Abstract
Whenever coherent radiation impinges on a scattering object, a speckled intensity pattern is produced. In the far field the speckle size and shape do not mirror any properties of the object. Here we show that, in spite of the limited spatial coherence of synchrotron radiation, speckles with remarkable properties can be observed when the sensor is placed in the near field. The statistical analysis of these speckles generates static and dynamic X-ray-scattering data, and the results from two typical scattering samples are given. When compared with conventional far-field techniques, the method enables a substantial increase of around four orders of magnitude in the beam size and power and opens the way to a previously inaccessible region of scattering angles. It also offers the possibility of tracking the spatio-temporal evolution of complex fluids and other inhomogeneous systems.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Goodman, J. W. Speckle Phenomena in Optics 1st edn (Roberts and Company Publishers, Greenwood Village, 2006).
Sutton, M. et al. Observation of speckle by diffraction with coherent X-rays. Nature 352, 608–610 (1991).
Mochrie, S. G. et al. Dynamics of block copolymer micelles revealed by X-ray intensity fluctuation spectroscopy. Phys. Rev. Lett. 78, 1275–1278 (1997).
Miao, J., Charalambous, P., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344 (1999).
Marchesini, S. et al. Coherent X-ray diffractive imaging: Applications and limitations. Opt. Express 11, 2344–2353 (2003).
Giglio, M., Carpineti, M. & Vailati, A. Space intensity correlations in the near field of the scattered light: A direct measurement of the density correlation function g(r). Phys. Rev. Lett. 85, 1416–1419 (2000).
Brogioli, D., Vailati, A. & Giglio, M. Heterodyne near-field scattering. Appl. Phys. Lett. 81, 4109–4111 (2002).
Ferri, F., Magatti, D., Pescini, D., Potenza, M. A. C. & Giglio, M. Heterodyne near-field scattering: A technique for complex fluids. Phys. Rev. E 70, 041405 (2004).
Cerbino, R. Correlations of light in the deep Fresnel region: An extended Van Cittert and Zernike theorem. Phys. Rev. A 75, 053815 (2007).
Giglio, M., Brogioli, D., Potenza, M. A. C. & Vailati, A. Near field scattering. Phys. Chem. Chem. Phys. 6, 1547–1550 (2004).
Narayanan, T., Diat, O. & Bösecke, P. SAXS and USAXS on the high brilliance beamline at the ESRF. Nucl. Instrum. Methods Phys. Res. A 177, 1005–1009 (2001).
Cipelletti, L., Carpineti, M. & Giglio, M. Fractal morphology, spatial order, and pore structure in microporous membrane filters. Langmuir 12, 6446–6451 (1996).
Guigay, J. P. et al. The partial Talbot effect and its use in measuring the coherence of synchrotron X-rays. J. Synchr. Rad. 11, 476–482 (2004).
Zabler, S., Cloetens, P., Guigay, J.-P., Baruchel, J. & Schlenker, M. Optimization of phase contrast imaging using hard x rays. Rev. Sci. Instrum. 76, 073705 (2005).
Trainoff, S. P. & Cannell, D. S. Physical optics treatment of the shadowgraph. Phys. Fluids 14, 1340–1363 (2002).
Talbot, H. F. Facts relating to optical science. No. IV. Phil. Mag. 9, 401–407 (1836).
Rehberg, I. et al. Thermally induced hydrodynamic fluctuations below the onset of electroconvection. Phys. Rev. Lett. 67, 596–599 (1994).
Croccolo, F., Brogioli, D., Vailati, A., Giglio, M. & Cannell, D. S. Effect of gravity on the dynamics of nonequilibrium fluctuations in a free-diffusion experiment. Ann. NY Acad. Sci. 1077, 365–379 (2006).
Batchelor, G. K. Brownian diffusion of particles with hydrodynamic interaction. J. Fluid Mech. 74, 1–29 (1976).
Cipelletti, L. & Ramos, L. Slow dynamics in glassy soft matter. J. Phys. Condens. Matter 17, R253 (2005).
Cosentino, M. Near Field Scattering, Laurea Degree Dissertation, Univ. Milan (June 2002).
Snigirev, A., Kohn, V., Snigireva, I. & Lengeler, B. A compound refractive lens for focusing high-energy X-rays. Nature 384, 49–51 (1996).
Mokso, R. & Cloetens, P. Nanoscale zoom tomography with hard x rays using Kirkpatrick–Baez optics. Appl. Phys. Lett. 90, 144104 (2007).
Chapman, H. N. et al. Femtosecond diffractive imaging with a soft-X-ray free-electron laser. Nature Phys. 2, 839–843 (2006).
Kim, G. B. & Lee, S. J. X-ray PIV measurements of blood flows without tracer particles. Exp. Fluids 41, 195–200 (2006).
Ziegler, E. et al. The ESRF BM05 metrology beamline: Instrumentation and performance upgrade. AIP Conf. Proc. 705, 436–439 (2004).
Kohn, V., Snigireva, I. & Snigirev, A. Direct measurement of transverse coherence length of hard X rays from interference fringes. Phys. Rev. Lett. 85, 2745–2748 (2000).
Acknowledgements
We acknowledge the ESRF for provision of synchrotron radiation facilities. We thank D. Cannell, P. Cloetens, G. Grübel, J. Harden, S. Mochrie, T. Narayanan, A. Snigirev, I. Snigireva, T. Weitkamp, D. Weitz and E. Ziegler for scientific discussion and encouragement. L. Claustre and J. Y. Massonnat are thanked for technical assistance at the beamline. Thanks are also due to M. Alaimo for bringing to our attention the results of ref. 25 and to C. Vozzi for help with the preparation of the figures.
Author information
Authors and Affiliations
Contributions
R.C., L.P., M.A.C.P. and M.G. made the speckle-based scattering measurements at the beamline BM05 (ESRF, Grenoble) and are responsible for the data analysis and for the writing of the manuscript. P.B. made the Bonse–Hart scattering measurement (microporous membrane) at the beamline ID02 (ESRF, Grenoble). A.R. made the traditional XPCS measurements (silica particles) at the beamline ID10A (ESRF, Grenoble).
Corresponding authors
Supplementary information
Supplementary Information
Supplementary Information, Supplementary Fig 1, Fig 2 and Fig 3 (PDF 1281 kb)
Rights and permissions
About this article
Cite this article
Cerbino, R., Peverini, L., Potenza, M. et al. X-ray-scattering information obtained from near-field speckle. Nature Phys 4, 238–243 (2008). https://doi.org/10.1038/nphys837
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphys837
This article is cited by
-
Quantitative analysis of speckle-based X-ray dark-field imaging using numerical wave-optics simulations
Scientific Reports (2021)
-
Quantitative X-ray phase contrast computed tomography with grating interferometry
European Journal of Nuclear Medicine and Molecular Imaging (2021)
-
Spectral Camera based on Ghost Imaging via Sparsity Constraints
Scientific Reports (2016)
-
Dynamic scaling for the growth of non-equilibrium fluctuations during thermophoretic diffusion in microgravity
Scientific Reports (2015)
-
Reconstructing state mixtures from diffraction measurements
Nature (2013)