Wow, a lot of serious conversation on this thread. So I thought I'd add my two cents. Myself, I'm no engineer (understatement). I've been reviewing projectors professionally for more than a decade, but I primarily review them from a subjective standpoint. I've also been an avid photographer, (I got my first film SLR just over 50 years ago - to date myself), and for my regular photography, and my reviews I use a Canon 60D. I use the standard zoom, and know that there are better optics Canon sells, where they have similar zoom lenses (in throw ratios), that cost more than my already pricey dSLR with lens.
First, despite spending 20+ minutes on this page, reading scanning, and looking at images, I do not see any way that having e-shift has a significant affect on how good a lens is needed. That's not to say, it doesn't call for slightly better resolving optics. But it definitely wouldn't need to be as good a lens as a true 4K would need.
1. "A pixel is a pixel" Whether e-shift is on, or off, the smallest pixel size any 1080p JVC pixel shifter can do, is always the same size. Firing twice in different positions does not change the amount of detail of either the first, or the delayed pixel.
2. When e-shift is on, that delayed pixel carries different info (color, sat, etc.) than the first, thanks to "fancy processing."
3. Perhaps most important. No projector I know of, pixel shifter or not, can produce a single pixel that has variation in it. Every aspect of that pixel will be exactly the same color/saturation, etc.)
4. Because of processing, the idea of pixel shifting, allows something "new." Right now, we have a single pixel which is X in size. Because of the overlap (and non-overlap) the original pixel and it's delayed partner, we end up with a "double pixel" which is not square, (looks like the usual diagram for pixel shifting) and it's probably close to 50% larger than a single pixel. So we have a "combined" pixel that has more than one color/sat, etc, but it is larger. Now we can have variation but in a larger pixel. Still, that variation can be done in a smaller area than with two discreet pixels (non-pixel shifter).
5. Each is still a 1080 sized pixel. If a lens can perfectly resolve 1 1080p pixel it should perfectly resolve two overlapping ones. But we're not talking perfect.
6. I think one could argue that if one's lens isn't high enough resolution it might blur the transitions between the overlapping pixels (lets' say they are different color or saturation, being different due to neighboring pixel information, but if that was the case, I would argue, that the lens would also be too soft of properly do 1080p pixels to begin with. Imagine the first firing is a medium red, and the 2nd firing of the same pixel (but shifted) is yellow. There will be three colors visible in our double pixel. one area (call it the lower left) would be red, the upper right would be yellow, and the area where they overlap would be orange. But the area that is orange, will be smaller than a single pixel. So there is the argument for needing more resolution,
hmm. Am I still making any sense.
Either way, though, the JVC does not need a lens that's "4K" Those overlapping pixel segments are each smaller than 1080p, but still, each pixel original pixel starts being four times the size of a true 3840x2160 4K pixel. So each of our three segments is still larger than a single 3840x2160 pixel.
Now with the new DLP UHD projectors and their native 2716x1528 chips, applying the same logic, one could argue that they need to be much closer to needing "4K" optics.
Generally, most projectors, unfortunately could use better glass, regardless. Less pincushioning, less barrel distortion, less blooming, and more even uniformity, and it sure would be nice if such lenses also rolled off brightness around 5% in the corners instead of the usual 10 - 15% or more.
One definitely can see the difference between the old VW1100 (or the 5000ES) and the lower end Sony 4Ks in terms of sharpness, and overall clarity. Not huge, but visibly superior. What that tells us, is that there are $15K true 4K projectors that still don't have "4K" optics (that can fully resolve 4K), because if they did, there wouldn't be a visible difference between those Sony's and their top of the lines. Also as is the nature of lenses, and as folks have pointed out, lenses can resolve more in the center than the edges of the image.
The sad part is, what we all really need is true 8K, so we can have proper, "big time" immersion. I look forward to the day when I can sit 5 feet from a 124" diagonal screen and have everything razor sharp. (BTW true 8K is still only 80 pixels per inch on a 100 inch wide screen - not exactly laser printer sharpness, but then we don't sit 18 inches from our screens.
Overall, I'd say most projectors - could use better lenses. I've got three different 4K UHD DLP's here, with one seeming to have a bit better lens than the other two. Two are $2500 projectors, so you know there are limits to what they can provide in terms of lens, unless of course, they can rack up the kind of sales volume that would allow the better economies of scale when it comes to manufacturing.
OK my ramble is over, perhaps I'm right, but at least I tried to be a little less technical, more subjective, for those like me, who might have had a problem understanding some of the comments and demonstrations. -art
"Reviewing projectors is fun, but watching the 5th Element for the 500th time..."
Which means I'm really looking forward to Valerian: City of 1000 Planets