I found myself often needing to calculate the collection efficiency of convex/Fresnel lenses and the hotspot+corona/spill breakdown of reflectors, so I whipped up this quick calculator to do it for me. Hope someone also finds it useful.
The core of the calculator is just a spherical cap area calculation, which follows from the (neat) result that: for a Lambertian emitter in 3 dimensions, any sphere centered directly in front of the emitter, with radius equal to the distance from center to emitter, has constant illuminance (lux) across its entire surface.
The calculator assumes that the LES is small relative to the secondary optic, but does not essentially depend on its exact size/shape.
Separating hotspot from corona is a harder task because both are captured by the reflector. I will try to come up with a decent approximation.