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In Season 2, Episode 1 ("Brother") of Star Trek Discovery, the crew takes images of an asteroid's surface using Discovery's "telescopic cameras".

Since one of the images shows

a starfleet vessel which has crash-landed on the surface,

the image is put on the main screen and we hear Michael Burnham say the following:

"There's no way to zoom in any further!
Commander Saru, I know your vision has a larger optical window than ours. Can you make out the registry number?"

which was not a nice thing to do, because it completely broke my suspension of disbelief in the middle of the episode.

Seriously? The Discovery's main screen has no "digital zoom" feature? My PC was able to do that back in the 20th century! Oh, and they could have also just walked a few steps closer to that huge view screen.

On the other hand, obviously, a lot of effort went into that scene (we even see Saru's eyes "zooming in"), so there might be a perfectly logical in-universe explanation that I have just missed.

Why weren't they able to just digitally zoom in on the image taken from the surface?

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    The only possible explanation I could come up with would be that Saru's vision has an enhance button (warning: TVTropes) which the Discovery's computer doesn't... – Heinzi Jan 20 at 12:46
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    I think this is just bad writing... Discovery probably has bazillion-pixel cameras with telescopic lenses better than Hubble, so that shouldn't happen... – Rebel-Scum Jan 20 at 13:00
  • This reminds me of the times that TNG went "Oh no, our massive state-of-the-art exploratory science starship doesn't have sensors that can scan that thing! Geordi, please look out the window"... After the first time, why didn't they upgrade their sensor suite? – Chronocidal Jan 23 at 9:18
  • I don't think this is about zooming, but about making out the actual letters from the image. In real life, this is also ridiciously easy for humans to do, but computers struggle with it (think about captchas). So, it's easier for Saru to make sense of the image. – Philipp Flenker Jan 25 at 13:29
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Short and sweet: there is no logical sound explanation for that ridiculous scene. It's bad writing on a facepalm level, showing the absolute lack of understanding of optical as well as digital image processing on the side of the writers and producers.

TL;DR - Version: The out-of-lore explanation is very likely that they wanted to put an emphasis on Sarus superior eyesight compared to humans, so they constructed a situation where they could showcase it. So far about the idea. The execution was outright naive, stupid and demonstrative of their incompetence.

The discovery has state-of-the-art cameras of the mid-23rd century aboard, so the first idea that those could not zoom in enough on meter high letters on a ship thats just a few kilometers away is silly enough. From here on, the levels of ridiculous just start growing.

A: If it was a somehow all-the-way analog display technology (which would require an extraordinary amount of dedication for a ship that is not focused on exploration), the image size could easily be increased, either by lenses or a high res (23rd century high-res, not 2019 high-res) digital zoom. However, the idea that it realy was an analog display mechanism seems realy far fetched for a star ships bridge display with overlay, navigational and tactical data etc.. No, just no.

B: The 99.9% more logical and practical assumption would be that it is a digital display. If that is the case, no god-like superior eyesight in the universe could enhance anything of a picture that was rasterized into pixels. If that is the maximum zoomlevel those cameras and the display system attached to them can achieve, than even watching the display with the hubble space telescope will only show you the pixels in large, but not reveal anymore details that you could not have made out with plain eyesight.

Synopsis: This is just another moment (in an otherwise quite entertaining fantasy show) where the producers utterly demonstrate their total lack in understanding OR the purposefull disregard of any believable technological pseudo-science, which is a watermark of everything Bad Robot, J.J. Abrahms and Alex Kurtzmann (who is a disciple and living fanboy of J.J.) touch.

Before those took over, Star Trek always at least tried to find a semi-justifiable way of explanation for their gadgets and deus-ex-machina technology that could somehow be put in context with science. This is a fundamental element of "SCIENCE fiction". If you take away the effort to at least try to base everything in sound science, it becomes pure fiction and you could as well have unicorns, dragons and magicians.

Fun Fact: The registry number on the crashed vessel is NCC-815, which is a bow down of producer Alex Kurtzmann to his mentor and buddy J.J. Abrahms. It's the registry number of the "Oceanic Flight 815" that Hurley Reyes crashed with on the Island in J.J.s TV series "LOST". And it is a part of the omnipresent magical numbers 4,8,15,16,23,42 in that series.

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Out of universe this is clearly a way to bring up peculiarities of Saru's species that will be relevant in following episodes.

In universe however is not completely unreal. Technology can't always replace or enhance biological abilities. Assuming the image on the screen was an optical representation of the image, in the same way an "optical" zoom works in nowadays DSLR cameras, it's perfectly possible for Saru's species to be able to appreciate something that the computer can't replicate. Note that there's no mention we're seeing a digital zoom, we may very well be looking at an optical zoom of the crash.

Analog is always better than digital. There's always some loss of data when you transform an image from analog to digital representation so it is perfectly plausible that a biological function works better over analog data than a computer does over digital data transformed from optical.

Note this already happens with today's technology. Both cam corders and still cameras work with something called Dynamic Range, which represents the maximum difference between the darker and brighter parts of an image. If the difference between those two on an image is greater than the dynamic range of the sensor on the camera, you'll lose detail on either the darkest parts or the brighter parts. However, the human eye does not suffer that limitation. It doesn't because it basically rapidly takes "snapshots" of the different areas and mix them up on your brain. You don't even realize your eyes are scanning the scene and adjusting your diaphragm (opening and closing it) to adjust to each part. Note this happens even if you're looking at a scene thorugh the optical viewfinder of a DSLR, you simply see more than the computer.

Now, while I'll admit it is a strech, given Saru's alien physiology, it is perfectly reasonable to assume the same principle will apply.

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You are right, it makes little sense, one cannot squeeze more information from a digital image, no matter how well your eyesight is. However, it was put there in order to draw attention to Saru's enhanced sight that is important for episode "The Sounds of Thunder" where He sees (directly, not via camera) something important that others haven't been able to. It may also come as a tribute to a previous member of star trek, Geordi La Forge, who helped the crew with enhanced, albeit artificial vision.

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I just assumed that as "Prey," Saru's brain has some really advanced image and environment enhancing built in that could supersede and augment a partial image in the analog realm where digital zoom just breaks down. An example being the ability to see the indirect effects of predators on the environment, or to find prized food sources, much in the way that a modern Human tracker can see signs that 99% of the rest of us miss.

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