Abstract

A geometric theory is developed for a spherical concave diffraction grating that has variable line spacing and curved grooves and can be produced with existing technology. The aberration coefficients of this grating are determined. A comparison of these coefficients with the corresponding coefficients of holographic gratings and with code v polynomial coefficients gives a clearer understanding of the similarity and difference between mechanically ruled and holographically recorded concave gratings and allows the optimization of these gratings with standard computer programs.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Noda, T. Namioka, and M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1036 (1974).
    [CrossRef]
  2. C. Palmer, “Theory of second-generation holographic diffraction gratings,” J. Opt. Soc. Am. A 6, 1175–1188 (1989).
    [CrossRef]
  3. T. Namioka and M. Koike, “Aspheric wave-front recording optics for holographic gratings,” Appl. Opt. 34, 2180–2186 (1995).
    [CrossRef] [PubMed]
  4. W. Cash, “Far-ultraviolet spectrographs: the impact of holographic grating design,” Appl. Opt. 34, 2241–2246 (1995).
    [CrossRef] [PubMed]
  5. M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
    [CrossRef] [PubMed]
  6. M. Duban, K. Dohlen, and G. R. Lemaitre, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
    [CrossRef]
  7. M. Duban, G. R. Lemaitre, and R. F. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
    [CrossRef]
  8. M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
    [CrossRef]
  9. M. Duban, “Third-generation holographic Rowland mounting: fourth-order theory,” Appl. Opt. 38, 3443–3449 (1999).
    [CrossRef]
  10. M. Duban, “Recording high-dispersion spherical holographic gratings in a modified Rowland mounting by use of a multimode deformable mirror,” Appl. Opt. 39, 16–19 (2000).
    [CrossRef]
  11. M. Duban, “Universal method for holographic grating recording: multimode deformable mirrors generating Clebsch-Zernike polynomials,” Appl. Opt. 40, 461–471 (2001).
    [CrossRef]
  12. M. Duban, “High-dispersion spherical holographic gratings in a modified Rowland mounting,” Appl. Opt. 40, 1599–1608 (2001).
    [CrossRef]
  13. E. Wilkinson and J. G. Green, “First-generation holographic, grazing-incidence gratings for use in converging, extreme-ultraviolet light beams,” Appl. Opt. 34, 4685–4696 (1995).
    [CrossRef] [PubMed]
  14. E. Wilkinson, M. Indebetouw, and M. Beasley, “First-generation holographic, grazing-incidence gratings for use in converging, extreme-ultraviolet light beams,” Appl. Opt. 40, 3244–3255 (2001).
    [CrossRef]
  15. E. Sokolova, “Concave diffraction gratings recorded in counterpropagating beams,” J. Opt. Technol. 66, 1084–1088 (1999).
    [CrossRef]
  16. E. Sokolova, “New-generation diffraction gratings,” J. Opt. Technol. 68, 584–589 (2001).
    [CrossRef]
  17. E. Sokolova, “Geometric theory of two steps recorded holographic diffraction gratings,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 113–124 (1998).
    [CrossRef]
  18. E. Sokolova, “Holographic diffraction gratings for flat-field spectrometers,” J. Mod. Opt. 47, 2377–2389 (2000).
  19. E. Sokolova, B. Kruizinga, T. Valkenburg, and J. Schaarsberg, “Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks,” J. Mod. Opt. 49, 1907–1917 (2002).
    [CrossRef]
  20. N. K. Pavlycheva, “Second- and third-generation holographic diffraction gratings in Rowland spectrographs,” J. Opt. Technol. 69, 278–282 (2002).
    [CrossRef]
  21. C. Webster and J. Cash, “Aspheric concave grating spectrographs,” Appl. Opt. 23, 4518–4522 (1984).
    [CrossRef]
  22. M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
    [CrossRef] [PubMed]
  23. T. Namioka, M. Koike, and D. Content, “Geometric theory of the ellipsoidal grating,” Appl. Opt. 33, 7261–7274 (1994).
    [CrossRef] [PubMed]
  24. M. Koike and T. Namioka, “Plane gratings for high-resolution grazing-incidence monochromators: holographic grating versus mechanically ruled varied-line-spacing grating,” Appl. Opt. 36, 6308–6318 (1997).
    [CrossRef]
  25. C. Palmer, R. C. Milton, and W. McKinney, “Imaging theory of plane-symmetric line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
    [CrossRef]
  26. C. Palmer and W. McKinney, “Imaging properties of varied-line-space (VLS) gratings with adjustable curvature,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 87–102 (1998).
    [CrossRef]
  27. C. Palmer and W. McKinney, “Equivalence of focusing conditions for holographic and varied-line-space grating systems,” Appl. Opt. 29, 47–51 (1990).
    [CrossRef] [PubMed]
  28. F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. U. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. 28, 423–426 (1979).
  29. T. Harada and T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980).
    [CrossRef] [PubMed]
  30. F. M. Gerasimov, E. A. Yakovlev, and V. U. Koshelev, “Mechanically fabricated stigmatic concave gratings on spherical blanks,” Opt. Spectrosc. 46, 1177–1182 (1979).
  31. Y. V. Bazshanov, “Connection between the parameters of ruled and holographic concave diffraction gratings,” Sov. J. Opt. Technol. 46, 1–3 (1979).
  32. E. A. Sokolova and M. N. Maleshin, “Ray path calculation in spectral instruments having stigmatic concave diffraction gratings,” Sov. J. Opt. Technol. 56, 346–348 (1991).
  33. zemax Optical Design Program, User’s Guide, Version 9.0 (Focus Software, Inc., Tucson, Ariz., 2000).
  34. code v Reference Manual, Version 8.20 (Optical Research Associates, Pasadena, Calif., 1997).

2002 (2)

E. Sokolova, B. Kruizinga, T. Valkenburg, and J. Schaarsberg, “Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks,” J. Mod. Opt. 49, 1907–1917 (2002).
[CrossRef]

N. K. Pavlycheva, “Second- and third-generation holographic diffraction gratings in Rowland spectrographs,” J. Opt. Technol. 69, 278–282 (2002).
[CrossRef]

2001 (4)

2000 (2)

1999 (2)

1998 (5)

E. Sokolova, “Geometric theory of two steps recorded holographic diffraction gratings,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 113–124 (1998).
[CrossRef]

M. Duban, K. Dohlen, and G. R. Lemaitre, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
[CrossRef]

M. Duban, G. R. Lemaitre, and R. F. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
[CrossRef]

M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
[CrossRef]

C. Palmer and W. McKinney, “Imaging properties of varied-line-space (VLS) gratings with adjustable curvature,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 87–102 (1998).
[CrossRef]

1997 (1)

1995 (3)

1994 (2)

C. Palmer, R. C. Milton, and W. McKinney, “Imaging theory of plane-symmetric line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

T. Namioka, M. Koike, and D. Content, “Geometric theory of the ellipsoidal grating,” Appl. Opt. 33, 7261–7274 (1994).
[CrossRef] [PubMed]

1991 (2)

E. A. Sokolova and M. N. Maleshin, “Ray path calculation in spectral instruments having stigmatic concave diffraction gratings,” Sov. J. Opt. Technol. 56, 346–348 (1991).

M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1987 (1)

1984 (1)

1980 (1)

1979 (3)

F. M. Gerasimov, E. A. Yakovlev, and V. U. Koshelev, “Mechanically fabricated stigmatic concave gratings on spherical blanks,” Opt. Spectrosc. 46, 1177–1182 (1979).

Y. V. Bazshanov, “Connection between the parameters of ruled and holographic concave diffraction gratings,” Sov. J. Opt. Technol. 46, 1–3 (1979).

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. U. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. 28, 423–426 (1979).

1974 (1)

Bazshanov, Y. V.

Y. V. Bazshanov, “Connection between the parameters of ruled and holographic concave diffraction gratings,” Sov. J. Opt. Technol. 46, 1–3 (1979).

Beasley, M.

Cash, J.

Cash, W.

Content, D.

Dohlen, K.

Duban, M.

M. Duban, “Universal method for holographic grating recording: multimode deformable mirrors generating Clebsch-Zernike polynomials,” Appl. Opt. 40, 461–471 (2001).
[CrossRef]

M. Duban, “High-dispersion spherical holographic gratings in a modified Rowland mounting,” Appl. Opt. 40, 1599–1608 (2001).
[CrossRef]

M. Duban, “Recording high-dispersion spherical holographic gratings in a modified Rowland mounting by use of a multimode deformable mirror,” Appl. Opt. 39, 16–19 (2000).
[CrossRef]

M. Duban, “Third-generation holographic Rowland mounting: fourth-order theory,” Appl. Opt. 38, 3443–3449 (1999).
[CrossRef]

M. Duban, K. Dohlen, and G. R. Lemaitre, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
[CrossRef]

M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
[CrossRef]

M. Duban, G. R. Lemaitre, and R. F. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
[CrossRef]

M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
[CrossRef] [PubMed]

M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
[CrossRef] [PubMed]

Gerasimov, F. M.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. U. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. 28, 423–426 (1979).

F. M. Gerasimov, E. A. Yakovlev, and V. U. Koshelev, “Mechanically fabricated stigmatic concave gratings on spherical blanks,” Opt. Spectrosc. 46, 1177–1182 (1979).

Green, J. G.

Harada, T.

Indebetouw, M.

Kita, T.

Koike, M.

Koshelev, B. U.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. U. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. 28, 423–426 (1979).

Koshelev, V. U.

F. M. Gerasimov, E. A. Yakovlev, and V. U. Koshelev, “Mechanically fabricated stigmatic concave gratings on spherical blanks,” Opt. Spectrosc. 46, 1177–1182 (1979).

Kruizinga, B.

E. Sokolova, B. Kruizinga, T. Valkenburg, and J. Schaarsberg, “Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks,” J. Mod. Opt. 49, 1907–1917 (2002).
[CrossRef]

Lemaitre, G. R.

Maleshin, M. N.

E. A. Sokolova and M. N. Maleshin, “Ray path calculation in spectral instruments having stigmatic concave diffraction gratings,” Sov. J. Opt. Technol. 56, 346–348 (1991).

Malina, R. F.

McKinney, W.

C. Palmer and W. McKinney, “Imaging properties of varied-line-space (VLS) gratings with adjustable curvature,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 87–102 (1998).
[CrossRef]

C. Palmer, R. C. Milton, and W. McKinney, “Imaging theory of plane-symmetric line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

C. Palmer and W. McKinney, “Equivalence of focusing conditions for holographic and varied-line-space grating systems,” Appl. Opt. 29, 47–51 (1990).
[CrossRef] [PubMed]

Milton, R. C.

C. Palmer, R. C. Milton, and W. McKinney, “Imaging theory of plane-symmetric line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

Namioka, T.

Noda, H.

Palmer, C.

C. Palmer and W. McKinney, “Imaging properties of varied-line-space (VLS) gratings with adjustable curvature,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 87–102 (1998).
[CrossRef]

C. Palmer, R. C. Milton, and W. McKinney, “Imaging theory of plane-symmetric line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

C. Palmer and W. McKinney, “Equivalence of focusing conditions for holographic and varied-line-space grating systems,” Appl. Opt. 29, 47–51 (1990).
[CrossRef] [PubMed]

C. Palmer, “Theory of second-generation holographic diffraction gratings,” J. Opt. Soc. Am. A 6, 1175–1188 (1989).
[CrossRef]

Pavlycheva, N. K.

Peisakhson, I. V.

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. U. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. 28, 423–426 (1979).

Schaarsberg, J.

E. Sokolova, B. Kruizinga, T. Valkenburg, and J. Schaarsberg, “Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks,” J. Mod. Opt. 49, 1907–1917 (2002).
[CrossRef]

Seya, M.

Sokolova, E.

E. Sokolova, B. Kruizinga, T. Valkenburg, and J. Schaarsberg, “Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks,” J. Mod. Opt. 49, 1907–1917 (2002).
[CrossRef]

E. Sokolova, “New-generation diffraction gratings,” J. Opt. Technol. 68, 584–589 (2001).
[CrossRef]

E. Sokolova, “Holographic diffraction gratings for flat-field spectrometers,” J. Mod. Opt. 47, 2377–2389 (2000).

E. Sokolova, “Concave diffraction gratings recorded in counterpropagating beams,” J. Opt. Technol. 66, 1084–1088 (1999).
[CrossRef]

E. Sokolova, “Geometric theory of two steps recorded holographic diffraction gratings,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 113–124 (1998).
[CrossRef]

Sokolova, E. A.

E. A. Sokolova and M. N. Maleshin, “Ray path calculation in spectral instruments having stigmatic concave diffraction gratings,” Sov. J. Opt. Technol. 56, 346–348 (1991).

Valkenburg, T.

E. Sokolova, B. Kruizinga, T. Valkenburg, and J. Schaarsberg, “Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks,” J. Mod. Opt. 49, 1907–1917 (2002).
[CrossRef]

Webster, C.

Wilkinson, E.

Yakovlev, E. A.

F. M. Gerasimov, E. A. Yakovlev, and V. U. Koshelev, “Mechanically fabricated stigmatic concave gratings on spherical blanks,” Opt. Spectrosc. 46, 1177–1182 (1979).

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. U. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. 28, 423–426 (1979).

Appl. Opt. (18)

T. Namioka and M. Koike, “Aspheric wave-front recording optics for holographic gratings,” Appl. Opt. 34, 2180–2186 (1995).
[CrossRef] [PubMed]

W. Cash, “Far-ultraviolet spectrographs: the impact of holographic grating design,” Appl. Opt. 34, 2241–2246 (1995).
[CrossRef] [PubMed]

M. Duban, “Third-generation Rowland holographic mounting,” Appl. Opt. 30, 4019–4025 (1991).
[CrossRef] [PubMed]

M. Duban, K. Dohlen, and G. R. Lemaitre, “Illustration of the use of multimode deformable plane mirrors to record high-resolution concave gratings: results for the Cosmic Origins Spectrograph gratings of the Hubble Space Telescope,” Appl. Opt. 37, 7214–7217 (1998).
[CrossRef]

M. Duban, G. R. Lemaitre, and R. F. Malina, “Recording method for obtaining high-resolution holographic gratings through use of multimode deformable plane mirrors,” Appl. Opt. 37, 3438–3439 (1998).
[CrossRef]

M. Duban, “Theory of spherical holographic gratings recorded by use of a multimode deformable mirror,” Appl. Opt. 37, 7209–7213 (1998).
[CrossRef]

M. Duban, “Third-generation holographic Rowland mounting: fourth-order theory,” Appl. Opt. 38, 3443–3449 (1999).
[CrossRef]

M. Duban, “Recording high-dispersion spherical holographic gratings in a modified Rowland mounting by use of a multimode deformable mirror,” Appl. Opt. 39, 16–19 (2000).
[CrossRef]

M. Duban, “Universal method for holographic grating recording: multimode deformable mirrors generating Clebsch-Zernike polynomials,” Appl. Opt. 40, 461–471 (2001).
[CrossRef]

M. Duban, “High-dispersion spherical holographic gratings in a modified Rowland mounting,” Appl. Opt. 40, 1599–1608 (2001).
[CrossRef]

E. Wilkinson and J. G. Green, “First-generation holographic, grazing-incidence gratings for use in converging, extreme-ultraviolet light beams,” Appl. Opt. 34, 4685–4696 (1995).
[CrossRef] [PubMed]

E. Wilkinson, M. Indebetouw, and M. Beasley, “First-generation holographic, grazing-incidence gratings for use in converging, extreme-ultraviolet light beams,” Appl. Opt. 40, 3244–3255 (2001).
[CrossRef]

C. Webster and J. Cash, “Aspheric concave grating spectrographs,” Appl. Opt. 23, 4518–4522 (1984).
[CrossRef]

M. Duban, “Holographic aspheric gratings printed with aberrant waves,” Appl. Opt. 26, 4263–4273 (1987).
[CrossRef] [PubMed]

T. Namioka, M. Koike, and D. Content, “Geometric theory of the ellipsoidal grating,” Appl. Opt. 33, 7261–7274 (1994).
[CrossRef] [PubMed]

M. Koike and T. Namioka, “Plane gratings for high-resolution grazing-incidence monochromators: holographic grating versus mechanically ruled varied-line-spacing grating,” Appl. Opt. 36, 6308–6318 (1997).
[CrossRef]

T. Harada and T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980).
[CrossRef] [PubMed]

C. Palmer and W. McKinney, “Equivalence of focusing conditions for holographic and varied-line-space grating systems,” Appl. Opt. 29, 47–51 (1990).
[CrossRef] [PubMed]

J. Mod. Opt. (2)

E. Sokolova, “Holographic diffraction gratings for flat-field spectrometers,” J. Mod. Opt. 47, 2377–2389 (2000).

E. Sokolova, B. Kruizinga, T. Valkenburg, and J. Schaarsberg, “Recording of concave diffraction gratings in counterpropagating beams using meniscus blanks,” J. Mod. Opt. 49, 1907–1917 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Technol. (3)

Opt. Eng. (1)

C. Palmer, R. C. Milton, and W. McKinney, “Imaging theory of plane-symmetric line-space grating systems,” Opt. Eng. 33, 820–829 (1994).
[CrossRef]

Opt. Spectrosc. (2)

F. M. Gerasimov, E. A. Yakovlev, I. V. Peisakhson, and B. U. Koshelev, “Concave diffraction gratings with variable spacing,” Opt. Spectrosc. 28, 423–426 (1979).

F. M. Gerasimov, E. A. Yakovlev, and V. U. Koshelev, “Mechanically fabricated stigmatic concave gratings on spherical blanks,” Opt. Spectrosc. 46, 1177–1182 (1979).

Sov. J. Opt. Technol. (2)

Y. V. Bazshanov, “Connection between the parameters of ruled and holographic concave diffraction gratings,” Sov. J. Opt. Technol. 46, 1–3 (1979).

E. A. Sokolova and M. N. Maleshin, “Ray path calculation in spectral instruments having stigmatic concave diffraction gratings,” Sov. J. Opt. Technol. 56, 346–348 (1991).

Other (4)

zemax Optical Design Program, User’s Guide, Version 9.0 (Focus Software, Inc., Tucson, Ariz., 2000).

code v Reference Manual, Version 8.20 (Optical Research Associates, Pasadena, Calif., 1997).

C. Palmer and W. McKinney, “Imaging properties of varied-line-space (VLS) gratings with adjustable curvature,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 87–102 (1998).
[CrossRef]

E. Sokolova, “Geometric theory of two steps recorded holographic diffraction gratings,” in Theory and Practice of Surface-Relief Diffraction Gratings: Synchrotron and Other Applications, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3450, 113–124 (1998).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Concave diffraction grating in the rectangular coordinate system.

Fig. 2
Fig. 2

Optical mounting of the flat-field spectrometer.

Fig. 3
Fig. 3

Spot diagrams calculated with code v for the spectrometer (Fig. 2) with, a, the point-source coordinates and b, the polynomial coefficients. The horizontal direction is parallel to the grating grooves.

Fig. 4
Fig. 4

Spot diagrams calculated with code v as a result of the optimization of polynomial coefficients with constraints, corresponding to the relationship between the coefficients belonging to the mechanically ruled grating: a, straight-groove grating; b, curved-groove grating. The horizontal direction is parallel to the grating grooves.

Fig. 5
Fig. 5

Spot diagrams calculated for the mechanically ruled grating with the same polynomial coefficients used for the calculations, results of which are shown in Fig. 4: a, visual basic program, straight grooves; b, visual basic program, curved grooves; c, zemax program, straight grooves. The horizontal direction is parallel to the grating grooves.

Fig. 6
Fig. 6

Possible geometric placement of recording sources, C and D, which can be used for fabricating the holographic grating, with the same defocusing, first-order astigmatism, meridional and sagittal coma aberrations, as the mechanically ruled grating with variable spacing and curved grooves.

Fig. 7
Fig. 7

Spot diagrams as a result of, a, a mechanically ruled concave diffraction grating; b, its polynomial approximation; c, its holographic approximation; d, the polynomial approximation of the holographic approximation. The vertical direction is parallel to the grating grooves.

Tables (3)

Tables Icon

Table 1 Coordinates of the Recording Sources and the Corresponding Parameters μ, ν, and γ

Tables Icon

Table 2 Polynomial Coefficients of the Mechanically Ruled Grating and Its Approximations

Tables Icon

Table 3 Root-Mean-Square Spot Diameters in Figs. 7b7d

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

x=R-R2-y2-z21/2.
F=AP+PB+nkλ,
F=F000+ypF100+zpF011+12yp2F200+12zp2F020+16yp3F300+12ypzp2F120+,,
Fijk=Mijk+kλHijk,
x sin γ+y cos γ-y0 cos γ=0,
y0=R-R2-y2-z21/2tan γ+y.
d=d01+μy+νy2,
N=1d01+μy+νy2.
n=y=0y01d01+μy+νy2dy.
n=2 arctanμ+2νy0-μ2+4ν1/2d0-μ2+4ν1/2-2 arctanμ-μ2+4ν1/2d0-μ2+4ν1/2.
Hijk=ijny, zyizj, H010=0, H100=1/d0, H020=tan γd0R, H110=0, H200=tan γ-μRd0R, H030=0, H120=-μ tan γd0R, H210=0, H300=2Rμ2-ν-3μ tan γd0R, H040=3 tan γμR tan γ-1d0R3, H130=0, H220=2 tan γ1+2μ2R2-2R2ν-μR tan γd0R3, H130=0, H400=3-2μ3+4μν+1+4μ2R2-4R2νtan γR3-μ tan2 γR2d0.
d=d01+μ-tanγ/Ry+νy2.
H200=-μd0, H120=-tan γμR+tan γd0R2, H300=2R2μ2-ν+μR tan γ-tan2 γd0R2, H040=3 tan γ-1+μR tan γ+tan2 γd0R3, H220=2 tan γ1+2μ2R2-2R2ν+3μR tan γ+tan2 γd0R3, H400=3-2μR3μ2-2ν+1-2μ2R2tan γ+μR tan2 γ+tan3 γd0R3.
μ=-tan γ/R.
Fijk=Mijk+k λλ0 Hijk,
H010=0, H110=0, H030=0, H210=0, H130=0, H230=0,H100=-sin γ+sin δ, H020=R1/rC-1/rD-cos γ+cos δR,H200=-cos γR+cos2 γrC+cos δR-cos2 δrD,H120=sin γrC2-cos γ sin γRrC-sin δrD2+cos δ sin δRrD,H300=3 cos γ sin γR cos γ-rCRrC2-3 cos δ sin δR cos δ-rDRrD2,H040=344R-rC cos γR3rC-2-2rC cos γR2rC3-4R-rD cos δR3rD+2-2rD cos δR2rD3,H220=144R-rC cos γR3rC-2-2rC cos γR2rC3-4R-rD cos δR3rD+2-2rD cos δR2rD3+62-2rC cos γRsin2 γrC3-2-2rD cos δRsin2 δrD3,H400=344R-rC cos γR3rC-2-2rC cos γR2rC3-4R-rD cos δR3rD+2-2rD cos δR2rD3+122-2rC cos γRsin2 γrC3-20 sin4 γrC3-122-2rD cos δRsin2 δrD3+20 sin4 δrD3,
rC=y12+z121/2,rD=y22+z221/2,sin γ=y1/rC,cos γ=z1/rC,sin δ=y2/rD,cos δ=z2/rD.
C1=H010=0, C2=H100,C3=H020/2, C4=H110=0,C5=H200/2, C6=H030=0,C7=-H120/2, C8=H210=0,C9=-H300/6, C10=H040/24,C11=H130=0, C12=H220/6,C13=H310=0, C14=H400/24.
C7=2C3C3-C5, C10=C3/4R2-C33+C32C5, C12=8C33/3-8C32C5/3+C31/4R2-2C9, C14=C3/4R2+C33+C32C5-2C53-3C5C9.
μ=-2C5, ν=-2C32-2C3C5+4C52-3C9,γ=arctanC3R.

Metrics