CAUSTIC WAVE ABERRATION THEORY FOR GENERAL OPTICAL SYSTEMS (LENS DESIGN, MERIT FUNCTIONS)

A new theory for evaluating the image properties of an optical system has been developed, using the caustic surfaces. Within the geometrical optics limit, a generalized wave front equation has been introduced in a new form that enables one to derive an exact formula for the wave aberration function. The wave aberration function has been evaluated for specific optical systems. These results have been compared to the corresponding values calculated by the third order aberration theory. A new technique for evaluating wave aberrations has been introduced. This technique is based upon the caustic surfaces of an optical system. The caustic wave aberration function has been evaluated for optical systems and shows very good agreement with the conventional wave aberration function. A caustic merit function, which measures the spread of the caustic surfaces from an ideal image point, has been introduced to minimize the aberrations of an optical system. Evaluation of this function requires a few rays to be traced through the optical system. For the singlet and doublet lenses, the caustic merit function has been compared to the RMS blur circle radius and the third order aberration theory as a function of the system variables and the field of view. For the triplet lens, the caustic merit function has been used to optimize several lenses. The resulting systems have been evaluated for several fields of view by comparing the RMS blur circle radius, transverse and wave aberration functions to the results obtained by conventional design of a similar triplet.; The present results are encouraging and suggest that increased use of the caustic surface in optical design can improve optical performance by reducing effects of higher order aberrations. In general, this new theory, caustic wave aberration theory, represents a strong bridge between the classical aberration theory and the caustic theory in geometrical optics.