Abstract

The imaging properties of aspherical diffraction gratings that have curved and variable spacing grooves are studied theoretically for simple rotational mountings. Methods for eliminating aberrations are examined by clarifying the relations of both the shape of the grating surface and the pattern of the grooves to the individual aberrations, such as astigmatism, coma, and curvature. Application of the methods to the Seya-Namioka mounting shows (i) a spherical grating with straight grooves of variable spacing, designed for elimination of coma, can give very sharp images over a wide spectral range; and (ii) a torus grating with curved grooves of variable spacing can give stigmatic images without serious image broadening. Therefore, resolution can be much improved in both spherical and torus gratings compared with those having conventional (straight and constant spacing) grooves.

© 1979 Optical Society of America

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  1. E. Schönheit, "Ein Seya-Namioka-Monochromator mit torischem Gitter für Photoionisations-Messungen," Optik (Stuttgart) 23, 305–312(1966).
  2. S. A. Strezhnev and A. L. Andreeva, "Toroidal diffraction gratings for Seya-Namioka monochromators," Opt. Spectrosc. 28, 426–428 (1970).
  3. R. J. Speer, "A comparative review of grazing incidence gratings, including recent measurements on the performance of stigmatic soft x-ray reflection gratings formed holographically," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 53–60(1974); R. J. Speer, D. Turner, R. L. Johnson, D. Rudolph, and G. Schmahl, "Holographically formed grazing-incidence reflection grating with stigmatic soft x-ray focal isolation", Appl. Opt. 13, 1258–1261 (1974).
  4. M. V. R. K. Murty, "Spherical zone-plate diffraction grating," J. Opt. Soc. Am. 50, 923(1960).
  5. Y. Sakayanagi, "A stigmatic concave grating with varying spacing," Sci. Light (Tokyo) 16, 129–137(1967); Y. Sakayanagi, "Theory of grating with circular grooves (curved grating)," Sci. Light (Tokyo) 3, 1–4(1954); Y. Sakayanagi, "Ruling of a curved grating," Sci. Light (Tokyo) 3, 79–83(1955).
  6. F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Kashelev, "Concave diffraction gratings with variable spacing," Opt. Spectrosc. 28, 423–426(1970).
  7. T. Namioka, H. Noda, and M. Seya, "Possibility of using the holograhic concave grating in vacuum monochromators," Sci. Light (Tokyo) 22, 77–99(1073); T. Namioka, M. Seya, and H. Noda, "Design and performance of holographic concave gratings," Jpn. J. Appl. Phys. 15, 1181–1197(1976).
  8. M. Pouey, "Imaging properties of ruled and holographic gratings," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 67–81(1974).
  9. M. V. R. K. Murty and N. C. Das, "Theory of certain diffraction gratings produced by the holographic method," J. Opt. Soc. Am. 61, 1001–1006 (1971).
  10. H. Noda, T. Namioka and M. Seya, "Geometric theory of the grating," J. Opt. Soc. Am. 64, 1031–1036(1974).
  11. C. H. F. Velzel, "On the imaging properties of holographic gratings,".J. Opt. Soc. Am. 67, 1021–1027(1977).
  12. Jobin Yvon Optical Systems, Diffraction gratings—ruled and holographic(Jobin Yvon Optical Systems, Metuchen, 1973), pp. 17–27.
  13. H. Noda, T. Namioka, and M. Seya, "Design of holographic concave gratings for Seya-Namioka monochromator," J. Opt. Soc. Am. 64, 1043–1048(1974); H. Noda, T. Namioka, and M. Seya, "Aberration-reduced holographic concave gratings for Seya-Namioka monochromators," Jpn. J. Appl. Phys. 14, Suppl. 1, 187– 191(1975).
  14. T. Harada, S. Moriyama, and T. Kita, "Mechanically ruled stigmatic concave gratings," Jpn. J. Appl. Phys. 14, Suppl. 1, 175–179 (1975).
  15. D. Llepère, "Monochromateur a simple rotation du rèseau, a rèseau holographique sur support torique pour l'ultraviolet lointain," Nouv. Rev. Opt. 6, 173–178(1975).
  16. F. Masuda, H. Noda, and T. Namioka, "Design and performance of toroidal holographic gratings," J. Spectrosc. Soc. Jpn 27, 211–223 (1978).
  17. T. Namioka, "Theory of the concave grating. III. Seya-Namioka monochromator," J. Opt. Soc. Am. 49, 951–961(1959).

1978 (1)

F. Masuda, H. Noda, and T. Namioka, "Design and performance of toroidal holographic gratings," J. Spectrosc. Soc. Jpn 27, 211–223 (1978).

1977 (1)

1975 (2)

T. Harada, S. Moriyama, and T. Kita, "Mechanically ruled stigmatic concave gratings," Jpn. J. Appl. Phys. 14, Suppl. 1, 175–179 (1975).

D. Llepère, "Monochromateur a simple rotation du rèseau, a rèseau holographique sur support torique pour l'ultraviolet lointain," Nouv. Rev. Opt. 6, 173–178(1975).

1974 (4)

H. Noda, T. Namioka, and M. Seya, "Design of holographic concave gratings for Seya-Namioka monochromator," J. Opt. Soc. Am. 64, 1043–1048(1974); H. Noda, T. Namioka, and M. Seya, "Aberration-reduced holographic concave gratings for Seya-Namioka monochromators," Jpn. J. Appl. Phys. 14, Suppl. 1, 187– 191(1975).

H. Noda, T. Namioka and M. Seya, "Geometric theory of the grating," J. Opt. Soc. Am. 64, 1031–1036(1974).

R. J. Speer, "A comparative review of grazing incidence gratings, including recent measurements on the performance of stigmatic soft x-ray reflection gratings formed holographically," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 53–60(1974); R. J. Speer, D. Turner, R. L. Johnson, D. Rudolph, and G. Schmahl, "Holographically formed grazing-incidence reflection grating with stigmatic soft x-ray focal isolation", Appl. Opt. 13, 1258–1261 (1974).

M. Pouey, "Imaging properties of ruled and holographic gratings," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 67–81(1974).

1971 (1)

1970 (2)

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Kashelev, "Concave diffraction gratings with variable spacing," Opt. Spectrosc. 28, 423–426(1970).

S. A. Strezhnev and A. L. Andreeva, "Toroidal diffraction gratings for Seya-Namioka monochromators," Opt. Spectrosc. 28, 426–428 (1970).

1967 (1)

Y. Sakayanagi, "A stigmatic concave grating with varying spacing," Sci. Light (Tokyo) 16, 129–137(1967); Y. Sakayanagi, "Theory of grating with circular grooves (curved grating)," Sci. Light (Tokyo) 3, 1–4(1954); Y. Sakayanagi, "Ruling of a curved grating," Sci. Light (Tokyo) 3, 79–83(1955).

1966 (1)

E. Schönheit, "Ein Seya-Namioka-Monochromator mit torischem Gitter für Photoionisations-Messungen," Optik (Stuttgart) 23, 305–312(1966).

1960 (1)

1959 (1)

1073 (1)

T. Namioka, H. Noda, and M. Seya, "Possibility of using the holograhic concave grating in vacuum monochromators," Sci. Light (Tokyo) 22, 77–99(1073); T. Namioka, M. Seya, and H. Noda, "Design and performance of holographic concave gratings," Jpn. J. Appl. Phys. 15, 1181–1197(1976).

Andreeva, A. L.

S. A. Strezhnev and A. L. Andreeva, "Toroidal diffraction gratings for Seya-Namioka monochromators," Opt. Spectrosc. 28, 426–428 (1970).

Das, N. C.

Gerasimov, F. M.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Kashelev, "Concave diffraction gratings with variable spacing," Opt. Spectrosc. 28, 423–426(1970).

Harada, T.

T. Harada, S. Moriyama, and T. Kita, "Mechanically ruled stigmatic concave gratings," Jpn. J. Appl. Phys. 14, Suppl. 1, 175–179 (1975).

Kashelev, B. V.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Kashelev, "Concave diffraction gratings with variable spacing," Opt. Spectrosc. 28, 423–426(1970).

Kita, T.

T. Harada, S. Moriyama, and T. Kita, "Mechanically ruled stigmatic concave gratings," Jpn. J. Appl. Phys. 14, Suppl. 1, 175–179 (1975).

Lepère, D

D. Llepère, "Monochromateur a simple rotation du rèseau, a rèseau holographique sur support torique pour l'ultraviolet lointain," Nouv. Rev. Opt. 6, 173–178(1975).

Masuda, F.

F. Masuda, H. Noda, and T. Namioka, "Design and performance of toroidal holographic gratings," J. Spectrosc. Soc. Jpn 27, 211–223 (1978).

Moriyama, S.

T. Harada, S. Moriyama, and T. Kita, "Mechanically ruled stigmatic concave gratings," Jpn. J. Appl. Phys. 14, Suppl. 1, 175–179 (1975).

Murty, M. V. R. K.

Namioka, T.

F. Masuda, H. Noda, and T. Namioka, "Design and performance of toroidal holographic gratings," J. Spectrosc. Soc. Jpn 27, 211–223 (1978).

H. Noda, T. Namioka and M. Seya, "Geometric theory of the grating," J. Opt. Soc. Am. 64, 1031–1036(1974).

H. Noda, T. Namioka, and M. Seya, "Design of holographic concave gratings for Seya-Namioka monochromator," J. Opt. Soc. Am. 64, 1043–1048(1974); H. Noda, T. Namioka, and M. Seya, "Aberration-reduced holographic concave gratings for Seya-Namioka monochromators," Jpn. J. Appl. Phys. 14, Suppl. 1, 187– 191(1975).

T. Namioka, "Theory of the concave grating. III. Seya-Namioka monochromator," J. Opt. Soc. Am. 49, 951–961(1959).

T. Namioka, H. Noda, and M. Seya, "Possibility of using the holograhic concave grating in vacuum monochromators," Sci. Light (Tokyo) 22, 77–99(1073); T. Namioka, M. Seya, and H. Noda, "Design and performance of holographic concave gratings," Jpn. J. Appl. Phys. 15, 1181–1197(1976).

Noda, H.

F. Masuda, H. Noda, and T. Namioka, "Design and performance of toroidal holographic gratings," J. Spectrosc. Soc. Jpn 27, 211–223 (1978).

H. Noda, T. Namioka, and M. Seya, "Design of holographic concave gratings for Seya-Namioka monochromator," J. Opt. Soc. Am. 64, 1043–1048(1974); H. Noda, T. Namioka, and M. Seya, "Aberration-reduced holographic concave gratings for Seya-Namioka monochromators," Jpn. J. Appl. Phys. 14, Suppl. 1, 187– 191(1975).

H. Noda, T. Namioka and M. Seya, "Geometric theory of the grating," J. Opt. Soc. Am. 64, 1031–1036(1974).

T. Namioka, H. Noda, and M. Seya, "Possibility of using the holograhic concave grating in vacuum monochromators," Sci. Light (Tokyo) 22, 77–99(1073); T. Namioka, M. Seya, and H. Noda, "Design and performance of holographic concave gratings," Jpn. J. Appl. Phys. 15, 1181–1197(1976).

Peisakhson, I. V.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Kashelev, "Concave diffraction gratings with variable spacing," Opt. Spectrosc. 28, 423–426(1970).

Pouey, M.

M. Pouey, "Imaging properties of ruled and holographic gratings," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 67–81(1974).

Sakayanagi, Y.

Y. Sakayanagi, "A stigmatic concave grating with varying spacing," Sci. Light (Tokyo) 16, 129–137(1967); Y. Sakayanagi, "Theory of grating with circular grooves (curved grating)," Sci. Light (Tokyo) 3, 1–4(1954); Y. Sakayanagi, "Ruling of a curved grating," Sci. Light (Tokyo) 3, 79–83(1955).

Schönheit, E.

E. Schönheit, "Ein Seya-Namioka-Monochromator mit torischem Gitter für Photoionisations-Messungen," Optik (Stuttgart) 23, 305–312(1966).

Seya, M.

H. Noda, T. Namioka and M. Seya, "Geometric theory of the grating," J. Opt. Soc. Am. 64, 1031–1036(1974).

H. Noda, T. Namioka, and M. Seya, "Design of holographic concave gratings for Seya-Namioka monochromator," J. Opt. Soc. Am. 64, 1043–1048(1974); H. Noda, T. Namioka, and M. Seya, "Aberration-reduced holographic concave gratings for Seya-Namioka monochromators," Jpn. J. Appl. Phys. 14, Suppl. 1, 187– 191(1975).

T. Namioka, H. Noda, and M. Seya, "Possibility of using the holograhic concave grating in vacuum monochromators," Sci. Light (Tokyo) 22, 77–99(1073); T. Namioka, M. Seya, and H. Noda, "Design and performance of holographic concave gratings," Jpn. J. Appl. Phys. 15, 1181–1197(1976).

Speer, R. J.

R. J. Speer, "A comparative review of grazing incidence gratings, including recent measurements on the performance of stigmatic soft x-ray reflection gratings formed holographically," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 53–60(1974); R. J. Speer, D. Turner, R. L. Johnson, D. Rudolph, and G. Schmahl, "Holographically formed grazing-incidence reflection grating with stigmatic soft x-ray focal isolation", Appl. Opt. 13, 1258–1261 (1974).

Strezhnev, S. A.

S. A. Strezhnev and A. L. Andreeva, "Toroidal diffraction gratings for Seya-Namioka monochromators," Opt. Spectrosc. 28, 426–428 (1970).

Velzel, C. H. F.

Yakovlev, E. A.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Kashelev, "Concave diffraction gratings with variable spacing," Opt. Spectrosc. 28, 423–426(1970).

J. Opt. Soc. Am. (6)

J. Spectrosc. Soc. Jpn (1)

F. Masuda, H. Noda, and T. Namioka, "Design and performance of toroidal holographic gratings," J. Spectrosc. Soc. Jpn 27, 211–223 (1978).

J. Spectrosc. Soc. Jpn. (1)

R. J. Speer, "A comparative review of grazing incidence gratings, including recent measurements on the performance of stigmatic soft x-ray reflection gratings formed holographically," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 53–60(1974); R. J. Speer, D. Turner, R. L. Johnson, D. Rudolph, and G. Schmahl, "Holographically formed grazing-incidence reflection grating with stigmatic soft x-ray focal isolation", Appl. Opt. 13, 1258–1261 (1974).

Jpn. J. Appl. Phys. (1)

T. Harada, S. Moriyama, and T. Kita, "Mechanically ruled stigmatic concave gratings," Jpn. J. Appl. Phys. 14, Suppl. 1, 175–179 (1975).

Nouv. Rev. Opt. (1)

D. Llepère, "Monochromateur a simple rotation du rèseau, a rèseau holographique sur support torique pour l'ultraviolet lointain," Nouv. Rev. Opt. 6, 173–178(1975).

Opt. Spectrosc. (2)

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. V. Kashelev, "Concave diffraction gratings with variable spacing," Opt. Spectrosc. 28, 423–426(1970).

S. A. Strezhnev and A. L. Andreeva, "Toroidal diffraction gratings for Seya-Namioka monochromators," Opt. Spectrosc. 28, 426–428 (1970).

Optik (1)

E. Schönheit, "Ein Seya-Namioka-Monochromator mit torischem Gitter für Photoionisations-Messungen," Optik (Stuttgart) 23, 305–312(1966).

Sci. Light (2)

Y. Sakayanagi, "A stigmatic concave grating with varying spacing," Sci. Light (Tokyo) 16, 129–137(1967); Y. Sakayanagi, "Theory of grating with circular grooves (curved grating)," Sci. Light (Tokyo) 3, 1–4(1954); Y. Sakayanagi, "Ruling of a curved grating," Sci. Light (Tokyo) 3, 79–83(1955).

T. Namioka, H. Noda, and M. Seya, "Possibility of using the holograhic concave grating in vacuum monochromators," Sci. Light (Tokyo) 22, 77–99(1073); T. Namioka, M. Seya, and H. Noda, "Design and performance of holographic concave gratings," Jpn. J. Appl. Phys. 15, 1181–1197(1976).

Soc. Jpn. (1)

M. Pouey, "Imaging properties of ruled and holographic gratings," J. Spectrosc. Soc. Jpn. 23, Suppl. 1, 67–81(1974).

Other (1)

Jobin Yvon Optical Systems, Diffraction gratings—ruled and holographic(Jobin Yvon Optical Systems, Metuchen, 1973), pp. 17–27.

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