"Ultra-Short Throw" Lens setup?

A thought occurred to me that it would be nice to build a little webcam type thing onto a whiteboard. I recently became aware that Ultra-Short Throw video projectors, which are able to project a 254cm (100") diagonal image from only about 8cm (3") away are a thing that exists.

My question is: What sort of lenses come to mind to do the opposite? That is, take a rectangular surface that is very close and accurately capture it, with minimal distortion.