The question has already been answered (the equivalent digital “resolution” of a frame of film being high enough that rescanning in 4K will yield plenty of detail) but “4K resolution” in itself doesn’t specifically mean a high quality image. “4K resolution” simply refers to one of two standardized pixel dimensions (depending on whether you’re referring to true 4K, which is a slightly wider aspect ratio, or UHD (which is the resolution of a 4K disc) which is 16:9 aspect ratio (3840×2160 pixels).
All of that said, you can theoretically make anything 4K resolution. You can upscale a VHS to 3840×2160 simply by transcoding it in a media encoding app. It will just resample the existing image at a much higher pixel density. The important thing is whether that higher pixel density actually yields more visual information. Imagine, for instance, that you’re viewing a photo you’ve taken on your phone. Let’s say your phone has a resolution of 1920×1080. If you pinch to zoom in on your photo, you’ll be cropping in closer on specific parts of that image, and that will wind up filling your phone’s 1920×1080 frame. So the image you’re looking at will still be displaying in 1080p resolution, but the actual raw photo file won’t have magically raised its resolution to reveal more details.
So when you purchase an older movie on 4K on physical media, for instance, you will often see blurbs on either the front or back of the box touting that the new digital transfer was created by rescanning the original camera negatives or an original print of the film. That means that the studio or distributor has actually gone back and rescanned every frame of the movie from an original film source rather than simply upscaled a lower resolution transfer from an inferior medium.
An example of this not being done is the exploitation slasher Killer Workout aka Aerobicide. I’ve got the Blu Ray, which is a 1080p (1920×1080 pixel) format. However, on the back of the box, there’s a disclaimer that says original prints of the film couldn’t be located, so the new Blu Ray transfer was made from the best sources available to the distributor. In some scenes, the best source was a VHS, which they simply re-sampled at 1080p resolution. The image quality in those scenes is therefore noticeably worse.
All of this said, many pieces of hardware and software have built in upscaling algorithms that effectively provide educated “guesses” as to what visual information might be missing in a lower quality image. Blu Ray players will often upscale an interlaced SD DVD image to make it run at a progressive resolution on an HDTV. It’s essentially creating new visual information from nothing, but it’s doing so based on guessing what that new information should be based on all of the frames of the image around it. So a properly upscaled image will still look better than simply zooming in or blowing up a lower resolution image to view at a larger resolution.
An infuriating example of this idea being brought up in a non-entertainment setting was the Kyle Rittenhouse trial. His attorneys made the argument that the “enhanced” security camera images of the shooting that seemed to show Rittenhouse acting aggressively instead of in self-defense couldn’t be trusted because the algorithms used to blow up the low quality image could have “inserted” any information randomly and might not reflect the reality of what happened. In other words, their argument was that a particular color or object seen in the image may only be a result of an upscaling algorithm and is merely a reflection of what the computer arbitrarily decided should be in the missing detail of the image rather than what was actually there. The prosecution pointed out that all of the upscaling algorithms in use are not arbitrarily inserting whatever pixel information they see fit at random – they’re using the context of surrounding pixels and surrounding frames of video to make a very educated guess. The judge in the case was an older gentleman who freely admitted to not understanding the premise and allowed the argument to move forward. It was infuriating as a video editor to watch that play out
I did a pretty bad job of describing this in text form, but hopefully this is somewhat helpful
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