Ray-tracing model of a perfect lens compliant with Fermat’s principle: the Cardinal Lens

Abstract

When using ray tracing for optical system design, it is often the case that the designer would like to implement simplified versions of one or more compound lens groups. This could be the case during initial layout when idealized versions of such compound lenses are needed or, perhaps alternatively, to mimic a well-corrected commercially available lens for which the prescription details are unavailable. One option is to use a paraxial thin lens as a proxy for the actual lens group, but doing so will yield a layout that is not consistent with Fermat’s principle or the Abbe sine condition. For example, a paraxial lens version of a compound microscope objective typically produces the wrong numerical aperture for a given entrance pupil diameter, and vice versa. A better option is to use a lens model that provides perfect imaging for a specified paraxial magnification and obeys Fermat’s principle. A variant of the model can yield a perfect Fourier transform lens. In addition, it is desirable to implement an idealized thick lens in which the principal planes are separated by a user-specified distance. This paper presents such a model, referred to as the Cardinal Lens, with implementation in Zemax OpticStudio via a user-defined surface.