Abstract

We explore the potential performance of soft x-ray spectrometers based on the use of varied-line-spacing spherical diffraction gratings (VLS-SG). The quantitative assessment is based on an optimization procedure to obtain both negligible optical aberrations at full illumination of the grating and a quasi linear focal curve. It involves high-order optical aberration cancellation to calculate the focal curves. We also examine the validity of small divergence closed-form formulas describing the light path function. Optimizing the optical and geometric parameters gives an ultimate resolving power, at 930 eV, of between 10 800 for a 3 m long instrument and 34 000 for an 11 m spectrometer according to the Rayleigh criterion. Typical fabrication tolerances would scale these values down by about 10%. The findings are validated by ray-tracing simulations.

© 2012 Optical Society of America

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  3. T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
    [CrossRef]
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  6. C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
    [CrossRef]
  7. D. Cocco, M. Matteucci, K. C. Prince, and M. Zangrando, “ComIXS: a compact inelastic x-ray spectrometer,” Proc. SPIE 4506, 46–227(2001).
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    [CrossRef]
  9. Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
    [CrossRef]
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    [CrossRef]
  11. G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
    [CrossRef]
  12. Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
    [CrossRef]
  13. L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  25. M. Sánchez del Río and R. J. Dejus, “Status of XOP: an x-ray optics software toolkit,” Proc. SPIE 5536, 171–174(2004).
    [CrossRef]
  26. M. Sánchez del Río and A. Marcelli, “Waviness effects in ray-tracing of “real” optical surfaces,” Nucl. Instrum. Methods Phys. Res. A 319, 170–177 (1992).
    [CrossRef]
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2012 (1)

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

2011 (2)

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[CrossRef]

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbăian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[CrossRef]

2006 (2)

T. Tokushima, Y. Harada, H. Ohashi, Y. Senba, and S. Shin, “High performance slit-less spectrometer for soft x-ray emission spectroscopy,” Rev. Sci. Instrum. 77, 063107 (2006).
[CrossRef]

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

2005 (2)

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

2004 (1)

M. Sánchez del Río and R. J. Dejus, “Status of XOP: an x-ray optics software toolkit,” Proc. SPIE 5536, 171–174(2004).
[CrossRef]

2001 (2)

D. Cocco, M. Matteucci, K. C. Prince, and M. Zangrando, “ComIXS: a compact inelastic x-ray spectrometer,” Proc. SPIE 4506, 46–227(2001).
[CrossRef]

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

1999 (1)

1997 (1)

1996 (1)

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

1995 (2)

S. Shin, A. Agui, M. Fujisawa, Y. Tezuka, and T. Ishii, “Soft x-ray emission spectrometer for undulator radiation,” Rev. Sci. Instrum. 66, 1584–1586 (1995).
[CrossRef]

K. D. Osborn and T. A. Callcott, “Two new optical designs for soft x-ray spectrometers using variable-line-space gratings,” Rev. Sci. Instrum. 66, 3131–3136 (1995).
[CrossRef]

1994 (1)

M. Koike and T. Namioka, “Merit function for the design of grating instruments,” Appl. Opt. 33, 2028–2056 (1994).

1992 (1)

M. Sánchez del Río and A. Marcelli, “Waviness effects in ray-tracing of “real” optical surfaces,” Nucl. Instrum. Methods Phys. Res. A 319, 170–177 (1992).
[CrossRef]

1986 (3)

B. Lai and F. Cerrina, “SHADOW: a synchrotron radiation ray tracing program,” Nucl. Instrum. Methods Phys. Res. A 246, 337–341 (1986).
[CrossRef]

J. Nordgren and R. Nyholm, “Design of a portable large spectral range grazing incidence instrument,” Nucl. Instrum. Methods Phys. Res. A 246, 242–245 (1986).
[CrossRef]

T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
[CrossRef]

1979 (1)

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

1974 (1)

1883 (1)

H. A. Rowland, “On concave gratings for optical purposes,” Philos. Mag. 16, 197–210 (1883).

Agren, H.

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Agui, A.

S. Shin, A. Agui, M. Fujisawa, Y. Tezuka, and T. Ishii, “Soft x-ray emission spectrometer for undulator radiation,” Rev. Sci. Instrum. 66, 1584–1586 (1995).
[CrossRef]

Ament, L. J. P.

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[CrossRef]

Arakawa, E. T.

T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
[CrossRef]

Avila, A.

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

Baluta, C.

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

Batson, P.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Betemps, R.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Braicovich, L.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Brookes, N. B.

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Burrows, D. N.

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

Callcott, T. A.

K. D. Osborn and T. A. Callcott, “Two new optical designs for soft x-ray spectrometers using variable-line-space gratings,” Rev. Sci. Instrum. 66, 3131–3136 (1995).
[CrossRef]

T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
[CrossRef]

Cerrina, F.

B. Lai and F. Cerrina, “SHADOW: a synchrotron radiation ray tracing program,” Nucl. Instrum. Methods Phys. Res. A 246, 337–341 (1986).
[CrossRef]

Chartas, G.

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

Chiuzbaian, G. S.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbăian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[CrossRef]

Chuang, Y.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Cocco, D.

D. Cocco, M. Matteucci, K. C. Prince, and M. Zangrando, “ComIXS: a compact inelastic x-ray spectrometer,” Proc. SPIE 4506, 46–227(2001).
[CrossRef]

Dallera, C.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Dejus, R. J.

M. Sánchez del Río and R. J. Dejus, “Status of XOP: an x-ray optics software toolkit,” Proc. SPIE 5536, 171–174(2004).
[CrossRef]

Delaunay, R.

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

Devereaux, T. P.

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[CrossRef]

Ederer, D. L.

T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
[CrossRef]

Fasana, A.

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Flechsig, U.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbăian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[CrossRef]

Fujisawa, M.

S. Shin, A. Agui, M. Fujisawa, Y. Tezuka, and T. Ishii, “Soft x-ray emission spectrometer for undulator radiation,” Rev. Sci. Instrum. 66, 1584–1586 (1995).
[CrossRef]

Garmire, G. P.

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

Ghiringhelli, G.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Goedkoop, J. B.

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Griep, S.

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Grioni, M.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Gullikson, E.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Hague, C. F.

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

Harada, T.

Harada, Y.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

T. Tokushima, Y. Harada, H. Ohashi, Y. Senba, and S. Shin, “High performance slit-less spectrometer for soft x-ray emission spectroscopy,” Rev. Sci. Instrum. 77, 063107 (2006).
[CrossRef]

Hasan, M. Z.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Hettrick, M. C.

M. C. Hettrick and J. H. Underwood, “Optical system for high resolution spectrometer/monochromator,” U.S. patent 4,776,696 (1988).

Hill, J. P.

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[CrossRef]

Horikawa, Y.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

Howells, M. R.

M. R. Howells, “Gratings and monochromators,” in X-ray Data Booklet (Lawrence Berkeley National Laboratory, 2001), pp. 4–17.

Hussain, Z.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Incorvaia, N.

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Ishii, T.

S. Shin, A. Agui, M. Fujisawa, Y. Tezuka, and T. Ishii, “Soft x-ray emission spectrometer for undulator radiation,” Rev. Sci. Instrum. 66, 1584–1586 (1995).
[CrossRef]

Kobayashi, M.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

Koch, J. A.

Koike, M.

M. Koike and T. Namioka, “Merit function for the design of grating instruments,” Appl. Opt. 33, 2028–2056 (1994).

Lai, B.

B. Lai and F. Cerrina, “SHADOW: a synchrotron radiation ray tracing program,” Nucl. Instrum. Methods Phys. Res. A 246, 337–341 (1986).
[CrossRef]

Marcelli, A.

M. Sánchez del Río and A. Marcelli, “Waviness effects in ray-tracing of “real” optical surfaces,” Nucl. Instrum. Methods Phys. Res. A 319, 170–177 (1992).
[CrossRef]

Marsi, M.

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

Matteucci, M.

D. Cocco, M. Matteucci, K. C. Prince, and M. Zangrando, “ComIXS: a compact inelastic x-ray spectrometer,” Proc. SPIE 4506, 46–227(2001).
[CrossRef]

McKinney, W.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Miyata, E.

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

Mori, K.

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

Namioka, T.

M. Koike and T. Namioka, “Merit function for the design of grating instruments,” Appl. Opt. 33, 2028–2056 (1994).

T. Namioka, “Diffraction gratings,” in Experimental Methods in the Physical Sciences Vol. 31, J. A. R. Samson and D. L. Ederer, eds. (Academic, 1998), pp. 347–377.

Niwa, H.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

Noda, H.

Nordgren, J.

J. Nordgren and R. Nyholm, “Design of a portable large spectral range grazing incidence instrument,” Nucl. Instrum. Methods Phys. Res. A 246, 242–245 (1986).
[CrossRef]

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Nordling, C.

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Nyholm, R.

J. Nordgren and R. Nyholm, “Design of a portable large spectral range grazing incidence instrument,” Nucl. Instrum. Methods Phys. Res. A 246, 242–245 (1986).
[CrossRef]

Ohashi, H.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

T. Tokushima, Y. Harada, H. Ohashi, Y. Senba, and S. Shin, “High performance slit-less spectrometer for soft x-ray emission spectroscopy,” Rev. Sci. Instrum. 77, 063107 (2006).
[CrossRef]

Osborn, K. D.

K. D. Osborn and T. A. Callcott, “Two new optical designs for soft x-ray spectrometers using variable-line-space gratings,” Rev. Sci. Instrum. 66, 3131–3136 (1995).
[CrossRef]

Oshima, M.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

Osyczka, A.

Patthey, L.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbăian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[CrossRef]

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Peatman, W. B.

W. B. Peatman, Gratings, Mirrors and Slits (Gordon and Breach Science, 1997).

Pepper, J.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Pettersson, L.

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Piazzalunga, A.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Prince, K. C.

D. Cocco, M. Matteucci, K. C. Prince, and M. Zangrando, “ComIXS: a compact inelastic x-ray spectrometer,” Proc. SPIE 4506, 46–227(2001).
[CrossRef]

Puppin, E.

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Qian, D.

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

Ringuenet, H.

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

Rowland, H. A.

H. A. Rowland, “On concave gratings for optical purposes,” Philos. Mag. 16, 197–210 (1883).

Sacchi, M.

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

Sakuma, H.

Sánchez del Río, M.

M. Sánchez del Río and R. J. Dejus, “Status of XOP: an x-ray optics software toolkit,” Proc. SPIE 5536, 171–174(2004).
[CrossRef]

M. Sánchez del Río and A. Marcelli, “Waviness effects in ray-tracing of “real” optical surfaces,” Nucl. Instrum. Methods Phys. Res. A 319, 170–177 (1992).
[CrossRef]

Schmitt, T.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbăian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[CrossRef]

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Selander, L.

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Senba, Y.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

T. Tokushima, Y. Harada, H. Ohashi, Y. Senba, and S. Shin, “High performance slit-less spectrometer for soft x-ray emission spectroscopy,” Rev. Sci. Instrum. 77, 063107 (2006).
[CrossRef]

Seya, N.

Shin, S.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

T. Tokushima, Y. Harada, H. Ohashi, Y. Senba, and S. Shin, “High performance slit-less spectrometer for soft x-ray emission spectroscopy,” Rev. Sci. Instrum. 77, 063107 (2006).
[CrossRef]

S. Shin, A. Agui, M. Fujisawa, Y. Tezuka, and T. Ishii, “Soft x-ray emission spectrometer for undulator radiation,” Rev. Sci. Instrum. 66, 1584–1586 (1995).
[CrossRef]

Siegbahn, K.

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Strocov, V. N.

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbăian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[CrossRef]

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Takahashi, K.

Tamioka, T.

Tezuka, Y.

S. Shin, A. Agui, M. Fujisawa, Y. Tezuka, and T. Ishii, “Soft x-ray emission spectrometer for undulator radiation,” Rev. Sci. Instrum. 66, 1584–1586 (1995).
[CrossRef]

Thomasset, M.

M. Thomasset, Synchrotron Soleil, France (personal communication, 2012).

Tokushima, T.

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

T. Tokushima, Y. Harada, H. Ohashi, Y. Senba, and S. Shin, “High performance slit-less spectrometer for soft x-ray emission spectroscopy,” Rev. Sci. Instrum. 77, 063107 (2006).
[CrossRef]

Trezzi, G.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

Tsang, K. L.

T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
[CrossRef]

Tsunemi, H.

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

Underwood, J. H.

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

J. H. Underwood and J. A. Koch, “High-resolution tunable spectrograph for x-ray laser linewidth measurements with a plane varied-line-spacing grating,” Appl. Opt. 36, 4913–4921 (1997).
[CrossRef]

M. C. Hettrick and J. H. Underwood, “Optical system for high resolution spectrometer/monochromator,” U.S. patent 4,776,696 (1988).

van den Brink, J.

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[CrossRef]

van Veenendaal, M.

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[CrossRef]

Wang, X.

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Zangrando, M.

D. Cocco, M. Matteucci, K. C. Prince, and M. Zangrando, “ComIXS: a compact inelastic x-ray spectrometer,” Proc. SPIE 4506, 46–227(2001).
[CrossRef]

Zhang, C. H.

T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
[CrossRef]

Appl. Opt. (3)

Astrophys. J. (1)

H. Tsunemi, K. Mori, E. Miyata, C. Baluta, D. N. Burrows, G. P. Garmire, and G. Chartas, “Improvement of the spatial resolution of the ACIS using split-pixel events,” Astrophys. J. 554, 496–504 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Chem. Solids (1)

Y. Chuang, J. Pepper, W. McKinney, Z. Hussain, E. Gullikson, P. Batson, D. Qian, and M. Z. Hasan, “High-resolution soft X-ray emission spectrograph at advanced light source,” J. Phys. Chem. Solids 66, 2173–2178 (2005).
[CrossRef]

J. Synchrotron Radiat. (2)

C. Dallera, E. Puppin, A. Fasana, G. Trezzi, N. Incorvaia, L. Braicovich, N. B. Brookes, and J. B. Goedkoop, “Soft x-ray emission spectroscopy at ESRF beamline 26 based on a helical undulator,” J. Synchrotron Radiat. 3, 231–238 (1996).
[CrossRef]

V. N. Strocov, T. Schmitt, U. Flechsig, L. Patthey, and G. S. Chiuzbăian, “Numerical optimization of spherical variable-line-spacing grating X-ray spectrometers,” J. Synchrotron Radiat. 18, 134–142 (2011).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (3)

B. Lai and F. Cerrina, “SHADOW: a synchrotron radiation ray tracing program,” Nucl. Instrum. Methods Phys. Res. A 246, 337–341 (1986).
[CrossRef]

M. Sánchez del Río and A. Marcelli, “Waviness effects in ray-tracing of “real” optical surfaces,” Nucl. Instrum. Methods Phys. Res. A 319, 170–177 (1992).
[CrossRef]

J. Nordgren and R. Nyholm, “Design of a portable large spectral range grazing incidence instrument,” Nucl. Instrum. Methods Phys. Res. A 246, 242–245 (1986).
[CrossRef]

Philos. Mag. (1)

H. A. Rowland, “On concave gratings for optical purposes,” Philos. Mag. 16, 197–210 (1883).

Physica Scripta (1)

J. Nordgren, H. Agren, L. Pettersson, L. Selander, S. Griep, C. Nordling, and K. Siegbahn, “A new 10 m grazing incidence instrument for molecular X-ray studies,” Physica Scripta 20, 623–626 (1979).
[CrossRef]

Proc. SPIE (2)

D. Cocco, M. Matteucci, K. C. Prince, and M. Zangrando, “ComIXS: a compact inelastic x-ray spectrometer,” Proc. SPIE 4506, 46–227(2001).
[CrossRef]

M. Sánchez del Río and R. J. Dejus, “Status of XOP: an x-ray optics software toolkit,” Proc. SPIE 5536, 171–174(2004).
[CrossRef]

Rev. Mod. Phys. (1)

L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011).
[CrossRef]

Rev. Sci. Instrum. (7)

C. F. Hague, J. H. Underwood, A. Avila, R. Delaunay, H. Ringuenet, M. Marsi, and M. Sacchi, “Plane-grating flat-field soft x-ray spectrometer,” Rev. Sci. Instrum. 76, 023110 (2005).
[CrossRef]

T. A. Callcott, K. L. Tsang, C. H. Zhang, D. L. Ederer, and E. T. Arakawa, “High-efficiency soft x-ray emission spectrometer for use with synchrotron radiation excitation,” Rev. Sci. Instrum. 57, 2680–2690 (1986).
[CrossRef]

S. Shin, A. Agui, M. Fujisawa, Y. Tezuka, and T. Ishii, “Soft x-ray emission spectrometer for undulator radiation,” Rev. Sci. Instrum. 66, 1584–1586 (1995).
[CrossRef]

K. D. Osborn and T. A. Callcott, “Two new optical designs for soft x-ray spectrometers using variable-line-space gratings,” Rev. Sci. Instrum. 66, 3131–3136 (1995).
[CrossRef]

T. Tokushima, Y. Harada, H. Ohashi, Y. Senba, and S. Shin, “High performance slit-less spectrometer for soft x-ray emission spectroscopy,” Rev. Sci. Instrum. 77, 063107 (2006).
[CrossRef]

G. Ghiringhelli, A. Piazzalunga, C. Dallera, G. Trezzi, L. Braicovich, T. Schmitt, V. N. Strocov, R. Betemps, L. Patthey, X. Wang, and M. Grioni, “SAXES, a high resolution spectrometer for resonant x-ray emission in the 400–1600 eV energy range,” Rev. Sci. Instrum. 77, 113108 (2006).
[CrossRef]

Y. Harada, M. Kobayashi, H. Niwa, Y. Senba, H. Ohashi, T. Tokushima, Y. Horikawa, S. Shin, and M. Oshima, “Ultrahigh resolution soft x-ray emission spectrometer at BL07LSU in SPring-8,” Rev. Sci. Instrum. 83, 013116 (2012).
[CrossRef]

Other (5)

M. C. Hettrick and J. H. Underwood, “Optical system for high resolution spectrometer/monochromator,” U.S. patent 4,776,696 (1988).

M. R. Howells, “Gratings and monochromators,” in X-ray Data Booklet (Lawrence Berkeley National Laboratory, 2001), pp. 4–17.

W. B. Peatman, Gratings, Mirrors and Slits (Gordon and Breach Science, 1997).

M. Thomasset, Synchrotron Soleil, France (personal communication, 2012).

T. Namioka, “Diffraction gratings,” in Experimental Methods in the Physical Sciences Vol. 31, J. A. R. Samson and D. L. Ederer, eds. (Academic, 1998), pp. 347–377.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of a VLS-SG spectrometer. The light arising from the source S impinges in the middle of the grating G on the way to the detector center D. G denotes arbitrary points on the grating.

Fig. 2.
Fig. 2.

Focal surfaces (upper panels) and the corresponding broadening of the resolving power (lower panels, logarithmic vertical axis) due to optical aberrations RA for successive approximations at full illumination of the grating. Left panels display the case of F20=0 and F20=F30=0 focal curves, while right panels show F20=F30=F40=0 and F40=0.

Fig. 3.
Fig. 3.

Contributions to the resolving power of a VLS-SG instrument with overall length r+r=8m (left panel) accompanied by ray-tracing simulations at 930 eV and full illumination of the grating. RS represents the source size contribution to the resolving power, RG the grating slope error weight, and RD the detector pixel limitation. Upper right panels show the spread of rays across the detector without detector pixel limitation; lower right panels take into account a detector pixel size S2min=13.5μm. The detector is oriented at γ=20° glancing incidence. The aberrations are minimized down to the RA values shown in Fig. 2 and are not displayed here.

Fig. 4.
Fig. 4.

Attainable theoretical resolving power, R, considered within the Rayleigh criterion, for different instrument lengths at full illumination for a 12 cm long grating. In practice, the displayed values should be scaled down by 5–10% (see Section 5). The results are considered for α0=88.4° at the optimization energy E0=930eV and magnification adjusted such that the orientation of the focal curve is conserved and makes γ=20° at E0.

Fig. 5.
Fig. 5.

Illustration of the resolving power criteria for Gaussian instrumental lines with identical width Δλ.

Tables (2)

Tables Icon

Table 1. Ideal Calculated Parameters and Global Theoretical Performance at 930 eV

Tables Icon

Table 2. Instrument Parameters Defined Within Attainable Tolerances

Equations (11)

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

F10=sinαsinβ+a0mλ,
F20=12(cos2αrcosαR)+12(cos2βrcosβR)+12a1mλ,
F30=sinα2r(cos2αrcosαR)+sinβ2r(cos2βrcosβR)+13a2mλ,
F40=cosα8R3+18r[1R2(cos2αrcosαR)2]+sinα2r(cos2αrcosαR)cosβ8R3+18r[1R2(cos2βrcosβR)2]+sinβ2r(cos2βrcosβR)+14a3mλ.
cos2αr+cos2βr+a0mλr(cosβtanγ+2sinβ)=1R[(cosα+cosβ)+a0mλtanβ].
R=λξRΔλ=EξRΔE,
Δλ=ΔλS2+ΔλG2+ΔλD2+ΔλA2.
ΔλS=S1cosαamr,
ΔλG=cosα+cosβam=2.3542σG,
ΔλD=S2cosβamr,
ΔλA=22ln2σdet=2.3542σdet,

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