The Transmission of Waves Through A Symmetric Optical Instrument.

Gaussian Parameter Method of Studying the Transmission of a Wave Surface through a Centered System of Symmetric Lenses.—Since for each point of an incident wave surface there is a corresponding point on the refracting surface, the parameter $\alpha$ of the refracting surface may be expressed in terms of the parameter $\beta$ of the wave surface, thus allowing the elimination of the parameter $\beta$. After expressing all quantities in terms of $\alpha$, certain invariant combinations are found among the coefficients of the wave and lens surfaces, these furnishing the determination of the refracted surface. This gives a point by point correspondence between all surfaces of the system. As an application, the focal distance and longitudinal aberration are calculated and a numerical case given. The method is applicable to aspherical surfaces as simply as to spherical ones, and it is hoped that many problems in practical optics may be simplified by the present method, combined with proper choices of the parameter.