yet another proposal of this "angular resolution" myth....you keep using this phrase....i do not think it means what you think it means.........
You can only see so much detail. There are limits imposed by what you are seeing by (visible light, radio, electrons, gamma radiation, etc.) There are limits imposed by the nature of space.
You can build a literally perfect detector, put it above the atmosphere, but you're not going to get enough resolution to see detail below a certain size at a given distance even without worrying about effects of the medium through which you're looking. There is a lower limit of subtended angle at which details may be resolved. Below that limit, you can see emitted radiation but it might as well be a point source going flicker, flicker for all you can tell about it.
Let's say we've got an object that is a geometric point that emits light. When I point a perfect imaging system at it, I do not get an image of a point, even though my perfect imaging system has no limitations like pixel sizes, and it otherwise does nothing that it shouldn't when forming an image on my perfect detector. Instead of a point, I see a disk surrounded by a number of rings. I can see them very well, thanks to the perfect sensitivity of my detector. There's a disk that's substantially larger than a point that fades out at the edge, then there's a dimmer ring that fades in, then out, and another ring that is outside that one. Since my system is perfect, I can see rings across my entire field of view, each only a few percent of the brightness of the one inside it.
Add a second point source of light. So long as it is well away from the original source, I see it as the same sort of disk and rings image as the first point, but in a different place. When they get closer, but don't actually touch, the disks and rings begin to merge together. At a point, they cease to be distinguishable as two separate sources. They are not lined up with each other, they are still separated, but the image no longer shows this. They appear as a single disk and ring structured image with the combined brightness of both. Even my perfect sensor system can't tell the difference. If you want to know anything about the points individually, you can't. If one goes out, I can't tell you which one did. If they move with respect to each other within this distance, it can't be seen. The image stays the same.
The resolving power you have is limited by many things, but the biggies are wavelength of the radiation you're capturing and the effective aperture or baseline of your observations. Even if you have an effectively infinite aperture by surrounding the subject of observation with a sensor sphere, the effects of wavelength are still there (I won't get into the other problems you get into or can make for yourself by trying to do this--physics creeps in through all the cracks so when you try to push something to either zero or infinity in one part of the equation, you're going to get physics you never dreamed of squeezing in with infinite force somewhere else.)
Now, this is in a best case scenario. Only two perfect point sources of light. When you start imaging something that isn't just two points but is what is called an "extended object" you get an image that is a mosaic of these disk and ring patterns. These patterns interact with each other. Varying frequencies, brightness levels, and so on mean that with any object that is bigger than a point source cannot be observed at the theoretical maximum resolving power of your system. Your ability to see detail diminishes dramatically. You can't tell where things are with respect to each other at even further angular separations from each other than when working with just the two points of light.
Even with perfect optics and a perfect detector with no limit to its resolution (infinitely small pixels, if you will.)
So, your ship's captain happens to have the best sensors available picked out of a snapshot camera found in a rubble heap of the ancients. 3I science can't tell them from perfect. He stumbles on the site of an attack, the ship still outgassing. He microjumps to one light hour away, real close, a smidge over 670 million miles. At this distance a 500 foot long craft subtends an angle of about one half of one millionth of an arcsecond. I'm not here to do real work unless you pay me
, but I can tell you easily off the top of my head that we're way below the limits of resolution of even a perfect sensor system operating at any wavelength that's going to interact with the subject in a useful way or be emitted by it. The craft could be a mile long and any details of or about the object are going to be lost. If you walk around in space using FTL a bit you can watch the two craft approach and separate, but you won't see any details.
You'll have better means of investigating the crime in detail.
