Characterization of first-order optical properties for asymmetric systems

First-order imaging properties are often represented in the form of a derivative matrix. This representation is not always expedient, however, since the elements of the matrix are not all independent; some elements can be written as functions of the others. Ideally, the first-order imaging properties should be represented without any redundant (and, therefore, possibly inconsistent) information. Further, it is convenient to characterize these properties in terms of entities with direct geometric interpretations. Hamilton’s methods are used here to determine a minimal set of geometric entities that is sufficient to characterize the first-order imaging properties of asymmetric systems. Although certain aspects of this problem have been discussed elsewhere, a particular facet has been consistently misinterpreted. This issue is resolved here by establishing that there is no unique first-order image plane for any optical system—regardless of symmetry.