Irradiance Calculation Using Radiance Measurement

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 has to 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 (white standard) - L is independent from angle and I varies cosine weighted from angle
Preferably the reflexion plate will be located perpendicular to the optical axis of the source. The measuring instrument (Luminance meter or spectroradiometer in Luminance mode) has to be positioned in an angle of 30 … 45° to the normal direction of the reflexion material.
	Scheme of the set up	Diffuse reflexion behaviour of the white standard
	Set up on the optical bench

The Illuminance E_vcan be calculated from the measured Luminance L_v according to the following formula:

Ω₀ - solid angle of 1 sr.
This formula is also valid for the spectral radiometric values E_e(λ), L_e(λ) and for the integral radiometric values E_e, L_e.