests a measurement distance at least ten times the maximum luminous dimension of omni-directional sources and twenty times that of directional sources, but care must be taken in applying the same. In the photometric far field the  inverse square law applies. It is due to this issue that the CIE published CIE 127 to report the luminous or radiant intensity of LED, values hitherto being reported incorrectly due to not respecting the requirement for point source conditions.

Radiant Intensity Measurement via Telescope

There are two means of measuring spectral radiant intensity, using an imaging technique or an irradiance technique making use of inverse square law.

In the former case, a telescope is used to measure the source, ensuring that the entire source area is encompassed in the measurement, in contrast to the manner in which a spectral radiance measurement is typically performed with the same entrance optic. The lens of the telescope sets the solid angle of measurement.

Alternatively, a measurement of spectral irradiance at a distance in the far field can be used with the inverse square law to report spectral radiant intensity. This is the technique which is at the heart of goniophotometers, in which the photometric equivalent of spectral irradiance, illuminance, is measured and luminous intensity reported from the product of this and the photometric distance squared. Whilst the irradiance technique may in many  cases be convenient, it represents a technique with a low optical throughput due to the use of a cosine-corrected input optic.


References

Categories: Entrance Optics