Why spot and beam uniformity are always not equal

Published by Optics for Hire.

For many LED optic projects a spot size and beam angle can be specified with a single uniformity value. But in cases of beam angles above 30 degrees things can be tricky. Please see the images below for a visual explanation.

Or if you prefer to understand the math...

Illuminance is changed by formula E=(I/r*r)*cos(A), where E - illuminance, I - luminous intensity, r - distance to spot, A - angle of ray.

usually distance r is constant. If dependence I from A is constant, we have illuminance falloff at high values of A, because cos (A) multiplier has smaller value.

With beam angles above 30 degrees, it is tricky to specifiy with a single uniformity value the spot size and beam angle

With beam angles above 30 degrees, it is tricky to specifiy with a single uniformity value the spot size and beam angle

Illuminance is dependent on  illuminance, luminous intensity, distance to spot, and angle of ray.

Illuminance is dependent on illuminance, luminous intensity, distance to spot, and angle of ray.