Compensation of off-axial aberrations using polarization-masked azimuthal Walsh filters

In the presence of astigmatism, the three-dimensional distribution of rays in the image region passes through two orthogonal lines, the vertical sagittal foci and the horizontal tangential foci. With increasing astigmatic behaviour of the imaging system, the sagittal and tangential foci will be farther removed from each other and the separation between these two planes serves as the measure of astigmatism. Midway between these planes, i.e., corresponding to the defocus term, W-20 = - W-22/2, where W-22 is the co-efficient of astigmatism, the intensity spread is found to be minimum and the transverse plane passing through this point is referred to as the plane of minimum aberration variance. For a diffraction-limited imaging system, the IPSF on this plane is the Airy pattern. In our study, each sector of the azimuthal Walsh aperture is masked by suitably oriented linear polarizers. The polarization phase introduced is a function of the state of polarization (SOP) of the input beam, the transmission axis of orientation of the masking polarizer and the orientation of the analyzer. A feasible method to assess the degree of astigmatic compensation is to compute the IPSF at the plane of minimum astigmatic variance and compare the intensity distribution with that of airy pattern. IPSFs for different values of W-22 are computed with the presence of compensating polarization masked azimuthal Walsh filters at 0 degrees and 90 degrees with input beam parameters a=b=1 , delta = 90 degrees and analyser kept at a particular angle. The results are compared with IPSFs computed for an unmasked lens and airy pattern.