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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 65, Iss. 1 — Jan. 1, 1975
  • pp: 13–21

New stigmatic, coma-free, concave-grating spectrograph

John-David F. Bartoe and Guenter E. Brueckner  »View Author Affiliations

JOSA, Vol. 65, Issue 1, pp. 13-21 (1975)

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Tandem use of two classical concave gratings makes it possible to design a double-dispersion spectrograph that is essentially free of astigmatism and coma over a large wavelength range near normal incidence. The first grating is used as a Wadsworth collimator. Light of different wavelengths is dispersed by the Wadsworth collimator so that it illuminates different portions of the second grating. The second grating is placed so that it acts as a Wadsworth camera, in which the light bundle of a certain wavelength illuminating a particular section of the second grating is diffracted along the local normal of that section. In this way, the Wadsworth condition for stigmatic and coma-free imaging is almost fulfilled for all wavelengths. Only two reflecting surfaces are needed. The instrument is a double-dispersion spectrograph with additive dispersion. It does not use an intermediate slit, but has the stray-light-suppression characteristics of such a mount. A comparison of its imaging capabilities with other stigmatic concave-grating spectrographs is presented.

John-David F. Bartoe and Guenter E. Brueckner, "New stigmatic, coma-free, concave-grating spectrograph," J. Opt. Soc. Am. 65, 13-21 (1975)

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  1. A classical concave grating has grooves arranged on a segment of a spherical surface such that the projection of the grooves onto a plane tangent to the vertex of the surface forms straight, equally spaced lines.
  2. F. L. O. Wadsworth, Astrophys. J. 3, 54 (1896).
  3. T. Namioka, J. Opt. Soc. Am. 51, 4 (1961).
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  13. H. G. Beutler, J. Opt. Soc. Am. 35, 349 (1945).
  14. Equations (5) are based upon the assumption that the ruling density of the second grating G2 is constant along the circle R. In practice, this is not the case for a classical concave grating, for which the ruling density is constant along a straight line tangent to the vertex of the sphere. Therefore, for a large grating with a small radius of curvature, the image of a particular wavelength will not be located exactly on the local normal. This second-order effect results in a very small amount of astigmatism, which has not been included in our analytical treatment.
  15. H. G. Beutler, J. Opt. Soc. Am. 35, 319 (1945).
  16. J-D. F. Bartoe, An Analysis of Some Stigmatic Concave Grating Spectrographs, M. S. thesis (Georgetown University, Washington, D. C., 1973).
  17. J. Cordelle, J. Flamand, G. Pieuchard, and A. Labeyrie, in Proceedings of Eighth Congress of the International Commission for Optics, Reading, England, 1969.
  18. The coma of a Wadsworth mount using a spherical collimating mirror is given by [Equations] where Δp is the linear size of the coma measured along the horizontal focal plane, W is the grating width, R is the grating radius, α and β are the angles of incidence and diffraction for the grating, and β0 is the angle of diffraction at which the coma is zero. If β0 = 0, then the source point must be on the normal of the mirror and the coma computed from the equation for ΔP is due to the grating only. Under this condition, the equation for Δp also gives the coma for the tandem Wadsworth mount, because the source point is on the normal of the first grating. The angular size of the coma is then given by θc ≅ Δp/γ′2h. M. Seya and T. Namioka, Science of Light 16, 167 (1967).
  19. Warren J. Smith, Modern Optical Engineering (McGraw-Hill, New York, 1966), p. 387.
  20. The laser wavelength presently used for production of type III holographic gratings is 4880 Å. Thus m = 0.297.

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