Abstract

The ability to factor expressions for the back focal distance and magnification of a multielement optical system in terms of the element powers and separations provides a simple means of investigating the dependence of the first-order optical properties (and their chromatic variations) on the system parameters. The Gaussian bracket expressions for the first-order properties of multielement systems consist of products and sums of the expressions for the elements rather than continued fractions. By examining the structure of the Gaussian bracket expressions for an arbitrary system, conclusions of a general nature may be formed. A rigorous proof is given that any achromatic image of a real object which is formed by an all-holographic imaging system must be virtual regardless of the number of holographic elements in the system. Also, a three-hologram imaging system is derived from the theory, and it Is shown to be the only three-element solution which is corrected for the chromatic difference of magnification and both primary and secondary longitudinal chromatic aberration. Although this solution has previously been found through other means, it was not known to be the only solution.

© 1987 Optical Society of America