We generalize the transfer matrix <i>ABCD</i> theorem for paraxial rays of the optical system to skew rays propagated off axis, whether or not the system possesses rotational symmetry. Furthermore, we apply the generalized <i>ABCD</i> theorem to evaluate the diffraction integral matrix elements <i>A</i>–<i>D</i> expressed in terms of the angle eikonal <i>T</i>, with the primary aberrations included. Finally, analysis and numerical calculation are given for propagation of a light beam through the optical system in the case in which spherical aberration and coma are present.
© 2004 Optical Society of America
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(080.1010) Geometric optics : Aberrations (global)
(080.2730) Geometric optics : Matrix methods in paraxial optics
(260.0260) Physical optics : Physical optics
Chaoying Zhao, Weihan Tan, and Qizhi Guo, "Generalized optical ABCD theorem and its application to the diffraction integral calculation," J. Opt. Soc. Am. A 21, 2154-2163 (2004)