Hi TA, about your set-up,
1) you may want to check for integration quality of the device.
If that is not good, your calibration will only work for emitters with comparable emission profile. For example, a flashlight that uses optics to make a radical different beam from a bare led, will read different from a bare led. Every type of emission pattern will require its own calibration.
If integration is good however, it does not matter what type of light source you measure, a fixed calibration is inherent to the design.
The easiest way to check integration is using a small zoomie in spot modus on low setting (actually the goal is a constant output, and flashlights are more constant on low settings, best is a constant current setting, like the lower settings on the BLF-A6 driver that uses an 7135, same for an old-school AK-47 or similar). Shine it into your device at various angles and record the reading. My sphere gives a maximal variation of 3% for any angle that the zoomie is pointed in. See here.
2) you may want to check for the influence that the to-be-measured lightsource in the entrance hole has on the calibration.
Unfortunately, with better integration, this influence increases. Your lightsource is part of the inner surface of the device where photons bounce around. In a well integrating device, photons will bounce around multiple times before being absorbed somewhere, so the photons have multiple chances to ‘meet’ the entrance hole. The entrance hole is a photon ‘leak’ which is is no problem at all because it is accounted for in your multiplier. However, if this leak is not constant (i.e. a shiny bezel shines light back into the sphere, while a black bezel absorbs the light) your multiplier will be influenced by that.
There is two ways to deal with that. Either you can accept this variation in which case you want to have an idea which order of magnitude this error is, or you are going to measure what the error is for each light source and correct the multiplier for that. you then need a build-in constant light source in your device for measuring the correction.
In my big 46cm sphere with 30mm entrance hole, that I use for emitter measurements, I find that entrance hole effects are minimal, I have a fixed multiplier for all emitter tests. For bigger flashlights I open up the hole to 80mm, in which case I do have to correct for the lightsource, if I do not do that, the error can be up to a few percent.
In my small 16cm sphere I need to compensate for the different reflectivities of what is in the 40mm hole every time, the error would be too large for my standard if I do not do that.