Abstract

We have developed a method for the manufacture of x-ray diffraction gratings with arbitrarily small blaze angles. These gratings are made by a process in which a high blaze angle grating made by anisotropic etching of Si (111) is subjected to planarization and reactive ion etching. Differential etching of the planarization medium and silicon ensures reduction of the blaze angle. Repeated application of this process leads to gratings of increasing perfection with an arbitrarily small blaze angle. This opens the way to highly efficient low line density gratings, to damage resistant gratings for ultra-high power applications such as free electron lasers, and for extension of the use of gratings into the hard x-ray energy range for dispersive spectroscopy.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  3. D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
    [Crossref]
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2018 (1)

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

2017 (2)

D. L. Voronov, E. M. Gullikson, and H. A. Padmore, “Large area nanoimprint enables ultra-precise x-ray diffraction gratings,” Opt. Express 25(19), 23334–23342 (2017).
[Crossref] [PubMed]

D. L. Voronov, P. Lum, and H. A. Padmore, “Full size x-ray grating fabrication using large area nanoimprint,” Proc. SPIE 10386, 1038607 (2017).

2016 (3)

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

D. L. Voronov, F. Salmassi, J. Meyer-Ilse, E. M. Gullikson, T. Warwick, and H. A. Padmore, “Refraction effects in soft x-ray Multilayer Blazed Gratings,” Opt. Express 24(11), 11334–11344 (2016).
[Crossref] [PubMed]

J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
[Crossref] [PubMed]

2015 (1)

2014 (1)

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A Multiplexed High-Resolution Imaging Spectrometer for Resonant Inelastic Soft X-ray Scattering Spectroscopy,” J. Synchrotron Radiat. 21(Pt 4), 736–743 (2014).
[Crossref] [PubMed]

2013 (1)

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

2012 (1)

2008 (1)

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

2007 (2)

K. F. Heidemann, B. Nelles, and R. Lenke, “Gratings with Blaze Angles Down to 0.1° for Photon Energies up to 10 keV,” AIP Conf. Proc. 879, 485–488 (2007).
[Crossref]

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

1992 (1)

L. E. Stillwagon and R. G. Larson, “Planarization during spin coating,” Phys. Fluids A Fluid Dyn. 4(5), 895–903 (1992).
[Crossref]

1981 (1)

Arnold, T.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Bajt, S.

Bianco, A.

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

Bisogni, V.

J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
[Crossref] [PubMed]

Buchheim, J.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Burian, T.

Cambie, R.

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Celestre, R.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Chalupský, J.

Chao, W.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Chapman, H. N.

Chuang, Y.-D.

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A Multiplexed High-Resolution Imaging Spectrometer for Resonant Inelastic Soft X-ray Scattering Spectroscopy,” J. Synchrotron Radiat. 21(Pt 4), 736–743 (2014).
[Crossref] [PubMed]

Coburn, S.

J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
[Crossref] [PubMed]

Cocco, D.

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

Coppola, N.

Doering, D.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Dvorak, J.

J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
[Crossref] [PubMed]

Eggenstein, F.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Eichert, D.

Erko, A.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Farahani, S. D.

Fedorov, A. V.

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

Firsov, A.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Follath, R.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Frost, F.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Galasso, G.

Gaudin, J.

Gullikson, E. M.

D. L. Voronov, E. M. Gullikson, and H. A. Padmore, “Large area nanoimprint enables ultra-precise x-ray diffraction gratings,” Opt. Express 25(19), 23334–23342 (2017).
[Crossref] [PubMed]

D. L. Voronov, F. Salmassi, J. Meyer-Ilse, E. M. Gullikson, T. Warwick, and H. A. Padmore, “Refraction effects in soft x-ray Multilayer Blazed Gratings,” Opt. Express 24(11), 11334–11344 (2016).
[Crossref] [PubMed]

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Gwalt, G.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Hájková, V.

Harmand, M.

Heidemann, K. F.

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

K. F. Heidemann, B. Nelles, and R. Lenke, “Gratings with Blaze Angles Down to 0.1° for Photon Energies up to 10 keV,” AIP Conf. Proc. 879, 485–488 (2007).
[Crossref]

Howells, M.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Jark, W.

Jarrige, I.

J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
[Crossref] [PubMed]

Juha, L.

Jurek, M.

Kaulich, B.

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

Kevan, S.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Kilcoyne, D.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Kirz, J.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Kondratenko, V. V.

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Krzywinski, J.

Kutz, O.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Larson, R. G.

L. E. Stillwagon and R. G. Larson, “Planarization during spin coating,” Phys. Fluids A Fluid Dyn. 4(5), 895–903 (1992).
[Crossref]

Lemke, S.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Lenke, R.

K. F. Heidemann, B. Nelles, and R. Lenke, “Gratings with Blaze Angles Down to 0.1° for Photon Energies up to 10 keV,” AIP Conf. Proc. 879, 485–488 (2007).
[Crossref]

Leonhardt, W.

J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
[Crossref] [PubMed]

Loch, R. A.

Löchel, B.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Lum, P.

D. L. Voronov, P. Lum, and H. A. Padmore, “Full size x-ray grating fabrication using large area nanoimprint,” Proc. SPIE 10386, 1038607 (2017).

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

Marchesini, S.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Mertin, M.

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

Meyer-Ilse, J.

Möller, S.

Nagasono, M.

Naulleau, P.

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

Nelles, B.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

K. F. Heidemann, B. Nelles, and R. Lenke, “Gratings with Blaze Angles Down to 0.1° for Photon Energies up to 10 keV,” AIP Conf. Proc. 879, 485–488 (2007).
[Crossref]

Ozkan, C.

Padmore, H. A.

D. L. Voronov, P. Lum, and H. A. Padmore, “Full size x-ray grating fabrication using large area nanoimprint,” Proc. SPIE 10386, 1038607 (2017).

D. L. Voronov, E. M. Gullikson, and H. A. Padmore, “Large area nanoimprint enables ultra-precise x-ray diffraction gratings,” Opt. Express 25(19), 23334–23342 (2017).
[Crossref] [PubMed]

D. L. Voronov, F. Salmassi, J. Meyer-Ilse, E. M. Gullikson, T. Warwick, and H. A. Padmore, “Refraction effects in soft x-ray Multilayer Blazed Gratings,” Opt. Express 24(11), 11334–11344 (2016).
[Crossref] [PubMed]

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A Multiplexed High-Resolution Imaging Spectrometer for Resonant Inelastic Soft X-ray Scattering Spectroscopy,” J. Synchrotron Radiat. 21(Pt 4), 736–743 (2014).
[Crossref] [PubMed]

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Pershin, Yu. P.

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Pietag, F.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Ponomarenko, A. G.

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Reichardt, G.

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

Roy, S.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Rudolph, I.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Saksl, K.

Salmassi, F.

Schaefers, F.

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

Schäfers, F.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Schirotzek, A.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Schulz, J.

Seliger, T.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Senf, F.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Seu, K. A.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Shapiro, D.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Siewert, F.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Sinn, H.

Sobierajski, R.

Sokolov, A.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Sovak, P.

Spence, J.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Stillwagon, L. E.

L. E. Stillwagon and R. G. Larson, “Planarization during spin coating,” Phys. Fluids A Fluid Dyn. 4(5), 895–903 (1992).
[Crossref]

Störmer, M.

Tiedtke, K.

Toleikis, S.

Tschentscher, T.

Tyliszczak, T.

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Visser, H.

Voronov, D. L.

D. L. Voronov, P. Lum, and H. A. Padmore, “Full size x-ray grating fabrication using large area nanoimprint,” Proc. SPIE 10386, 1038607 (2017).

D. L. Voronov, E. M. Gullikson, and H. A. Padmore, “Large area nanoimprint enables ultra-precise x-ray diffraction gratings,” Opt. Express 25(19), 23334–23342 (2017).
[Crossref] [PubMed]

D. L. Voronov, F. Salmassi, J. Meyer-Ilse, E. M. Gullikson, T. Warwick, and H. A. Padmore, “Refraction effects in soft x-ray Multilayer Blazed Gratings,” Opt. Express 24(11), 11334–11344 (2016).
[Crossref] [PubMed]

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A Multiplexed High-Resolution Imaging Spectrometer for Resonant Inelastic Soft X-ray Scattering Spectroscopy,” J. Synchrotron Radiat. 21(Pt 4), 736–743 (2014).
[Crossref] [PubMed]

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Vyšín, L.

Waberski, C.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Warwick, T.

D. L. Voronov, F. Salmassi, J. Meyer-Ilse, E. M. Gullikson, T. Warwick, and H. A. Padmore, “Refraction effects in soft x-ray Multilayer Blazed Gratings,” Opt. Express 24(11), 11334–11344 (2016).
[Crossref] [PubMed]

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A Multiplexed High-Resolution Imaging Spectrometer for Resonant Inelastic Soft X-ray Scattering Spectroscopy,” J. Synchrotron Radiat. 21(Pt 4), 736–743 (2014).
[Crossref] [PubMed]

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

Werner, W.

Wolf, J.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Yashchuk, V. V.

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Zeschke, T.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

Zizak, I.

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

AIP Conf. Proc. (2)

K. F. Heidemann, B. Nelles, and R. Lenke, “Gratings with Blaze Angles Down to 0.1° for Photon Energies up to 10 keV,” AIP Conf. Proc. 879, 485–488 (2007).
[Crossref]

D. Cocco, A. Bianco, B. Kaulich, F. Schaefers, M. Mertin, G. Reichardt, B. Nelles, and K. F. Heidemann, “From Soft to Hard X‐ray with a Single Grating Monochromator,” AIP Conf. Proc. 879, 497–500 (2007).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. L. Voronov, P. Lum, P. Naulleau, E. M. Gullikson, A. V. Fedorov, and H. A. Padmore, “X-ray diffraction gratings: precise control of ultra-low blaze angle via anisotropic wet etch,” Appl. Phys. Lett. 109(4), 043112 (2016).
[Crossref]

J. Phys. Conf. Ser. (1)

D. Shapiro, S. Roy, R. Celestre, W. Chao, D. Doering, M. Howells, S. Kevan, D. Kilcoyne, J. Kirz, S. Marchesini, K. A. Seu, A. Schirotzek, J. Spence, T. Tyliszczak, T. Warwick, D. L. Voronov, and H. A. Padmore, “Development of coherent scattering and diffractive imaging and the COSMIC facility at the Advanced Light Source,” J. Phys. Conf. Ser. 425(19), 192011 (2013).
[Crossref]

J. Synchrotron Radiat. (2)

F. Siewert, B. Löchel, J. Buchheim, F. Eggenstein, A. Firsov, G. Gwalt, O. Kutz, S. Lemke, B. Nelles, I. Rudolph, F. Schäfers, T. Seliger, F. Senf, A. Sokolov, C. Waberski, J. Wolf, T. Zeschke, I. Zizak, R. Follath, T. Arnold, F. Frost, F. Pietag, and A. Erko, “Gratings for synchrotron and FEL beamlines: a project for the manufacture of ultra-precise gratings at Helmholtz Zentrum Berlin,” J. Synchrotron Radiat. 25(Pt 1), 91–99 (2018).
[Crossref] [PubMed]

T. Warwick, Y.-D. Chuang, D. L. Voronov, and H. A. Padmore, “A Multiplexed High-Resolution Imaging Spectrometer for Resonant Inelastic Soft X-ray Scattering Spectroscopy,” J. Synchrotron Radiat. 21(Pt 4), 736–743 (2014).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

Phys. Fluids A Fluid Dyn. (1)

L. E. Stillwagon and R. G. Larson, “Planarization during spin coating,” Phys. Fluids A Fluid Dyn. 4(5), 895–903 (1992).
[Crossref]

Proc. SPIE (2)

D. L. Voronov, P. Lum, and H. A. Padmore, “Full size x-ray grating fabrication using large area nanoimprint,” Proc. SPIE 10386, 1038607 (2017).

D. L. Voronov, R. Cambie, E. M. Gullikson, V. V. Yashchuk, H. A. Padmore, Yu. P. Pershin, A. G. Ponomarenko, and V. V. Kondratenko, “Fabrication and characterization of a new high density Sc/Si multilayer sliced grating,” Proc. SPIE 7077, 707708 (2008).
[Crossref]

Rev. Sci. Instrum. (1)

J. Dvorak, I. Jarrige, V. Bisogni, S. Coburn, and W. Leonhardt, “Towards 10 meV resolution: The design of an ultrahigh resolution soft X-ray RIXS spectrometer,” Rev. Sci. Instrum. 87(11), 115109 (2016).
[Crossref] [PubMed]

Other (3)

http://cxro.lbl.gov/reflectometer

http://www.pcgrate.com

http://www.capitolscientific.com/Dow-Electronic-Materials-AR3-600-DUV-Anti-Reflectant-1-Gallon-Glass-Bottle

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Figures (7)

Fig. 1
Fig. 1 Process flow for reduction of the blaze angle of an original saw-tooth grating: original Si grating with large blaze angle (a), planarization of the grating surface with a sacrificial layer (b), plasma etching of the sacrificial layer with an etch rate of VSL/ VSi ≈2 (c), a final blazed grating with a reduced blaze angle (d).
Fig. 2
Fig. 2 AFM image of the blazed gratings with blazed angles of 5.7° before (a) and after (b) planarization. The full vertical range is 2 μ m and 50 nm respectively.
Fig. 3
Fig. 3 Cross-sectional SEM images of an original 100 lines/mm grating with ablaze angle of 5.7°, planarized with AR3 coating (a), (b) the same grating in the middle of the RIE reduction etch: the AR3 is still observed in the bottom part of the grooves, and the upper part of the grooves has a reduced blaze angle.
Fig. 4
Fig. 4 Profiles of the grating before and after successive reduction cycles
Fig. 5
Fig. 5 AFM image and the average groove profile of the final blazed grating with a groove density of 100 lines/mm and a blaze angle of 0.17°.
Fig. 6
Fig. 6 Experimental (blue line with symbols) and simulated (red and grey bars) diffraction from the fabricated blazed grating at an energy of 700 eV and an incidence angle of 88.46° (a). Experimental (red line with symbols) and simulated (grey bars) diffraction efficiency of the 100 lines/mm lamellar grating from the Cosmic monochromator (b).
Fig. 7
Fig. 7 Experimental efficiency of the 1st positive diffraction order of the 100 lines/mm Cosmic lamellar grating (red curve with triangular symbols) and the blazed grating under blaze conditions (blue curve with circle symbols) and for the constant Cff = 1.2 geometry (green curve with square symbols).

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