This whole area of imaging something with many different lightsources was pioneered by HP labs. The full name "Polynomial Texture Mapping" refers to the technique of using all the images taken in order to make a virtual image for any light source (it is easier to look at an example to understand this). Early "rigs" looked like this one:

This is the National Gallery London prototype made by Joseph Padfield. It uses fixed lights on a strong structure and a camera can be seen at the top.
He has a nice demonstration of images of paintings.
Building these structures is quite complex and they are not very portable - so when I was asked by Graeme Earl from our Archaeology dept. to investigate a more portable unit for their digs I was interested to see what could be done on battery power, with powerful white LEDs and a moving structure. We came up with this:

Here you can see a motor controlled arm with all the high power white LEDs (fast and avoid heat). The tripod support makes it easy to deploy on strange surfaces in digs. The lights and camera are all controlled by a laptop/PC using custom software. The current camera is a Nikon D300. The rig captures all the images for the lights in one position, then the arm is moved slightly for the next set and so on. The whole system fits in a suitcase for travel and can be powered from a large battery if necessary. A revised version of this has been used extensively. by the Archaeological Computing Research Group.

Photo of "Amazon head" under the rig.
PTM Viewer demo (requires Java - which should not be a problem)