Caustic merit function for optical design

Abstract

The two caustic surfaces, which are in turn the loci of the image points, are formed in the image region by each element of the source of an optical system. Lens optimization is achieved herein by adjusting parameters so that the caustic surfaces formed by rays from selected points of the object coalesce and converge to the corresponding Gaussian image points. A merit function, specifying the sum of the distances between each caustic surface and the corresponding Gaussians image, is defined and minimized subject to the constraints that the system focal length and physical length are constant and that the third-order aberrations of the system are zero. An optimization procedure, based on minimizing the caustic merit function, is used to design a singlet, doublet, and triplet lens system.