An investigation into consequences of classifying orthogonal aberrations by degree.

Abstract

The motivation for this research stems from the optical design problem. From a mathematical perspective the problem can be stated as follows: given a starting optical configuration and a set of variable parameters, determine the specific configuration which yields the global minimum of the merit function which represents the imaging quality of the system. Currently, no satisfactory solution to this problem has been found, although a process called "simulated annealing" has shown some potential. The idea behind this research is that perhaps a merit function can be constructed in such a way that information contained in higher order polychromatic aberration coefficients can be used to indicate the region of the global minimum. In pursuit of this, the construction of two physically significant merit functions (the wavefront variance and the mean square ray aberration) is formulated in such a way as to allow the segregation of aberration coefficients by order within the merit function. This suggests a sequence of merit "subfunctions" can be constructed in such a way that each member of the sequence is associated with a particular order of aberration, and that the sequence itself converges to the complete merit function. In order to compute the polychromatic aberration coefficients needed to construct the merit functions, an algorithmic approach to proximate ray tracing is developed. This is shown to be an extension of the original form of proximate ray tracing and has proved highly successful in the computation of polychromatic aberration coefficients. The behavior of three optical systems with respect to their effective design parameters is then investigated. The investigation takes the form of topographic maps of the merit subfunctions. A study of the maps reveals that the global topography of the subfunctions remains relatively invariant with respect to order. Also, any minima present tend to remain relatively stationary with respect to order, although any particular one can slowly migrate within some small region of parameter space.