Irradiance and Illuminance

Irradiance is the radiant flux received by the detector area. The unit of irradiance is W/m². Irradiance is denoted by E_e,λ,



φ_s is the received radiant flux on the detector surface and A_D is the detector area or surface. Irradiance always follows the Inverse Square Law. Suppose from a point source the radiant flux is being received by two surfaces of A₁ and A₂ where they are equal surface area. They are placed at r₁ and r₂ distance. Now the flux received by the surface

 

And the flux received by the surface

 


Where, I_e,λ radiant intensity and ω solid angle. Again the radiant flux received per unit area for A₁ and A₂ are

 


Here A₁ and A₂ are equal. Putting the φ_e,λ = I_e,λ ω in the equation we get
 

This is Inverse Square Law of irradiance. If we convert this irradiance into Illuminance then we should follow the conversion equation i.e.

 

Where, K_m is the constant which is called maximum spectral luminous efficacy and its value is 683 lm/W. By definition the luminous flux received by unit area of the detector is called Illuminance. Its unit is Lux or Lumen per sq. meter (lm/sq. m). It also follows the same inverse square law, i.e.




E_v is related to the surface dA where luminous flux is falling on this surface perpendicularly. E'_v is related to the surface dA' where this surface creates an angle Ɵ to the base plane. As per figure above,



 This above equation can be written making it generalized,