3D object reconstruction from random orientations

The featured item this time is “Structure from Fleeting Illumination of Faint Spinning Objects in Flight with Application to Single Molecules” by Russell Fung and co-authors at U Wisconsin Milwaukee.

The promise of solving atomic-resolution 3D structure of biological proteins with X-ray Free Electron Lasers has several obstacles. First one is to have fast enough x-ray pulse to image molecules before it starts to undergo “Coulomb explosion”. But even that is not sufficient to produce atomic-scale structure due to low scattering cross-section of hard x-rays – so the experiment will need to be repeated many (thousands?) times to improve statistics. Luckily, protein molecules are identical, so the fundamental 3D structure of the sample could be considered the same – however, the orientation of protein molecule is going to be different each time.

There are two ways to solve the “random orientation” problem – one is to try to align the molecule, for example with a laser beam. However this has to be done with a very high precision and is difficult to achieve in practice. Another approach is to do experiment thousands of times with random orientations of molecules, catalogue all resulting projections, and then use mathematical algorithms to “fold” the projections into a unique 3D object that is consistent with all resulting projections.

Russel Fung et al. provide an algorithm that does just that – by simulating realistic conditions of 4th generation synchrotron source, X-ray Free Electron Laser, with collection of 100,000 photons, 72,000 repeated diffraction patterns from single shot experiments and scattering rates as low as 0.01 photons per pixel at large wavevectors corresponding to 1.8 Angstrom.

The result of folding using Generative Topographic Mapping for protein chignolin in random orientations is shown in figure above, for 3D movie of this reconstructed molecule see Abbas Ourmazd’s webpage at UW Milwaukee.

two PRLs on x-ray phasing

Two new PRLs are dealing with x-ray phasing.

The first paper is de Jonge et al., “Quantitative Phase Imaging with a Scanning Transmission X-Ray Microscope” Phys. Rev. Lett. 100, 163902 (2008). Typically the differential phase contrast measurements become non-trivial for thick specimens, when the adsorption and phase-wrapping effects become significant. This paper resolves this problems when differential phase contrast measurements are done in scanning transmission x-ray microscopy mode (STXM), since the solution is overconstrained, allowing to arrive at unique phase and adsorption values.

The second paper is Johnson et al., “Coherent Diffractive Imaging Using Phase Front Modifications” Phys. Rev. Lett. 100, 155503 (2008).

Since phase is lost during the measurements, it is impossible to simply fourier-transform the coherent x-ray diffraction pattern to obtain a real-space image of an object with nanoscale resolution. There are numerous numerical approaches of phase-retrieval based on oversampling the diffraction pattern. This paper presents an alternative approach of introducing a phase plate, and deconvolving the set of phases resulting from the sample by scanning the phase object around, making the contribution from the phase plate known, and providing information on un-altered phases that would be observed if no phase plate was present. This technique is similar to ptychography, as it provides additional constraints that help arriving at unique solution in a rapidly convergent manner, except it scans the known phase plate, rather than the object being imaged.

Dark-field X-ray Phase Contrast Imaging

This week’s featured paper is the paper by Franz Pfeiffer and colleagues at Paul Scherrer Institute in Switzerland:

Hard-X-ray dark-field imaging using a grating interferometer, Nature Materials 7, 134 – 137 (2008) .

This Nature Materials paper is related to the previous papers by the same group: Pfeiffer et al., Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources, Nature Physics 2, 258 – 261 (2006)

as well as Pfeiffer et al., Shearing Interferometer for Quantifying the Coherence of Hard X-Ray Beams, Phys. Rev. Lett. 94, 164801 (2005).

The use of shearing inteferometer, which to x-rays look like series of micron-sized “combs” or diffraction gratings, allows imaging of milimeter-sized objects using the differential phase contrast, rather than adsorption, as a contrast mechanism. These are the techniques that can be adopted using rather primitive “highly incoherent” in-house x-ray sources – such as x-ray tubes and rotating anodes, and therefore do not require a trip to a synchrotron.