If you use an array of LEDs spaced a given distance apart, both ways, you get nearly uniform PAR over most of the substrate. Such an array would be:
You can see that at a spot under one LED, there are others offset a few inches that can also contribute some PAR. So, you need to determine the PAR contribution for each LED, close enough to contribute any, and add them up for that spot. For example if the LEDs are spaced 3.5 inches apart, 4 LEDs will be offset by 3.5 inches, 4 at 4.9 inches, 4 at 7 inches, 8 at 7.7 inches, etc. The PAR contributions from the ones farther away is small, but with 4 or 8 of them added up, they are significant.
When I did this for the 3.5 inches spacing I got a total of about 50 micromols of PAR. So, I tried it with the rows staggered, and that reduced the PAR down to about 40 micromols. That was about what I want, so I chose 3.5 inches for my spacing.
I have other graphs I use to make this is a little easier, but that's the process.
The array I selected is: