As someone who has been developing Projection Screen coatings since 2003, I feel I can offer some definitive information, and perhaps some advice here.
Even back in the days of 800 x 600 & 480i projected resolution, there were marked differences of how pixel grids were resolved between various screen textures.
But back then the case was that texture was your friend...for two reasons.
: It helped diffuse the incoming Projected light, because most screens...textured surfaces not withstanding...were coming it at over 1.0 gain because most Projectors were far more dim than today's units (<sub 900 lumen) , and what with most every single projector (CRTs get a pass) not having light-uniformity values much above 65-70%....that being the case, the center of most images would be noticeably brighter than at the edges. Light that was effectively scattered via diffusion mitigated the tendency of such surfaces to "Hot Spot".
The contours (bumps) of texture would break up the uniform pixel grid pattern (Screen Door Effect ie: SDE), making it less discernible at the distances most felt constrained to view imagery at.
That last point is validated by the fact that has image resolution has increased, the old standards set down as Law that one must observe 1.8 to 2.0 to 1 viewing ratios (eyes to screen) became outdated. And again, when some PJs improved their light uniformity values to be above 70%, eye strain issues became less a concern. But then SDE became more of an issue, because people did not want anything so distracting to ruin their viewing pleasure.
At this point a clarification between SDE and Pixels must be made. SDE is most commonly thought of as the Grid Lines that show because projector
optics typically have significantly higher pixel density than the image they project, allowing the fine lines, which are much smaller than the pixels themselves, to be seen.
DLP Projectors had less of an issue than did LCD Projectors because they use a single Mirror instead of 3 Panels, but when an image is blown up to 100"s and beyond, many can still see the actual Pixel structure of an image. Especially Lasik Altered Mutants.
As far as Painted Screens go, initially rolling on coatings was initially the order of the day, and if done correctly resulted in surface textures that were smoother than their Mfg Screen counterparts. Problem was....that smoother surface let the SDE be all the more noticeable. Just the same, such surfaces were "4K Ready" long before we ever imagined 4K as being a reality.
First there had to come 720p and then 1080p, resolutions that reduced the size of the LCD Grids (and increased Pixel density). That combined with better light uniformity (usually) helped push in the Viewing Distance to Screen Width ratio distances more akin to 1.5:1 But darn....the closer you got to a screen with smaller Pixels, the larger those pixels became. A Catch-22 scenario was the result. But by that time (2008> )image quality concerns had gravitated to Contrast being more important...and those who wanted to remove SDE from the equation turned to SXRD & LyCos projectors. That took care of the SDE.....but
So bringing us back to today.....4K resolution (Native or EShift) Pixel density is even more increased.....but in many cases, so has Contrast, and the latter is now playing a critical part in how easily any artifact, screen or PJ induced, is resolved by the viewer's eyesight.
The higher the contrast, the more defined the differences in light/dark image content. This also means the Gradient Grey Scale is increased, allowing for far more of an increase in shadow depth perception. In the case of individual Pixels, there is always going to be some space between them, and when again...an image is blown up to huge proportions, the difference between a lit area (used Pixel) and the unused space becomes more apparent. Smaller...but still there. And since 4K means people are moving in still closer to their screens....some can begin to see even the much smaller Pixels. Or the much smaller Grid Lines of the LCD Panels. SXRD & LyCos PJs are not wholly exempt from this, just far more proficient in increasing the "visible" difference between a active and inactive Pixel. Image Smoothing technology (Panasonic's LCD-oriented Smooth Screen Tech) was the very best at eliminating all vestiges of Pixelation and SDE, but there was a cost....sharpness would suffer a bit.
Finally, with 4K rising in popularity, Mfg Screen concerns started to jump on the "4K Ready" Band Wagon. At the start, that really was just a Promotional Slogan...nothing had been done to smooth out the Screen surfaces. So Non-Mfg Screen surfaces (Painted Walls and Boards...Inexpensive PCV Materials) and curiously, the very least expensive PVC Mfg Screens all ruled the roost in that respect. That opened the eyes of the Screen MFg, and of a sudden...Smooth was in...because a lot of End Users had complained about seeing even the greatly reduced LCD Grid Lines and /or Pixels because textured surfaces would present areas that allowed shadowing differences due to texture high & low points.
And of course, the closer one sat, the more easily resolved such artifacts would become.
A ultra smooth surface is unforgiving as far as one discerning any projected artifact, where as a textured surface can and does highlight such artifacts even more....destroying what advantage higher resolution brings to the viewing experience. Because...once you see such "artifact-ing", you can't "un-see" it...your always looking for it in the brighter areas of an image.
So on one hand, @bix26
is correct in stating that texture does not reduce the ability to resolve 4K Resolution......but it does indeed distract from the ability to view an image as pristine as possible. Any texture will distract one's perception that they are looking into a different reality....a "Window" into another place in time.
Moving on......a UST
perform effectively on any screen that is in any appreciable way Angular or Retro Reflective, or that has a gain exceeding much higher than 1.0. That pretty much encompasses virtually all Ambient Light "Rejection" Screens....screens that accept light coming in from a specific angle different from the Projector. Only recently developed specialized Screens that collect and redirect the Image coming in at such a extreme angle of incidence can effectively employ both Gain and Ambient Light performance when a UST
Projector is in use. That criteria is severely limiting...there are not many screens available that fit that definition...fewer that actually do what they portend to do...and almost none that do actually work and don't come down the Pike prohibitively expensive.
There is a good reason most advertising of UST Projectors involve showing them projecting directly onto a Wall. Most Walls are under 1.0 gain...ergo very suitable for UST Projection.
does make great good sense for Family Room "TV Replacement", there will be a period where ALR Screens intended to work well with UST PJs will cost more than they should, because the demand to offset ambient light is a real issue. But not an intractable one.
For many, simply employing a "SMOOTH" 1.0 gain (or less) Grey surface...Mfg or Painted, will mitigate some degree of diffused ambient light that strikes the Screen, helping to maintain Blacks and Color vibrancy. Such a Screen is known as being ALR (Ambient Light Resistant)
And USTs that have an abundance of Lumen output (...and decent Contrast...) make such simple surfaces all the more readily acceptable....overcoming the limitations of a screen having a lower gain.
So knowing what to get, and what to expect is the surest route to satisfaction. Unrealistic expectations have shot down many end users, who tend to blame the equipment / Screens or Mfg claims before they can accept that they themselves were self-misguided due to not knowing exactly what the complete picture involves.
DIY Screen making has had a handle at delivering Contrast Boosting and Gain and greatly overcoming Ambient Light without overtly creating Angular reflection for some years now, so in that respect has always been ahead of the Game. But UST Projection is the absolute most limiting application. Again...not wholly intractable, but limiting as far as how much ALR and Gain increase can be done without drastically attenuating the image.
..............but that is something best left for discussion on the DIY Screen Forum.