Optimization of three and four-element lens systems by minimizing the caustic merit function

For an imaging optical system, it is, in general, desirable to transform a collection of point sources of light into point images distributed over the focal plane with the appropriate magnification. In practice, this is achieved by varying the lens system parameters (radii of curvature, lens spacings, and indicies of refraction) such that the spread of a bundle of rays from each object point over the image plane has been minimized. Traditionally, optical design is performed by minimizing a merit function based on the spread of rays over the image plane or the deviation of the image wavefront from a reference spherical wavefront. In this study, the caustic surfaces, which are the loci of the wavefront centers of curvature, are used to construct a merit function that describe the spread of the caustic surfaces from an ideal image point. A generalized ray tracing algorithm has been used to calculate the principal radii of curvature of the wavefront for a bundle of rays passing through the optical system. From the generalized ray tracing algorithm, the caustic surfaces can be determined and provide important information about the structure of the image which is used in this study for lens design and analysis.; The caustic merit function has been used to optimize a large collection of three and four-element lenses. The performance of the optimized systems has been evaluated for different field angles by comparing the RMS blur circle radii with systems designed by conventional techniques. Results indicate that minimizing the caustic merit function reduces the RMS blur radii over the field of view and the total aberrations of the lens system when a few rays are traced through the system. During the optimization process, the caustic merit function has been minimized by varying the system parameters subject to the constraint of constant total focal length for the lens. A quasi-Newton algorithm has been used as the optimization technique.