You know this whole lumens thing really got me going on a huge research project and I discovered a lot of things.
But the one thing worth sharing is there's a dead simple formula commonly used in the home theater world that removes a lot of variables from the very science-based approach I was obsessing about earlier.
Besides knowing the dimensions of your screen, the formula requires just one input:
A measurement, in lux, of a 'white' test pattern, taken facing the projector lens, *with the meter's lens in the exact plane of the screen surface*.
This last bit is surprisingly hard to accomplish.
First, real world meters have a lens that is contained in a boxy enclosure with some kind of non-negligible depth. Even placing the back of the meter in contact with the screen surface puts the lens an inch or more closer to the projector than the actual screen is, and this changes the outcome. You could maybe go off to the side somewhere but the screen sorta by definition occupies all areas that are lit up by the projector so now you're in the dark. There's also uniformity issues: real world projectors unfortunately may send measurably more light to the northwest part of the imaging area than the southeast part etc. Somewhere near the dead center of the image is probably where you'll get the highest values (I know I did, and I searched pretty thoroughly). Lastly, the orientation of the meter matters somewhat, since you may get higher or lower readings based on whether the enclosure is being held horizontally or vertically or not pointed exactly straight at the projector, etc. Basically you try em all while taking continuous readings and just record the max value you get.
So last night I reset everything (this time zooming the image to the other end of the zoom range, sorry) and tore up the room and hunted around for the brightest possible readings in various locations and made some new measurements. Then I plugged them into this formula:
lumens = (lux / 10.76) * area of screen in sq ft
If you stay in metric that's simply
lumens = lux * area of screen in sq meters
I got this formula from the surprisingly helpful thread
which is still relevant 13 years later.
Regarding an earlier question you asked, can you determine screen gain using a light meter, there's another formula mentioned in that thread I found intriguing: once you have this screen-facing, in-plane measurement in lux, you can compare it to the reading you're getting *facing the screen* in Foot Lamberts (both readings should involve the exact same location within the image as much as possible-- see note above about image uniformity). The two readings should be related by the formula
ftL = lumens * screen gain / (area of screen in sq ft)
This works fine, but I was starting with metric numbers. So I prefer to use a simpler formula that states nits = lux / pi (assuming a perfect 1.0 gain surface)
Using a little junior high algebra I get
gain = (nits * pi) / lux
Again, this supposes you are using two very well-matched readings from the same spot on the screen. Every other method based on a meter reading taken in some other way is a compromise and starts to involve a lot of math.
Final disclaimer, I took these values using a white full field pattern instead of a smaller window pattern centered on the reading location. That brings all the room reflections into play.
So even trying as hard as I could to simplify, these values are contaminated somewhat and you can't pretend there's much precision in the result. Maybe I'll repeat this whole process someday with tiny test patterns and black felt everywhere, but anyway here are the numbers from last night:
I got 236 lux facing the PJ, taken from the exact plane of the screen.
The area of the image being thrown was 4.10 meters-squared
By my calculations that comes to 967 lumens (with a 1900 hour old lamp mind you).
I also got 48.5 nits measured facing the other way, pointed at the exact same part of the screen where the meter was for the first measurement.
So that led to a shockingly low computation for gain, 0.65
I was willing to believe it might be as low as 0.85 but 0.65? Yikes. I think I'll go buy a "white" screen knowing the gain's going to end up being way lower than whatever the manufacturer claims.
But that's my problem, not yours. The general takeaway for HT 2050 owners is even a bulb in the middle of its lifespan still gives around 1000 calibrated lumens. Good stuff.