Radiant Exitance and Luminous Exitance

Radiant Exitance is defined as the radiant flux emitted from a source per unit area surface of that source.Radiant flux is the source quantity. It is denoted as M_e,λ and its unit is W/m².



One important thing is that radiance is related to the source whereas the irradiance is related to the detector. Both have same unit i.e. W/m². By applying Plank’s Law in the specific blackbody
radiation, the radiant Exitance can be expressed as






Now we can define the Luminous Exitance and we can get Luminous Exitance by using the radiometric to photometric conversion equation.

 

Where, K_m is the constant which is called maximum spectral luminous efficacy and its value is 683 lm/W. So, the Luminous Exitance can be defined as the Luminous flux emitted from a source per unit surface area of that source. The unit of Luminous Exitance is lm/m².

Radiant Intensity and Luminous Intensity

The energy flux per unit solid angle in certain direction is called radiant intensity. If the intensity is denoted by



Here, ω is the solid angel in steradian and φ_λ is the energy flux at λ wavelength. A filled detector with its active area is placed at r₁ distance from a source and another detector with a different area is placed r₂ in such a manner that they are in same solid angle. The received flux by each other must be same. But in photometric, the luminous flux per unit solid angle in a given direction is called Luminous intensity. Its unit is Candela (Cd) or Lumen/steradian (lm/sr) The relation between the photometric and the radiometric intensity is given by



I_{e, λ} is measured in W/sr and I_v is measured in lm/sr.