Meaning of first-order optics

Abstract

The concept of first-order properties of axially symmetric optical systems is well known. Of course, the same concept is fundamental in the context of nonaxially symmetric systems. To determine the first-order properties of a system, it is common to perform a differential ray trace, the results of which are conveniently represented in the form of a derivative matrix. From this matrix, any first-order property (e.g., focal length and magnification) of the system can be determined. For imaging systems, one important property is the location of the first-order image. For axially symmetric systems, the derivative matrix can be used to determine the position of the image of the axial point of the object. However, the location of the firstorder image of any other point on the object cannot be determined uniquely. Consequently, there is never a unique paraxial image plane. This concept and its extension to the nonaxially symmetric case are discussed. Although the extension is straightforward, it has caused some confusion in the literature (e.g., see Ref. 1 and the references cited therein). The aspects of the problem that have contributed to this confusion are addressed in an attempt to shed some light on this situation.