Abstract

An elegant and comprehensive treatment of image formation by a general optical system is shown to be possible by the use of Hamilton’s method. Lagrange’s theorem is used to show how the eikonal, or angle characteristic function, can be calculated for a single refracting or reflecting surface and for an optical system composed of an arbitrary number of elements. We review the imaging properties of a general system in the linear approximation and show how the aberrations of second and third order can be calculated. We consider briefly the influence of symmetry on the type and number of aberrations. We give a simple deviation of the optical cosine condition of Smith and show how it is related to the imaging properties of the system.

© 1987 Optical Society of America

Characteristic functions and the aberrations of symmetric optical systems. I. Transverse aberrations when the eikonal is given

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