Effects of introducing astigmatism aberration to spiral elements of diverse geometrical shapes

In this study, we explore the impact of astigmatism on the focusing characteristics of various spiral zone plates with different geometries. We examine four types of spiral zone plates: spiral circular, spiral square, spiral orthogonal, and spiral checkerboard. Our theoretical analysis of the spiral circular zone plate indicates that introducing astigmatism aberration changes the focused vortex into Hermite beams, producing a series of interference lines. The quantity of dark fringes reflects the topological charge of the vortex beam and the orientation reveals determines whether the vorticity is clockwise or counterclockwise. This phenomenon is consistent across the other spiral zone plates as well, as astigmatism modifies the resulting beam into an interference pattern that indicates both the magnitude and direction of the topological charge.