Theory of the Concave Grating I*†

The theory of the concave grating has been examined in considerable detail by methods of geometrical optics. The results derived by means of geometrical optics were checked by comparing them with those based on physical optics in special cases. The conditions for image formation and aberrations in the image may be expressed by equations somewhat different from those given by Beutler which are shown to be in error. The astigmatism and other aberrations are treated with respect to finite length of slit illumination, finite grating size and deviations of the optical components from the Rowland plane but still lying on the Rowland cylinder. Within certain limitations, it is shown that the aberrations present in an off-plane Eagle mounting may be corrected by a very small rotation of the slit in a plane perpendicular to the optic axis. The optimum width of the grating, instrumental line half-width, and resolving power of the grating are also discussed. Finally, the Beutler treatment of the concave grating is examined in detail and the important errors are pointed out.