Camera Obscura
With the laser painter done, the next major component is a camera to capture the laser-painted object. A nice hi-res camera would be nice, but I'm doing this on the cheap, so a $20 discount webcam will have to suffice.
There's one small catch. Lens distortion. Lenses bend light, and not uniformly.
If you follow a ray of light from Dot C on the left, you'll see that it strikes the glass of the lens straight on. When light hits a refracting medium, like say glass, perpendicular to the surface, it goes straight through. This is the theory that drives "window" technology.
But if you follow the ray from Dot A, you'll notice it strikes the glass at an angle. The bit of glass near the edge of the lens is less like a window, and more like a prism. The bottom line is, the closer to the edge of the lens light strikes, the more it gets bent. This is why lenses can do the nifty trick of focusing light, which comes in pretty handy in photography. However, when we're trying to capture undistorted information to accurately recreate a 3D version of the object we're photographing, this lens distortion becomes a pain in the butt.
Digression
To paraphrase Samuel Johnson, there are two kinds of knowledge, the kind we know, and the kind we know where to find.*
Frequently in the process of mad scientific inquiry, I am drawing on knowledge I know, at least well enough to get by. But just as frequently, I am using different resources to jog my memory, or fill in the details I've forgotten. For these occasions, old college textbooks help out (either from my old college days, of from yard sales). Odd little reference books that I've picked up over the years also help (Geigy, "Scientific Tables" Seventh edition; The Universal Encyclopedia of Mathematics.
But my very best friend in these endeavors is Google. So here's the deal: Google is not God. Google keeps more personal information about all it's users than I'm comfortable with, but hey, I'm old-fashioned that way. But when I need to brush up on how refraction works, or what research is being done in the field of structured light for computer vision, Google's the Igor to my Dr. Frankenstein. So, keep adding to the knowledge you know, and keep the other resources handy for the other bits.
* I did a search on "two kinds knowledge" to find the full quote & attribution.
A Non-Distorting Imager
There are ways, in software to compensate for lens distortion. They all use a great deal of math, and are therefore unattractive to me. There are also some traditional methods for reducing distortion in photography, chief among them being the use of a telephoto lens.
Sadly, for a desktop scanner, a telephoto lens is not a good choice, unless we want to greatly expand the definition of desktop.
There is a class of imaging devices, however, that work on the principle of diffraction, rather than refraction. This imaging devices has no linear distortion, and a near infinite depth of field, meaning all objects are equally in focus. It also happens to be one of the oldest imaging systems, the pinhole camera, or by it's Latin name, camera obscura.
It has it's problems; low light sensitivity, frequently all objects are equally out-of-focus, but it pluses make it worth exploring.
Time to build a digital pinhole camera!