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Fast Deterministic Ptychographic Imaging Using X-Rays

Published online by Cambridge University Press:  23 May 2014

Ada W. C. Yan ,
Adrian J. D’Alfonso ,
Andrew J. Morgan ,
Corey T. Putkunz  and
Leslie J. Allen
Ada W. C. Yan
Affiliation:
School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
Adrian J. D’Alfonso
Affiliation:
School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
Andrew J. Morgan
Affiliation:
School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
Corey T. Putkunz
Affiliation:
School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
Leslie J. Allen*
Affiliation:
School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
*
*Corresponding author. [email protected]
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Abstract

We present a deterministic approach to the ptychographic retrieval of the wave at the exit surface of a specimen of condensed matter illuminated by X-rays. The method is based on the solution of an overdetermined set of linear equations, and is robust to measurement noise. The set of linear equations is efficiently solved using the conjugate gradient least-squares method implemented using fast Fourier transforms. The method is demonstrated using a data set obtained from a gold–chromium nanostructured test object. It is shown that the transmission function retrieved by this linear method is quantitatively comparable with established methods of ptychography, with a large decrease in computational time, and is thus a good candidate for real-time reconstruction.

Keywords

coherent diffractive imagingexit-wave reconstructionptychographylensless imagingphase retrievalX-ray imaging
Type
FEMMS Special Issue
Information
Microscopy and Microanalysis , Volume 20 , Issue 4 , August 2014 , pp. 1090 - 1099
Copyright
© Microscopy Society of America 2014 

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References

Bao, P., Zhang, F., Pedrini, G. & Osten, W. (2008). Phase retrieval using multiple illumination wavelengths. Opt Lett 33, 309–311.CrossRefGoogle ScholarPubMed
Chapman, H.N., Barty, A., Bogan, M.J., Boutet, S., Frank, M., Hau-Riege, S.P., Marchesini, S., Woods, B.W., Bajt, S., Benner, W.H., London, R.A., Plönjes, E., Kuhlmann, M., Treusch, R., Düsterer, S., Tschentscher, T., Schneider, J.R., Spiller, E., Möller, T., Bostedt, C., Hoener, M., Shapiro, D.A., Hodgson, K.O., van der Spoel, D., Burmeister, F., Bergh, M., Caleman, C., Huldt, G., Seibert, M.M., Maia, F.R.N.C., Lee, R.W., Szöke, A., Timneanu, N. & Hajdu, J. (2006). Femtosecond diffractive imaging with a soft-X-ray free-electron laser. Nat Phys 2, 839–843.CrossRefGoogle Scholar
D’Alfonso, A.J., Morgan, A.J., Martin, A.V., Quiney, H.M. & Allen, L.J. (2012). Fast deterministic approach to exit-wave reconstruction. Phys Rev A 85, 013816.Google Scholar
D’Alfonso, A.J., Morgan, A.J., Yan, A.W.C., Wang, P., Sawada, H., Kirkland, A.I. & Allen, L.J. (2013). Deterministic electron ptychography at atomic resolution. Phys Rev B 89, 064101.Google Scholar
Elser, V. (2003). Phase retrieval by iterated projections. J Opt Soc Am A 20, 40–55.Google Scholar
Fienup, J.R. (1978). Reconstruction of an object from the modulus of its Fourier transform. Opt Lett 3, 27–29.Google Scholar
Gureyev, T.E., Roberts, A. & Nugent, K.A. (1995). Phase retrieval with the transport-of-intensity equation: Matrix solution with use of Zernike polynomials. J Opt Soc Am A 12, 1932–1942.Google Scholar
Hansen, P.C. (1992). Analysis of discrete ill-posed problems by means of the L-curve. SIAM Rev 34, 561–580.CrossRefGoogle Scholar
Hansen, P.C. (2010). Discrete Inverse Problems: Insight and Algorithms. Philadelphia: SIAM.Google Scholar
Hawkes, P.W. (2009). Aberration correction past and present. Phil Trans R Soc A 367, 3637–3664.Google Scholar
Henderson, R. (1995). The potential and limitations of neutrons, electrons and X-rays for atomic resolution microscopy of unstained biological molecules. Q Rev Biophys 28, 171–193.CrossRefGoogle ScholarPubMed
Hestenes, M.R. & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems. J Res Nat Bur Stand 49, 409–436.Google Scholar
Hoppe, W. (1969). Diffraction in inhomogeneous primary wave fields.1. Principle of phase determination from electron diffraction interference. Acta Crystallogr A 25, 495–501.Google Scholar
Leith, E. & Upatnieks, J. (1962). Reconstructed wavefronts and communication theory. J Opt Soc Am 52, 1123–1128.CrossRefGoogle Scholar
Maiden, A.M. & Rodenburg, J.M. (2009). An improved ptychographical phase retrieval algorithm for diffractive imaging. Ultramicroscopy 109, 1256–1262.CrossRefGoogle ScholarPubMed
Martin, A.V. & Allen, L.J. (2008). Direct retrieval of a complex wave from its diffraction pattern. Opt Commun 281, 5114–5121.Google Scholar
Miao, J., Charalambous, P., Kirz, J. & Sayre, D. (1999). Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344.CrossRefGoogle Scholar
Morgan, A.J., D’Alfonso, A.J., Wang, P., Sawada, H., Kirkland, A.I. & Allen, L.J. (2013). Fast deterministic single-exposure coherent diffractive imaging at sub-Ångström resolution. Phys Rev B 87, 094115.Google Scholar
Ostermeier, C. & Michel, H. (1997). Crystallization of membrane proteins. Curr Opin Struct Biol 7, 697–701.Google Scholar
Putkunz, C.T., Clark, J.N., Vine, D.J., Williams, G.J., Pfeifer, M.A., Balaur, E., McNulty, I., Nugent, K.A. & Peele, A.G. (2011). Phase-diverse coherent diffractive imaging: High sensitivity with low dose. Phys Rev Lett 106, 013903.Google Scholar
Quiney, H.M., Peele, A.G., Cai, Z., Paterson, D. & Nugent, K.A. (2006). Diffractive imaging of highly focused X-ray fields. Nat Phys 2, 101–104.Google Scholar
Rodenburg, J.M. & Bates, R.H.T. (1992). The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Phil Trans R Soc Lond A 339, 521–553.Google Scholar
Rodenburg, J.M. & Faulkner, H.M.L. (2004). A phase retrieval algorithm for shifting illumination. Appl Phys Lett 85, 4795–4797.Google Scholar
Scherzer, O. (1936). Some defects of electron lenses. Zeitschrift für Physik 101, 593–603.CrossRefGoogle Scholar
Shapiro, D., Thibault, P., Beetz, T., Elser, V., Howells, M., Jacobsen, C., Kirz, J., Lima, E., Miao, H., Neiman, A.M. & Sayre, D. (2005). Biological imaging by soft X-ray diffraction microscopy. Proc Natl Acad Sci USA 102, 15343–15346.Google Scholar
Stroke, G.W., Brumm, D. & Funkhouser, A. (1965). Three-dimensional holography with “lensless” Fourier-transform holograms and coarse P/N polaroid film. J Opt Soc Am 55, 1327–1328.Google Scholar
Thibault, P., Dierolf, M., Menzel, A., Bunk, O., David, C. & Pfeiffer, F. (2008). High-resolution scanning X-ray diffraction microscopy. Science 321, 379–382.Google Scholar
Uhlemann, S., Müller, H., Hartel, P., Zach, J. & Haider, M. (2013). Thermal magnetic field noise limits resolution in transmission electron microscopy. Phys Rev Lett 111, 046101.Google Scholar
Wiener, N. (1930). Generalized harmonic analysis. Acta Math 55, 117–258.Google Scholar
Zhang, F., Pedrini, G. & Osten, W. (2007). Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation. Phys Rev A 75, 043805.CrossRefGoogle Scholar