Abstract

X-ray speckle visibility spectroscopy (XSVS) is a method for studying dynamics in disordered systems. This method was originally developed in the visible-light region, in which an intense laser can be used. When applied in the X-ray region, where the number of photons is much smaller than in the visible-light region, it suffers from photon statistics. In this paper, we quantitatively discuss the effect of photon shot noise on XSVS analyses. The effect is experimentally confirmed using sequential speckle patterns from Brownian polystyrene nanospheres in glycerol.

©2012 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Single shot speckle and coherence analysis of the hard X-ray free electron laser LCLS

Sooheyong Lee, W. Roseker, C. Gutt, B. Fischer, H. Conrad, F. Lehmkühler, I. Steinke, D. Zhu, H. Lemke, M. Cammarata, D.M. Fritz, P. Wochner, M. Castro-Colin, S. O. Hruszkewycz, P. H. Fuoss, G. B. Stephenson, G. Grübel, and A. Robert
Opt. Express 21(21) 24647-24664 (2013)

Pushing x-ray photon correlation spectroscopy beyond the continuous frame rate limit

Eric M. Dufresne, Suresh Narayanan, Alec R. Sandy, David M. Kline, Qingteng Zhang, Eric C. Landahl, and Steve Ross
Opt. Express 24(1) 355-364 (2016)

Measuring temporal speckle correlations at ultrafast x-ray sources

C. Gutt, L.-M. Stadler, A. Duri, T. Autenrieth, O. Leupold, Y. Chushkin, and G. Grübel
Opt. Express 17(1) 55-61 (2009)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010).
    [Crossref]
  2. M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
    [Crossref]
  3. G. Grübel and F. Zontone, “Correlation spectroscopy with coherent X-rays,” J. Alloy. Comp. 362(1-2), 3–11 (2004).
    [Crossref]
  4. M. Sutton, “A review of X-ray intensity fluctuation spectroscopy,” C. R. Phys. 9(5-6), 657–667 (2008).
    [Crossref]
  5. S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
    [Crossref] [PubMed]
  6. T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
    [Crossref] [PubMed]
  7. L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
    [Crossref] [PubMed]
  8. D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
    [Crossref] [PubMed]
  9. S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
    [Crossref]
  10. P. Falus, M. A. Borthwick, and S. G. J. Mochrie, “Fluctuation dynamics of block copolymer vesicles,” Phys. Rev. Lett. 94(1), 016105 (2005).
    [Crossref] [PubMed]
  11. C. Caronna, Y. Chushkin, A. Madsen, and A. Cupane, “Dynamics of nanoparticles in a supercooled liquid,” Phys. Rev. Lett. 100(5), 055702 (2008).
    [Crossref] [PubMed]
  12. S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
    [Crossref] [PubMed]
  13. M. Leitner, B. Sepiol, L.-M. Stadler, B. Pfau, and G. Vogl, “Atomic diffusion studied with coherent X-rays,” Nat. Mater. 8(9), 717–720 (2009).
    [Crossref] [PubMed]
  14. O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
    [Crossref] [PubMed]
  15. M. Sutton, K. Laaziri, F. Livet, and F. Bley, “Using coherence to measure two-time correlation functions,” Opt. Express 11(19), 2268–2277 (2003).
    [Crossref] [PubMed]
  16. P. K. Dixon and D. J. Durian, “Speckle visibility spectroscopy and variable granular fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
    [Crossref] [PubMed]
  17. R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
    [Crossref]
  18. H. Abe, S. Adachi, K. Amemiya, K. Asakura, L. Chavas, N. Funamori, T. Furuya, R. Hajima, K. Hirano, T. Honda, E. Kako, H. Kawata, S. Kishimoto, Y. Kitajima, Y. Kobayashi, S. Michizono, Y. Murakami, H. Nakai, N. Nakamura, M. Nomura, T. Obina, S. Sakanaka, N. Sei, and Y. Shinohara, Yoshio Takahashi, Yukio Takahashi, K. Tsuchiya, S. Wakatsuki, M. Yamamoto, and W. Yashiro, “Energy Recovery Linac preliminary design report” (2011), http://pfwww.kek.jp/ERLoffice/detabase/ERL%20Preliminary%20Design%20Report_web.pdf .
  19. A. Fluerasu, L. Wiegart, and M. C. Dayton, “Preliminary design report for the coherent hard X-ray (CHX) beamline at NSLS-II” (2010), http://www.bnl.gov/nsls2/beamlines/files/pdf/CHX_pdr.pdf .
  20. B. J. Berne and R. Pecora, Dynamic Light Scattering With Application to Chemistry, Biology, and Physics (Dover Publications, 2000).
  21. E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
    [Crossref]
  22. Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
    [Crossref]
  23. T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
    [Crossref]
  24. Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
    [Crossref] [PubMed]
  25. S. M. Gruner, M. W. Tate, and E. F. Eikenberry, “Charge-coupled device area x-ray detectors,” Rev. Sci. Instrum. 73(8), 2815–2842 (2002).
    [Crossref]
  26. S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express 18(14), 14519–14534 (2010).
    [Crossref] [PubMed]
  27. C. Gutt, L.-M. Stadler, A. Duri, T. Autenrieth, O. Leupold, Y. Chushkin, and G. Grübel, “Measuring temporal speckle correlations at ultrafast x-ray sources,” Opt. Express 17(1), 55–61 (2009).
    [Crossref] [PubMed]
  28. W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
    [Crossref] [PubMed]
  29. W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
    [Crossref] [PubMed]

2011 (1)

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

2010 (3)

Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
[Crossref] [PubMed]

S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express 18(14), 14519–14534 (2010).
[Crossref] [PubMed]

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010).
[Crossref]

2009 (3)

2008 (2)

C. Caronna, Y. Chushkin, A. Madsen, and A. Cupane, “Dynamics of nanoparticles in a supercooled liquid,” Phys. Rev. Lett. 100(5), 055702 (2008).
[Crossref] [PubMed]

M. Sutton, “A review of X-ray intensity fluctuation spectroscopy,” C. R. Phys. 9(5-6), 657–667 (2008).
[Crossref]

2007 (2)

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

2005 (2)

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[Crossref]

P. Falus, M. A. Borthwick, and S. G. J. Mochrie, “Fluctuation dynamics of block copolymer vesicles,” Phys. Rev. Lett. 94(1), 016105 (2005).
[Crossref] [PubMed]

2004 (1)

G. Grübel and F. Zontone, “Correlation spectroscopy with coherent X-rays,” J. Alloy. Comp. 362(1-2), 3–11 (2004).
[Crossref]

2003 (2)

P. K. Dixon and D. J. Durian, “Speckle visibility spectroscopy and variable granular fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
[Crossref] [PubMed]

M. Sutton, K. Laaziri, F. Livet, and F. Bley, “Using coherence to measure two-time correlation functions,” Opt. Express 11(19), 2268–2277 (2003).
[Crossref] [PubMed]

2002 (1)

S. M. Gruner, M. W. Tate, and E. F. Eikenberry, “Charge-coupled device area x-ray detectors,” Rev. Sci. Instrum. 73(8), 2815–2842 (2002).
[Crossref]

2001 (2)

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
[Crossref] [PubMed]

2000 (1)

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

1997 (1)

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

1996 (1)

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

1995 (3)

S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
[Crossref] [PubMed]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
[Crossref]

1991 (1)

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Abernathy, D. L.

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

Aeppli, G.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Als-Nielsen, J.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

Amemiya, Y.

Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
[Crossref] [PubMed]

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

Autenrieth, T.

Bandyopadhyay, R.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[Crossref]

Berman, L.

S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
[Crossref] [PubMed]

Berman, L. E.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Bizen, T.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Bley, F.

Borthwick, M. A.

P. Falus, M. A. Borthwick, and S. G. J. Mochrie, “Fluctuation dynamics of block copolymer vesicles,” Phys. Rev. Lett. 94(1), 016105 (2005).
[Crossref] [PubMed]

D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

Brauer, S.

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

Brüning, R.

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
[Crossref]

Caronna, C.

C. Caronna, Y. Chushkin, A. Madsen, and A. Cupane, “Dynamics of nanoparticles in a supercooled liquid,” Phys. Rev. Lett. 100(5), 055702 (2008).
[Crossref] [PubMed]

Cerbino, R.

Chushkin, Y.

Cupane, A.

C. Caronna, Y. Chushkin, A. Madsen, and A. Cupane, “Dynamics of nanoparticles in a supercooled liquid,” Phys. Rev. Lett. 100(5), 055702 (2008).
[Crossref] [PubMed]

Dierker, S. B.

S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
[Crossref] [PubMed]

Dixon, P. K.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[Crossref]

P. K. Dixon and D. J. Durian, “Speckle visibility spectroscopy and variable granular fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
[Crossref] [PubMed]

Dufresne, E.

E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
[Crossref]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

Duri, A.

Durian, D. J.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[Crossref]

P. K. Dixon and D. J. Durian, “Speckle visibility spectroscopy and variable granular fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
[Crossref] [PubMed]

Ehnes, A.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

Eikenberry, E. F.

S. M. Gruner, M. W. Tate, and E. F. Eikenberry, “Charge-coupled device area x-ray detectors,” Rev. Sci. Instrum. 73(8), 2815–2842 (2002).
[Crossref]

Falus, P.

P. Falus, M. A. Borthwick, and S. G. J. Mochrie, “Fluctuation dynamics of block copolymer vesicles,” Phys. Rev. Lett. 94(1), 016105 (2005).
[Crossref] [PubMed]

D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

Feng, Y.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Fischer, E. W.

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

Fleming, R. M.

S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
[Crossref] [PubMed]

Franz, H.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

Gittings, A. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[Crossref]

Greytak, T.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Grübel, G.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

C. Gutt, L.-M. Stadler, A. Duri, T. Autenrieth, O. Leupold, Y. Chushkin, and G. Grübel, “Measuring temporal speckle correlations at ultrafast x-ray sources,” Opt. Express 17(1), 55–61 (2009).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

G. Grübel and F. Zontone, “Correlation spectroscopy with coherent X-rays,” J. Alloy. Comp. 362(1-2), 3–11 (2004).
[Crossref]

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

Gruner, S. M.

S. M. Gruner, M. W. Tate, and E. F. Eikenberry, “Charge-coupled device area x-ray detectors,” Rev. Sci. Instrum. 73(8), 2815–2842 (2002).
[Crossref]

Gutt, C.

Hara, T.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Held, G. A.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Imai, R.

Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
[Crossref] [PubMed]

Inoue, K.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Isaacs, E. D.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Jaramillo, R.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Kim, H. C.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Kishimoto, H.

Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
[Crossref] [PubMed]

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

Kitamura, H.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Kohda, T.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Laaziri, K.

Lee, S.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

Leitner, M.

M. Leitner, B. Sepiol, L.-M. Stadler, B. Pfau, and G. Vogl, “Atomic diffusion studied with coherent X-rays,” Nat. Mater. 8(9), 717–720 (2009).
[Crossref] [PubMed]

Leupold, O.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

C. Gutt, L.-M. Stadler, A. Duri, T. Autenrieth, O. Leupold, Y. Chushkin, and G. Grübel, “Measuring temporal speckle correlations at ultrafast x-ray sources,” Opt. Express 17(1), 55–61 (2009).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

Livet, F.

Logan, J. M.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Lumma, D.

D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

Lurio, L. B.

D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

Madsen, A.

C. Caronna, Y. Chushkin, A. Madsen, and A. Cupane, “Dynamics of nanoparticles in a supercooled liquid,” Phys. Rev. Lett. 100(5), 055702 (2008).
[Crossref] [PubMed]

Maejima, T.

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

Malik, A.

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

Maréchal, X.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Mayes, A. M.

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

Meier, G.

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

Mochrie, S. G. J.

P. Falus, M. A. Borthwick, and S. G. J. Mochrie, “Fluctuation dynamics of block copolymer vesicles,” Phys. Rev. Lett. 94(1), 016105 (2005).
[Crossref] [PubMed]

D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Nagler, S. E.

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Narayanan, S.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Nishikawa, H.

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

Nugent, K. A.

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010).
[Crossref]

Oka, T.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Patkowski, A.

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

Pelletier, J. F.

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

Peuser, J.

Pfau, B.

M. Leitner, B. Sepiol, L.-M. Stadler, B. Pfau, and G. Vogl, “Atomic diffusion studied with coherent X-rays,” Nat. Mater. 8(9), 717–720 (2009).
[Crossref] [PubMed]

Pindak, R.

S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
[Crossref] [PubMed]

Regan, L.

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

Robert, A.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

Robinson, I. K.

S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
[Crossref] [PubMed]

Rodricks, B.

E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
[Crossref]

Roseker, W.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

Rosenbaum, T. F.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Sandy, A. R.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

Scheffold, F.

Schulte-Schrepping, H.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

Seike, T.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Sepiol, B.

M. Leitner, B. Sepiol, L.-M. Stadler, B. Pfau, and G. Vogl, “Atomic diffusion studied with coherent X-rays,” Nat. Mater. 8(9), 717–720 (2009).
[Crossref] [PubMed]

Shinohara, Y.

Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
[Crossref] [PubMed]

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

Shpyrko, O. G.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Skipetrov, S. E.

Sprung, M.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Stadler, L.-M.

Steffen, W.

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

Stephenson, G. B.

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
[Crossref]

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Suh, S. S.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[Crossref]

Sutton, M.

M. Sutton, “A review of X-ray intensity fluctuation spectroscopy,” C. R. Phys. 9(5-6), 657–667 (2008).
[Crossref]

M. Sutton, K. Laaziri, F. Livet, and F. Bley, “Using coherence to measure two-time correlation functions,” Opt. Express 11(19), 2268–2277 (2003).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
[Crossref]

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Suzuki, T.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Tanaka, T.

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Tate, M. W.

S. M. Gruner, M. W. Tate, and E. F. Eikenberry, “Charge-coupled device area x-ray detectors,” Rev. Sci. Instrum. 73(8), 2815–2842 (2002).
[Crossref]

Thurn-Albrecht, T.

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

Vogl, G.

M. Leitner, B. Sepiol, L.-M. Stadler, B. Pfau, and G. Vogl, “Atomic diffusion studied with coherent X-rays,” Nat. Mater. 8(9), 717–720 (2009).
[Crossref] [PubMed]

Weber, B.

Yagi, N.

Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
[Crossref] [PubMed]

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Zakharov, P.

Zontone, F.

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, A. Robert, and G. Grübel, “Performance of a picosecond x-ray delay line unit at 8.39 keV,” Opt. Lett. 34(12), 1768–1770 (2009).
[Crossref] [PubMed]

G. Grübel and F. Zontone, “Correlation spectroscopy with coherent X-rays,” J. Alloy. Comp. 362(1-2), 3–11 (2004).
[Crossref]

Zschack, P.

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

Adv. Phys. (1)

K. A. Nugent, “Coherent methods in the X-ray sciences,” Adv. Phys. 59(1), 1–99 (2010).
[Crossref]

C. R. Phys. (1)

M. Sutton, “A review of X-ray intensity fluctuation spectroscopy,” C. R. Phys. 9(5-6), 657–667 (2008).
[Crossref]

J. Alloy. Comp. (1)

G. Grübel and F. Zontone, “Correlation spectroscopy with coherent X-rays,” J. Alloy. Comp. 362(1-2), 3–11 (2004).
[Crossref]

J. Synchrotron Radiat. (2)

Y. Shinohara, R. Imai, H. Kishimoto, N. Yagi, and Y. Amemiya, “Indirectly illuminated X-ray area detector for X-ray photon correlation spectroscopy,” J. Synchrotron Radiat. 17(6), 737–742 (2010).
[Crossref] [PubMed]

W. Roseker, H. Franz, H. Schulte-Schrepping, A. Ehnes, O. Leupold, F. Zontone, S. Lee, A. Robert, and G. Grübel, “Development of a hard X-ray delay line for X-ray photon correlation spectroscopy and jitter-free pump-probe experiments at X-ray free-electron laser sources,” J. Synchrotron Radiat. 18(3), 481–491 (2011).
[Crossref] [PubMed]

Jpn. J. Appl. Phys. (1)

Y. Shinohara, H. Kishimoto, T. Maejima, H. Nishikawa, N. Yagi, and Y. Amemiya, “X-ray photon correlation spectroscopy of filler in rubber,” Jpn. J. Appl. Phys. 46(4), L300–L302 (2007).
[Crossref]

Nat. Mater. (1)

M. Leitner, B. Sepiol, L.-M. Stadler, B. Pfau, and G. Vogl, “Atomic diffusion studied with coherent X-rays,” Nat. Mater. 8(9), 717–720 (2009).
[Crossref] [PubMed]

Nature (2)

O. G. Shpyrko, E. D. Isaacs, J. M. Logan, Y. Feng, G. Aeppli, R. Jaramillo, H. C. Kim, T. F. Rosenbaum, P. Zschack, M. Sprung, S. Narayanan, and A. R. Sandy, “Direct measurement of antiferromagnetic domain fluctuations,” Nature 447(7140), 68–71 (2007).
[Crossref] [PubMed]

M. Sutton, S. G. J. Mochrie, T. Greytak, S. E. Nagler, L. E. Berman, G. A. Held, and G. B. Stephenson, “Observation of speckle by diffraction with coherent X-rays,” Nature 352(6336), 608–610 (1991).
[Crossref]

Nucl. Instrum. Methods Phys. Res. Sect. A (2)

E. Dufresne, R. Brüning, M. Sutton, B. Rodricks, and G. B. Stephenson, “A statistical technique for characterizing X-ray position sensitive detectors,” Nucl. Instrum. Methods Phys. Res. Sect. A 364(2), 380–393 (1995).
[Crossref]

T. Hara, T. Tanaka, T. Seike, T. Bizen, X. Maréchal, T. Kohda, K. Inoue, T. Oka, T. Suzuki, N. Yagi, and H. Kitamura, “In-vacuum X-ray helical undulator for high flux beamline at SPring-8,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468, 165–168 (2001).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. Lett. (9)

P. K. Dixon and D. J. Durian, “Speckle visibility spectroscopy and variable granular fluidization,” Phys. Rev. Lett. 90(18), 184302 (2003).
[Crossref] [PubMed]

S. B. Dierker, R. Pindak, R. M. Fleming, I. K. Robinson, and L. Berman, “X-Ray photon correlation spectroscopy study of Brownian motion of gold colloids in glycerol,” Phys. Rev. Lett. 75(3), 449–452 (1995).
[Crossref] [PubMed]

T. Thurn-Albrecht, W. Steffen, A. Patkowski, G. Meier, E. W. Fischer, G. Grübel, and D. L. Abernathy, “Photon correlation spectroscopy of colloidal palladium using a coherent x-ray beam,” Phys. Rev. Lett. 77(27), 5437–5440 (1996).
[Crossref] [PubMed]

L. B. Lurio, D. Lumma, A. R. Sandy, M. A. Borthwick, P. Falus, S. G. J. Mochrie, J. F. Pelletier, M. Sutton, L. Regan, A. Malik, and G. B. Stephenson, “Absence of scaling for the intermediate scattering function of a hard-sphere suspension: Static and dynamic x-ray scattering from concentrated polystyrene latex spheres,” Phys. Rev. Lett. 84(4), 785–788 (2000).
[Crossref] [PubMed]

D. Lumma, M. A. Borthwick, P. Falus, L. B. Lurio, and S. G. J. Mochrie, “Equilibrium dynamics in the nondiffusive regime of an entangled polymer blend,” Phys. Rev. Lett. 86(10), 2042–2045 (2001).
[Crossref] [PubMed]

S. G. J. Mochrie, A. M. Mayes, A. R. Sandy, M. Sutton, S. Brauer, G. B. Stephenson, D. L. Abernathy, and G. Grübel, “Dynamics of block copolymer micelles revealed by x-ray intensity fluctuation spectroscopy,” Phys. Rev. Lett. 78(7), 1275–1278 (1997).
[Crossref]

P. Falus, M. A. Borthwick, and S. G. J. Mochrie, “Fluctuation dynamics of block copolymer vesicles,” Phys. Rev. Lett. 94(1), 016105 (2005).
[Crossref] [PubMed]

C. Caronna, Y. Chushkin, A. Madsen, and A. Cupane, “Dynamics of nanoparticles in a supercooled liquid,” Phys. Rev. Lett. 100(5), 055702 (2008).
[Crossref] [PubMed]

S. Brauer, G. B. Stephenson, M. Sutton, R. Brüning, E. Dufresne, S. G. J. Mochrie, G. Grübel, J. Als-Nielsen, and D. L. Abernathy, “X-ray intensity fluctuation spectroscopy observations of critical dynamics in Fe3Al,” Phys. Rev. Lett. 74(11), 2010–2013 (1995).
[Crossref] [PubMed]

Rev. Sci. Instrum. (2)

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, “Speckle-visibility spectroscopy: A tool to study time-varying dynamics,” Rev. Sci. Instrum. 76(9), 093110 (2005).
[Crossref]

S. M. Gruner, M. W. Tate, and E. F. Eikenberry, “Charge-coupled device area x-ray detectors,” Rev. Sci. Instrum. 73(8), 2815–2842 (2002).
[Crossref]

Other (3)

H. Abe, S. Adachi, K. Amemiya, K. Asakura, L. Chavas, N. Funamori, T. Furuya, R. Hajima, K. Hirano, T. Honda, E. Kako, H. Kawata, S. Kishimoto, Y. Kitajima, Y. Kobayashi, S. Michizono, Y. Murakami, H. Nakai, N. Nakamura, M. Nomura, T. Obina, S. Sakanaka, N. Sei, and Y. Shinohara, Yoshio Takahashi, Yukio Takahashi, K. Tsuchiya, S. Wakatsuki, M. Yamamoto, and W. Yashiro, “Energy Recovery Linac preliminary design report” (2011), http://pfwww.kek.jp/ERLoffice/detabase/ERL%20Preliminary%20Design%20Report_web.pdf .

A. Fluerasu, L. Wiegart, and M. C. Dayton, “Preliminary design report for the coherent hard X-ray (CHX) beamline at NSLS-II” (2010), http://www.bnl.gov/nsls2/beamlines/files/pdf/CHX_pdr.pdf .

B. J. Berne and R. Pecora, Dynamic Light Scattering With Application to Chemistry, Biology, and Physics (Dover Publications, 2000).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1 Dependence of visibility on exposure time based on Eq. (16). Four cases of a Brownian motion system are calculated: β〈 N(q,T) 〉= 0.1, 1, 10, and ∞ when ε = 1. The vertical and horizontal axes represent visibility divided by β and exposure time normalized by τ, respectively. For clarity, the plots are moderately shifted.

Download Full Size | PPT Slide | PDF

Fig. 2
Fig. 2 Typical scattering images for T = (a) 36 ms ( Δt ), (b) 180 ms ( 5Δt ), and (c) 900 ms ( 25Δt ). The lower-right part is covered by a beamstop.

Download Full Size | PPT Slide | PDF

Fig. 3
Fig. 3 (a) Relaxation times determined by XSVS (red circles) and XPCS (blue diamonds). (b) Dependence of the visibility of speckle patterns at q = 0.0335 nm−1 on exposure time (red circles) and its fitted result using Eq. (18) (solid line) and that for the case where the effect of shot noise is neglected (dotted line). (c) Average number of counted photons per frame per pixel normalized by ε determined by fitting Eq. (18) to experimental data (red circles) and circularly averaged intensity of speckle patterns (black line).

Download Full Size | PPT Slide | PDF

Equations (18)

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

g 2 (q,t)= 〈 I(q,t')I(q,t+t') 〉 〈 I(q,t') 〉 2 ,
g 2 (q,t=k'Δt)= 1 N(K−k') ∑ n=1 N ∑ k=1 K−k' S n,k S n,k+k' ( 1 N(K−k') ∑ n=1 N ∑ k=1 K−k' S n,k )( 1 Nk' ∑ n=1 N ∑ k=K−k'+1 K S n,k ) ,
g 2 (q,t)=1+β | f(q,t) | 2 ,
v(q,T)= 〈 S 2 (q,t) 〉− 〈 S(q,t) 〉 2 〈 S(q,t) 〉 2 ,
v(q,T)= 1 NK−1 ∑ n=1 N ∑ k=1 K ( S n,k − 1 NK ∑ n=1 N ∑ k=1 K S n,k ) 2 ( 1 NK ∑ n=1 N ∑ k=1 K S n,k ) 2 .
v(q,t)=2β/T ∫ 0 T (1−t/T) | f(q,t) | 2 dt .
〈 S(q,T) 〉=C 〈 〈 ∫ 0 T n m (q,t)dt 〉 p 〉 c ==C 〈 〈 ∫ 0 T n(q,t)dt 〉 p 〉 c =C〈 ∫ 0 T n(q,t)dt 〉,
〈 S 2 (q,T) 〉= C 2 〈 〈 ( ∫ 0 T n m (q,t)dt ) 2 〉 p 〉 c = C 2 〈 〈 ( ∫ 0 T n(q,t)dt ) 2 + ∫ 0 T n(q,t)dt 〉 p 〉 c = C 2 〈 ( ∫ 0 T n(q,t)dt ) 2 〉+ C 2 〈 ∫ 0 T n(q,t)dt 〉,
〈 S(q,T) 〉=C〈 ∫ 0 T n e (q,t)dt 〉=C〈 ∫ 0 T n(q,t)dt 〉,
〈 S 2 (q,T) 〉= C 2 〈 ( ∫ 0 T n e (q,t)dt ) 2 〉= C 2 〈 ( ∫ 0 T n(q,t)dt ) 2 〉+ C 2 ε〈 ∫ 0 T n(q,t)dt 〉,
v(q,T)= v 0 (q,T)+ ε 〈 N(q,T) 〉 ,
v 0 (q,t)= 〈 ( ∫ 0 T n(q,t)dt ) 2 〉− 〈 ∫ 0 T n(q,t)dt 〉 2 〈 ∫ 0 T n(q,t)dt 〉 2 ,
〈 N(q,T) 〉=〈 ∫ 0 T n e (q,t)dt 〉=〈 ∫ 0 T n(q,t)dt 〉.
v(q,T)=2β/T ∫ 0 T (1−t/T) | f(q,t) | 2 dt + ε 〈 N(q,T) 〉 .
v(q,T)=2β/T ∫ 0 T (1−t/T) | f(q,t) | 2 dt + ε 〈 N(q,T) 〉 + 〈 σ 2 (T) 〉 〈 ∫ 0 T I(q,t)dt 〉 2 ,
v(q,T)=β exp(−2T/τ)−1+2T/τ 2 (T/τ) 2 + ε 〈 N(q,T) 〉 .
g 2 (q,t)=1+βexp(−2t/τ),
v(q,T=kΔt)=β exp(−2kΔt/τ)−1+2kΔt/τ 2 (kΔt/τ) 2 + ε k〈 N(q,Δt) 〉 .

Metrics