Multinodal fifth-order optical aberrations of optical systems without rotational symmetry: the astigmatic aberrations.

Building on earlier work on the nodal aberration theory of third-order aberrations and a subset of fifth-order terms, this paper presents the multinodal field dependence of the family of aberrations describing the shape of the medial focal surface (the focal surface upon which the minimum RMS wavefront error is measured) and the astigmatic aberrations with respect to this surface through the fifth order. Specifically, the multinodal field dependence for W(420M) and W₄₂₂ (the field-quartic medial surface and field-quartic astigmatism) are derived and presented as well as their influence on the magnitude and nodal field dependence of the companion lower-order terms, W(220M) and W₂₂₂. This paper provides the first derivations of field-quartic aberrations presented by the author in the refereed literature.