Method of solving triplets consisting of a singlet and air-spaced doublet with given primary aberrations

Abstract

An effective algebraic algorithm is proposed as a computational tool for solving the thin-lens structure of a triplet which consists of a singlet and an air-spaced doublet. The triplet is required to yield specified amounts of lens power and four primary aberrations: spherical aberration, coma, longitudinal chromatic aberration and secondary spectrum. In addition, the air spacing is used to control the zonal spherical aberration and spherochromatism. The problem is solved in the following manner. First, the equations for power and chromatic aberration are combined into a quartic polynomial equation if the object is at a finite distance, or combined into a quadratic polynomial equation if the object is at infinity. The roots give the element powers. Second, the lens shapes are obtained by solving the quartic polynomial equation which is obtained by combining the equations of spherical aberration and coma. Since quartic and quadratic equations can be solved using simple algebraic methods, the algorithm is rapid and guarantees that all the lens forms can be found.