Abstract

Geometric theory of the grating is developed, with special emphasis on the relation between the properties of holographic gratings and those of mechanically ruled gratings. The theory is applicable to practically all types of holographic and mechanically ruled gratings, including aspheric gratings. General expressions are given for the effective grating constant, the grating equation, the focal curves, and the light-path function. Possible applications of the theory to the design of aberration-corrected gratings are also described.

© 1974 Optical Society of America

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  1. F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Koshelev, Opt. Spektrosk. 28, 790 (1970) [Opt. Spectrosc. 28, 423 (1970)].
  2. T. Harada (private communication, 1973).
  3. Y. Sakayanagi, Sci. Light (Tokyo) 3, 79 (1954/55).
  4. H. Haber, J. Opt. Soc. Am. 40, 153 (1950).
  5. H. Greiner and E. Schäffer, Optik 16, 288 (1959); Optik 16, 350 (1959).
  6. I. V. Peisakhson and I. N. Tarnakin, Zh. Prikl. Spektrosk. 1, 289 (1964); Zh. Prikl. Spektrosk. 2, 218 (1965).
  7. S. C. Miller, Special Report No. 2, Upper Air Laboratory, University of Colorado (1950).
  8. T. Namioka, J. Opt. Soc. Am. 51, 4 (1961); J. Opt. Soc. Am. 51, 13 (1961).
  9. B. E. Woodgate, J. Opt. Soc. Am. 64, 654 (1974).
  10. Yu. P. Shchepetkin, Opt. Spektrosk. 4, 383 (1958); Opt. Spektrosk. 4, 513 (1958).
  11. E. Schönheit, Optik 23, 305 (1966).
  12. S. A. Strezhnev and A. L. Andreeva, Opt. Spektrosk. 28, 796 (1970) [Opt, Spectrosc. 28, 426 (1970)].
  13. R. P. Madden and D. L. Ederer, J. Opt. Soc. Am. 62, 722 (1972).
  14. A. Cornu, C. R. Acad. Sci. (Paris) 80, 645 (1875); C. R. Acad. Sci. (Paris) 116, 1215 (1893); C. R. Acad. Sci. (Paris) 116, 1421 (1893); C. R. Acad. Sci. (Paris) 117, 1032 (1893).
  15. B. Gale, Opt. Acta 13, 41 (1966).
  16. Y. Sakayanagi, Sci. Light (Tokyo) 16, 129 (1967).
  17. Y. Sakayanagi, Sci. Light (Tokyo) 3, 1 (1954/55).
  18. M. V. R. K. Murty, J. Opt. Soc. Am. 52, 768 (1962).
  19. M. Singh and K. Majumder, Sci. Light (Tokyo) 18, 57 (1969).
  20. J. D. Baumgardner, Ph.D. thesis (University of Rochester, 1970).
  21. J. Cordelle, J. Flamand, G. Pieuchard, and A. Labeyrie, in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle, 1970), p. 117.
  22. M. V. R. K. Murty and N. C. Das, J. Opt. Soc. Am. 61, 1001 (1971).
  23. G. Pieuchard (private communication, 1972).
  24. T. Namioka and H. Noda, in Proceedings of International Symposium for Synchrotron Radiation Users, edited by G. V. Marr and I. H. Munro (Daresbury Nuclear Physics Laboratory, Daresbury, 1973), p. 51.
  25. T. Namioka, H. Noda, and M. Seya, Sci. Light (Tokyo) 22, 77 (1973).
  26. M. Pouey, C. R. Acad. Sci. (Paris) B276, 531 (1973).
  27. W. T. Welford, Opt. Acta 10, 121 (1963).
  28. M. Pouey, Opt. Commun. 2, 339 (1970).
  29. Commercial classification by Jobin-Yvon.

Harada, T.

T. Harada (private communication, 1973).

Pieuchard, G.

G. Pieuchard (private communication, 1972).

Andreeva, A. L.

S. A. Strezhnev and A. L. Andreeva, Opt. Spektrosk. 28, 796 (1970) [Opt, Spectrosc. 28, 426 (1970)].

Baumgardner, J. D.

J. D. Baumgardner, Ph.D. thesis (University of Rochester, 1970).

Cordelle, J.

J. Cordelle, J. Flamand, G. Pieuchard, and A. Labeyrie, in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle, 1970), p. 117.

Cornu, A.

A. Cornu, C. R. Acad. Sci. (Paris) 80, 645 (1875); C. R. Acad. Sci. (Paris) 116, 1215 (1893); C. R. Acad. Sci. (Paris) 116, 1421 (1893); C. R. Acad. Sci. (Paris) 117, 1032 (1893).

Das, N. C.

M. V. R. K. Murty and N. C. Das, J. Opt. Soc. Am. 61, 1001 (1971).

Ederer, D. L.

R. P. Madden and D. L. Ederer, J. Opt. Soc. Am. 62, 722 (1972).

Flamand, J.

J. Cordelle, J. Flamand, G. Pieuchard, and A. Labeyrie, in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle, 1970), p. 117.

Gale, B.

B. Gale, Opt. Acta 13, 41 (1966).

Gerasimov, F. M.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Koshelev, Opt. Spektrosk. 28, 790 (1970) [Opt. Spectrosc. 28, 423 (1970)].

Greiner, H.

H. Greiner and E. Schäffer, Optik 16, 288 (1959); Optik 16, 350 (1959).

Haber, H.

H. Haber, J. Opt. Soc. Am. 40, 153 (1950).

Koshelev, B. V.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Koshelev, Opt. Spektrosk. 28, 790 (1970) [Opt. Spectrosc. 28, 423 (1970)].

Labeyrie, A.

J. Cordelle, J. Flamand, G. Pieuchard, and A. Labeyrie, in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle, 1970), p. 117.

Madden, R. P.

R. P. Madden and D. L. Ederer, J. Opt. Soc. Am. 62, 722 (1972).

Majumder, K.

M. Singh and K. Majumder, Sci. Light (Tokyo) 18, 57 (1969).

Miller, S. C.

S. C. Miller, Special Report No. 2, Upper Air Laboratory, University of Colorado (1950).

Murty, M. V. R. K.

M. V. R. K. Murty and N. C. Das, J. Opt. Soc. Am. 61, 1001 (1971).

M. V. R. K. Murty, J. Opt. Soc. Am. 52, 768 (1962).

Namioka, T.

T. Namioka, J. Opt. Soc. Am. 51, 4 (1961); J. Opt. Soc. Am. 51, 13 (1961).

T. Namioka and H. Noda, in Proceedings of International Symposium for Synchrotron Radiation Users, edited by G. V. Marr and I. H. Munro (Daresbury Nuclear Physics Laboratory, Daresbury, 1973), p. 51.

T. Namioka, H. Noda, and M. Seya, Sci. Light (Tokyo) 22, 77 (1973).

Noda, H.

T. Namioka, H. Noda, and M. Seya, Sci. Light (Tokyo) 22, 77 (1973).

T. Namioka and H. Noda, in Proceedings of International Symposium for Synchrotron Radiation Users, edited by G. V. Marr and I. H. Munro (Daresbury Nuclear Physics Laboratory, Daresbury, 1973), p. 51.

Peisakhson, I. V.

I. V. Peisakhson and I. N. Tarnakin, Zh. Prikl. Spektrosk. 1, 289 (1964); Zh. Prikl. Spektrosk. 2, 218 (1965).

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Koshelev, Opt. Spektrosk. 28, 790 (1970) [Opt. Spectrosc. 28, 423 (1970)].

Pieuchard, G.

J. Cordelle, J. Flamand, G. Pieuchard, and A. Labeyrie, in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle, 1970), p. 117.

Pouey, M.

M. Pouey, Opt. Commun. 2, 339 (1970).

M. Pouey, C. R. Acad. Sci. (Paris) B276, 531 (1973).

Sakayanagi, Y.

Y. Sakayanagi, Sci. Light (Tokyo) 16, 129 (1967).

Y. Sakayanagi, Sci. Light (Tokyo) 3, 1 (1954/55).

Y. Sakayanagi, Sci. Light (Tokyo) 3, 79 (1954/55).

Schäffer, E.

H. Greiner and E. Schäffer, Optik 16, 288 (1959); Optik 16, 350 (1959).

Schönheit, E.

E. Schönheit, Optik 23, 305 (1966).

Seya, M.

T. Namioka, H. Noda, and M. Seya, Sci. Light (Tokyo) 22, 77 (1973).

Shchepetkin, Yu. P.

Yu. P. Shchepetkin, Opt. Spektrosk. 4, 383 (1958); Opt. Spektrosk. 4, 513 (1958).

Singh, M.

M. Singh and K. Majumder, Sci. Light (Tokyo) 18, 57 (1969).

Strezhnev, S. A.

S. A. Strezhnev and A. L. Andreeva, Opt. Spektrosk. 28, 796 (1970) [Opt, Spectrosc. 28, 426 (1970)].

Tarnakin, I. N.

I. V. Peisakhson and I. N. Tarnakin, Zh. Prikl. Spektrosk. 1, 289 (1964); Zh. Prikl. Spektrosk. 2, 218 (1965).

Welford, W. T.

W. T. Welford, Opt. Acta 10, 121 (1963).

Woodgate, B. E.

B. E. Woodgate, J. Opt. Soc. Am. 64, 654 (1974).

Yakovlev, E. A.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Koshelev, Opt. Spektrosk. 28, 790 (1970) [Opt. Spectrosc. 28, 423 (1970)].

Other (29)

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Koshelev, Opt. Spektrosk. 28, 790 (1970) [Opt. Spectrosc. 28, 423 (1970)].

T. Harada (private communication, 1973).

Y. Sakayanagi, Sci. Light (Tokyo) 3, 79 (1954/55).

H. Haber, J. Opt. Soc. Am. 40, 153 (1950).

H. Greiner and E. Schäffer, Optik 16, 288 (1959); Optik 16, 350 (1959).

I. V. Peisakhson and I. N. Tarnakin, Zh. Prikl. Spektrosk. 1, 289 (1964); Zh. Prikl. Spektrosk. 2, 218 (1965).

S. C. Miller, Special Report No. 2, Upper Air Laboratory, University of Colorado (1950).

T. Namioka, J. Opt. Soc. Am. 51, 4 (1961); J. Opt. Soc. Am. 51, 13 (1961).

B. E. Woodgate, J. Opt. Soc. Am. 64, 654 (1974).

Yu. P. Shchepetkin, Opt. Spektrosk. 4, 383 (1958); Opt. Spektrosk. 4, 513 (1958).

E. Schönheit, Optik 23, 305 (1966).

S. A. Strezhnev and A. L. Andreeva, Opt. Spektrosk. 28, 796 (1970) [Opt, Spectrosc. 28, 426 (1970)].

R. P. Madden and D. L. Ederer, J. Opt. Soc. Am. 62, 722 (1972).

A. Cornu, C. R. Acad. Sci. (Paris) 80, 645 (1875); C. R. Acad. Sci. (Paris) 116, 1215 (1893); C. R. Acad. Sci. (Paris) 116, 1421 (1893); C. R. Acad. Sci. (Paris) 117, 1032 (1893).

B. Gale, Opt. Acta 13, 41 (1966).

Y. Sakayanagi, Sci. Light (Tokyo) 16, 129 (1967).

Y. Sakayanagi, Sci. Light (Tokyo) 3, 1 (1954/55).

M. V. R. K. Murty, J. Opt. Soc. Am. 52, 768 (1962).

M. Singh and K. Majumder, Sci. Light (Tokyo) 18, 57 (1969).

J. D. Baumgardner, Ph.D. thesis (University of Rochester, 1970).

J. Cordelle, J. Flamand, G. Pieuchard, and A. Labeyrie, in Optical Instruments and Techniques, edited by J. Home Dickson (Oriel, Newcastle, 1970), p. 117.

M. V. R. K. Murty and N. C. Das, J. Opt. Soc. Am. 61, 1001 (1971).

G. Pieuchard (private communication, 1972).

T. Namioka and H. Noda, in Proceedings of International Symposium for Synchrotron Radiation Users, edited by G. V. Marr and I. H. Munro (Daresbury Nuclear Physics Laboratory, Daresbury, 1973), p. 51.

T. Namioka, H. Noda, and M. Seya, Sci. Light (Tokyo) 22, 77 (1973).

M. Pouey, C. R. Acad. Sci. (Paris) B276, 531 (1973).

W. T. Welford, Opt. Acta 10, 121 (1963).

M. Pouey, Opt. Commun. 2, 339 (1970).

Commercial classification by Jobin-Yvon.

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