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. 2012 Jun 4;20(12):13129-37.
doi: 10.1364/OE.20.013129.

Solving structure with sparse, randomly-oriented x-ray data

Hugh T Philipp  1 , Kartik Ayyer, Mark W Tate, Veit Elser, Sol M Gruner
Affiliations

Solving structure with sparse, randomly-oriented x-ray data

Hugh T Philipp et al. Opt Express. .

Abstract

Single-particle imaging experiments of biomolecules at x-ray free-electron lasers (XFELs) require processing hundreds of thousands of images that contain very few x-rays. Each low-fluence image of the diffraction pattern is produced by a single, randomly oriented particle, such as a protein. We demonstrate the feasibility of recovering structural information at these extremes using low-fluence images of a randomly oriented 2D x-ray mask. Successful reconstruction is obtained with images averaging only 2.5 photons per frame, where it seems doubtful there could be information about the state of rotation, let alone the image contrast. This is accomplished with an expectation maximization algorithm that processes the low-fluence data in aggregate, and without any prior knowledge of the object or its orientation. The versatility of the method promises, more generally, to redefine what measurement scenarios can provide useful signal.

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Figures

Fig. 1
Fig. 1
(a) The lead x-ray mask mounted within an aperture in an aluminum disk. (b) A static x-ray image of the pattern collected as 432 individual frames with approximately 1/5 photon per pixel per frame. The frames were thresholded and averaged. (c) A reconstruction using randomly-oriented data having an average 11.5 photons/frame and 1.2 million recorded photons. (d) A reconstruction using randomly-oriented data having an average 2.5 photons/frame and 1.2 million recorded photons ( Media 1).
Fig. 2
Fig. 2
(a–c) Three sample frames from the 2.5 photon/frame data set with detected x-ray photons circled. (d) Occupancy histogram compared with the Poisson distribution. (e) The sum of all thresholded frames from the 2.5 photon/frame data set showing a uniform angular distribution of data.
Fig. 3
Fig. 3
Effect of background on reconstruction quality. (a) Reconstruction from 2.5 photons/frame data set and no added background. This is the same as Fig. 1(d). (b) Reconstruction from the 11.5 photons/frame data set with an average of 11.5 photons of background added per frame ‘by hand’ with a Poisson distribution. The background level was subtracted before rendering to facilitate comparison to (a). As can be seen, the quality of the reconstructions is about the same, and much reduced from the original 11.5 photons/frame data (Fig. 1(c)).
Fig. 4
Fig. 4
Reduction in the rate at which pixels measuring photons acquire information as a function of signal-to-noise. Plotted is the ratio R of the information rate, acquired with and without background. SN is the ratio of signal to background photon counts. This plot applies to the model where half the pixels receive only background (covered by mask) and the other half receive signal and background (not covered by mask).
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References

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