Wigner Distribution Deconvolution for ptychography: blind solution of the illumination function

Session

Stream 4: Diamond Light Source Session 1

Authors

Mr Wenjie Mei (1), Professor John Rodenburg (1)

Affiliations

1. University of Sheffield

Keywords

Phase retrieval, Ptychography, Wigner Distribution Deconvolution 

Abstract text

Long before the advent of iterative methods for the solution of the ptychographical phase-retrieval problem for lensless, high-fidelity transmission microscopy [1], a direct deconvolution method was well-developed in the 1990s, called Wigner Distribution Deconvolution [2]. This included work showing that the ptychographic data set could be inverted ‘blindly’, i.e. without any knowledge of the illumination optics [3]. However, there were problems with the method reported. The technique used a process called ‘stepping out’ that could only employ a tiny fraction of the massive data set involved in WDD. Since then, Li et al [4] have developed a much more comprehensive way of dealing with all pairs of phase differences in a typical WDD data set. The present work revisits the blind deconvolution problem in the light of this more recent work. Whether WDD will compete with the iterative solution methods, all of which solve for both the object function and the illumination field, and which are very well developed and flexible in their application, is yet to be determined. Whatever the case, handling the blind deconvolution issue robustly is a key requirement for handling this sort of ‘4D STEM’ data. We present recent progress in achieving this goal.

References

1. Rodenburg, J. and A. Maiden, Ptychography, in Springer Handbook of Microscopy, P.W. Hawkes and J.C.H. Spence, Editors. 2019, Springer International Publishing: Cham. p. 2-2.

2. Rodenburg, J. and R. Bates, The theory of super-resolution electron microscopy via Wigner-distribution deconvolution. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 1992. 339(1655): p. 521-553.

3.  McCallum, B. and J. Rodenburg, Simultaneous reconstruction of object and aperture functions from multiple far-field intensity measurements. JOSA A, 1993. 10(2): p. 231-239.

4. Li, P., T.B. Edo and J.M. Rodenburg, Ptychographic inversion via Wigner distribution deconvolution: noise suppression and probe design. Ultramicroscopy, 2014. 147: p. 106-113.