Method of solving a triplet comprising a singlet and a cemented doublet with given primary aberrations

Abstract

A simple algebraic algorithm is proposed as a computational tool for the thin-lens design of a triplet which consists of a singlet and a cemented doublet. The triplet is required to yield specified amounts of lens power, primary spherical aberration, central coma, longitudinal chromatic aberration and secondary spectrum. The three element powers of the triplet are first obtained by solving the simultaneous linear equations of the total lens power, longitudinal chromatic aberration and secondary spectrum. A quadratic equation is obtained by combining the equations of spherical aberration and central coma, and the lens shapes are then obtained by solving this quadratic equation. The solving process is purely algebraic and is therefore easy to calculate and guarantees that all the solutions can be found.