Abstract

We develop a novel method for structure determination of confined fluids using diffraction-grating-based x-ray interferometry. Within this approach, diffraction from a microfluidic array, which acts both as confinement and transmission diffraction grating, provides the reference wave, whereas the density modulations of the confined fluid, acting as a weak phase object, generate the object wave. The ensemble-averaged density profile of the fluid perpendicular to the confining channel is then unambiguously obtained from the interference between the reference and object waves by direct Fourier inversion.

© 2008 Optical Society of America

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  1. W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
    [CrossRef]
  2. H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
    [CrossRef] [PubMed]
  3. B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995).
    [CrossRef]
  4. M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
    [CrossRef] [PubMed]
  5. O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
    [CrossRef]
  6. A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
    [CrossRef]
  7. A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007).
    [CrossRef]
  8. O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
    [CrossRef]
  9. O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
    [CrossRef]
  10. H. N. Chapman, A. Barty, S. Marchesini, A. Moy, S. P. Hau-Riege, C. Cui, M. R. Howells, R. Rosen, H. He, J. C. H. Spence, U. Weierstall, T. Beetz, C. Jacobsen, and D. Shapiro, "High-resolution ab initio three-dimensional x-ray diffraction microscopy," J. Opt. Soc. Am. A 23, 1179-1200 (2006).
    [CrossRef]
  11. J. N. Clark, G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, and A. G. Peele, "Quantitative phase measurement in coherent diffractive imaging," Opt. Express 16, 3342-3348 (2008).
    [CrossRef] [PubMed]
  12. P. W. Wachulak, M. C. Marconi, R. A. Bartels, C. S. Menoni, and J. J. Rocca, "Soft x-ray laser holography with wavelength resolution," J. Opt. Soc. Am. B 25, 1811-1814 (2008).
    [CrossRef]
  13. A. Szöke, "Holographic methods in x-ray crystallography. II. Detailed theory and connection to other methods of crystallography," Acta Crystallogr. Sect. A 49, 853-866 (1993).
    [CrossRef]
  14. G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
    [CrossRef]
  15. D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
    [CrossRef]
  16. Since Δβ/Δδ ~ 10-2 in the present study (Δδ denoting the average change in the imaginary part of the refractive index across the grating-fluid interface), absorption can be neglected.
  17. It follows from the definition of (x) that A0 = 0.
  18. The reference diffraction efficiencies |0 m are obtained from the diffraction efficiencies |e m of the empty grating as |0 m _ (m_=0 |m/m_=0 |e m) |e m.
  19. K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
    [CrossRef]
  20. J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999).
    [CrossRef]
  21. T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987).
    [CrossRef]
  22. D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
    [CrossRef] [PubMed]
  23. C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
    [CrossRef] [PubMed]

2008 (4)

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

J. N. Clark, G. J. Williams, H. M. Quiney, L. Whitehead, M. D. de Jonge, E. Hanssen, M. Altissimo, K. A. Nugent, and A. G. Peele, "Quantitative phase measurement in coherent diffractive imaging," Opt. Express 16, 3342-3348 (2008).
[CrossRef] [PubMed]

P. W. Wachulak, M. C. Marconi, R. A. Bartels, C. S. Menoni, and J. J. Rocca, "Soft x-ray laser holography with wavelength resolution," J. Opt. Soc. Am. B 25, 1811-1814 (2008).
[CrossRef]

2007 (3)

A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

2006 (1)

2005 (1)

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

2003 (1)

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

2002 (1)

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

2001 (1)

D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
[CrossRef]

2000 (2)

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999).
[CrossRef]

1997 (1)

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

1995 (1)

B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995).
[CrossRef]

1993 (2)

A. Szöke, "Holographic methods in x-ray crystallography. II. Detailed theory and connection to other methods of crystallography," Acta Crystallogr. Sect. A 49, 853-866 (1993).
[CrossRef]

G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
[CrossRef]

1987 (1)

T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987).
[CrossRef]

Abernathy, D.

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

Altissimo, M.

Bartels, R. A.

Barty, A.

Basu, J. K.

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

Beetz, T.

Bhushan, B.

B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995).
[CrossRef]

Bongaerts, J. H. H.

M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
[CrossRef] [PubMed]

Bunk, O.

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

Chamard, V.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Chapman, H. N.

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999).
[CrossRef]

Clark, J. N.

Cui, C.

David, C.

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

de Jonge, M. D.

de Vries, S. A.

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

Denk, M.

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

Diaz, A.

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

Dosch, H.

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

Eisenberg, D.

T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987).
[CrossRef]

Ghaderi, T.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Grübel, G.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Guo, H.

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

Gutt, C.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Hanssen, E.

Harder, R.

D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
[CrossRef]

Hau-Riege, S. P.

He, H.

Hoch, J. C.

G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
[CrossRef]

Honkimäki, V.

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

Howells, M. R.

Huisman, W. J.

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

Israelachvili, J. N.

B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995).
[CrossRef]

Jacobsen, C.

Jefimovs, K.

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

Kaendler, I. D.

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

Keymeulen, H.

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

Kim, H.

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

Kim, S.-H.

T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987).
[CrossRef]

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999).
[CrossRef]

Klein, O.

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

Landmann, U.

B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995).
[CrossRef]

Lee, D. R.

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

Lippmann, T.

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

Maalouf, G. J.

G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
[CrossRef]

Madsen, A.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Marchesini, S.

Marconi, M. C.

Menoni, C. S.

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999).
[CrossRef]

Moritz, W.

D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
[CrossRef]

Moy, A.

Nugent, K. A.

Nygård, K.

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

Padeste, C.

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

Patterson, B. D.

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

Peele, A. G.

Perret, E.

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

Peters, J. F.

M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
[CrossRef] [PubMed]

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

Pfeiffer, F.

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

Quiney, H. M.

Reichert, H.

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

Reiter, G.

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

Riese, D. O.

M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
[CrossRef] [PubMed]

Robinson, I. K.

D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
[CrossRef]

Rocca, J. J.

Rosen, R.

Saldin, D. K.

D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
[CrossRef]

Satapathy, D. K.

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999).
[CrossRef]

Schmitt, B.

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

Seeck, O. H.

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

Seydel, T.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Shapiro, D.

Shu, D.

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

Sinha, S. K.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

Spence, J. C. H.

Sprung, M.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Stern, A. S.

G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
[CrossRef]

Szöke, A.

G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
[CrossRef]

A. Szöke, "Holographic methods in x-ray crystallography. II. Detailed theory and connection to other methods of crystallography," Acta Crystallogr. Sect. A 49, 853-866 (1993).
[CrossRef]

Szöke, H.

G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
[CrossRef]

Terry, T. E.

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

Terwilliger, T.

T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987).
[CrossRef]

Tolan, M.

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

van der Veen, J. F.

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
[CrossRef] [PubMed]

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

Vogler, H.

D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
[CrossRef]

Wachulak, P. W.

Wegdam, G.

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

Wegdam, G. H.

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

Weierstall, U.

Weitkamp, T.

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

Whitehead, L.

Williams, G. J.

Willmott, P. R.

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

Zwanenburg, M. J.

M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
[CrossRef] [PubMed]

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

Acta Crystallogr. Sect. A (4)

O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen, "Diffractive imaging for periodic samples: retrieving one-dimensional concentration profiles across microfluidic channels," Acta Crystallogr. Sect. A 63, 306-314 (2007).
[CrossRef]

A. Szöke, "Holographic methods in x-ray crystallography. II. Detailed theory and connection to other methods of crystallography," Acta Crystallogr. Sect. A 49, 853-866 (1993).
[CrossRef]

G. J. Maalouf, J. C. Hoch, A. S. Stern, H. Szöke, and A. Szöke, "Holographic methods in x-ray crystallography. III. First numerical results," Acta Crystallogr. Sect. A 49, 866-871 (1993).
[CrossRef]

T. Terwilliger, S.-H. Kim, and D. Eisenberg, "Generalized method of determining heavy-atom positions using the difference Patterson function," Acta Crystallogr. Sect. A 43, 1-5 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

K. Nygård, D. K. Satapathy, O. Bunk, F. Pfeiffer, C. David, and J. F. van der Veen, "Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects," Appl. Phys. Lett. 92, 214105 (2008).
[CrossRef]

Comput. Phys. Commun. (1)

D. K. Saldin, R. Harder, H. Vogler, W. Moritz, and I. K. Robinson, "Solving the structure completion problem in surface crystallography," Comput. Phys. Commun. 137, 12-24 (2001).
[CrossRef]

Europhys. Lett. (1)

O. H. Seeck, H. Kim, D. R. Lee, D. Shu, I. D. Kaendler, J. K. Basu, and S. K. Sinha, "Observation of thickness quantization in liquid films confined to molecular dimension," Europhys. Lett. 60, 376-382 (2002).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

Nature (London) (4)

W. J. Huisman, J. F. Peters, M. J. Zwanenburg, S. A. de Vries, T. E. Terry, D. Abernathy, and J. F. van der Veen, "Layering of a liquid metal in contact with a hard wall," Nature (London) 390, 379-381 (1997).
[CrossRef]

H. Reichert, O. Klein, H. Dosch, M. Denk, V. Honkimäki, T. Lippmann, and G. Reiter, "Observation of five-fold local symmetry in liquid lead," Nature (London) 408, 839-841 (2000).
[CrossRef] [PubMed]

B. Bhushan, J. N. Israelachvili, and U. Landmann, "Nanotribology: friction, wear and lubrication at the atomic scale," Nature (London) 374, 607-616 (1995).
[CrossRef]

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, "Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens," Nature (London) 400, 342-344 (1999).
[CrossRef]

Opt. Express (1)

Phys. Rev. E (1)

O. Bunk, A. Diaz, F. Pfeiffer, C. David, C. Padeste, H. Keymeulen, P. R. Willmott, B. D. Patterson, B. Schmitt, D. K. Satapathy, J. F. van der Veen, H. Guo, and G. H. Wegdam, "Confinement-induced liquid ordering investigated by x-ray phase retrieval," Phys. Rev. E 75, 021501 (2007).
[CrossRef]

Phys. Rev. Lett. (3)

M. J. Zwanenburg, J. H. H. Bongaerts, J. F. Peters, D. O. Riese, and J. F. van der Veen, "X-ray waveguiding studies of ordering phenomena in confined fluids," Phys. Rev. Lett. 85, 5154-5157 (2000).
[CrossRef] [PubMed]

D. K. Satapathy, O. Bunk, K. Jefimovs, K. Nygård, H. Guo, A. Diaz, E. Perret, F. Pfeiffer, C. David, G. H. Wegdam, and J. F. van der Veen, "Colloidal monolayer trapped near a charged wall: A synchrotron x-ray diffraction study," Phys. Rev. Lett. 101, 136103 (2008).
[CrossRef] [PubMed]

C. Gutt, T. Ghaderi, V. Chamard, A. Madsen, T. Seydel, M. Tolan, M. Sprung, G. Grübel, and S. K. Sinha, "Observation of heterodyne mixing in surface x-ray photon correlation spectroscopy experiments," Phys. Rev. Lett. 91, 076104 (2003).
[CrossRef] [PubMed]

Physica B (1)

A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen, "Microcavity arrays for X-ray diffraction studies of ordering phenomena in confined colloid solutions," Physica B 357, 199-203 (2005).
[CrossRef]

Thin Solid Films (1)

A. Diaz and J. F. van der Veen, "Theory of X-ray scattering from a complex fluid confined by a nanocavity array," Thin Solid Films 515, 5645-5653 (2007).
[CrossRef]

Other (3)

Since Δβ/Δδ ~ 10-2 in the present study (Δδ denoting the average change in the imaginary part of the refractive index across the grating-fluid interface), absorption can be neglected.

It follows from the definition of (x) that A0 = 0.

The reference diffraction efficiencies |0 m are obtained from the diffraction efficiencies |e m of the empty grating as |0 m _ (m_=0 |m/m_=0 |e m) |e m.

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the experimental setup and geometric definitions. The SEM image shows the cross section of a typical microfluidic array with period p=400 nm, height h≃2.4 µm, and channel width in the range w≃120–190 nm.

Fig. 2.
Fig. 2.

Typical diffraction pattern acquired from a fluid-filled grating. Due to symmetry, only the positive diffraction orders are shown. Inset: Magnified view of the 42nd to 53rd diffraction orders.

Fig. 3.
Fig. 3.

Difference autocorrelation function ΔP(x) for selected channel widths w (vertically offset for clarity).

Fig. 4.
Fig. 4.

Contour plot of the confinement-induced fluid density modulations perpendicular to the confining channel as function of the channel width w.

Fig. 5.
Fig. 5.

Phase-shift profile across the confining channel (w=142 nm). The solid line is obtained using the present interferometric approach, while the dashed line depicts the corresponding profile (including the grating) as obtained using an iterative phase-retrieval algorithm [8] (vertically offset in order to facilitate comparison). Inset: Unshifted phase profiles.

Equations (6)

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t ( x ) = 1 + { e i [ Φ + α ( x ) ] 1 } f ( x ) .
T m ( e i Φ 1 ) F m + i A m e i Φ = T m 0 + i A m e i Φ ,
η m η m 0 + 2 A m F m sin⁡ Φ + A m 2 .
a ( x ) = m = M M A m cos ( 2 π m x p ) ,
A m η m η m 0 2 F m sin Φ .
Δ P ( x ) = m = M M ( η m η m 0 ) cos ( 2 π m x p ) = 2 sin Φ p a ( x ) f ( x ) + 1 p a ( x ) a ( x ) ,

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