In the design of optical systems, it is expedient to consider only those systems that possess the desired first-order imaging properties. For asymmetric systems, however, the requisite methods for performing such a first-order layout have not been established. The foundations of suitable methods, based on the work of Hamilton, are developed here. The utility of these techniques is demonstrated by resolving a fundamental issue in the context of the characterization of first-order properties of optical systems. Specifically, it is well known that the smallest number of quantities required to characterize the first-order imaging properties of an asymmetric system is, at most, eleven, and it is established here that precisely eleven quantities are required in general. That is, there are no hidden constraints among these conventional quantities.

© 1992 Optical Society of America

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