Application of the pupil astigmatism criteria in optical design

We developed the pupil astigmatism criteria for correcting the quadratic field-dependent aberrations. These criteria provide an elegant way to determine and correct aberrations that have quadratic field dependence and arbitrary pupil dependence in the same way that the Abbe sine condition is used for aberrations with linear field dependence. Like the sine condition, the pupil astigmatism criteria involve only the properties of the rays originating from the on-axis object point, so it is convenient to implement them in optical design. We introduce an algorithm to apply the criteria in designing new well-corrected optical systems. Some example designs are presented.