Abstract

X-ray fluorescence imaging using perfect planar square pore micro-channel plate x-ray optics (MPO) is investigated through the modeling of the MPO point spread function (PSF). A semi-continuous model based on the use of a simplified two parameters reflectivity curve is developed including, in particular, three kinds of contributions. A validation of this model is carried out by calculating variations of several PSF characteristics with the MPO and fluorescence imaging parameters and comparing the results with ray-tracing simulations. A good agreement is found in a large range of x-ray energies; however, it is shown that for the lower values of the working distance a discrete model should be used to take into account the periodic nature of the PSF. Ray-tracing simulated images of extended monochromatic sources are interpreted in light of both the semi-continuous and discrete models. Finally, solutions are proposed to improve the imaging properties of the MPOs.

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

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  1. K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
    [Crossref]
  2. M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
    [Crossref]
  3. I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
    [Crossref]
  4. L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
    [Crossref]
  5. P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
    [Crossref]
  6. D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.
  7. R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  14. F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
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    [Crossref]
  17. R. Willingale, G. W. Fraser, and J. F. Pearson, “Optimization of square pore optics for the x-ray spectrometer on Bepi-Columbo,” Proc. SPIE 5900, 590012 (2005).
    [Crossref]
  18. R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
    [Crossref]

2018 (1)

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

2017 (2)

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

2016 (2)

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

2015 (1)

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

2013 (1)

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

2012 (1)

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

2011 (1)

M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
[Crossref]

2005 (1)

R. Willingale, G. W. Fraser, and J. F. Pearson, “Optimization of square pore optics for the x-ray spectrometer on Bepi-Columbo,” Proc. SPIE 5900, 590012 (2005).
[Crossref]

2004 (1)

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

2000 (1)

C. T. Chantler, “Detailed tabulation of atomic form factors, photoelectric absorption and scattering cross section, and mass attenuation coefficients in the vicinity of absorption edges in the soft x-ray (z = 30–36, z = 60–89, e = 0.1 kev–10 kev), addressing convergence issues of earlier work,” J. Phys. Chem. Ref. Data 29, 597–1056 (2000).
[Crossref]

1993 (1)

1991 (1)

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using square channel-capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[Crossref]

1979 (1)

J. R. P. Angel, “Lobster eyes as x-ray telescopes,” Astrophys. J. 233, 364–373 (1979).
[Crossref]

Albéric, M.

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Alberti, R.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Alfeld, M.

M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
[Crossref]

Angel, J. R. P.

J. R. P. Angel, “Lobster eyes as x-ray telescopes,” Astrophys. J. 233, 364–373 (1979).
[Crossref]

Aresi, N.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Bertrand, L.

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

Bjeoumikhov, A.

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Blake, D.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Bombelli, L.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Bristow, T.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Caliri, C.

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Cartechini, L.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Chalumeau, C.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

Chantler, C. T.

C. T. Chantler, “Detailed tabulation of atomic form factors, photoelectric absorption and scattering cross section, and mass attenuation coefficients in the vicinity of absorption edges in the soft x-ray (z = 30–36, z = 60–89, e = 0.1 kev–10 kev), addressing convergence issues of earlier work,” J. Phys. Chem. Ref. Data 29, 597–1056 (2000).
[Crossref]

Chapman, H. N.

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
[Crossref]

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using square channel-capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[Crossref]

Cohen, S. X.

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

Cosentino, L.

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

de Nolf, W.

M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
[Crossref]

Di Martino, S.

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

Dik, J.

M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
[Crossref]

Downs, R.

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Fairbend, R.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Feldman, C. H.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Fraser, G. W.

R. Willingale, G. W. Fraser, and J. F. Pearson, “Optimization of square pore optics for the x-ray spectrometer on Bepi-Columbo,” Proc. SPIE 5900, 590012 (2005).
[Crossref]

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

Frizzi, T.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Gailhanou, M.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Gammino, S.

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Gironda, M.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Hasegawa, T.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Hérouard, D.

P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
[Crossref]

Holland, A. D.

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

Hutchinson, I. B.

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

Janssens, K.

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
[Crossref]

Kato, S.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Kawahara, N.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Kometani, N.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Marchis, F.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Martindale, A.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Mascali, D.

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Matsuno, T.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Miliani, C.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Ming, D.

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Morris, R.

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Müller, K.

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Nicotra, P.

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

Nugent, K. A.

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
[Crossref]

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using square channel-capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[Crossref]

Nussey, J. P.

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

O’Brien, P. T.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Osborne, J. P.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Pappalardo, L.

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Pearson, J. F.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

R. Willingale, G. W. Fraser, and J. F. Pearson, “Optimization of square pore optics for the x-ray spectrometer on Bepi-Columbo,” Proc. SPIE 5900, 590012 (2005).
[Crossref]

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

Petit, S.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Price, G. J.

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

Pullan, D.

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

Radtke, M.

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Reiche, I.

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Rizzo, F.

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Robinet, L.

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

Romano, F. P.

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Rosi, F.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Santos, H. C.

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Sarrazin, P.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Sasaki, Y. C.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Scharf, O.

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Schöder, S.

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

Schyns, E.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Shoji, T.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Simon, R.

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Solé, V. A.

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Takimoto, Y.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Talarico, F.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Thompson, K.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Thoury, M.

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

Tranquilli, G.

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Tsuji, K.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Turner, K.

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

van der Snickt, G.

M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
[Crossref]

Verney, A.

P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
[Crossref]

Wähning, A.

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

Walter, P.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Webb, S.

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Wilkins, S. W.

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using cylindrical-channel capillary arrays. I. Theory,” Appl. Opt. 32, 6316–6332 (1993).
[Crossref]

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using square channel-capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[Crossref]

Willingale, R.

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

R. Willingale, G. W. Fraser, and J. F. Pearson, “Optimization of square pore optics for the x-ray spectrometer on Bepi-Columbo,” Proc. SPIE 5900, 590012 (2005).
[Crossref]

Wilson, M.

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Yamada, T.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Yamanashi, M.

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

Yen, A.

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

Anal. Chem. (2)

I. Reiche, K. Müller, M. Albéric, O. Scharf, A. Wähning, A. Bjeoumikhov, M. Radtke, and R. Simon, “Discovering vanished paints and naturally formed gold nanoparticles on 2800 years old Phoenician ivories using SR-FF-MicroXRF with the color x-ray camera,” Anal. Chem. 85, 5857–5866 (2013).
[Crossref]

F. P. Romano, C. Caliri, L. Cosentino, S. Gammino, D. Mascali, L. Pappalardo, F. Rizzo, O. Scharf, and H. C. Santos, “Micro x-ray fluorescence imaging in a tabletop full field-x-ray fluorescence instrument and in a full field-particle induced x-ray emission end station,” Anal. Chem. 88, 9873–9880 (2016).
[Crossref]

Appl. Opt. (1)

Appl. Phys. A (1)

L. Bertrand, L. Robinet, M. Thoury, K. Janssens, S. X. Cohen, and S. Schöder, “Cultural heritage and archaeology materials studied by synchrotron spectroscopy and imaging,” Appl. Phys. A 106, 377–396 (2012).
[Crossref]

Astrophys. J. (1)

J. R. P. Angel, “Lobster eyes as x-ray telescopes,” Astrophys. J. 233, 364–373 (1979).
[Crossref]

J. Anal. At. Spectrom. (2)

M. Alfeld, K. Janssens, J. Dik, W. de Nolf, and G. van der Snickt, “Optimization of mobile scanning macro-XRF systems for the in situ investigation of historical paintings,” J. Anal. At. Spectrom. 26, 899–909 (2011).
[Crossref]

F. P. Romano, C. Caliri, P. Nicotra, S. Di Martino, L. Pappalardo, F. Rizzo, and H. C. Santos, “Real-time elemental imaging of large dimension paintings with a novel mobile macro x-ray fluorescence (MA-XRF) scanning technique,” J. Anal. At. Spectrom. 32, 773–781 (2017).
[Crossref]

J. Instrum. (1)

P. Sarrazin, D. Blake, M. Gailhanou, F. Marchis, C. Chalumeau, S. Webb, P. Walter, E. Schyns, K. Thompson, and T. Bristow, “MapX: 2D XRF for planetary exploration—image formation and optic characterization,” J. Instrum. 13, C04023 (2018).
[Crossref]

J. Phys. Chem. Ref. Data (1)

C. T. Chantler, “Detailed tabulation of atomic form factors, photoelectric absorption and scattering cross section, and mass attenuation coefficients in the vicinity of absorption edges in the soft x-ray (z = 30–36, z = 60–89, e = 0.1 kev–10 kev), addressing convergence issues of earlier work,” J. Phys. Chem. Ref. Data 29, 597–1056 (2000).
[Crossref]

Proc. SPIE (2)

R. Willingale, G. W. Fraser, and J. F. Pearson, “Optimization of square pore optics for the x-ray spectrometer on Bepi-Columbo,” Proc. SPIE 5900, 590012 (2005).
[Crossref]

R. Willingale, J. F. Pearson, A. Martindale, C. H. Feldman, R. Fairbend, E. Schyns, S. Petit, J. P. Osborne, and P. T. O’Brien, “Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes,” Proc. SPIE 9905, 99051Y (2016).
[Crossref]

Rev. Sci. Instrum. (2)

G. J. Price, G. W. Fraser, J. F. Pearson, J. P. Nussey, I. B. Hutchinson, A. D. Holland, K. Turner, and D. Pullan, “Prototype imaging x-ray fluorescence spectrometer based on microchannel plate optics,” Rev. Sci. Instrum. 75, 2314–2319 (2004).
[Crossref]

H. N. Chapman, K. A. Nugent, and S. W. Wilkins, “X-ray focusing using square channel-capillary arrays,” Rev. Sci. Instrum. 62, 1542–1561 (1991).
[Crossref]

Spectrochim. Acta Part B (1)

K. Tsuji, T. Matsuno, Y. Takimoto, M. Yamanashi, N. Kometani, Y. C. Sasaki, T. Hasegawa, S. Kato, T. Yamada, T. Shoji, and N. Kawahara, “New developments of x-ray fluorescence imaging techniques in laboratory,” Spectrochim. Acta Part B 113, 43–53 (2015).
[Crossref]

X-Ray Spectrom. (1)

R. Alberti, T. Frizzi, L. Bombelli, M. Gironda, N. Aresi, F. Rosi, C. Miliani, G. Tranquilli, F. Talarico, and L. Cartechini, “Crono: a fast and reconfigurable macro x-ray fluorescence scanner for in-situ investigations of polychrome surfaces,” X-Ray Spectrom. 46, 297–302 (2017).
[Crossref]

Other (3)

P. Walter, P. Sarrazin, M. Gailhanou, D. Hérouard, A. Verney, and D. Blake, “Full-field XRF instrument for cultural heritage: application to the study of a Caillebotte painting,” X-Ray Spectrom. (2018).
[Crossref]

D. Blake, P. Sarrazin, T. Bristow, R. Downs, M. Gailhanou, F. Marchis, D. Ming, R. Morris, V. A. Solé, K. Thompson, P. Walter, M. Wilson, A. Yen, and S. Webb, “The mapping x-ray fluorescence spectrometer (MapX),” in 3rd International Workshop on Instrumentation for Planetary Missions (2016), p. 4006.

J. Daillant and A. Gibaud, eds., “Chap. 3: Specular reflectivity from smooth and rough surfaces,” in X-Ray and Neutron Reflectivity, Theory and Applications (Springer, 1999).

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Figures (22)

Fig. 1.
Fig. 1. MPO geometrical parameters. (a) Point source imaged in the 1 1 arrangement. (b) Detail showing the precise position ( x 0 , y 0 ) of the optical axis with respect to the nearest pore center.
Fig. 2.
Fig. 2. Example of the simplified version of the reflectivity curve used for analytic calculations (blue line) compared with the simulated reflectivity of an Ir layer on a silica substrate at 6400 eV (red line).
Fig. 3.
Fig. 3. Ray-tracing simulated PSF. The reflecting material is a 25 nm Ir layer on SiO 2 , with both the surface and interface roughness equal to 2 nm. E = 15    keV , l s = 0.05    m , D = 20    μm , T = 26    μm , and t = 4.8    mm . Normalized intensity in log scale.
Fig. 4.
Fig. 4. Distribution of rays, contributing to the PSF central spot, at the entrance surface of the MPO. In the notation ( n x , n y ) , n x is the number of reflections in the xz plane, and n y is the number of reflections in the yz plane. Because of the parameters used here, n x and n y are either 1 or 0. Parameters: D = 20    μm , T = 26    μm , t = 1.2    mm , l s = 10    cm , E = 6400    eV , and reflective layer: Ir.
Fig. 5.
Fig. 5. Plots of S odd 2 ( α , Δ R ) as a function of α for different values of Δ R showing the influence of absorption and roughness induced loss on Ω 2 d .
Fig. 6.
Fig. 6. External total reflection critical angle γ c and reflectivity loss Δ R as a function of energy in the case of Ir reflective material. Δ R is shown for two values of the rms surface roughness σ . The insert shows the 2–3 keV region where effective values γ c eff [Eq. (4)] replace, in the case of the 2 nm roughness (dotted line), the critical angle value used in the case of a perfect flat surface (continuous line). In this region and in the case of the 2 nm rms roughness, Δ R = Δ R eff is constant and equal to 1 .
Fig. 7.
Fig. 7. Ω 2 d as a function of x-ray energy and t / D in the case of an Ir top layer with a 2 nm rms roughness. Discontinuities induced by M and L absorption edges of Ir are clearly visible.
Fig. 8.
Fig. 8. Ω eff / γ c 2 as a function of α = t γ c / D . Variations of α are obtained for each energy by changing the MPO thickness t , with D being constant. Ray-tracing simulations results (symbols) are compared with the model of Eq. (17) (continuous lines). Parameters: Ir layer with σ = 2    nm , l s = 10    cm , t = 1.2    mm , D = 20    μm , and T = 26    μm .
Fig. 9.
Fig. 9. Ω eff , Ω 2 d , Ω 1 d , and Ω 0 d dependence with l s . Ray-tracing simulations results (symbols) are compared with the model of Eqs. (12), (14), (16), and (17) (continuous lines). Parameters: Ir layer with σ = 2    nm , t = 1.2    mm , D = 20    μm , T = 26    μm , and E = 6400    eV .
Fig. 10.
Fig. 10. Central spot profiles for a series of MPO thicknesses t. Ray-tracing simulations results (symbols) are compared with the model of Eq. (20) (continuous lines). Parameters: d S = 0.25    μm 2 , Ir layer with σ = 2    nm , l s = 0.1    m , D = 20    μm , T = 26    μm , and E = 6400    eV .
Fig. 11.
Fig. 11. Central spot x direction profile relative integral breadth W/D as a function of t represented as a function of α = t γ c / D for three different energies: ray-tracing simulations results (symbols) and model of Eq. (20) (continuous lines). Parameters: Ir layer with σ = 2    nm , l s = 0.1    m , D = 20    μm , and T = 26    μm .
Fig. 12.
Fig. 12. Ω arms / Ω 2 d : (a) as a function of α for values of Δ R in the range 0 to 1 ; (b) as a function of energy for different values of t / D , (60,120,240,480), in the case of an Ir layer with a 2 nm surface rms roughness. Continuous lines are obtained using Eq. (24); symbols are results from ray-tracing simulations.
Fig. 13.
Fig. 13. Relative reach of the cross and pseudo background as a function of x-ray energy for t / D ratios ranging from 60 to 480.
Fig. 14.
Fig. 14. Ray-tracing simulation showing the enhancement of the periodic nature of the MPO PSF at short distance. (a) Source; (b) image showing a periodic modulation at places where the source is uniform. Reflective material: Ir. E = 6400    eV , l s = 1.2    mm , D = 20    μm , T = 26    μm , and t = 1.2    mm .
Fig. 15.
Fig. 15. Side view of a channel with the distances and angles used in the discrete model.
Fig. 16.
Fig. 16. Ω eff as a function of x for y = 0 . The continuous line was calculated using Eq. (28). The first series of ray-tracing simulations was carried out using the simplified reflectivity curve (circles) and the second series using the real reflectivity (squares). The x profile is quite sensitive to the exact reflectivity profile. Parameters: Ir, energy = 6400    eV , σ = 2    nm , l s = 5    mm , t = 2.4    mm , D = 20    μm , and T = 26    μm .
Fig. 17.
Fig. 17. Ω eff as a function the x-ray energy in the case of a short l s distance. RT1 and RT2 are ray-tracing simulations using two kinds of reflectivity curves (see text). These ray-tracing simulations were done using a point source at x = 0 , y = 0 (square symbols), a point source at x = T / 2 , y = T / 2 (diamond symbols), or a uniform square source of side length T (circle symbols). The ray-tracing simulations are compared with the discrete and the semi-continuous model (lines). Parameters: Ir, l s = 2.5    mm , σ = 2    nm , t = 2.4    mm , D = 20    μm , and T = 26    μm .
Fig. 18.
Fig. 18. Ray-tracing simulations of a Siemens star imaged at different energies using an MPO for a relatively large distance l s = l i = 100    mm . MPO parameters: Ir with a 2 nm rms roughness as reflecting material, pore size D = 20    μm , period T = 26    μm , and thickness 1.2 mm. The number of rays generated and the intensity scale are the same for the four simulations.
Fig. 19.
Fig. 19. Ray-tracing simulations of the MPO imaging of a Siemens star for different distances l s = l i . MPO parameters: Ir with a 2 nm rms roughness is the reflecting material, x-ray energy is 6400 eV, pore size D = 20    μm , period T = 26    μm , and thickness 2.4 mm. The number of rays generated and the intensity scale are the same for the four simulations.
Fig. 20.
Fig. 20. Ray-tracing simulations of a grid imaged with MPOs of different thicknesses. For each MPO thickness, two images with a different grid orientation (0 deg and 45 deg) are shown. The pitch of the grid is 10 μm; the holes are squares with a side length of 5 μm. MPO parameters: Ir with a 2 nm rms roughness is the reflecting material, x-ray energy is 6400 eV, pore size D = 20    μm , and period T = 26    μm . The intensity is normalized for each image.
Fig. 21.
Fig. 21. Ray-tracing simulations of the MPO PSF. (a) Using a standard MPO with a fixed orientation. (b) Using a modified static MPO with a random orientation of the pores square cross section. (c) A standard MPO with a continuous rotation. The rotation axis is parallel to the pore axis with a position at 150 μm from the PSF center. MPO parameters: l s = l i = 100    mm , Ir with a 2 nm rms roughness is the reflecting material, pore size D = 20    μm , period T = 26    μm , and thickness 1.2 mm. The number of rays generated and the intensity scale are the same for the three simulations.
Fig. 22.
Fig. 22. Effect of a random square orientation (central row) or an MPO rotation (bottom row) on imaging for two working distances (100 mm, left column, and 5 mm, right column) compared to the standard MPO (top row). MPO parameters: Ir with a 2 nm rms roughness is the reflecting material, pore size D = 20    μm , period T = 26    μm , and thickness 1.2 mm. The intensity is normalized for each image.

Equations (45)

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γ c = λ r e 2 π N av ρ m K 1.643 10 3 λ ρ m K [ γ c ( rad ) , λ ( Å ) , ρ m ( g · cm 3 ) ] K = 2 i c i ( f 0 i + f i ( λ ) ) i c i M i ,
R ¯ ( λ ) = 1 γ c ( λ ) 0 γ c ( λ ) R ( γ , λ ) d γ ,
R ( γ , λ ) = { 1 + 2 ( R ¯ ( λ ) 1 ) γ / γ c ( λ ) γ γ c ( λ ) 0 γ > γ c ( λ ) .
R ¯ < 0.5 { R ¯ eff = 0.5 γ c eff = 2 R ¯ γ c .
Ω eff = Ω 2 d + Ω 1 d + Ω 0 d .
δ n s ( θ r s ) D = { 0 | θ r s | n s 1 | θ r s | ( n s 1 ) n s 1 < | θ r s | n s n s + 1 | θ r s | n s < | θ r s | < n s + 1 0 | θ r s | n s + 1 ,
δ 0 ( θ r s ) D = { 1 | θ r s | 0 | θ r s | < 1 0 | θ r s | 1 .
Ω p ( θ x , θ y ) = δ n x ( θ r x ) δ n y ( θ r y ) ( l s t / 2 ) 2 R n x ( θ x ) R n y ( θ y ) .
d 2 N ( θ x , θ y ) = η ( l s t / 2 ) 2 D 2 d θ x d θ y ,
η = D 2 / T 2 .
Ω ( n x , n y ) = θ x = + θ y = + Ω p ( θ x , θ y ) d 2 N ( θ x , θ y ) = 4 η γ c 2 S n x S n y
S n = { 1 α 0 α δ n ( θ r s ) D R n ( θ r s t / D ) d θ r s n 0 1 2 α n = 0 ,
α = t γ c D .
α S n = { 0 α n 1 F n ( Δ R ) F n ( ( n 1 ) Δ R / α ) n 1 < α < n F n ( n Δ R / α ) F n ( ( n 1 ) Δ R / α ) + G n ( Δ R ) G n ( n Δ R / α ) n α < n + 1 F n ( n Δ R / α ) F n ( ( n 1 ) Δ R / α ) + G n ( ( n + 1 ) Δ R / α ) G n ( n Δ R / α ) α n + 1 ,
F n ( U ) = ( α Δ R ) 2 ( U ( 1 + U ) n + 1 n + 1 ( 1 + U ) n + 2 ( n + 1 ) ( n + 2 ) ) ( n 1 ) α Δ R ( 1 + U ) n + 1 n + 1 , G n ( U ) = α Δ R ( 1 + U ) n + 1 ( α Δ R ) 2 ( U ( 1 + U ) n + 1 n + 1 ( 1 + U ) n + 2 ( n + 1 ) ( n + 2 ) ) .
Ω 2 d = 4 η γ c 2 S odd 2 ( α , Δ R )
S odd ( α , Δ R ) = k = 0 + S 2 k + 1 .
Θ 1 x ( n x ) = θ x = + η ( l s t / 2 ) D δ n x ( θ r x ) ( l s t / 2 ) R n x ( θ x ) d θ x = 2 η γ c S n x
Ω 1 d = D l s + t / 2 k ( Θ 1 x ( 2 k + 1 ) + Θ 1 y ( 2 k + 1 ) )
= 4 D η γ c l s + t / 2 S odd ( α , Δ R ) = 2 D l s + t / 2 Ω 2 d .
Ω 0 d = D 2 ( l s + t / 2 ) 2 ,
Ω eff = 4 η γ c 2 S odd 2 ( α , Δ R ) + 4 D η γ c l s + t / 2 S odd ( α , Δ R ) + D 2 ( l s + t / 2 ) 2 = n = 0 2 g ( n ) [ η γ c S odd ( α , Δ R ) ] n ( D l s + t / 2 ) 2 n ,
P 1 x ( x ) = { η γ c D | Δ R | k = 0 + [ ( 1 U ) 2 ( k + 1 ) 2 ( k + 1 ) ] U min ( k , x ) U max ( k , x ) | x | D < 1 0 | x | D 1 P 2 x ( x ) = { 1 2 l s | x | < D l s l s + t / 2 0 otherwise ,
D = 1 1 t / ( 2 l s ) D U min ( k , x ) = ( 2 k + | x | / D ) | Δ R | / α U max ( k , x ) = min ( U m ( k , x ) , max ( | Δ R | , U min ( k , x ) ) ) U m ( k , x ) = ( 2 ( k + 1 ) | x | / D ) | Δ R | / α .
P 2 d ( x , y ) = P 1 x ( x ) P 1 y ( y ) P 1 d ( x , y ) = P 1 x ( x ) P 2 y ( y ) + P 2 x ( x ) P 1 y ( y ) P 0 d ( x , y ) = P 2 x ( x ) P 2 y ( y ) .
d 2 Ω eff ( x , y ) = P eff ( x , y ) d x d y = ( P 2 d ( x , y ) + P 1 d ( x , y ) + P 0 d ( x , y ) ) d x d y .
Ω arms = 8 η γ c 2 S even ( α , Δ R ) S odd ( α , Δ R ) Ω 1 d ,
Ω arms 0 = 4 η γ c 2 α S odd ( α , Δ R ) Ω 1 d .
S even ( α , Δ R ) = k = 0 + S 2 k .
Ω arms Ω eff Ω arms Ω 2 d = 2 S even S odd ,
Ω arms 0 Ω eff Ω arms 0 Ω 2 d = 1 α S odd .
Ω p . background Ω eff Ω p . background Ω 2 d = S even 2 S odd 2 = 1 4 ( Ω arms Ω 2 d ) 2 .
W cross = max ( 4 l s D / t , 4 l s γ c ) .
θ i = | x i | l s t / 2 Δ θ = D l s t / 2 .
θ min ( i ) = θ i Δ θ / 2 θ max ( i ) = θ i + Δ θ / 2.
θ min + ( 0 ) = 0 θ max + ( 0 ) = θ i + Δ θ / 2 θ min ( 0 ) = 0 θ max ( 0 ) = θ i + Δ θ / 2.
n min ( i ) = θ min ( i ) t D n max ( i ) = θ max ( i ) t D + 1 ,
Δ θ eff ( n , x i ) = θ 1 θ 2 R n ( λ , γ ) d γ = γ c Δ R [ ( 1 + U ) n + 1 n + 1 ] Δ R θ 1 / γ c Δ R θ 2 / γ c ,
θ 1 , θ 2 = { min ( θ min , γ c ) , min ( θ x i ( n min + 1 ) , γ c ) n = n min min ( θ x i ( n ) , γ c ) , min ( θ x i ( n + 1 ) , γ c ) n min < n < n max min ( θ x i ( n max ) , γ c ) , min ( θ max , γ c ) n = n max
θ x i ( n ) = 1 l s + t / 2 [ | x i | + ( n 1 / 2 ) D ] .
Σ x , odd = i = + k = 0 + Δ θ eff ( 2 k + 1 , x i ) Σ y , odd = j = + k = 0 + Δ θ eff ( 2 k + 1 , y j ) .
Σ x , 0 = k , n min x = 0 [ min ( θ x k ( 1 ) , D / ( 2 l s ) ) min ( θ min xk , D / ( 2 l s ) ) ] Σ y , 0 = k , n min y = 0 [ min ( θ y k ( 1 ) , D / ( 2 l s ) ) min ( θ min yk , D / ( 2 l s ) ) ] .
Ω effective , d = ( Σ x , odd + Σ x , 0 ) ( Σ y , odd + Σ y , 0 ) .
d 4 n = N s 4 π T 2 d S d Ω = N s η 4 π D 2 d S d Ω .
d 2 n = δ n x ( θ r x ) δ n y ( θ r y ) R n x ( θ x ) R n y ( θ y ) N s η 4 π D 2 d θ x d θ y .

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