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ANSI lumens is based on measuring 9 points on a screen, not a checkerboard pattern, but an imaginary grid (or use a real grid with 100 IRE white divided by black lines). This is the standard method of measuring ANSI Lumens. Projectors vary by as much as 35% or more by unevenly illuminating the screen, that is why you have to measure different points.
The C6 or D3 will not provide the correct results, you cannot find the max lumens point unless you take 15-20 minutes at each imaginary square. You may think you've found the right max fL point, but you haven't, not only does angle affect it, but so does distance to screen, so there are literally hundreds of possibilities to try to find the max reading.
No-one measures brightness with a colorimeter if they want to be accurate.
This is one reason why some reviewers using colorimeters to measure contrast have ridiculous results. That said, you can measure contrast somewhat accurately with a C6 by taking the peak reading with the cheap light meter, but taking the black floor reading AMP'd up at the lens with the c6, or you can just use a white piece of paper in front of the lens. This will provide the most accurate measurement of contrast within the limitations of the C6. I personally would do two methods if wanting to read contrast and then average the error of the two to be honest.