厚みのある乱視用眼鏡レンズに対するEqual-Astigmatismの条件

抄録

The general condition for “equal astigmatism” in Seidel region for a single lens used as a spectacle lens for correcting astigmatic vision have been deduced for a lens with a toric surface in front and a spherical in the rear. The condition takes the form of an equation of the 11th order with respect to the reciprocal of the radius of curvature of the lens surface in case when the thickness of the lens is finite and the object plane is at finite distance, while it is reduced to an equation of the 8 th order in case when the object plane is at infinity. Gleichen's condition for equal astigmatism for a thin lens with its object plane placed at infinity can readily be deduced as a special case of our general condition. Several examples of spectracle lenses for astigmatic eyes, designed from the solutions of our general equation as the starting values and later refined by fine correction, showed excellent performance of equal astigmatism within an angular field as large as 80°.