Astigmatism together with longitudinal focal shift in off-axis optical systems

In many laser applications optical systems are employed to focus off-axis beams that only partially fill the system aperture. In this paper analytical expressions that give the position of the diffraction focus, normalized peak intensity, and tolerance conditions for uniform and Gaussian off-axis beams in an optical system which suffers from astigmatism together with longitudinal focal shift aberration are obtained on the basis of diffraction theory. The results are useful for designing focusing systems for use with laser beams.