Exact relations between wave aberration and the sagitta difference, and between ray aberration and the slope difference

From parametric forms for the normal lines of the aberrated wavefront and the reference sphere we write in exact form the wave aberration as the sagitta difference, and the ray aberration as the slope difference. It is shown that the accuracy in the approximate equations of aberration, depends on the effective F/#F/# of the optical system besides how much smaller the wave aberration is than the radius of the reference sphere. We find that the errors in the approximations do not depend on the shape of the aberrated wavefront.