ABERRATION FIELDS IN TILTED AND DECENTERED OPTICAL SYSTEMS

In the process of designing a lens, the designer is faced with two major tasks. One is to find a design that provides the required performance across the specified field. The second is to find the tolerances on the fabrication and alignment of the system during manufacture.; Currently, there are two distinct approaches to lens design. Some designers use aberration coefficients to construct a merit function for optimization and use the values of the coefficients to guide the design. Others use real rays to construct the merit function and ray fans to follow the progress of the design. In studying the effects of tilts and decenters on the ensuing design in order to determine the tolerances, both groups have been forced to use real ray analysis. This is because the wave aberration expansion used by designers assumes that the system being studied is rotationally symmetric. Tilts and decenters destroy this symmetry.; In this work a formulation of the wave aberration expansion is developed that accounts for the effects of tilts and decenters in the context of the aberration fields in an aligned system. Techniques for displaying the properties of the third and fifth order terms in the wave aberration expansion in a perturbed system are developed. The methods of display allow a designer who is well acquainted with the behavior of the terms in a rotationally symmetric system to envision their behavior in a perturbed system without being well acquainted with the theory that is developed.; Once the wave aberration expansion for the perturbed systems is developed, it is applied to calculating the rms wavefront error or the rms spot size in a perturbed system. The resulting analytic expressions are considerably faster than real ray calculations. The increase in speed makes it economical, for the first time, to evaluate image quality over the entire image plane in nonsymmetric systems. This is an important new tool for providing a complete picture of the effects of a set of arbitrarily oriented tilts and decenters on an optical design.; The theory that is developed allows the tilts and decenters to be arbitrarily oriented at any surface, i.e., they are not restricted to be either meridional or coplanar. This is accomplished by beginning the development with a vector formulation of the wave aberration expansion. This new form has some important implications even for aligned systems. In particular, it is shown that the sagittal and tangential focal surfaces located by a Coddington skew ray trace are not continuous in a misaligned system. There continue though, to be two continuous focal surfaces on which line imagery is obtained in the presence of pure astigmatism. These surfaces are found directly, in both perturbed and aligned systems, when the vector formulation is used. These surfaces are inherently more significant than the sagittal and tangential focal surfaces.; The expressions for describing the performance of a perturbed optical system are used to develop an interactive computer program that relies heavily on computer graphics to provide an efficient method of studying the effects of tilts and decenters on an optical design. The use of computer graphics greatly reduces the amount of output required to obtain a detailed picture of the response of the system to perturbations. The graphic routines are illustrated by studying the effects of tilts and decenters on a Ritchey-Chretien telescope and a triplet design.