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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 59, Iss. 9 — Sep. 1, 1969
  • pp: 1189–1194

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

JOSEPH READER  »View Author Affiliations

JOSA, Vol. 59, Issue 9, pp. 1189-1194 (1969)

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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.

© 1969 Optical Society of America

JOSEPH READER, "Optimizing Czerny-Turner Spectrographs: A Comparison between Analytic Theory and Ray Tracing," J. Opt. Soc. Am. 59, 1189-1194 (1969)

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  1. M. Czerny and A. F. Turner, Z. Physik 61, 792 (1930).
  2. G. Chandler, J. Opt. Soc. Am. 58, 895 (1968).
  3. A. Shafer, L. Megill, and L. Droppleman, J. Opt. Soc. Am. 54, 879 (1964).
  4. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
  5. G. Rosendahl, J. Opt. Soc. Am. 52, 412 (1962).
  6. W. G. Fastie, U. S. Patent 3,011,391 (1961).
  7. S. A. Khrshanovskii, Opt. Spectry. (USSR) 9, 207 (1960).
  8. K. Mielenz, J. Res. Natl. Bur. Std. (U. S.) 68C, 205 (1964).
  9. The diameter of the camera mirror is determined by the requirement that the entire grating be visible from all points of the plate holder. This gives D>W cosβ + 2L(l-m/r).
  10. This change was necessitated by a statement in the Megill program which sets the direction cosines of the central ray relative to the x, y, and z axes equal to -1, 0, and 0, respectively. Thus, the central ray is assumed by the program to be parallel to the x axis. If the geometry is not changed, the calculated spot diagram and image width do not refer to rays which actually form the image. This is equivalent to tracing rays through a system that is different from the one specified by the input parameters.
  11. W. G. Fastie, private communication.

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