Abstract
A ray-tracing computer programme has been developed to analyse and design Ebert spectrometers. Using this programme the author has found families of spectrometers that have no astigmatism or coma. In general these spectrometers are usable over only a narrow spectral range, but special cases were found that are suitable for use as scanning monochromators. The monochromators are corrected for these aberrations at all wavelengths, but they require auxiliary folding mirrors. The good performance of the monochromators is due to zero incidence angles of the chief ray at both reflections from the spherical mirror.

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