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

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