Calculation of conic constants for thick lenses to get diffraction-limited images using 3rd order design and marginal skew ray tracing

Abstract

We calculate equations to obtain the exact and third-order design of thick lenses free from spherical and coma aberrations at two points, at the edge and center of the lens, considering the shape factor and the conic constants. We obtained analytical expressions based on the equality of the optical path and the Abbe sine condition calculated for an object located in infinite and finite positions. Examples developed with this method show an alternative way of designing diffraction-limited thick lenses that are equal or better than results obtained when the conic constants are optimized using commercial optical design software. As the shape of the lens changes, the spherical and coma aberrations vary; so, the presented method offers better results for shape factors ranging from −0.5 to 0.9.