Thanks for the clarification! I can verify the <9% error relative to peak intensity, and agree that it is quite good for how general the model is.
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Another thing about the sharp drop at straight angle is that it may even represent the reality quite well.
With the T6 I can read a book with all the ‘stray’ light beyond the spill that shouldn’t be there but it is, and it does drop suddenly at 90°. With TIRs seeing one’s feet is a feature.
Yep, with a reflector, the cutoff is indeed abrupt, which the model does represent.
I’m curious whether the model also happens to estimate well the height of the dropoff. The ratio of peak intensity to spill intensity at zero offset angle, or equivalently, the magnification factor (by area) of the optic, works out to be A^2 for acuity index A. This means the spill dropoff should have 1/A^2 the height of the peak intensity, which works out to 1/(A*\sqrt(pi)).
The Gaussian density at pi/2 evaluates to A/sqrt{pi} * exp(-A^2pi^2/4), which is much faster-decaying for larger values of A. So for very throwy lights, the predicted spill is much dimmer than the actual spill. But that’s ok and unsurprising since the Gaussian model does not care about the specifics of the optic type/geometry.