"I thought they used a Reflective WHITE coating?"
Not in the way most people understand reflection. An integrating sphere uses the relevant property of diffusion and scattering to minimize the original direction of the light incident to any part of it. Light applied to the sphere is distributed over all angles by minimizing specific angles such as what a mirror does.
I should have clarified this in my original post.
Labsphere's description of their coating is a reflective white - not a non-reflective black coating as you SEEM to describe. This
IS very unclear in your post, as your post implies the exact opposite. IE: To a lay person, the difference appears to be more black and white.
Perhaps if you were to clarify why the non-relective black coating you described, is described by them as a reflective white coating, it would help to clarify what you meant?
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Tim - It sounds like a lot of factors might be cancelling out in a nice way here.
Your losses in light due to the transmission through the glass plate used to stand the light on to fix the height/alignment are subtracting from the lumens into the pipe.
Your reflection of the light by the PVC inside the pipe might be increasing the detected lumens...according to the above post, but I don't think absorbing light would change the lumens except by reducing the amount making it to the end of the pipe/detector...and reflectance can't increase the OTF lumens themselves, as only what is there can be reflected, etc.
Your losses to the pipe opening (Light reflected back out the top, around the light) would reduce the lumens detected.
Your losses to the lumens lost around the detector would reduce the lumens detected.
Your meter may or may not be reporting an accurate lux value.
You already know you are currently getting good correlation of lumen values with known references...and your Lux = Lumens ratio is a happy coincidence.
This says to me that while you are losing light from both open ends of the pipe, and due to the glass plate the light stands on, the square footage of the interior surfaces and the involved angles, whatever your meter is reporting, etc, all seem to be in a good ratio to have your end result work.
Having your meter calibrated, and having some reference lights across a broad spectrum of light sources calibrated, would of course help...but may simply result in your current Lux = Lumen ratio being skewed - and you needing to use a conversion factor to get back to what you already get.
Food for thought.