Abstract

In the context of aberration-corrected holographic spherical gratings used in the Rowland-circle mounting, we have investigated the off-Rowland recording geometries with stigmatic sources that nullify the defocus and meridional coma at all wavelengths. We introduce the additional requirement that astigmatism vanishes at a given wavelength. Then we demonstrate that a family of solutions exists and has a quasi-zero sagittal coma at the wavelength adopted for the astigmatism correction. This simultaneous reduction of sagittal coma and astigmatism greatly enhances the spectral performances of the Rowland mount. We also point out that a subfamily is found when the derivative of astigmatism is equal to zero at the wavelength of correction; the performances are then extended to a wider spectral range. Finally ray traces and performances of two representative examples of the new family of gratings are presented.

© 1993 Optical Society of America

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References

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  1. M. P. Chrisp, “Aberration-corrected holographic gratings and their mountings,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol 10, pp. 391–454.
  2. M. C. Hutley, “Diffraction Gratings,” in Diffusion Gratings, N. H. March, H. N. Daglish, eds. (Academic, London, 1982), Chap. 7, p. 215.
  3. J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. Home Dikson, ed. (Oriel, Newcastle upon Tyne, UK, 1970), pp. 117–124.
  4. B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount I,” Opt. Acta 28, 1587–1599 (1981).
    [CrossRef]
  5. B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount II,” Opt. Acta 28, 1601–1610 (1981).
    [CrossRef]
  6. T. Namioka, H. Noda, M. Seya, “Possibility of using the holographic concave grating in vacuum monochromators,” Sci. Light 22, 77–99 (1973).
  7. M. Pouey, “Conditions de stigmatisme pour les montages de Rowland équipés de réseaux holographiques concaves,” C. R. Acad. Sci. Paris B 276, 531–534 (1973).
  8. Yu. V. Bazhanov, “Determination of optimal parameters of concave diffraction gratings in devices with a Rowland circle,” Opt. Spectrosc. (USSR) 55, 639–642 (1983).
  9. R. Grange, “Aberration-reduced holographic spherical gratings for Rowland circle spectrographs,” Appl. Opt. 31, 3744–3749 (1992).
    [CrossRef] [PubMed]
  10. H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1048 (1974).
    [CrossRef]
  11. G. Pieuchard, J. Flamand, Jobin-Yvon Company, 16-18 rue du Canal, B.P. 118, 91165 Longjumeau Cedex, France (personal communication, 1992).

1992 (1)

1983 (1)

Yu. V. Bazhanov, “Determination of optimal parameters of concave diffraction gratings in devices with a Rowland circle,” Opt. Spectrosc. (USSR) 55, 639–642 (1983).

1981 (2)

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount I,” Opt. Acta 28, 1587–1599 (1981).
[CrossRef]

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount II,” Opt. Acta 28, 1601–1610 (1981).
[CrossRef]

1974 (1)

1973 (2)

T. Namioka, H. Noda, M. Seya, “Possibility of using the holographic concave grating in vacuum monochromators,” Sci. Light 22, 77–99 (1973).

M. Pouey, “Conditions de stigmatisme pour les montages de Rowland équipés de réseaux holographiques concaves,” C. R. Acad. Sci. Paris B 276, 531–534 (1973).

Bazhanov, Yu. V.

Yu. V. Bazhanov, “Determination of optimal parameters of concave diffraction gratings in devices with a Rowland circle,” Opt. Spectrosc. (USSR) 55, 639–642 (1983).

Brown, B. J.

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount I,” Opt. Acta 28, 1587–1599 (1981).
[CrossRef]

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount II,” Opt. Acta 28, 1601–1610 (1981).
[CrossRef]

Chrisp, M. P.

M. P. Chrisp, “Aberration-corrected holographic gratings and their mountings,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol 10, pp. 391–454.

Cordelle, J.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. Home Dikson, ed. (Oriel, Newcastle upon Tyne, UK, 1970), pp. 117–124.

Flamand, J.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. Home Dikson, ed. (Oriel, Newcastle upon Tyne, UK, 1970), pp. 117–124.

G. Pieuchard, J. Flamand, Jobin-Yvon Company, 16-18 rue du Canal, B.P. 118, 91165 Longjumeau Cedex, France (personal communication, 1992).

Grange, R.

Hutley, M. C.

M. C. Hutley, “Diffraction Gratings,” in Diffusion Gratings, N. H. March, H. N. Daglish, eds. (Academic, London, 1982), Chap. 7, p. 215.

Labeyrie, A.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. Home Dikson, ed. (Oriel, Newcastle upon Tyne, UK, 1970), pp. 117–124.

Namioka, T.

H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1048 (1974).
[CrossRef]

T. Namioka, H. Noda, M. Seya, “Possibility of using the holographic concave grating in vacuum monochromators,” Sci. Light 22, 77–99 (1973).

Noda, H.

H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1048 (1974).
[CrossRef]

T. Namioka, H. Noda, M. Seya, “Possibility of using the holographic concave grating in vacuum monochromators,” Sci. Light 22, 77–99 (1973).

Pieuchard, G.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. Home Dikson, ed. (Oriel, Newcastle upon Tyne, UK, 1970), pp. 117–124.

G. Pieuchard, J. Flamand, Jobin-Yvon Company, 16-18 rue du Canal, B.P. 118, 91165 Longjumeau Cedex, France (personal communication, 1992).

Pouey, M.

M. Pouey, “Conditions de stigmatisme pour les montages de Rowland équipés de réseaux holographiques concaves,” C. R. Acad. Sci. Paris B 276, 531–534 (1973).

Seya, M.

H. Noda, T. Namioka, M. Seya, “Geometric theory of the grating,” J. Opt. Soc. Am. 64, 1031–1048 (1974).
[CrossRef]

T. Namioka, H. Noda, M. Seya, “Possibility of using the holographic concave grating in vacuum monochromators,” Sci. Light 22, 77–99 (1973).

Wilson, I. J.

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount II,” Opt. Acta 28, 1601–1610 (1981).
[CrossRef]

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount I,” Opt. Acta 28, 1587–1599 (1981).
[CrossRef]

Appl. Opt. (1)

C. R. Acad. Sci. Paris B (1)

M. Pouey, “Conditions de stigmatisme pour les montages de Rowland équipés de réseaux holographiques concaves,” C. R. Acad. Sci. Paris B 276, 531–534 (1973).

J. Opt. Soc. Am. (1)

Opt. Acta (2)

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount I,” Opt. Acta 28, 1587–1599 (1981).
[CrossRef]

B. J. Brown, I. J. Wilson, “Holographic grating aberration correction for a Rowland circle mount II,” Opt. Acta 28, 1601–1610 (1981).
[CrossRef]

Opt. Spectrosc. (USSR) (1)

Yu. V. Bazhanov, “Determination of optimal parameters of concave diffraction gratings in devices with a Rowland circle,” Opt. Spectrosc. (USSR) 55, 639–642 (1983).

Sci. Light (1)

T. Namioka, H. Noda, M. Seya, “Possibility of using the holographic concave grating in vacuum monochromators,” Sci. Light 22, 77–99 (1973).

Other (4)

M. P. Chrisp, “Aberration-corrected holographic gratings and their mountings,” in Applied Optics and Optical Engineering, R. R. Shannon, J. C. Wyant, eds. (Academic, London, 1987), Vol 10, pp. 391–454.

M. C. Hutley, “Diffraction Gratings,” in Diffusion Gratings, N. H. March, H. N. Daglish, eds. (Academic, London, 1982), Chap. 7, p. 215.

J. Cordelle, J. Flamand, G. Pieuchard, A. Labeyrie, “Aberration-corrected concave gratings made holographically,” in Optical Instruments and Techniques, J. Home Dikson, ed. (Oriel, Newcastle upon Tyne, UK, 1970), pp. 117–124.

G. Pieuchard, J. Flamand, Jobin-Yvon Company, 16-18 rue du Canal, B.P. 118, 91165 Longjumeau Cedex, France (personal communication, 1992).

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Figures (5)

Fig. 1
Fig. 1

Schematic diagram of the Rowland-circle mounting. The entrance slit, A, and the image, B, are located on the Rowland circle. The recording sources, C and D, can be positioned anywhere in the dispersion plane.

Fig. 2
Fig. 2

Plot of the regions in the αOβ plane where solutions can be found for an arbitrary ratio (mλ/λ0)−1 equal to 2. R refers to both real sources. V refers to one virtual and one real source.

Fig. 3
Fig. 3

Three-dimensional plots at the same scale of sagittal coma terms R2F12 for α and β values corresponding with most of the solutions. (a) Holographically corrected spherical gratings generated with the recording geometries described in this study. (b) Uncorrected spherical gratings with straight and equally spaced grooves.

Fig. 4
Fig. 4

Spot diagrams for an on-axis point source and five wavelengths in the spectrum corresponding to the Lyman/Fuse 5767-groove/mm grating.

Fig. 5
Fig. 5

Comparison of the spot diagrams for two designs with an equal Rowland-circle diameter (200 mm), groove density (400 grooves/mm), and geometry (α = 8.117°): (a) conventional holographic grating (straight and equally spaced grooves), (b) grating of the new family recorded using the parameters listed in Table 2.

Tables (2)

Tables Icon

Table 1 Mounting and Recording Parameters for a Lyman/Fuse 5767-groove/mm Grating

Tables Icon

Table 2 Mounting and Recording Parameters for a 400-groove/mm Spherical Grating

Equations (21)

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F i j = M i j + ( m λ / λ 0 ) H i j ,
sin α + sin β = N m λ ,
N = ( sin δ sin γ ) / λ 0 and sin δ sin γ > 0 ,
R c = R ( sin γ cos 2 δ cos 2 γ sin δ ) sin δ ( cos δ cos γ ) ,
R d = R c sin δ sin γ ,
R F 02 = R M 02 + m λ / λ 0 R H 02 = 0 .
R H 02 = R ( S c S d ) ,
R / R c = 1 / ( sin γ sin δ ) sin δ ( cos δ cos γ ) ( 1 + sin δ sin γ ) .
R H 02 = sin γ sin δ ( cos δ cos γ ) ( 1 + sin δ sin γ ) .
R M 02 = sin 2 α cos α + sin 2 β cos β .
( λ 0 / m λ ) ( sin 2 α cos α + sin 2 β cos β ) = sin γ sin δ ( cos δ cos γ ) ( 1 + sin δ sin γ ) .
R 2 M 12 = sin 3 α cos 2 α + sin 3 β cos 2 β .
R 2 H 12 = R 2 ( S c / R c ) sin γ R 2 ( S d / R d ) sin δ .
R 2 H 12 = sin γ ( R / R c ) R H 02 .
R 2 H 12 = 1 / ( sin γ sin δ ) [ sin γ sin δ ( cos δ cos γ ) ] 2 ( 1 + sin δ sin γ ) 2 .
m λ / λ 0 R 2 H 12 = 1 / ( sin α + sin β ) ( sin 2 α cos α + sin 2 β cos β ) 2 .
R 2 F 12 = sin α sin β sin 2 ( α β ) cos 2 α cos 2 β ( sin α + sin β ) .
M 02 / λ + m H 02 / λ 0 = 0 .
M 02 / λ M 02 / λ = 0 .
sin α + sin β cos β ( sin β cos 2 β + sin β ) ( sin 2 α cos α + sin 2 β cos β ) = 0 .
sin δ sin γ = N λ 0

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