My impression is that doing a flat image in the middle of a piece is a matter of adhesive that matches the index of refraction of the acrylic so you don’t see a joint. There’s also the thing with a 3D image, which AFAIK is some kind of variable-focus thing, possibly with multiple beams, so that the material only changes at the particular focal point (but that requires a wavelength that your material is mostly transparent to, just not at superhigh power levels.
So this process generally uses two lasers. One from the top and one from the side. Where the two lasers intersect there is enough energy to vaporize a small portion of material. This turns into a small bubble. They can pattern these bubbles in x y z space to create whatever geometry you are looking for.
Its a pretty neat process. Its also the same concept for radiation treatment of cancer.
Long ago I ran across info on holographic computer data storage, and I had actually contacted Professor Glenn Sincerbox referenced in the linked article below to ask him how it works, simply out of my own curiosity. He kindly responded to my email, and I haven’t forgotten his name since. In fact I was able to Google him and locate this article, with a similar explanation: