An optical beam transformation system includes a first and a second optical element, each of which has a non-reentrant surface. The system transforms a substantially non-uniform optical input beam (such as a Gaussian) to a substantially uniform output beam. The first and second optical elements are arranged in either a Keplerian or Galilean configuration. The aspheric surface of the second optical element is related to the aspheric surface of the first optical element by a ray-tracing function that maps substantially all of an input light beam that is incident on the first optical element to a collimated output light beam that is output from the second optical element. Preferably, the output light beam has a Fermi-Dirac intensity distribution, and the ray-tracing function maps the input light beam to the output beam out to the (1/e)6 intensity radius of the input light beam.