Theoretical Considerations on the Achievability of Uniform Distribution of Irradiance on the Surface

The growing demand for industrial illuminators with various parameters prompts work on new solutions. One of them is to build an illuminator that emits electromagnetic radiation to the surface in a uniform manner in terms of irradiation intensity. The article presents mathematical considerations regarding the possibility of achieving uniform irradiance on a surface perpendicular to the optical axis of an LED emitting Lambertian luminous intensity radiation. The article also presents a theoretical photometric solid that would allow achieving uniform irradiance on the surface perpendicular to the optical axis of the LED. Theoretically, it is possible to achieve uniformity on a surface with a different shape, as presented.