Ptychography: A different approach to sub-nanometer resolution imaging

It has been a notable phenomenon since considerable time that almost every major university invents their own nano-imaging techniques. Usually, this results in a particular piece of technology with limited applications that does not necessarily become industry standard. Although it may produce interesting results and demonstrate alternative options, it does not necessarily mean that it will end up relevant. While it is quite worthwhile taking a close look at the strengths and benefits of individual approaches, extolling their virtues remains to be postponed for years if not decades in certain cases until the consensus of market forces has articulated a clear preference along with reasons for it.

That said, one needs to take into consideration that all technology, even what has become the industry standard, is provisional and its continued development is cross-fertilized by alternative approaches. In the longer term, there is no room in technology development for ‘not invented here,’ of ignoring third-party solutions because of their external origins. With few exceptions, looking sideways to leverage other people’s work behooves all further R&D, since it avoids reinventing the wheel while highlighting potential for improvements.

While scanning electron microscopy (Ernst Ruska and Max Knoll, 1931, ~ 50 nm resolution) opened the door to imaging the molecular dimension, the scanning tunneling microscope (Gerd Binnig and Heinrich Rohrer,[1] 1981, ~ 0.1-0.01 nm resolution) enabled imaging and manipulating individual atoms in a sample. It has since been refined into deterministic electron ptychography at atomic resolution levels. Ruska as well as Binnig/Rohrer received the 1986 Nobel Prize in Physics for their contributions to electron microscopy. The next leap came in scanning transmission x-ray microscopy (STXM) of which a special case is ptychography, a form of diffractive imaging using inverse computation of scattered intensity data. The name derives from Greek ptyx for fold or layer as in diptychon, triptychon, polyptychon. Developed by Walter Hoppe in the late 1960s,[2] further developments arrived at applications for use in both x-ray and visible spectrum, resulting in a resolution improvement by more than a factor of 3 so that it can, in principle, reach wavelength-scale resolution. Even with typical resolutions of just 0.24 nm its image quality is improved over standard scanning tunneling microscopy and therefore useful in the nanoscale. Its principal limitation was, until recently, the need to avoid vibrations in the x-ray microscope. A sample is scanned through a minimal aperture with a narrow and coherent x-ray generated by a synchrotron. Smart algorithms based on Fourier transformations replace optical or magnetic lenses.  Or, as John Rodenburg put it,

“We measure diffraction patterns rather than images. What we record is equivalent to the strength of the electron, X-ray or light waves which have been scattered by the object – this is called their intensity. However, to make an image, we need to know when the peaks and troughs of the waves arrive at the detector – this is called their phase.
     The key breakthrough has been to develop a way to calculate the phase of the waves from their intensity alone. Once we have this, we can work out backwards what the waves were scattered from: that is, we can form an aberration-free image of the object, which is much better than can be achieved with a normal lens.”

As a 2013 study conducted jointly by Switzerland’s Paul Scherrer Institute (PSI) and Technical University Munich showed, progress in imaging and metrology increasingly correlates with sophisticated control of and comprehensive characterization of wave fields. This technology makes it possible to image an entire class of specimens that could not previously be observed particularly well. Not only can remaining vibrations of the x-ray microscope be compensated for by purely mathematical and statistical methods, arriving at much higher image quality, but ptychography also makes it possible to characterize fluctuations within the specimen itself, even if they occur at a speed transcending that of individual frames. It may become possible to determine changes in magnetization of individual bits in high-density magnetic storage media.

Qualitative image improvements accomplished by this technology are notable:

Computer simulation enables testing the diffraction imaging composed by the system’s algorithms, which allows both simulation of instrumentation effects and of effects of and within the specimen.  This matters because it proves that the specimen and its dynamics are accurately reflected in the algorithmic images. 3D images may be generated by repeat scans of de facto 2D samples at different tilt angles. The PSI/TU Munich method renders high-resolution images of mixed states within the sample. These may include quantum mixtures or fast stationary stochastic processes such as vibrations, switching or steady flows that can be generally described as low-rank mixed states since the dynamics of samples are often the very objective of an experiment.

[1] Nanotechnology – as well as I personally – owe Heinrich Rohrer an immense debt of gratitude. The passing in May 2013 of this disciple of Wolfgang Pauli and Paul Scherrer as well as an IBM Fellow was an immense loss. IBM’s Binnig and Rohrer Nanotechnology Center in RĂ¼schlikon, Zurich was named after both physicists.
[2] Walter Hoppe. “Towards three-dimensional “electron microscopy” at atomic resolution.” 61 (6) Die Naturwissenschaften (1974), 239–249.

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