Abstract

An optical design for spherical-grating monochromators for application to synchrotron radiation is presented. High spectral and spatial performance is obtained with a spherical variable-line-spaced grating coupled to a spherical mirror with its tangential plane coincident with the grating’s equatorial plane. The monochromator works without an entrance slit in an off-Rowland configuration with a fixed entrance arm and demagnification on the exit slit. The law for groove-space variation of the grating compensates for the main spectral aberrations; spectral focusing in an extended energy range is ensured by a slight change in the exit arm with translations of the order of a few tens of millimeters. The inclusion of a spherical mirror ensures focusing on a plane perpendicular to the plane of spectral dispersion. The ultimate resolution is limited by the slope errors of a single spherical surface. The layout is applied to the design of a high-resolution monochromator for the 1000–250-eV region.

© 2000 Optical Society of America

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References

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  1. G. P. Williams, “Effects of optical component surface figure errors on resolving power of soft x-ray monochromators,” Nucl. Instrum. Meth. A 246, 294–300 (1986).
    [CrossRef]
  2. G. Bonfante, G. Naletto, G. Tondello, “High-resolution soft-x-ray monochromators of new design,” Nucl. Instrum. Meth. A 291, 213–218 (1990).
    [CrossRef]
  3. C. T. Chen, “Concept and design procedure for cylindrical element monochromators for synchrotron radiation,” Nucl. Instrum. Meth. A 256, 595–604 (1987).
    [CrossRef]
  4. H. A. Padmore, “Application of a simple rotational spherical grating mounting to high resolution soft x-ray spectroscopy,” in Soft X-Ray Optics and Technology, E. Koch, G. A. Schmahl, eds., Proc. SPIE733, 274–285 (1986).
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    [CrossRef]
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  7. H. A. Padmore, “Optimization of soft x-ray monochromators,” Rev. Sci. Instrum. 60, 1608–1615 (1989).
    [CrossRef]
  8. T. Kita, T. Harada, N. Nakano, H. Kuroda, “Mechanically ruled aberration corrected concave grating for a flat-field grazing incidence spectrograph,” Appl. Opt. 22, 819–825 (1983).
    [CrossRef]
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    [CrossRef]
  11. L. Poletto, G. Naletto, G. Tondello, “Optical design of a grazing incidence spectrometer with varied line-space flat grating for high-order harmonic diagnostic,” in Ultraviolet and X-Ray Detection, Spectroscopy, and Polarimetry III, S. Fineschi, ed., Proc. SPIE3764, 85–93 (1999).
    [CrossRef]
  12. T. Harada, T. Kita, “Mechanically ruled aberration-corrected concave gratings,” Appl. Opt. 19, 3987–3993 (1980).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  14. L. Poletto, G. Tondello, “Design of a high-throughput grazing-incidence flat-field spectrometer,” Appl. Opt. 39, 4000–4006 (2000).
    [CrossRef]
  15. G. Bonfante, G. Tondello, “Grazing incidence Czerny–Turner monochromator utilizing sagittal focusing mirrors,” Appl. Opt. 29, 4250–4254 (1990).
    [CrossRef] [PubMed]
  16. G. Naletto, G. Tondello, “Configurations for a monochromator with variable-line-spaced gratings,” (Department of Electronics and Informatics, University of Padova, Padova, Italy, 1989).
  17. L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
    [CrossRef]
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    [CrossRef] [PubMed]

2000 (1)

1999 (2)

T. Harada, K. Takahashi, H. Sakuma, A. Osyczka, “Optimum design of a grazing-incidence flat-field spectrograph with a spherical varied-line-space grating,” Appl. Opt. 38, 2743–2748 (1999).
[CrossRef]

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

1990 (3)

1989 (1)

H. A. Padmore, “Optimization of soft x-ray monochromators,” Rev. Sci. Instrum. 60, 1608–1615 (1989).
[CrossRef]

1987 (1)

C. T. Chen, “Concept and design procedure for cylindrical element monochromators for synchrotron radiation,” Nucl. Instrum. Meth. A 256, 595–604 (1987).
[CrossRef]

1986 (1)

G. P. Williams, “Effects of optical component surface figure errors on resolving power of soft x-ray monochromators,” Nucl. Instrum. Meth. A 246, 294–300 (1986).
[CrossRef]

1984 (1)

1983 (1)

1980 (1)

1959 (1)

1948 (1)

Baez, A. V.

Bonfante, G.

G. Bonfante, G. Tondello, “Grazing incidence Czerny–Turner monochromator utilizing sagittal focusing mirrors,” Appl. Opt. 29, 4250–4254 (1990).
[CrossRef] [PubMed]

G. Bonfante, G. Naletto, G. Tondello, “High-resolution soft-x-ray monochromators of new design,” Nucl. Instrum. Meth. A 291, 213–218 (1990).
[CrossRef]

Chen, C. T.

C. T. Chen, “Concept and design procedure for cylindrical element monochromators for synchrotron radiation,” Nucl. Instrum. Meth. A 256, 595–604 (1987).
[CrossRef]

Cvetko, D.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Floreano, L.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Gotter, R.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Harada, T.

Hettrick, M.

Hogrefe, M.

M. Hogrefe, M. R. Howells, E. Hoyer, “Applications of spherical gratings in synchrotron radiation spectroscopy,” in Soft X-Ray Optics and Technology, E. Koch, G. A. Schmahl, eds., Proc. SPIE733, 253–261 (1986).

Howells, M. R.

M. Hogrefe, M. R. Howells, E. Hoyer, “Applications of spherical gratings in synchrotron radiation spectroscopy,” in Soft X-Ray Optics and Technology, E. Koch, G. A. Schmahl, eds., Proc. SPIE733, 253–261 (1986).

Hoyer, E.

M. Hogrefe, M. R. Howells, E. Hoyer, “Applications of spherical gratings in synchrotron radiation spectroscopy,” in Soft X-Ray Optics and Technology, E. Koch, G. A. Schmahl, eds., Proc. SPIE733, 253–261 (1986).

Kirkpatrick, P.

Kita, T.

Kuroda, H.

Malvezzi, M.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Marassi, L.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Morgante, A.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Nakano, N.

Naletto, G.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

G. Bonfante, G. Naletto, G. Tondello, “High-resolution soft-x-ray monochromators of new design,” Nucl. Instrum. Meth. A 291, 213–218 (1990).
[CrossRef]

L. Poletto, G. Naletto, G. Tondello, “Optical design of a grazing incidence spectrometer with varied line-space flat grating for high-order harmonic diagnostic,” in Ultraviolet and X-Ray Detection, Spectroscopy, and Polarimetry III, S. Fineschi, ed., Proc. SPIE3764, 85–93 (1999).
[CrossRef]

G. Naletto, G. Tondello, “Configurations for a monochromator with variable-line-spaced gratings,” (Department of Electronics and Informatics, University of Padova, Padova, Italy, 1989).

Osyczka, A.

Padmore, H. A.

H. A. Padmore, “Optimization of soft x-ray monochromators,” Rev. Sci. Instrum. 60, 1608–1615 (1989).
[CrossRef]

H. A. Padmore, “Application of a simple rotational spherical grating mounting to high resolution soft x-ray spectroscopy,” in Soft X-Ray Optics and Technology, E. Koch, G. A. Schmahl, eds., Proc. SPIE733, 274–285 (1986).

Poletto, L.

L. Poletto, G. Tondello, “Design of a high-throughput grazing-incidence flat-field spectrometer,” Appl. Opt. 39, 4000–4006 (2000).
[CrossRef]

L. Poletto, G. Naletto, G. Tondello, “Optical design of a grazing incidence spectrometer with varied line-space flat grating for high-order harmonic diagnostic,” in Ultraviolet and X-Ray Detection, Spectroscopy, and Polarimetry III, S. Fineschi, ed., Proc. SPIE3764, 85–93 (1999).
[CrossRef]

Rense, W. A.

Sakuma, H.

Santaniello, A.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Takahashi, K.

Tommasini, F.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Tondello, G.

L. Poletto, G. Tondello, “Design of a high-throughput grazing-incidence flat-field spectrometer,” Appl. Opt. 39, 4000–4006 (2000).
[CrossRef]

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

G. Bonfante, G. Naletto, G. Tondello, “High-resolution soft-x-ray monochromators of new design,” Nucl. Instrum. Meth. A 291, 213–218 (1990).
[CrossRef]

G. Bonfante, G. Tondello, “Grazing incidence Czerny–Turner monochromator utilizing sagittal focusing mirrors,” Appl. Opt. 29, 4250–4254 (1990).
[CrossRef] [PubMed]

L. Poletto, G. Naletto, G. Tondello, “Optical design of a grazing incidence spectrometer with varied line-space flat grating for high-order harmonic diagnostic,” in Ultraviolet and X-Ray Detection, Spectroscopy, and Polarimetry III, S. Fineschi, ed., Proc. SPIE3764, 85–93 (1999).
[CrossRef]

G. Naletto, G. Tondello, “Configurations for a monochromator with variable-line-spaced gratings,” (Department of Electronics and Informatics, University of Padova, Padova, Italy, 1989).

Verdini, A.

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Violett, T.

Williams, G. P.

G. P. Williams, “Effects of optical component surface figure errors on resolving power of soft x-ray monochromators,” Nucl. Instrum. Meth. A 246, 294–300 (1986).
[CrossRef]

Appl. Opt. (7)

J. Opt. Soc. Am. (2)

Nucl. Instrum. Meth. A (3)

G. P. Williams, “Effects of optical component surface figure errors on resolving power of soft x-ray monochromators,” Nucl. Instrum. Meth. A 246, 294–300 (1986).
[CrossRef]

G. Bonfante, G. Naletto, G. Tondello, “High-resolution soft-x-ray monochromators of new design,” Nucl. Instrum. Meth. A 291, 213–218 (1990).
[CrossRef]

C. T. Chen, “Concept and design procedure for cylindrical element monochromators for synchrotron radiation,” Nucl. Instrum. Meth. A 256, 595–604 (1987).
[CrossRef]

Rev. Sci. Instrum. (2)

H. A. Padmore, “Optimization of soft x-ray monochromators,” Rev. Sci. Instrum. 60, 1608–1615 (1989).
[CrossRef]

L. Floreano, G. Naletto, D. Cvetko, R. Gotter, M. Malvezzi, L. Marassi, A. Morgante, A. Santaniello, A. Verdini, F. Tommasini, G. Tondello, “Performance of the grating-crystal monochromator of the ALOISA beamline at the Elettra synchrotron,” Rev. Sci. Instrum. 70, 3855–3864 (1999).
[CrossRef]

Other (4)

L. Poletto, G. Naletto, G. Tondello, “Optical design of a grazing incidence spectrometer with varied line-space flat grating for high-order harmonic diagnostic,” in Ultraviolet and X-Ray Detection, Spectroscopy, and Polarimetry III, S. Fineschi, ed., Proc. SPIE3764, 85–93 (1999).
[CrossRef]

G. Naletto, G. Tondello, “Configurations for a monochromator with variable-line-spaced gratings,” (Department of Electronics and Informatics, University of Padova, Padova, Italy, 1989).

H. A. Padmore, “Application of a simple rotational spherical grating mounting to high resolution soft x-ray spectroscopy,” in Soft X-Ray Optics and Technology, E. Koch, G. A. Schmahl, eds., Proc. SPIE733, 274–285 (1986).

M. Hogrefe, M. R. Howells, E. Hoyer, “Applications of spherical gratings in synchrotron radiation spectroscopy,” in Soft X-Ray Optics and Technology, E. Koch, G. A. Schmahl, eds., Proc. SPIE733, 253–261 (1986).

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Figures (7)

Fig. 1
Fig. 1

Optical layout for a grazing-incidence SVLS grating.

Fig. 2
Fig. 2

Schematic of the grazing-incidence spherical-grating monochromator with a SVLS grating.

Fig. 3
Fig. 3

Variation of the exit arm of the monochromator with fixed entrance arm p 0 = 21 m: 1800- and 900-line/mm gratings.

Fig. 4
Fig. 4

Ray-traced images on the slit plane without slope errors: top, 1800-line/mm grating; bottom, 900-line/mm grating.

Fig. 5
Fig. 5

FWHM resolution with slit widths for 50% or 80% transmission: top, 1800-line/mm grating; bottom, 900-line/mm grating. The corresponding slit widths are shown in Fig. 6.

Fig. 6
Fig. 6

Slit width for 50% or 80% transmission: top, 1800-line/mm grating; bottom, 900-line/mm grating.

Fig. 7
Fig. 7

Grating translation in the mounting proposed by Hettrick12 for maintaining the exit arm fixed at 4200 mm: top, 1800-line/mm grating; bottom, 900-line/mm grating.

Tables (2)

Tables Icon

Table 1 Parameters for the Emission from the Undulator Considered in This Studya

Tables Icon

Table 2 FWHM Spot Sizes on the Center of the Experimental Test Chamber with Slit Translationa

Equations (16)

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σy=σ01+2a2y+3a3y2+4a4y3,
α=k+a sinmλσ02 cosk/2,
k=α-β.
12cos2 αp0+cos2 βq-cos α+cos βR+mλσ0a2=0  spectral defocusing,
12sin αp0cos2 αp0-cos αR+sin βqcos2 βq-cos βR+mλσ0a3=0  coma,
184 sin2 αp02cos2 αp0-cos αR-1p0cos2 αp0-cos αR2+1R21p0-cos αR+184 sin2 βq2cos2 βq-cos βR-1qcos2 βq-cos βR2+1R21q-cos βR+mλσ0a4=0  spherical aberration.
R=λcos α+cos β-λcos α+cos βλcos2 αp0+cos2 βq0-λcos2 αp0+cos2 βq0,
a2=12mσ0cos2 αp0+cos2 βq0cos α+cos β-cos2 αp0+cos2 βq0cos α+cos βλcos α+cos β-λcos α+cos β,
minλ,λ |qλ-q0|max=minλ,λcos2 βcos α+cos βR-cos2 αp0-2sin α+sin β-q0max,
Σsam=|q-q0| qmpmp0qcos βcos α Σver,
λΔλ=|m|λσ0q0NRΣslit cos β=|m|λσ0p0NRΣver cos α,
λΔλ=|m|λσ0p0NR cos αΣver2+121+cos βcos α2p02δγ2-1/2,
W=NSΣslit=NSqp0cos αcos βΣver2+121+cos βcos α2p02δγ21/2,
12cos2 αp0+cos2 βq0-cos α+cos βR+mλσ0a2-3a3Δy+6a4Δy2=0,
α=k+a sinmλσy2 cosk/2,  β=α-k.
Δθ=α-ΔyR-k2.

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