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The imaging properties of aspherical diffraction gratings that have curved and variable spacing grooves are studied theoretically for simple rotational mountings. Methods for eliminating aberrations are examined by clarifying the relations of both the shape of the grating surface and the pattern of the grooves to the individual aberrations, such as astigmatism, coma, and curvature. Application of the methods to the Seya-Namioka mounting shows (i) a spherical grating with straight grooves of variable spacing, designed for elimination of coma, can give very sharp images over a wide spectral range; and (ii) a torus grating with curved grooves of variable spacing can give stigmatic images without serious image broadening. Therefore, resolution can be much improved in both spherical and torus gratings compared with those having conventional (straight and constant spacing) grooves.
Iwanaga et al. (1979) studied this question.