用辐射亮度值计算辐射照度值

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

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.

 
Reflexion plate

Scheme of the set up

 

 
reflexionsstandart

Diffuse reflexion behaviour of the white standard

 

 
irradiance reflektion 300Set up on the optical bench
 
         

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

EnuOmega

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 EeLe.





     
 
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