Ptychography

Collection of a ptychographic imaging data set in the simplest single-aperture configuration. (a) Coherent illumination incident from the left is locally confined onto an area of the specimen. A detector downstream of the specimen records an interference pattern. (b) The specimen is shifted (in this case, upwards) and a second pattern is recorded. Note that regions of illumination must overlap with one another to facilitate the ptychographic shift-invariance constraint. (c) A whole ptychographic data set uses many overlapping regions of illumination. (d) The entire data set is four-dimensional: for each 2D illumination position (x, y), there is a 2D diffraction pattern (k_x, k_y).

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" (Ancient Greek: πτυχή, "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.