METHOD OF SOLVING TRIPLETS CONSISTING OF A SINGLET AND AIR-SPACED DOUBLET WITH GIVEN PRIMARY ABERRATIONS

An effective algebraic algorithm is proposed as a computational tool f or solving the thin-lens structure of a triplet which consists of a si nglet and an air-spaced doublet. The triplet is required to yield spec ified amounts of lens power and four primary aberrations: spherical ab erration, coma, longitudinal chromatic aberration and secondary spectr um. In addition, the air spacing is used to control the zonal spherica l aberration and spherochromatism. The problem is solved in the follow ing manner. First, the equations for power and chromatic aberration ar e combined into a quartic polynomial equation if the object is at a fi nite 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 w hich is obtained by combining the equations of spherical aberration an d coma. Since quartic and quadratic equations can be solved using simp le algebraic methods, the algorithm is rapid and guarantees that all t he lens forms can be found.