| This thesis explores techniques for and applications of free-space beam shaping. After reviewing the basic principles of scalar diffraction theory, I discuss and experimentally demonstrate several approaches to two- and three-dimensional transverse beam synthesis; these include analytical solutions of varying complexity as well as methods for computer optimization of beams with arbitrary constraints. Analytical solutions are also presented for the temporal analogy of nondiffracting beams, i.e., nondispersing pulses, and repercussions to time-dependent diffraction theory are discussed.; Next these beam shaping methods are applied to imaging photolithography, addressing ways to improve both resolution and focal depth therein with the use and proper design of phase masks. In this work it is evident that computation time plays a critical role in the applicability of phase masks to photolithography, because phase mask design algorithms tend to scale unfavorably with mask size. I therefore introduce an approximation to the Hopkins equation which reduces the computation time for partially coherent imaging by one to two orders of magnitude. Following this the question of spatial coherence in phase mask-assisted photolithography becomes interesting, and the optimal coherence for such systems is investigated both theoretically and experimentally. The properties of incoherent imaging are next applied to a slightly different problem--imaging through random media. A new technique for ballistic imaging is presented, discussed theoretically, simulated, and demonstrated experimentally, and its advantages and drawbacks are analyzed. Finally, a theoretical overview of the fundamental limits to space-time beam shaping is presented, several results of which are demonstrated.; Due to the diversity of the subjects discussed, introductions and brief histories are given at the beginning of relevant chapters. |
