Quality factors of a slightly inclined Gaussian beam passing through a zone plate: Effect of stop shifts

We discuss the influence of a movement of the stop on the quality of a slightly inclined Gaussian beam focused with a zone plate. First we examine the diffraction of a complex-source-point spherical wave through a zone plate which is not in contact with an aperture stop. Then we find an expression of the fourth order-corrected Gaussian beam which is represented in terms of Seidel-type wavefront aberrations. The derived formula is also used to analyze how the aberrations work on the quality of the diffracted Gaussian beam. In cases where the spot size of the incident beam is small compared with the principal focal length of the zone plate, we show that the quality of a slightly inclined beam of diffracted order m > 0 (or m < 0) can be improved by shifting the stop from the zone plate in the negative (or positive) z direction.