Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects
Appl. Phys. Lett. 92, 214105 (2008); doi:10.1063/1.2938050
Published 28 May 2008
You are not logged in to this journal. Log in
A dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects is derived by solving the Helmholtz equation in the parabolic approximation using the coupled-wave theory. A method to account for volume-diffraction effects, based on propagating backwards the eigenmodes of the microfluidic array, is demonstrated for a colloidal suspension in confinement.
©2008 American Institute of Physics
| History: | Received 2 April 2008; accepted 10 May 2008; published 28 May 2008 |
| Permalink: |
http://link.aip.org/link/?APPLAB/92/214105/1 |
REFERENCES (23)
For access to fully linked references, you need to log in.
For access to fully linked references, you need to Log in.
- J. Miao, P. Charalambous, J. Kirz, and D. Sayre,
Nature (London) 400, 342 (1999) . - M. A. Pfeifer, G. J. Williams, I. A. Vartanyants, R. Harder, and I. K. Robinson,
Nature (London) 442, 63 (2006) . - D. Shapiro, P. Thibault, T. Beetz, V. Elser, M. Howells, C. Jacobsen, J. Kirz, E. Lima, H. Miao, A. M. Neiman, and D. Sayre,
Proc. Natl. Acad. Sci. U.S.A. 102, 15343 (2005) . - 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, Phys. Rev. E 75, 021501 (2007).
- P. Thibault, V. Elser, C. Jacobsen, D. Shapiro, and D. Sayre,
Acta Crystallogr., Sect. A: Found. Crystallogr. 62, 248 (2006) . - R. Harder, M. A. Pfeifer, G. J. Williams, I. A. Vartaniants, and I. K. Robinson, Phys. Rev. B 77, 115425 (2007).
- O. Bunk, A. Diaz, F. Pfeiffer, C. David, B. Schmitt, D. K. Satapathy, and J. F. van der Veen,
Acta Crystallogr., Sect. A: Found. Crystallogr. 63, 306 (2007) . - G. Schneider, Appl. Phys. Lett. 71, 2242 (1997).
- F. Pfeiffer, C. David, J. F. van der Veen, and C. Bergemann, Phys. Rev. B 73, 245331 (2006).
- C. G. Schroer, Phys. Rev. B 74, 033405 (2006).
- M. J. Zwanenburg, J. F. Peters, J. H. H. Bongaerts, S. A. de Vries, D. L. Abernathy, and J. F. van der Veen, Phys. Rev. Lett. 82, 1696 (1999).
-
/
~10−2 for Si at the present wavelength. - The eigenstates and eigenvalues for |m|
70, are obtained by transforming the coefficient matrix in Eq. (4) to Hessenberg form and solving the linear matrix equation using the QR algorithm (Ref. 23). - C. Fuhse and T. Salditt,
Opt. Commun. 265, 140 (2006) . - A. Diaz, C. David, H. Guo, H. Keymeulen, F. Pfeiffer, G. Wegdam, T. Weitkamp, and J. F. van der Veen,
Physica B 357, 199 (2005) . - D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, 1991).
- We use the longitudinal step size
z=10 nm. - R. L. Jones, T. Hu, E. K. Lin, W.-L. Wu, R. Kolb, D. M. Casa, P. J. Bolton, and G. B. Barclay, Appl. Phys. Lett. 83, 4059 (2003).
- We use the Crank–Nicolson scheme (Ref. 23) with step sizes
x=
z=1 nm. - A. Jarre, C. Fuhse, C. Ollinger, J. Seeger, R. Tucoulou, and T. Salditt, Phys. Rev. Lett. 94, 074801 (2005).
- The duty cycle w/p, and the tapering angle
, are determined from the diffraction efficiencies of the empty grating. The other parameters are obtained using the model-independent approach of Ref. 7. - G. Schneider, Appl. Phys. Lett. 73, 599 (1998).
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, 1992).







