It is an interesting measurement, but quite incorrect. What you are referring to is the light output ratio, also called LOR. The 81% is not correct. Send the fixture to a professional lighting company which has a large scale photogoniometer to get the correct results, instead of trying to integrate points on a grid. In fact it is a lot more, but you just can not measure that accurately with an integrated point measurement. Which btw is also discussed in the same paper.An interesting metric I came up with the other day that uses data from this thread is what I called reflector 'photosynthetic radiation efficiency.' This provides the relative percentage of PAR range umol/s that exit the reflector as compared to the PAR range umol/s that is emitted by the lamp.
Just divide the reflector's umol/s per joule in PAR range by the lamp's umol/s per joule in PAR range, and multiply by 100. The lamp's total output is often reported by the manufacturer, as total PPF, or PPF per watt.
I was a bit surprised to learn, for example, Gavita PRO DE 1000W HPS reflector has a photosynthetic radiation efficiency of about 81%, that is, about 19% of radiant PPF emitted by the lamp is absorbed by the reflector/fixture.
https://www.icmag.com/ic/showpost.php?p=6738657&postcount=6837
It is interesting that you came across LOR "the other day" because that is what professional lighting companies work with and specify all day long. It shows how uninformed you are, and I see you are quoting every time from the same documents and source. As a scientist you should know that you can not rely on a single source.
LOR is the basis of reflector ratings as in efficiency. Then we haven really talked about spread and uniformity yet, or exit angle of the reflector, or light losses to the ceiling with open reflectors. We haven't talked about how the lamp temperature can influence the lamp voltage and the output of a lamp, and we certainly have not discussed yet why you should change your lamp at 4% depreciation, and not ten, because you are not growing tomatoes in a greenhouse but silver on a stick in a climate room. You have a lot still to learn.