Abstract

The spatial characterization of laser beam profiles and the analysis of their quality changes under propagation through optical systems are topics of current interest in the literature.^1-4 In this connection, one of the major problems is to find general optimization criteria for beam quality parameters (rigorously defined in terms of the so-called moments of boththe intensity and the radiant intensity of the field) as well as to improve them. In this sense, use of pure phase transmittances, through which the beam is made to propagate, has recently revealed to be an appropriate procedure because the total power is maintained. Thus, it has been shown⁵ that spherical aberration (or, more generally, quartic phase distortions) could improve the beam quality under certain conditions. This rather surprising conclusion was derived for the bidimensional (2-D) case and symmetric-intensity beams. However, as it is shown in the present work, the generalization of these previous results to 3-D optical systems and non-cylindrical beams involves not straightforward properties, mainly due to the appearance of crossed moments in the analytical expressions. In particular, it is well known in Fourier optics that two identical but orthogonal cylindrical lenses in contact with one another are optically equivalent (in the absence of aberrations) to a single spherical lens of the same focal length. But this equivalence, however, is no longer valid when spherical aberrations take place. In fact, we have found beams (for example, cylindrical Gaussian fields) for which use of the pair of cylindrical lenses produces better output quality parameters than the equivalent single spherical lens (provided that the optical systems were aberrated).

© 1994 IEEE