Ptychography

Ptychography (/t(a)ɪˈkɒgrəfi/ t(a)i-KO-graf-ee) is a computational microscopy technique that reconstructs the complex-valued image (amplitude and phase) of a specimen from a series of coherent diffraction patterns recorded as a localized probe is scanned with overlap across the sample. It unifies the principles of microscopy and crystallography, combining the real-space imaging of microscopy with the reciprocal-space diffraction analysis of crystallography to produce high-resolution, quantitative images free from lens aberrations. Ptychography has been demonstrated with visible light, X-rays, electrons and extreme-ultraviolet radiation, enabling quantitative phase contrast imaging across nine orders of magnitude in length scales. Its defining characteristic is translational invariance, which means that the interference patterns are generated by one constant function (e.g. a field of illumination or an aperture stop) moving laterally by a known amount with respect to another constant function (the specimen itself or a wave field). The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" ( , "ptychē" is 'fold' ) into one another as shown in the figure. Unlike conventional lens imaging, ptychography is unaffected by lens-induced aberrations or diffraction effects caused by limited numerical aperture.…

Ptychography (/t(a)ɪˈkɒgrəfi/ t(a)i-KO-graf-ee) is a computational microscopy technique that reconstructs the complex-valued image (amplitude and phase) of a specimen from a series of coherent diffraction patterns recorded as a localized probe is scanned with overlap across the sample. It unifies the principles of microscopy and crystallography, combining the real-space imaging of microscopy with the reciprocal-space diffraction analysis of crystallography to produce high-resolution, quantitative images free from lens aberrations. Ptychography has been demonstrated with visible light, X-rays, electrons and extreme-ultraviolet radiation, enabling quantitative phase contrast imaging across nine orders of magnitude in length scales. Its defining characteristic is translational invariance, which means that the interference patterns are generated by one constant function (e.g. a field of illumination or an aperture stop) moving laterally by a known amount with respect to another constant function (the specimen itself or a wave field). The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" ( , "ptychē" is 'fold' ) into one another as shown in the figure. Unlike conventional lens imaging, ptychography is unaffected by lens-induced aberrations or diffraction effects caused by limited numerical aperture. This is particularly important for atomic-scale wavelength imaging, where it is difficult and expensive to make good-quality lenses with high numerical aperture. Another advantage is its high phase sensitivity, enabling clear imaging of transparent or weakly absorbing specimens. This is because it is sensitive to the phase of the radiation that has passed through a specimen, and so it does not rely on the object absorbing radiation. In the case of visible-light biological microscopy, this means that cells do not need to be stained or labelled to create contrast. Modern ptychography, developed in the 2000s and now the most widely used form of the technique, combines scanning microscopy with coherent diffractive imaging (CDI) through iterative phase-retrieval algorithms. In this approach, a coherent probe—such as an X-ray, electron, or optical beam—is scanned across the specimen with overlapping illumination regions, and a diffraction pattern is recorded at each position. The overlap between adjacent probe positions in real space and diffraction data in reciprocal space provide sufficient redundancy to enable the simultaneous reconstruction of both the probe and the sample transmission functions. This yields quantitative, aberration-free phase images that are robust to partial coherence and experimental imperfections, while providing both high spatial resolution and a large field of view. Modern ptychography has been demonstrated with X-rays, electrons, and visible light, providing sub-ångström resolution in electron microscopy and quantitative three-dimensional imaging through X-ray ptychotomography. d_z = \frac{\lambda}{2\sin^2(\theta / 2)}, where λ is the wavelength of the illumination, and θ is the maximum scattering angle captured by the detector. The depth resolution is typically much poorer than the lateral resolution, which is the primary current limitation. Recent applications of multislice ptychography include atomic-scale imaging of oxygen vacancies in zeolites and high temperature superconductors, oxygen anion displacements in 3D in ferroelectrics, interface mapping in van der Waals heterostructures and moiré phasons in 2D materials. Multislice ptychography continues to evolve rapidly. Decades later, Rodenburg and collaborators extended Hoppe's concept by developing non-iterative algorithms such as Wigner Distribution Deconvolution (WDD) and the Single-Side-Band SSB, method (which is an approximation of WWD when the specimen is weakly scattering). These methods were first demonstrated experimentally in one dimension and 2 dimensions using light, and electrons . In the early to mid-1990s, Nellist, McCallum, and Rodenburg demonstrated the first experimental proof of crystalline electron ptychography in the exact scattering geometry first proposed by Hoppe, achieving resolution beyond the 'information limit', which until that time was regarded as the insuperable limit of resolution in the transmission electron microscope Around the same time, Chapman implemented the first X-ray ptychography using the WDD formalism. However, progress was limited at the time because ptychographic reconstruction generally required prior knowledge of the probe, although it had been shown that in principle both functions could be separated using the WWD formulation . Furthermore, the scanning step size had to be approximately half the target resolution. , leading to massive 4D STEM data sets that could not be easily accommodated by even the largest computers available at that time. Nowadays, 4D STEM data can be recorded trivially: it is a major area of research.

External links

Cornell researchers see atoms at record resolution, cornell.edu at 20 May 2021

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