For many LED optic projects, a spot size and beam angle can be specified with a single uniformity value. In cases of beam angles above 30 degrees, things get tricky. Please see the images below for an explanation.
If you prefer to understand the math…
Illuminance is changed by formulaE=(I/r*r)*cos(A), whereE– illuminance, I – luminous intensity,r– distance to spot,A– angle of ray.
Distanceris usually constant. If the dependence ofIfromAis constant, we have illuminance falloff at highAvalues becausecos (A)multiplier is smaller.

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

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