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 β that is a dimensionless measure of how well the geometrical optics approximation holds. An analytical method is given for determining the lens when β is large. The sensitivity of this solution to various imperfections in the system alignment is also analyzed.
© 1996 Optical Society of America
L. A. Romero and F. M. Dickey, "Lossless laser beam shaping," J. Opt. Soc. Am. A 13, 751-760 (1996)