Abstract

We describe the aberrations of diffraction gratings without any restrictions on the symmetry of the substrate, the curvature of the grooves, or the position of the entrance slit. The theory can also be applied to holographic gratings, holographic lenses, synthetic holograms, zone plates, and other diffracting instruments. The description comprises second-order focusing conditions, including the generalization of the Rowland circle and the conditions for astigmatism, length, slope, and curvature of the focal lines, comatic and fourth-order aberrations. In particular we show the relations between the aberrations óf second and higher orders. The theory is applied in this paper to astigmatic mountings of the Rowland type, and to mountings of the Wadsworth and Eagle type that we call anastigmatic. We give special attention to the conditions for freedom of coma of anastigmatic mountings.

© 1976 Optical Society of America

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  1. W. Werner, Appl. Opt. 6, 1691 (1967).
  2. W. Werner, thesis (Delft, 1970) (unpublished).
  3. H. Noda, T. Namioka, and M. Seya, J. Opt. Soc. Am. 64, 1031 (1974).
  4. F. Zernike, in Festschrift, Pieter Zeeman (Martinus Nijhoff, The Hague, 1935), p. 323.
  5. H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).
  6. T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).
  7. G. Stroke, Handbuch der Physik XXIX (Springer, Berlin, 1967), p. 447.
  8. W. T. Welford, Progress in Optics, Vol. IV (North-Holland, Amsterdam, 1965).
  9. G. S. Monk, Light, Principles and Experiments, 1st ed. (McGraw-Hill, New York, 1937), p. 424.
  10. A. Danielson and P. Lindblom, Optik 41, 441 (1974).
  11. A. Danielson and P. Lindblom, Optik 41, 465 (1975).
  12. M. Pouey, J. Opt. Soc. Am. 64, 1616 (1974).

Beutler, H. G.

H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).

Danielson, A.

A. Danielson and P. Lindblom, Optik 41, 465 (1975).

A. Danielson and P. Lindblom, Optik 41, 441 (1974).

Lindblom, P.

A. Danielson and P. Lindblom, Optik 41, 441 (1974).

A. Danielson and P. Lindblom, Optik 41, 465 (1975).

Monk, G. S.

G. S. Monk, Light, Principles and Experiments, 1st ed. (McGraw-Hill, New York, 1937), p. 424.

Namioka, T.

T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).

H. Noda, T. Namioka, and M. Seya, J. Opt. Soc. Am. 64, 1031 (1974).

Noda, H.

H. Noda, T. Namioka, and M. Seya, J. Opt. Soc. Am. 64, 1031 (1974).

Pouey, M.

M. Pouey, J. Opt. Soc. Am. 64, 1616 (1974).

Seya, M.

H. Noda, T. Namioka, and M. Seya, J. Opt. Soc. Am. 64, 1031 (1974).

Stroke, G.

G. Stroke, Handbuch der Physik XXIX (Springer, Berlin, 1967), p. 447.

Welford, W. T.

W. T. Welford, Progress in Optics, Vol. IV (North-Holland, Amsterdam, 1965).

Werner, W.

W. Werner, Appl. Opt. 6, 1691 (1967).

W. Werner, thesis (Delft, 1970) (unpublished).

Zernike, F.

F. Zernike, in Festschrift, Pieter Zeeman (Martinus Nijhoff, The Hague, 1935), p. 323.

Other (12)

W. Werner, Appl. Opt. 6, 1691 (1967).

W. Werner, thesis (Delft, 1970) (unpublished).

H. Noda, T. Namioka, and M. Seya, J. Opt. Soc. Am. 64, 1031 (1974).

F. Zernike, in Festschrift, Pieter Zeeman (Martinus Nijhoff, The Hague, 1935), p. 323.

H. G. Beutler, J. Opt. Soc. Am. 35, 311 (1945).

T. Namioka, J. Opt. Soc. Am. 49, 446 (1959).

G. Stroke, Handbuch der Physik XXIX (Springer, Berlin, 1967), p. 447.

W. T. Welford, Progress in Optics, Vol. IV (North-Holland, Amsterdam, 1965).

G. S. Monk, Light, Principles and Experiments, 1st ed. (McGraw-Hill, New York, 1937), p. 424.

A. Danielson and P. Lindblom, Optik 41, 441 (1974).

A. Danielson and P. Lindblom, Optik 41, 465 (1975).

M. Pouey, J. Opt. Soc. Am. 64, 1616 (1974).

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