METHOD OF SOLVING A TRIPLET COMPRISING A SINGLET AND A CEMENTED DOUBLET WITH GIVEN PRIMARY ABERRATIONS

A simple algebraic algorithm is proposed as a computational tool for t he thin-lens design of a triplet which consists of a singlet and a cem ented doublet. The triplet is required to yield specified amounts of l ens power, primary spherical aberration, central coma, longitudinal ch romatic aberration and secondary spectrum. The three element powers of the triplet are first obtained by solving the simultaneous linear equ ations 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 shape s are then obtained by solving this quadratic equation. The solving pr ocess is purely algebraic and is therefore easy to calculate and guara ntees that all the solutions can be found.