I understand this isn't a common request for most people, but it's highly common in industrial image/vision systems for quality inspection, etc.
Sure there are a lot of ways you could do it. It's no secret you could simply use mirrors, or multiple cameras (cameras are cheap these days) but then you'd have to have further image processing to correctly assemble and stitch together all those bits and pieces. Why complicate matters? All you need is the right tool for the job: in this case, a pericentric lens.
Think of it as the exact opposite of a wide angle "fisheye" lens, allowing you to capture images like these:
... well, maybe it's simpler to show it to yout this way:
[images from opto-engineering]
Indeed, the side image shows up highly distorted (but that can be easily fixed by digital image processing if that happens to be necessary) but it solves the problem of acquiring an image of such an object in just one shot.
This special type of lens, along with entocentric and telecentric lens (not to mention spectral imaging lens) are highly specialized and you won't likely ever see one outdoors... But I thought it would be interesting to show you the secret these lens hold. :)
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