Optimizing Czerny–Turner Spectrographs: A Comparison between Analytic Theory and Ray Tracing

The analytic theory of aberrations has been used to derive an expression for the magnitude of the coma width of the image in the meridional plane in a Czerny–Turner spectrograph with unequal mirror radii. The calculated properties of a 4-m spectrograph with equal radii and a recently constructed 3.34-m spectrograph with unequal radii are compared with the results obtained by tracing individual rays. The agreement is excellent, in contrast to the results of Chandler [ J. Opt. Soc. Am.58, 895 ( 1968)]. The lateral position of the grating for complete elimination of coma found experimentally with the 3.34-m instrument is in fair agreement with the theory. A correction to the 3 longitudinal grating position is given for a Czerny–Turner spectrograph which results in a flatter focal surface.