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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 62, Iss. 6 — Jun. 1, 1972
  • pp: 756–762

Theory of the Two-Mirror Plane-Grating Spectrograph

PETER LINDBLOM  »View Author Affiliations


JOSA, Vol. 62, Issue 6, pp. 756-762 (1972)
http://dx.doi.org/10.1364/JOSA.62.000756


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Abstract

The central-ray aberrations of the two-mirror plane-grating spectrograph are studied in three dimensions. Two mounts are discussed. Astigmatism is found to be reduced in both mounts by a reduction of the ruled length of the grating and/or by reduction of the mirror-tilt angles. When the rulings are orthogonal to the meridional plane, the coma-free condition from the two-dimensional theory is found not to eliminate horizontal coma completely; the residual coma is reduced by the same arrangements that will reduce astigmatism and by placing the mirrors close to each other. For the case in which the rulings are parallel with the meridional plane, an expression for complete elimination of horizontal coma in the central image is given. In both mounts, the conditions for elimination of coma should be satisfied by variation of the curvatures of the mirrors while the tilt angles should be kept as small as possible. Criteria for elimination of astigmatism and spherical aberration are also given.

Citation
PETER LINDBLOM, "Theory of the Two-Mirror Plane-Grating Spectrograph," J. Opt. Soc. Am. 62, 756-762 (1972)
http://www.opticsinfobase.org/josa/abstract.cfm?URI=josa-62-6-756


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References

  1. M. Czerny and A. F. Turner, Z. Physik 61, 792 (1930).
  2. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
  3. T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).
  4. A. B. Shafer, L. R. Megill, and L. Dropplemann, J. Opt. Soc. Am. 54, 879 (1964).
  5. C. D. Allemand, J. Opt. Soc. Am. 58, 159 (1968).
  6. J. Reader, J. Opt. Soc. Am. 59, 1189 (1969).
  7. D. J. Schroeder, Appl. Opt. 6, 1976 (1967).
  8. See Fig. 4 in Ref. 4.
  9. A similar expression has been given in Ref. 4, which is an approximation of Eq. (38). The expression for the spherical aberration given in Ref. 5 is, however, believed to be incomplete, probably because of errors in the higher-order terms of the Beutler expansion of the light-path function.

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