Velocity map imaging is used to map the 3D momentum distribution of charged particles such as ions and electrons into 2D image. This equipment relies on its ability to map particles having the same initial momentum vectors but emitted at different locations to arrive in (approximately) the same point at the detector. There have been a couple of methods to recover the 3D distribution from the measured 2D image, this includes Abel inversion, onion peeling, basis set expansion (BASEX), and many others. May be the second chapter in this pdf will help.