Originally Posted by RLBURNSIDE
You're not getting it, the 2.7K DMD gets shifted and thus there are two sets of independent light paths to consider. So, the lens needs to resolve both of them. Meaning, if they are offset by a 1/2 pixel, then the lens needs to be effectively 4K capable in order to not smear the detail from one of the shifted images away.
This is pretty straightforward.
You are thinking in a digital mindset, which is where the logic is breaking down.
I will make it more basic:
A lens is round.
A lens has highest resolution in the center, and lower resolution near the edges.
A lens is fully analog, meaning there is no "pixel grid" like a digital device has
A rectangular image from the DMD is projected on the round surface of the lens
The resolution of that image is 2716x1528
If that resolution is fully resolved by the lens, this means it is fully sharp with no significant artifacts, blur, etc when this resolution is projected through it
Finally, when the image is shifted half a pixel, it will make zero difference because the lens is not a digital device. If it was completely sharp in position A, when position B is only half a pixel away it is also going to be completely sharp there as well
Where a lens would have to be "4k" is if the native resolution of the DMD were actually 3840x2140 and thus the pixels would be much smaller than the pixels projected by the 2716x1528 DMD. Even though our brain interprets smaller pixels with XPR, the lens never actually has to resolve smaller pixels with 2716x1528 XPR.