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Dynamical theory for diffractive x-ray imaging of one-dimensional periodic objects
3.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).
4.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).
7.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).
12. for Si at the present wavelength.
13.The eigenstates and eigenvalues for , 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).
16.D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, San Diego, 1991).
17.We use the longitudinal step size .
19.We use the Crank–Nicolson scheme (Ref. 23) with step sizes .
21.The duty cycle , 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.
23.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).
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