We develop new methods for diffractive imaging of nanoscale objects, primarily using X-rays. Within this area, we work on developing analysis algorithms, often involving the solving of ill-posed inverse problems, and applying them to experimental data.
Coherent diffractive imaging (CDI) is a technique to determine the structure of an object from the far-field diffraction pattern produced when it interacts with a coherent wave. Among other things, one variation of this technique can be used to determine the 3D structure of biomolecules and other nanoscale objects using X-rays. Unfortunately, these small objects scatter too little to see much in a single image before radiation damage kicks in and destroys the particle.
X-ray free electron lasers (XFELs) have bright enough and short enough pulses that one can combine the information from a large number of molecules and generate a 3D structure by computationally determining the orientation and other unmeasured variables.
We participate (and sometimes lead) XFEL experiments which push the limits of these techniques, and then execute the entire analysis pipeline from raw data to structure. In addition, we develop new algorithms to improve the efficiency of these techniques and broaden the range of applications.
1. Loh, Elser. "Reconstruction algorithm for single-particle diffraction imaging experiments", Physical Review E 80.2, 026705 (2009)
2. Ayyer, Lan, et al. "Dragonfly: an implementation of the expand–maximize–compress algorithm for single‐particle imaging." J. Appl. Cryst. 49.4, 1320 (2016)
X-ray crystallography remains the dominant method to obtain high resolution structures of proteins and other biomolecules. This is because the diffraction signal is concentrated in bright Bragg peaks, giving good signal-to-noise and making subtracting the diffuse background easier.
However, part of this diffuse 'background' is cause by the disorder in these crystals. And in fact, if the disorder is correlated i.e. multiple atoms moving coherently, the scattering pattern has features which inform us about this coherent motion1. Thus, we get information about how the proteins move naturally.
One simple form of disorder seen in some crystals is rigid-body-like motion where the entire molecule moves together, primarily because the crystal contacts are much weaker than the internal structure. In these cases, the diffuse scattering is directly related to the molecular transform, and so can be used to get a higher resolution structural model of the protein2,3.
We are interested in refining this method of inproving resolution in the case of rigid-body-like disorder, but also in developing methods to reliably extract more complex modes of motion from any protein crystal diffaction pattern.
1. Ayyer, Chapman, Yefanov. "Structure Determination by Continuous Diffraction from Imperfect Crystals" In X-ray Free Electron Lasers - A Revolution in Structural Biology, In Press
2. Ayyer, Yefanov, et al. "Macromolecular Imaging with Imperfect Crystals", Nature 530 (7589), 202 (2016)
3. Chapman, Yefanov, et al. "Continuous diffraction of molecules and disordered molecular crystals", J. Appl. Cryst. 50(4) 1084 (2017)
Diffractive imaging experiments often involve exposing thousands to millions of objects one at a time before using computational methods to assemble them into a single dataset.
As an example, in X-ray SPI, patterns are oriented and merged to produce a single 3D intensity distribution. This requires all objects to be identical, upto orientation. Unfortunately, this is almost never the case. Thus the algorithmic challenge is not just to deal with the weak signal, conformational heterogeneity etc. but also to separate out the "junk".
Alternatively, we may be interested in a few different polymorphic classes of a certain biomolecular assembly like a fiber. Or we may want to assemble a time series of a reaction in a 2D imaging experiment by recognizing and removing outliers.
In all these cases, machine learning methods such as manifold learning, clustering, deep learning etc. using an appropriate feature set is our favoured approach to deal with this problem.
Incoherent light does not produce stable interference patterns (the overlapping light from two red LEDs won't create fringes). However, they do produce transient patterns which are stable over the coherence time. If we can measure these transient patterns and somehow average the information, we can obtain the structure of the source distribution.
The interference is not stable because each wave packet produced has a random initial phase. However, if we average the 2-point intensity correlation of each pattern, the random phases average out and we are left with the phase difference due to path difference (the structural part). This effect was first demonstrated in astronomy by Hanbury Brown and Twiss.
We want to demonstrate and use the effect with atomic fluorescence, which also has the same random phases. One powerful application of this technique would be sensitivity to the energy of the emitted photon. The degree of interference would depend on the electronic states of the interfering atoms. We thus have the tantalizing possibility of atomically spatially resolved spectroscopy.
1. Classen, Ayyer, et al. "Incoherent Diffactive Imaging via Intensity Correlations of hard X-rays", Phys. Rev. Lett 119, 053401 (2017)
2. Schneider, Mehringer, et al. "Quantum imaging with incoherently scattered light from a free-electron laser", Nature Phys. 14.2, 126 (2018)