Integrating sphere #4 (the fast and cheap one)

So I’m learning that my DIY sphere (shown back at post# 64) is apparently wildly inaccurate at higher lumen levels (/- 400 lumens and above) and it doesn’t seem to matter what size flashlight is in the hole (so I don’t believe it’s related to light reflecting off the bezel/glass lens). I’m wondering if it’s related to light loss through the sphere wall, where lower lumen levels wouldn’t see much light loss, but higher outputs would. Thoughts? A few years back I posted these lux readings where I experimented with covering my sphere with a thick black towel, but I only used my Convoy S2 EDC (high mode on that light is only/- 500 lumens). FYI - my sphere calibration/multiplier is derived from measuring three different Fenix HL55 headlamps and averaging the results. (Note that I’ve never had a light that shows steady well regulated output at levels about /- 400 lumens, so my multiplier(s) are computed with “low” and “medium” output levels). I’m not trying to nail down exact lumen #’s from lights (I understand I’ll be off/-10% of “true”), but looking to have a multiplier that works consistenly from 1 lumen to +/- 2,000 lumens.

Here are 3 sphere results that have led me to question my calulated lumens at higher levels (all lights measured using fully charged hi-drain cells):

Sofirn SP40 (XP-L 4,000k):
Low = 6.6 Lumens
Med = 62.8 Lumens
High = 306 Lumens
Turbo = 798 Lumens

Sofirn SD05 (on a brand new Molicel P42A 21700)
Low = 277 Lumens
Med = 792 Lumens
High = 2,223 Lumens

Astrolux HL01 (XP-L 4,000k)
Stepped Ramp Levels:
Step 1 – 13.0 lumens
Step 2 – 43.9 lumens
Step 3 – 124 lumens
Step 4 – 162 lumens
Step 5 – 253 lumens
Step 6 – 404 lumens
Step 7 – 690 lumens
Turbo – 992 lumens

I immediately questioned my results on all three lights above 300 lumens. In this post, user YogibearAl gave me his calculations for the SP40 (which sound good to me) and so I used those to re-calculate new multipliers for each mode. My previous multiplier was 0.4275, and now trying to calibrate to Yogi’s #’s I am getting varying multipliers, with the #’s for the high outputs being significantly higher (my expectation – that my sphere is “good” at low outputs, but gets exponentially worse at higher levels). Multiplier’s I get:

SP40
Low – 0.4516
Med – 0.4422
High – 0.5000
Turbo – 0.5158

If I then run with the multiplier of 0.5000 from high mode, run that back against my SP40 measurements and also on my SD05 & Astrolux HL01 (XP-L 4000k) measurements, I get:

SP40
Low – 7.8 lumens
Med – 73.5 lumens
High – 358 lumens
Turbo – 934 lumens

SD05
Low – 324 lumens
Med- 926 lumens
High- 2600 lumens

Astrolux HL01
Stepped Ramp Levels:
Step 1 – 15.2 lumens
Step 2 – 51.3 lumens
Step 3 – 145 lumens
Step 4 – 190 lumens
Step 5 – 296 lumens
Step 6 – 472 lumens
Step 7 – 807 lumens
Turbo – 1160 lumens

So now my higher numbers seem much more in line with expectations, but I suspect I’m showing lumen #’s that are too high for the lower levels. So what am I supposed to do, use different multipliers for different lumen output ranges? And how would I know what I am doing is reasonably accurate Is anyone else using these round styrofoam spheres seeing the same issue I am? Do I need to paint the outside of my sphere to stop light loss? Should I test lux readings with the towel again with higher output lights? Is a towel really causing light not to get “lost”.

Thanks,
-Garry