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

Building on an earlier work on the nodal aberration theory of the 3rd-order aberrations [J. Opt. Soc. Am. A22, 1389 (2005)] and the first paper in this series on the nodal aberration theory of higher-order aberrations [J. Opt. Soc. Am. A26, 1090 (2009)], this paper continues the derivation and presentation of the intrinsic, characteristic, often multinodal geometry for each type/family of the 3rd- and 5th-order optical aberrations as categorized by parallel developments for rotationally symmetric optics. The first paper in this series on the higher-order terms developed the nodal properties of the spherical aberration family, including W(060), W(240M), and W(242), and for completeness 7th-order spherical aberration W(080). This second paper in the series develops and presents the intrinsic, characteristic, often multinodal properties of the family of comatic aberrations through 5th order, specifically W(151), W(331M), and W(333) [field-linear, 5th-order aperture coma; field-cubed, 3rd-order aperture coma; and field-cubed, elliptical coma (a 3rd-order in aperture 5th-order vector aberration)]. This paper will present the first derivations of trinodal aberrations by the author.