Aberrations of holographic toroidal grating systems

Expressions are derived for the sixteen wave front aberration coefficients of a single grating. These give the wave aberrations to the fourth order for a plane symmetric grating system. The contributions from each mirror and grating can be added to give the aberrations in the final image. Problems encountered with intermediate astigmatic images are overcome by defining the wave front aberration with respect to an astigmatic reference surface. There is one field variable describing displacement of the object point from the symmetry plane. The aperture stop may be placed anywhere in the system, and equations are given for the aberration changes produced by sifting this position.