Brad:
I'm sorry to keep beating this somewhat dead horse, but I think what you are saying is quite simply wrong, and that we as professionals need to have our facts straight.
First of all ANSI Lumens are not a direct measure of the light output of the projector, but rather a measure of the light reflected from the screen. From Hiretec "Choosing an LCD Projector": "ANSI lumens is an average Lumen measurement around the screen. This is accomplished by dividing the screen into 9 rectangles (three vertical coulombs and three rows). Take a measurement of light using a good spot light meter 1 foot away from the screen pointing at the center of each of the nine areas. Then you take the average of the nine areas and that is your average (ANSI) Fl (foot-Lambert) light output."
Let's consider your extreme example of alternating light and dark pixels. I agree the ANSI Lumen measurement (as described above) would be the same whether the projectors were aligned or not since the same amount of light is falling on the screen so one would expect the same amount of light to be reflected back to the measuring device. In fact, at any reasonable distance back from the screen, I submit that the screen would look to the eye almost exactly the same, a smooth bright gray, whether the projectors were aligned or misaligned. As you get closer to the perfectly aligned screen it would begin to look a little grainer than the misaligned screen, but no brighter.
Karl,
Just because a lot of people believe an urban legend doesn't make it any more true. A major point of the DaLite paper Brad so kindly directed me to is that there is "misconception prevalent in our industry" that stacking identical projectors produces less that twice the light output, but that is what you and Brad have both been trying to say in spite of the evidence put forth in the DaLite paper. Or, in Brad's case, he's saying even though they may measure twice as bright, stacked projectors won't look as bright as a single projector that measures the same.
I would like to say one more thing. I agree that stacked projectors do not tend look as good as a single projector of similar brightness and quality and I will always prefer one bright projector if that is easily available. The reason is that it does take longer to stack projectors and there is always a risk of reduced sharpness of the image, especially around the edges and in the corners. Brightness is not an issue.
And I want to thank Brad for directing me to the paper that had the answer to the question I was asking, even if he doesn't want to believe it.
Jerry