The torus grating is defined as a calotte of a circular torus bearing a grating ruling on its concave side. In contrast to the spherical grating, the torus grating is capable of eliminating astigmatism, in general, for two points in the spectrum. These two stigmatic points can be adjusted to any desired wave-length within a wide range of the spectrum by choosing suitable values for the angles of incidence and diffraction. In the rest of the spectrum produced by a torus grating, astigmatism is considerably smaller than that prevailing in spectra of spherical gratings. Moreover, astigmatism is negligible in the proximity of the two stigmatic points, giving rise to “quasi-stigmatic” ranges in the torus grating spectrum. The extension of these quasi-stigmatic ranges depends on the size of tolerable astigmatism. If based upon an astigmatism equal to the diffraction width of the spectral images, a quasi-stigmatic range can be wider than 1000A. With light sources of small size a considerable gain in spectral intensity results from the lack of astigmatism. The theory of the torus grating which has been attempted in this paper further demonstrates that coma, aberration, and curvature of spectral lines in the torus grating spectrum are generally smaller than the same image imperfections in the spectrum of the spherical grating.
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