Tutorial

The human eye a a certain sensitivity to radiations.

The visibility curve V ( λ ) represents the normalized sensitivity of the human eye to radiations depending on the wavelength for daytime vision. The curve is not flat. It has a bell shape with a maximum at 555 nm. This means that for instance, a flux at 555 nm is seen brighter than the same flux at 650 nm. Therefore, a higher flux at 650 nm is needed to be seen at the same brightness than at 555 nm.

V ( λ ) is calculated in the visible range ( from ~ 400 nm to ~ 800 nm).

Whatever the considered parameter, if P_r is the value in SI radiometric and P_p, its value in SI photometric unit, for a monochromatic radiation :

.

K₅₅₅ is a constant defined with the intensity. It is the intensity in SI photometric unit ( which is the candela - abbreviation : Cd) corresponding to an intensity of 1 W/Sr at 555 nm. Therefore, K₅₅₅ is expressed in Cd .Sr / W.

K₅₅₅ = 683 Cd .Sr / W.

At any wavelength λ :

.

The different photometric units and their corrsepondance in radiometric units for monochromatic radiations are therefore :

- Intensity : Cd (Candela) ( ),

- flux or power : lumen ( ),

- irradiance : lux ( ),

- emittance : lux ( ),

- luminance or radiance (in radiometry ) : Cd /m2 ( ).

For polychromatic radiations, whatever the parameter P ( intensity, radiance or luminance, flux or power, irradiance, emittance) Pr can be expressed as follows :

.

Therefore :

.

For instance, it is possible to calculate the luminance of a balck body at a cetain temperature in Cd/m2 ( photometric unit ) , using the precedent formula.