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 OSA

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,” Nature352(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,” Nature447(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. Express11(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. A364(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. A467–468, 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. Express18(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. Express17(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]

Adv. Phys.

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

C. R. Phys.

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

J. Alloy. Comp.

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

J. Synchrotron Radiat.

• 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.

• 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.

• 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

• 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,” Nature447(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,” Nature352(6336), 608–610 (1991). [CrossRef]

Nucl. Instrum. Methods Phys. Res. Sect. A

• 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. A364(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. A467–468, 165–168 (2001). [CrossRef]

Opt. Express

• S. E. Skipetrov, J. Peuser, R. Cerbino, P. Zakharov, B. Weber, and F. Scheffold, “Noise in laser speckle correlation and imaging techniques,” Opt. Express18(14), 14519–14534 (2010). [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. Express17(1), 55–61 (2009). [CrossRef] [PubMed]
• M. Sutton, K. Laaziri, F. Livet, and F. Bley, “Using coherence to measure two-time correlation functions,” Opt. Express11(19), 2268–2277 (2003). [CrossRef] [PubMed]

Opt. Lett.

• 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]

Phys. Rev. Lett.

• 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.

• 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

• 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).

Click here to see a list of articles that cite this paper

Related Journal Articles

• Reduction of quantum noise in transmittance estimation using photon-correlated beams (JOSAA)
• Intensity correlations of a noise-driven diode laser (JOSAB)
• Traveling-wave atom cavity interaction in the single-atom microlaser (OL)
• Two-photon apodization in lithium niobate (OL)
• Photon statistics of amplified spontaneous emission noise in a 10-Gbit/s optically preamplified direct-detection receiver (OL)

Related Conference Papers

• Tests for non-randomness in quantum jumps
• Super-poissonian intensity fluctuations and correlations between pump and probe fields in electromagnetically induced transparency
• Towards Multimode Memories with Atomic Ensembles in the Solid State
• Time Evolution of Entangled Excitonic State in Two Coupled Quantum Dots Interacting with a Squeezed Coherent Field
• Correlations and Anti-Correlations in EIT: Laser Noise Versus Atomic Dipole Noise