Publisher Summary Ptychography is a nonholographic solution of the phase problem. It is a method for calculating the phase relationships among different parts of a scattered wave disturbance in a situation where only the magnitude (intensity or flux) of the wave can be physically measured. Its usefulness lies in its ability (like holography) to obtain images without the use of lenses, and hence to lead to resolution improvements and access to properties of the scattering medium that cannot be easily obtained from conventional imaging methods. The chapter discusses ptychography in the context of other phase-retrieval methods in both historical and conceptual terms. In an original and oblique approach to the phase problem, it was Hoppe who proposed the first version of the particular solution to the phase problem. The word “ptychography” was introduced to suggest a solution to the phase problem using the convolution theorem, or rather the “folding” of diffraction orders into one another via the convolution of the Fourier transform of a localized aperture or illumination function in the object plane. Apart from computers, the two most important experimental issues that affect ptychography, relate to the degree of coherence in the illuminating beam and the detector efficiency and dynamic range.

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Ptychography and Related Diffractive Imaging Methods

Scanning transmission electron microscopy (STEM) is widely used for imaging, diffraction, and spectroscopy of materials down to atomic resolution. Recent advances in detector technology and computational methods have enabled many experiments that record a full image of the STEM probe for many probe positions, either in diffraction space or real space. In this paper, we review the use of these four-dimensional STEM experiments for virtual diffraction imaging, phase, orientation and strain mapping, measurements of medium-range order, thickness and tilt of samples, and phase contrast imaging methods, including differential phase contrast, ptychography, and others.

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Four-Dimensional Scanning Transmission Electron Microscopy (4D-STEM): From Scanning Nanodiffraction to Ptychography and Beyond.

X-ray ptychographic microscopy combines the advantages of raster scanning X-ray microscopy with the more recently developed techniques of coherent diffraction imaging. It is limited neither by the fabricational challenges associated with X-ray optics nor by the requirements of isolated specimen preparation, and offers in principle wavelength-limited resolution, as well as stable access and solution to the phase problem. In this Review, we discuss the basic principles of X-ray ptychography and summarize the main milestones in the evolution of X-ray ptychographic microscopy and tomography over the past ten years, since its first demonstration with X-rays. We also highlight the potential for applications in the life and materials sciences, and discuss the latest advanced concepts and probable future developments.

X-ray ptychography

The theory of deconvolving the microdiffraction data-set available in a scanning transmission electron microscope or, equivalently, the set of all bright- and dark-field images available in a conventional transmission electron microscope to obtain super- resolution micrographs (which are not limited by the transfer function of the objective lens) is developed and described with reference to holography and other phase-retrieval schemes. By the use of a Wigner distribution, influences of the instrument function can be entirely separated from the information pertaining to the specimen. The final solution yields an unambiguous estimate of the complex value of the specimen function at a resolution which in theory is only limited by the electron wavelength. The faithfulness of the image processing is shown to be not seriously affected by specimen thickness or partial coherence in the illuminating beam. The inversion procedure is remarkably noise insensitive, implying that it should result in a robust and practicable experimental technique, though one that will require very large computing facilities.

The theory of super-resolution electron microscopy via Wigner-distribution deconvolution

Advances in microscopy techniques based on x-rays have opened unprecedented opportunities in terms of spatial resolution, combined with chemical and morphology sensitivity, to analyze solid, soft and liquid matter. The advent of ultrabright third and fourth generation photon sources and the continuous development of x-ray optics and detectors has pushed the limits of imaging and spectroscopic analysis to structures as small as a few tens of nanometers. Specific interactions of x-rays with matter provide elemental and chemical sensitivity that have made x-ray spectromicroscopy techniques a very attractive tool, complementary to other microscopies, for characterization in all actual research fields. The x-ray penetration power meets the demand to examine samples too thick for electron microscopes implementing 3D imaging and recently also 4D imaging which adds time resolution as well. Implementation of a variety of phase contrast techniques enhances the structural sensitivity, especially for the hard x-ray regime. Implementation of lensless or diffraction imaging helps to enhance the lateral resolution of x-ray imaging to the wavelength dependent diffraction limit.

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Transmission and emission x-ray microscopy: operation modes, contrast mechanisms and applications.

http://xrm.phys.northwestern.edu/research/pdf_papers/1989/bates_ultramic_1989.pdf

R.H.T. Bates

Papers

Sub-ångström transmission microscopy: A fourier transform algorithm for microdiffraction plane intensity information