Abstract

The most general optical system is considered, in which the object and image may also be curved surfaces. For each object point a base ray is chosen, whose intersection with the image surface defines the geometrical image point. It is shown that, with suitable choices of axes for the object and image spaces, principal azimuths always exist around the object space and image space parts of the base ray. These azimuths are such that, in a paraxial type approximation, rays entering with coordinates (XS,O) and (O,yT), respectively, emerge with coordinates (XS,O) and (O,yT). This theorem enables the definition of canonical entrance and exit pupil variables, (xS,yT) and (xS,yT), and object and image space variables, (GS,HT) and (GS,HT), such that the geometrical image of (GS,HT) is at GS=GS,HT=HT, and (for an isoplanatic image point) any finite aperture ray entering with coordinates (xS,yT) emerges with xS=xS,yT=yT. The analysis also leads to formulas for the two principal local magnifications of the image and to the sine condition for a general optical system. Both the geometrical and diffraction theory of image formation for a general optical system are in this manner shown to reduce to exactly the same forms as for an axially symmetric system. In Part 2, the necessary computing methods are obtained for the practical application of the theory.

© 1985 Optical Society of America

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