Irradiance calculation using radiance measurement

Recommended products: specbos 1211-2/spectraval 1501

Sometimes Irradiance (Illuminance) has to be measured indirectly by Radiance (Luminance),  e.g. in case of limited space behind the measuring plane, if a luxmeter is not available or for comparing/ testing  purposes. In this case it is necessary to use a white standard with known (spectral) Reflectance ρ (ρ(λ)) in addition to the Radiance meter. This standard plate must be positioned in the plane where the Irradiance shall be measured. The precondition to the plate is, that it reflects diffusely (Lambertian behaviour, see the figures below). Common commercial names of such material are Spectralon and Optopolymer.

Lambertian Reflexion Plate
Lambertian Reflexion Plate
Scheme of the set up
Scheme of the set up

Lambertian Reflexion Plate (white standard) – the radiance L is angle-independent and the Radiant Intensity I changes cosine-dependent with the angle

Preferably the reflexion plate will be located perpendicularly to the optical axis of the source. The measuring instrument (Luminance meter or spectroradiometer in Luminance mode) must be positioned in an angle of 30 … 45° to the normal direction of the reflexion material.

The Illuminance Ev can be calculated from the measured Luminance Lv according to the following formula:

Ω0 - solid angle of 1 sr

This formula is also valid for the spectral radiometric values Ee(λ), Le(λ) and for the integral radiometric values Ee, Le.

Set up on the optical bench
Set up on the optical bench
Diffuse reflexion behaviour of the white standard
Diffuse reflexion behaviour of the white standard
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