Aspheric wave-front recording optics for holographic gratings

The geometric theory of aspheric wave-front recording optics is extended to include the fourth-order groove parameters that correspond to the fourth-order holographic terms in the light-path function. We derived explicit expressions of the groove parameters by analytically following an exact ray-tracing procedure for a double-element optical system that consists of a point source, an ellipsoidal mirror, and an ellipsoidal grating blank. Design examples of holographic gratings for an in-plane Eagle-type vacuum-UV monochromator are given to demonstrate the capability of the present theory in the design of aspheric wave-front recording optics.