Uniform versus Gaussian beams: a comparison of the effects of diffraction, obscuration, and aberrations

Much is said in the literature about Gaussian beams. However, there is little in terms of a quantitative comparison between the propagation of uniform and Gaussian beams. Even when results for both types of beam are given, they appear in a normalized form in such a way that some of the quantitative difference between them is lost. In this paper we first consider an aberration-free beam and investigate the effect of Gaussian amplitude across the aperture on the focal-plane irradiance and encircled-power distributions. The axial irradiance of focused uniform and Gaussian beams is calculated, and the problem of optimum focusing is discussed. The results for a collimated beam are obtained as a limiting case of a focused beam. Next, we consider the problem of aberration balancing and compare the effects of primary aberrations on the two types of beam. Finally, the limiting case of weakly truncated Gaussian beams is discussed, and simple results are obtained for the irradiance distribution and the balanced aberrations.