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Were you able to document your results with images?
Sorry Mark, but numbers speak louder than screen shots. It doesn't matter whether your images are RAW or medium rare, it's only the geometry that's the issue here.
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Last night I projected a green version of my test pattern onto the curved AT screen, then placed and alloy track in front of the screen rig so I had a guide to run a flat vertical panel.
I used a tape measure on the screen surface so that each time the projected single pixel display lines projected onto the tape marking. The circles on the curved screen were 350mm wide each representing a zero grid distortion. The flat panel was slightly closer to the projector, so the circles were slightly smaller. There was a slight difference between centre and edge here as would be expected.
That "slight difference between edge and center"
IS the Grid Distortion. The rest we know: use a curved screen and reduce distortion. That's not rocket science.
Unless you're prepared to quantify the difference between edge and center, on a flat screen, at the same throw and throw ratio as the curved screen, then "a slight difference" is not good enough.
The way to do the test is as follows.
1. Accurately measure the throw ratio.
This gives us a benchmark for comparison with other lenses at the same throw ratio.
2. Measure the widths - edge, 3/4 position and center - of smaller grid panels than you have measured.
The smaller the better. Typically, a distance equal to about 1/16th to 1/20th of the distance from edge to center. Otherwise you're just averaging-out the progressive distortions present in a large distance. That's a no-no. The bigger the size of the grid panel measure the more meaningless are the results.
Something like this:

The full sized version of this consists of 60x60 pixel grid squares. Suggest you make one similar and measure widths as indicated by the white squares.
3. Report your numbers.
Screen shots and statements like "small difference" are, frankly, inadequate for depicting GD, or substantiating any claims about it.
Some immediate observations on your photos are that your screen curve appears to be too steep for the MK-4. The outer projected circles are smaller in width than the inner circle, judging by the "control"outline circles you have superimposed.
If those
superimposed outline circles you inserted over the projected circles are all the same size then I don't see how you can say all your
projected circles are the same size. The ones on the outer are clearly well within the drawn circles, while the one in the middle is virtually the same size. In other words how can they all be the same size (350mm) if some are smaller than others? It doesn't make sense.
Secondly, placing your piece of flat screen panel out a few inches from the deepest part of your curved screen will make the projected circles appear smaller than they would be on a flat screen. This has a bearing on GD measurement.
The way you have measured this is messy and confused. You are not comparing like with like.
Lastly, I'd be careful of producing photographs (however flawed in execution) that seem to show GD is the same on both a curved
and a flat screen in the same photograph at the same throw ratio setup. That is
flat-out impossible.