GENERALIZED RAY TRACING, GENERALIZED BENDING, AND USE OF CAUSTIC SURFACES AS MERIT FUNCTIONS IN OPTICAL DESIGN

Generalized ray tracing is an algorithm for calculating the geometrical parameters of a wavefront in the neighborhood of a traced ray. These calculations are applied, surface by surface, for each traced ray, to an optical system being designed. These calculations determine the two points of contact of each traced ray with the two sheets of caustic surface. The caustic surfaces are, in fact, aberrated three-dimensional images of object points and therefore contain all information on the geometrical aberrations of the subject lens. Caustic surfaces can be thought of as three-dimensional geometrical point spread functions. Generalized bending is a procedure by which the curvature of a pair of adjacent spherical refracting surfaces, their spearation, and the distance to the next succeeding or next preceding surface may be changed so that any paraxial ray is left invariant except between the two affected surfaces. In this study we discuss some characteristics of generalized bending and also show that the displacement of a caustic point caused by a generalized bending is in essentially a straight line, that the direction of the displacement is determined by which refracting surfaces are selected, and that the magnitude of the displacement is proportional to the logarithm of the bending parameter. This suggests that caustic surfaces can be used as a merit function in the optical process, that the merit functions can be calculated by means of generalized ray tracing, and that generalized bending provides an effective means of optimizing the design when included in a feedback loop.