Hey thanks for sending this! A couple items I’d like to ask more about:
(1) How do you justify the assumption of Gaussian beam profile? Almost every beam profile (esp. mules and aspherics) is well-known to be non-Gaussian, though I suppose that Gaussian is a reasonable distribution for modeling any distribution that is unimodal and symmetric, which describes most beams. I suppose I could use my exact simulation to determine the accuracy of the Gaussian approximation.
(2) The 50%-of-total-output threshold is a sensible definition of hotspot, and will be very close to my purely geometric definition for most lights. However, assuming Gaussian beam profile, the right FWHM angle is not 2.35 times the standard deviation, but possibly around 1.1774 times the standard deviation. The 2.35 comes from a one-dimensional Gaussian distribution, but beams in 3D space are approximated by a 2-dimensional Gaussian, which is slightly more radially concentrated. I would suggest going through all of the calculations (e.g., etendue) and checking for dimensional inconsistencies like this.
BTW, here’s a new version dedicated to computing hotspot/corona/spill angles. I like geometric approaches because they are essentially dimension-independent.