Not knowing how a CAT scan works, beyond a vague intuition from already knowing what the acronym stands for, and not wanting to look it up before making a guess: can I assume it’s akin to this, in that radiation is shot from an emission source, through the target, to a detector on the other side, with the density of the material attenuating the signal in predictable ways, from which we can apply a transformation to some large number of such measurements to achieve a computed 3D result?
In a closer analogy to a CAT scan, each nail would have a string connecting it to a ~10 degree spread of nails on the opposite side, and each string would be grayscale.
The real physics is quite tricky, because you actually emit a variety of x-ray energies at once, each with different penetrating power, and xray flux varies spatially as well. this means each of your angular strings has its own grayscale response curve.
