Question

Assuming I have a light diffuser with an area A (approximately planar, not spherical) and measure the light intensity directly at the surface (23 mW/cm²), how could I determine the intensity at distance d away from the diffuser?

I'm aware, that I can't simply use the inverse square law for near distances, but nevertheless, I can assume that any point on the surface still follows the inverse square law, the problem is, that the photons emittet by the sourronding points add up again making the intensity greater. How can I calculate the correct intensity from a (rather near) distance d away?

Answer 1

To calculate the light intensity at a distance from a planar light diffuser, modify the inverse square law to account for the multiple light paths from the surface area to the observation point, especially at closer ranges. The intensity diminishes but not directly as per the inverse square due to contributions across the diffuser's surface.

Step-by-step explanation:

To determine the correct intensity of light at a certain distance d from a planar diffuser, it's true that the inverse square law is the foundation, but it needs to be adapted because the light isn't emanating from a point source. The key complication arises from the light emitted at different points on the diffuser's surface that can add up at the observation point, especially at closer distances.

For a planar light source, the intensity will decrease as you move away, but not strictly according to the inverse square law used for point sources. Instead, we need to consider the contributions of each point on the surface of the diffuser to the total intensity at the point of interest. The intensity calculation therefore becomes an integration problem over the area of the diffuser, considering how each element contributes to the total intensity at d, and accounting for the angle at which each element's light reaches the point.

If the distance is sufficiently large compared to the size of the diffuser (several times greater than the largest dimension of the diffuser), the contributions from the edges become less significant, and the inverse square law starts to become a more accurate approximation.