If you shine a laser into diamond centered and perpendicular to the table face, the beam will be split and returned out of the table to show a pattern of dots (some bright, some dim). The pattern is unique to each diamond.
I did something similar in college in the 90's, except using cut crystals. One laser in, hundreds of beams out (faded, of course). You know the kind of faceted crystal balls that some people put in their cars and hang from the rearview mirror that cast rainbows everywhere when the sun hits it. Looked cool with a fog machine in the dorm.
Sounds like a Swiss watch company could use that for proving authenticity.
Company Seals are also a pretty big deal in East Asia, which are usually a red stamp. If several could be combined (e.g. CEO, CTO, CFO seals all generating a unique interference pattern), that would be a provable signature that the document is legitimate.
X-rays are just one frequency of light. You can use any.
Also you can use electrons to get electron crystallography which is (arguably) more powerful as you can reform the original image after, it requires WAY smaller crystals, can see lighter atoms, and more.
Using Differentiable Rendering (reconstructing scene setup parameter(s) from an image), possibly, although it would depend on the number of unknown params.
Mitsuba2 had an example of matching caustic patterns by modifying geometry I think...
My gut tells me it would work like a hash function, the diamond -> dot pattern function being trivial, but the dot pattern -> diamond function taking exponentially more effort
Gemprint.com uses this to fingerprint diamonds. You can see some images of "gemprints" here: https://www.gemprint.com/light-performance.html