An Analytical Solution of Vector Diffraction for Focusing Optical Systems with Seidel Aberrations

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Abstract
In this paper, a method developed by the author is used to study the image formation in various aplanatic systems with Seidel (fourth-order) aberrations. We study the spherical aberration, the distortion aberration and the curvature of field aberration. Just as in the case of scalar diffraction theory, it is shown that the distortion produces a shifted intensity pattern while in contrast with the scalar theory it is shown that the curvature of the field aberration produces a different intensity distribution. We also provide expressions for the location of the diffraction foci and calculate the Strehl intensity. We find that for the case of spherical aberration, the Strehl intensity increases with the increase in the numerical aperture whereas for the case of curvature of field aberration the Strehl intensity decreases with the increase in the numerical aperture. For distortion aberration the Strehl intensity is same as the Gaussian intensity. The computations are carried out for a focusing lens. The diffraction integrals are evaluated in terms of the spherical Bessel functions and the Gegenbauer polynomials of the first kind. The computations are easy since both of these functions are evaluated with the use of very stable recurrence relations. In addition to studying the diffraction pattern associated with a single aberration the method presented here allows us to study the diffraction pattern produced by a combined effect of all three aberrations.

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