Abstract

A merit function is proposed and applied to design holographic concave gratings for moderate-resolution monochromators. To justify the validity of the merit function, imaging properties of gratings used for the coma-correction Seya-Namioka monochromator, designed by the present authors, Noda, and Takahashi, are compared through ray tracing and their aberration-correction mechanisms are also analyzed. The capability of the merit function is well demonstrated in the design of holographic gratings for another two moderate-resolution monochromators with different requirements. All the results obtained show that the merit function is not only straight and effective but also manages to balance various aberrations of the concave holographic grating very well.

© 2011 Optical Society of America

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References

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  1. H. Noda, T. Namioka, and M. Seya, “Design of holographic concave gratings for Seya-Namioka monochromators,” J. Opt. Soc. Am. 64, 1043–1048 (1974).
    [CrossRef]
  2. T. Namioka, M. Seya, and H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
    [CrossRef]
  3. W. R. McKinney and C. Palmer, “Numerical design method for aberration-reduced concave grating spectrometers,” Appl. Opt. 26, 3108–3118 (1987).
    [CrossRef] [PubMed]
  4. R. Grange, “Holographic spherical gratings: a new family of quasistigmatic designs for the Rowland-circle mounting,” Appl. Opt. 32, 4875–4880 (1993).
    [CrossRef] [PubMed]
  5. T. Namioka and M. Koike, “Aspheric wave-front recording optics for holographic gratings,” Appl. Opt. 34, 2180–2186(1995).
    [CrossRef] [PubMed]
  6. M. Koike, Y. Harada, and H. Noda, “New blazed holographic grating fabricated by using an aspherical recording with an ion-etching method,” Proc. SPIE 815, 96–101 (1987).
  7. H. Noda, Y. Harada, and M. Koike, “Holographic grating recorded using aspheric wave fronts for a Seya—Namioka monochromator,” Appl. Opt. 28, 4375–4380 (1989).
    [CrossRef] [PubMed]
  8. T. Namioka, “Theory of the ellipsoidal concave grating. I,” J. Opt. Soc. Am. 51, 4–12 (1961).
    [CrossRef]
  9. T. Namioka, “Theory of the ellipsoidal concave grating. II. Application the theory to the specific grating mountings,” J. Opt. Soc. Am. 51, 13–16 (1961).
    [CrossRef]
  10. T. Namioka, M. Koike, and D. Content, “Geometric theory of the ellipsoidal grating,” Appl. Opt. 33, 7261–7274 (1994).
    [CrossRef] [PubMed]
  11. M. P. Crisp, “Aberration of holographic toroidal grating systems,” Appl. Opt. 22, 1508–1518 (1983).
    [CrossRef]
  12. M. Koike and T. Namioka, “Merit function for the design of grating instruments,” Appl. Opt. 33, 2048–2056 (1994).
    [CrossRef] [PubMed]
  13. M. Koike, Y. Ueno, and T. Namioka, “Application of the hybrid design method to VUV double-element optical systems equipped with holographic gratings recorded with aspheric wave fronts,” Proc. SPIE 3150, 31–39 (1997).
    [CrossRef]
  14. S. Masuia and T. Namioka, “Geometric aberration theory of double-element optical systems,” J. Opt. Soc. Am. A 16, 2253–2268 (1999).
    [CrossRef]
  15. S. Masuia and T. Namioka, “Aberration theory and a design method of double-element optical systems,” Proc. SPIE 3737, 498–508 (1999).
    [CrossRef]
  16. A. Takahashi and T. Katayama, “Automatic design of holographic gratings for Seya-Namioka monochromators,” J. Opt. Soc. Am. 68, 1254–1256 (1978).
    [CrossRef]
  17. H. Noda, T. Namioka, and M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1036 (1974).
    [CrossRef]

1999

S. Masuia and T. Namioka, “Geometric aberration theory of double-element optical systems,” J. Opt. Soc. Am. A 16, 2253–2268 (1999).
[CrossRef]

S. Masuia and T. Namioka, “Aberration theory and a design method of double-element optical systems,” Proc. SPIE 3737, 498–508 (1999).
[CrossRef]

1997

M. Koike, Y. Ueno, and T. Namioka, “Application of the hybrid design method to VUV double-element optical systems equipped with holographic gratings recorded with aspheric wave fronts,” Proc. SPIE 3150, 31–39 (1997).
[CrossRef]

1995

1994

1993

1989

1987

M. Koike, Y. Harada, and H. Noda, “New blazed holographic grating fabricated by using an aspherical recording with an ion-etching method,” Proc. SPIE 815, 96–101 (1987).

W. R. McKinney and C. Palmer, “Numerical design method for aberration-reduced concave grating spectrometers,” Appl. Opt. 26, 3108–3118 (1987).
[CrossRef] [PubMed]

1983

1978

1976

T. Namioka, M. Seya, and H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

1974

1961

Content, D.

Crisp, M. P.

Grange, R.

Harada, Y.

H. Noda, Y. Harada, and M. Koike, “Holographic grating recorded using aspheric wave fronts for a Seya—Namioka monochromator,” Appl. Opt. 28, 4375–4380 (1989).
[CrossRef] [PubMed]

M. Koike, Y. Harada, and H. Noda, “New blazed holographic grating fabricated by using an aspherical recording with an ion-etching method,” Proc. SPIE 815, 96–101 (1987).

Katayama, T.

Koike, M.

Masuia, S.

S. Masuia and T. Namioka, “Geometric aberration theory of double-element optical systems,” J. Opt. Soc. Am. A 16, 2253–2268 (1999).
[CrossRef]

S. Masuia and T. Namioka, “Aberration theory and a design method of double-element optical systems,” Proc. SPIE 3737, 498–508 (1999).
[CrossRef]

McKinney, W. R.

Namioka, T.

S. Masuia and T. Namioka, “Aberration theory and a design method of double-element optical systems,” Proc. SPIE 3737, 498–508 (1999).
[CrossRef]

S. Masuia and T. Namioka, “Geometric aberration theory of double-element optical systems,” J. Opt. Soc. Am. A 16, 2253–2268 (1999).
[CrossRef]

M. Koike, Y. Ueno, and T. Namioka, “Application of the hybrid design method to VUV double-element optical systems equipped with holographic gratings recorded with aspheric wave fronts,” Proc. SPIE 3150, 31–39 (1997).
[CrossRef]

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

M. Koike and T. Namioka, “Merit function for the design of grating instruments,” Appl. Opt. 33, 2048–2056 (1994).
[CrossRef] [PubMed]

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

T. Namioka, M. Seya, and H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

H. Noda, T. Namioka, and M. Seya, “Design of holographic concave gratings for Seya-Namioka monochromators,” J. Opt. Soc. Am. 64, 1043–1048 (1974).
[CrossRef]

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

T. Namioka, “Theory of the ellipsoidal concave grating. I,” J. Opt. Soc. Am. 51, 4–12 (1961).
[CrossRef]

T. Namioka, “Theory of the ellipsoidal concave grating. II. Application the theory to the specific grating mountings,” J. Opt. Soc. Am. 51, 13–16 (1961).
[CrossRef]

Noda, H.

Palmer, C.

Seya, M.

Takahashi, A.

Ueno, Y.

M. Koike, Y. Ueno, and T. Namioka, “Application of the hybrid design method to VUV double-element optical systems equipped with holographic gratings recorded with aspheric wave fronts,” Proc. SPIE 3150, 31–39 (1997).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

T. Namioka, M. Seya, and H. Noda, “Design and performance of holographic concave gratings,” Jpn. J. Appl. Phys. 15, 1181–1197 (1976).
[CrossRef]

Proc. SPIE

M. Koike, Y. Harada, and H. Noda, “New blazed holographic grating fabricated by using an aspherical recording with an ion-etching method,” Proc. SPIE 815, 96–101 (1987).

S. Masuia and T. Namioka, “Aberration theory and a design method of double-element optical systems,” Proc. SPIE 3737, 498–508 (1999).
[CrossRef]

M. Koike, Y. Ueno, and T. Namioka, “Application of the hybrid design method to VUV double-element optical systems equipped with holographic gratings recorded with aspheric wave fronts,” Proc. SPIE 3150, 31–39 (1997).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of monochromator.

Fig. 2
Fig. 2

Spot diagrams obtained by tracing rays through gratings, mounted in coma-correction Seya-Namioka monochromator, designed by (a) Noda, (b) Takahashi, and the (c) present authors, respectively.

Fig. 3
Fig. 3

Amount of defocus term F 200 as a function of diffracted wavelength. The solid, dashed, and dotted–dashed curves describe the gratings designed by Noda, Takahashi, and the present authors, respectively.

Fig. 4
Fig. 4

Amount of coma term F 300 as a function of diffracted wavelength. The solid, dashed, and dotted–dashed curves describe the gratings designed by Noda, Takahashi, and the present authors, respectively.

Fig. 5
Fig. 5

Spot diagrams obtained by tracing rays through gratings mounted in (a) constant-deviation monochromators 1 and 2.

Fig. 6
Fig. 6

Amount of defocus term F 200 as a function of diffracted wavelength. The solid and dashed curves describe the gratings designed for monochromators 1 and 2, respectively.

Fig. 7
Fig. 7

Amount of coma term F 300 as a function of diffracted wavelength. The solid and dashed curves describe the gratings designed for monochromators 1 and 2, respectively.

Tables (2)

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Table 1 Optimum Grating Parameters

Tables Icon

Table 2 Optimum Results for the Two Constant-Deviation Monochromators

Equations (3)

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F = A P + P B + n m λ .
F = F 000 + ω F 100 + l F 011 + 1 2 ω 2 F 200 + 1 2 l 2 F 020 + 1 2 ω 3 F 300 + 1 2 ω l 2 F 120 + ω l F 111 + 1 8 ω 4 F 400 + 1 4 ω 2 l 2 F 220 + ,
I = η ε ( λ η ) [ μ 1 F 200 2 ( λ η ) + μ 2 F 020 2 ( λ η ) + μ 3 F 300 2 ( λ η ) + μ 4 F 120 2 ( λ η ) + μ 5 F 400 2 ( λ η ) + ] ,

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