The camera handles everything automatically. It generates dynamic patterns on the screen and adjusts several times until it is satisfied with the result. It does this for red, green, blue, and white across 10IRE, 20IRE, ect up to 100IRE. The LUT is human readable and able to be uploaded and downloaded from the FPGA.
I imagine the process is Capture > Analyze > Generate > Apply > Repeat until all test images are within bounds and color matched, not stage 1: capture, stage 2: calculate, done. That's how it worked for our projection, at least.
I'd bet that they do some of that, too, but if you've got 100 images you want to get "perfect", it's probably faster to capture 10 of them uncalibrated, guess at the curve, capture those same 10 and 10 more calibrated with guess #1, and make a second guess, for a couple iterations than it is to capture all 100 images before any calibration and then all 100 again afterwards to confim, especially if there's any slop in the calibration curve.