Lossless laser beam shaping

The Fresnel approximation is used in the design of a lens that turns a beam with one intensity distribution into a beam with a different distribution at the focal plane of a Fourier transform lens. In general, this cannot be done exactly, so one must be satisfied with approximate solutions to this problem. It is shown that the difficulty of this problem depends on a parameter beta that is a dimensionless measure of how well the geometrical optics approximation holds. An analytical method is given for determining the lens when beta is large. The sensitivity of this solution to various imperfections in the system alignment is also analyzed. (C) 1996 Optical Society of America