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.

Recent Coherent X-ray Literature Round-Up

Electrospray approach to single-particle diffraction at XFEL facilities:

M. Bogan, W. Benner, S. Boutet et al., “Single Particle X-ray Diffractive Imaging,” Nano Letters 8, 310-316 (2008)

A study of SiN etched “logo” pattern x-ray induced destruction, similar to Chapman’s Nature Physics 2006 work (Cowboys holding hands logo, doi:10.1038/nphys461):

A. Barty, S. Boutet, M. J. Bogan et al., “Ultrafast single-shot diffraction imaging of nanoscale dynamics,” Nat Photon 2, 415-419 (2008)

Lens-less imaging of Fresnel Zone Plate using ptychography – scanning coherent diffraction – improvement in resolution and illumination function from FZP reconstruction by Rodenburg et al. PRL 98, 034801 (2007):

P. Thibault, M. Dierolf, A. Menzel et al., “High-Resolution Scanning X-ray Diffraction Microscopy,” Science321, 379-382 (2008)

Tabletop coherent soft x-ray microscopy by UColorado group – an exciting alternative to large XFEL machines:

R. L. Sandberg, C. Song, P. W. Wachulak et al., “High numerical aperture tabletop soft x-ray diffraction microscopy with 70-nm resolution,” Proceedings of the National Academy of Sciences of the United States of America 105, 24-7 (2008)

X-ray holography with 5 reference beams is obviously better than holography with 3 or 1 reference beams. How about 1,000,000 reference beams? This is what can be accomplished with uniformly redundant arrays:

S. Marchesini, S. Boutet, A. E. Sakdinawat et al., “Massively parallel X-ray holography,” Nat Photon 2, 560-563 (2008)

Coherent imaging of 80-100nm particle (in SAXS mode, similar to work by Miao group) with 5nm resolution, but done at 15 keV. Coherent fraction of the beam drops off as lambda^2, and efficiency of area x-ray detectors is substantially reduced at higher energies too. But at higher energies one can capture more of the Q range for the same solid angle defined by scattering geometry. Still, 5 nm number is better resolution that I expected – this should imply there are at least 15-20 highly visible fringes in diffraction pattern, instead of 7 or so. Maybe it’s log scale of intensity that hides extra fringes…

C. G. Schroer, P. Boye, J. M. Feldkamp et al., “Coherent X-Ray Diffraction Imaging with Nanofocused Illumination,” Physical Review Letters 101, 090801-4 (2008)

A review article on coherent x-ray diffractive imaging of small particles:

J. Miao, T. Ishikawa, Q. Shen and T. Earnest, “Extending X-ray crystallography to allow the imaging of noncrystalline materials, cells, and single protein complexes,” Annual Review of Physical Chemistry 59, 387-410 (2008)

First example of x-ray holography in hard x-ray regime. Sample preparation is quite a bit more challenging.

L. Stadler, C. Gutt, T. Autenrieth et al., “Hard X Ray Holographic Diffraction Imaging,” Physical Review Letters 100, 245503-4 (2008)

More coherent x-ray lens-less image reconstructions

New paper in Science by Pierre Thibault et al. “High-Resolution Scanning X-ray Diffraction Microscopy” Science 321, 379 (2008).

Authors use an approach identical to ptychography  to demonstrate the power of the technique by reconstructing the Fresnel Zone Plate – similar to work by Rodenburg et al., PRL 98, 034801 (2007).

John Miao and his UCLA group has used lensless imaging to reconstruct image of a single virus:

C. Song et al., “Quantitative Imaging of Single, Unstained Viruses with Coherent X-rays” arXiv:0806.2875.

And Stadler et al. “Hard X Ray Holographic Diffraction Imaging” Phys. Rev. Lett. 100, 245503 (2008) show that the x-ray holographic approach similar to the one previously used by Eisebitt et al., Nature 432, 885 (2004) works in hard-xray regime as should be expected. They cleverly used five carefully positioned nanoparticles as the negative sources of reference beam, and successfully demonstrated that letter “P” can be reconstructed, adding to an impressive alphabet of reconstructed letters and logos. While use of hard x-rays paves the road for imaging of thick speciments, it’s not clear if one could take advantage of the same principle in high-angle diffraction geometry, which is where real action is for hard x-rays.

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.

Giant molecules or tiny crystals?

Nature Materials has a News and Views article by Ian Robinson titled “Coherent diffraction: Giant molecules or tiny crystals?”, which reviews recent coherent electron diffraction results by Huang et al. featured here earlier. One of the interesting points made in this mini-review is the phase diagram on the left showing a transition from bulk cubic crystal to decahedral and icosahedral structures, including quasi-molten and liquid phases.

Keyhole Imaging, Relaxation in Nanoparticles, CDW correlations

In advanced publication of Nature Physics, Brian Abbey and colleagues present a new technique, called “Keyhole Coherent Diffractive Imaging”, which enables them to study extended objects (in similar fashion as ptychography, but based on a somewhat different geometry). The basic idea of KCDI is to combine Fresnel and Fraunhoffer imaging in a divergent (curved) wavefront by placing an imaged object behind the focal spot of a lens and use this additional information to reconstruct the wavefront. It is somewhat counter-intuitive to understand why curved wavefronts should provide a faster phase-retrieval algorithm convergence than flat wavefronts, but it’s a bit like mixing near-field and far-field techniques.

In advanced publication of Nature Materials, Urbana group lead by Jim Zuo show how application of coherent electron diffraction imaging (very similar to x-ray techniques) can reveal the relationship between the coordination number of Au atoms within a ~4 nm nanoparticle and the out-of-plane bond length. Electrons interact much stronger with matter than x-rays and one could argue that electrons are better for imaging of small nanosized objects, while x-rays are better for imaging extended micron-sized objects. Surface relaxation is a well-known phenomenon in surface science – due to reduced number of near-neighbors, atoms in the near-surface region end up with “dangling bonds” effect – and by turning these bonds inward the atoms can reduce out-of-plane atomic distance. Zuo and his group provide a very detailed analysis of surface relaxation for various facets of Au nanoparticles, as a function of near-neighbor coordination number.

And in a recent issue of Physical Review Letters, David LeBolloch’ and colleagues show that charge density wave condensate in blue bronze compound can spontaneously develop long-range correlations (up to micron-size) when the charge density waves is depinned due to applied current and is in a sliding state (imagine a particle on a washboard potential which is getting tilted).

X-ray lens-less imaging of buried nanostructures

Coherent X-ray Diffraction allows reconstruction of small particles with ~15 nanometer resolution. However, High Resolution Transmission Electron Microscopy (see current issue of MRS Bulletin for review) can achieve an atomic-scale resolution for crystalline nanoscale objects.

But since electrons interact very strongly with positively charged ions in the lattice, electron microscopy cannot see deep inside of materials. X-rays have deep penetrating power, and can provide detailed structural information about deeply buried structures. In small-angle scattering regime all of the material in the path of the x-rays will contribute to the coherent speckle. However, using the energy tunability feature of synchrotron sources, one could scan the energy across the resonant edge of a specific element, changing the effective electron density of specific atomic species. The difference between density maps will reveal the specific elemental distribution of this atomic species, since all other elements will subtract off. Changyong Song from John Miao’s Coherent X-ray Imaging group at UCLA and co-workers have demonstrated this by imaging a Bi nanostructure buried deep within Si matrix (Phys. Rev. Lett. 100, 025504 (2008) ). This microscopy technique, which combines lens-less imaging based on phase-retrieval of coherent x-ray diffraction pattern and the resonant measurements could be extended to samples containing multiple elements – repeating these measurements at various adsorption edges of different elements will produce detailed elemental maps of deeply buried structures (microns or more beneath the surface).

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.

Near-Field X-ray Speckle

There is a brand new paper that appeared today in Nature Physics by Cerbino and co-workers that describes a new x-ray coherent technique based on observations of Near-Field Speckle pattern.

Typically x-ray speckles (or visible light speckles) are observed in Fraunhoffer, or far-field diffraction regime, in which parallel beam approximation can be applied.

The other extreme regime is the near-field (aka Fresnel) geometry, where the detector is placed in the relative vicinity of the sample. This regime is often ignored by scientists because of the complicated scattering patterns caused by interference between scattered and transmitted beams.

However, recently it was shown that Fresnel geometry has some advantages – both in terms of performing lensless imaging microscopy: curved wavefronts, resulting from for example focusing Fresnel Zone Plate optics, result in faster convergence of lensless imaging algorythms – see this paper by Williams et al. Phys. Rev. Lett. 97, 025506 (2006) - and now in terms of using near-field x-ray speckle for X-ray Photon Correlation Spectroscopy.

The Near-Field Speckle setup is limited to relatively small Q-range – the example used in the featured paper by Cerbino et. al is covering ultra-small angle scattering range of Q<0.001 inverse nanometers, corresponding to lengthscales on the order of 10 microns. While such low angles are difficult to access with far-field hard x-ray speckle, the same lengthscales can in principle be reached with visible light (laser) speckle – dynamic light scattering techniques. However, one big advantage of x-rays here is their penetrating
ability and no complications due to multiple scattering effects. Therefore, Near Field X-ray Speckle has a lot of potential for use in non-transparent materials and thick specimens where multiple light scattering effects make laser-based measurements difficult.

Partially Wetting Thin Films show no capillary dynamics

This week’s very short item is featuring recently published work by Christian Gutt et al. on XPCS studies of thin partially wetting liquid films: Phys. Rev. Lett. 99, 096104 (2007).

The basic summary of the result is that thin (unlike the partially wetting macroscopic droplet shown on the left) liquid films apeear to be heavily pinned (at least at longer wavelengths) – and as a result do not show the capillary fluctuations that exist at free surfaces of liquids. Dynamically these liquid films appear very similar to solids.

Sudoku, folding proteins and coherent diffraction

…all of these problems have a lot in common – they involve exhaustive search with a huge number of parameters, accompanied by a similarly large number of constraints, or rules.

The picture on the left is from the cover illustration to PNAS issue back in January of this year, accompanied by the paper by Elser et al., “Searching with iterated maps” PNAS 104, 418 (2007).

One of the key applications is in coherent x-ray imaging – coherent diffraction patterns are fourier transforms of real-space density of an object, but due to phase problem (loss of phases during the measurements of x-ray intensities) one can’t simply perform inverse fourier transform to get back to real-space image. But oversampling – measuring intensities at at least twice the spatial frequency of the object – can solve the phase problem by bringing the number of equations equal to the number of unknown variables again. One can solve for phases by considering restraints, or rules, imposed by such experiments – for example, intensities are known (while phases are not), real space densities are real positive numbers, typically contained within a finite volume (support). There may be more elaborate restraints.

By using an approach based on differential map algorithm one can alternate performing simple projections in real and reciprocal space, using the restraints mentioned above, alternated with Fourier transforms to go from real space to reciprocal space and back.

This approach can be applied to other problems – from finding the local minimum in energy landscape for protein folding, packing and tiling probelms to finding a unique solution for sudoku problems, jumble and other puzzles.

For more info see this wikipedia page or slides of talk by Veit Elser from his Cornell webpage.

Glass on cooling OR heating

This week’s item is a paper that just appeared on arxiv.org by Simon Mochrie’s Yale group and Argonne collaborators on a unique situation that occurs in a liquid that becomes a glass upon cooling OR heating: X. Lu et al., “How a liquid becomes a glass both on cooling and on heating” arxiv.org/0708.3663v1

Typically we think of glasses that vitrify when the temperature is (suddenly) lowered. The unique situation explored in this paper is a situation where at high temperature system forms a glass dominated by repulsive interactions, and at low temperatures due to attractive interactions.

By tracking the glass transition using coherent x-ray scattering techniques (XPCS in this case) the authors look in great detail at the logarithmically decaying slow fluctuations in the same system under very different circumstances – and therefore able to study not a single but two glass transitions with either repulsive or attractive interactions.

Lensless x-ray imaging with tabletop sources

This week’s item is the PRL paper by Sandberg et al., “Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams” Phys. Rev. Lett. 99, 098103 (2007).

It is essentially a collaboration between JILA/Colorado groups of Henry Kapteyn and Margaret Murnane specializing in coherent soft x-ray tabletop sources, and John Miao’s UCLA group which specializes in lensless imaging, as well as folks from LBNL. The fact that these are very “soft” x-rays – wavelengths of 29 nm means that the spatial resolution is still rather limited (on the order of 100-200nm), compared to synchrotron sources such as ALS or APS, but on the flip side they can do measurements in their in-house lab, instead of relying on scarce synchrotron beamtime, which is a huge benefit. Traditional x-ray sources such as rotating anode and fixed tube can typically operate in hard x-ray range (8keV and higher), but the energy is also fixed and the sources are very incoherent.

I am looking forward to the times when the tabletop sources can become cheap and commonplace enough for other groups to do their characterization using these and other coherent x-ray scattering probes.

XFEL trifecta in Science, Nature

Last week was the “perfect storm” of XFEL ultrafast science, with four papers in Nature and Science:

Nature featured a paper by Henry Chapman et al. on Femtosecond time-delay X-ray Holography. By recording an interference pattern of a particle and it’s mirror image it is possible to record an ultrafast “explosive” motion of the particle due to exposure of the x-ray beam. It’s the ultimate pump-probe experiment where both pump and probe are one and the same.
This paper is accompanied by News and Views article “Femtophysics: Double vision” by Andrea Cavalleri.

Science has two review papers out – one is “Harnessing Attosecond Science in the Quest for Coherent X-rays” by Kaptey et. al from Margaret Murnane’s group at Colorado Boulder.

There is also a Review paper by Phil Bucksbaum on “The Future of Attosecond Spectroscopy”.

Thee two papers are part of the special section on attosecond spectroscopy, also featured as a cover story.

Coherent X-ray Imaging of Antiphase Domain Boundaries

Today’s featured paper is a PRB by Lorenz-M. Stadler et al. on coherent x-ray imaging of antiphase domain boundaries in FeAl alloy.

The basic idea of antiphase boundary is simple, and illustrated for a binary 2D alloy on the diagram to the left. In the checkerboard pattern of two kinds of atoms the antiphase domain is created when the black-white-black-white-black order is skipped by a “phase shift” of pi, resulting in “white-black-black-white-…” after which regular order is restored again.

In three dimensions the antiphase domain can be a little more complicated to visualize, but the basic idea is precisely the same.

Persistence of memory

Persistence of memory – how does a magnet “remember” it’s state? Does it remember what it used to look like if you cycle the magnetic field? It appears the answer is yes, and disorder is the driving force behind the “persistence” factor.

Mike Pierce and collaborators have studied CoPt magnetic films using soft x-rays tuned to Co L2-3 adsorption edge, where circular dichroism provides a significant contrast between different orientations of magnetisation in the film. The speckle resulting in small-angle x-ray scattering pattern codes the information about specific magnetic domain orientation within the sample. By cycling the magnetic field and comparing the speckles one can calculate the “persistence” of memory or correlation of magnetic domain configurations between the cycles, as the fingerprint-like domains are forced to nucleate, grow and disappear.

Coherent X-ray imaging and dynamics

This week’s journal club item is a Science magazine review article by Gaffney and Chapman on imaging of atomic structure and dynamics using coherent x-ray beams, ultrafast x-ray beams and the combination of the two. Even though most of the coherent x-ray imaging part of the review is understandably focused on single-molecule imaging, the paper provides a very nice overview of the extremely bright future, and also of some key challenges.

This quote is quite remarkable, in providing a nice comparison of future vs. present/past sources: “At the LCLS, the integrated x-ray production in 10 s of lasing will exceed the total x-ray photon production at the SPPS during its 3-year lifetime.”

It’s also interesting to note that the review is published in Science, a relative newcomer to coherent x-ray field heavily dominated by Nature and more recently also by Nature Physics.

Mmmm… PIE!

The title should be pronounced using your best Homer Simpson voice.

PIE stands for “Ptychographical Iterative Engine”, and it’s the most interesting development in lens-less imaging this year. The idea is to use diffraction patterns from overlapping regions (which look like a Venn diagram, or olympic logo) by moving an aperture by a known amount, and use this knowledge to speed up real-space reconstruction process.

The most recent PRL paper is by John Roderburg, and was listed in my GoogleNews feed soon after it came out in January of this year. This most recent work is an experimental extension of simulations done previously by Faulkner and Rodenburg.

Move to wordpress and this week’s items (4)

This is my first post since recent move to wordpress.

This week we have four items:

1. An excellent review in this week’s Science by Simon Billinge and Igor Levin titled “The Problem with Determining Atomic Structure at the Nanoscale”. The fundamental problem of determining atomic structure of non-periodic materials is an old one, but is becoming especially critical in context of nano-structures, where finite correlation lengths on the order of nanometers, even in case of crystalline structures, makes it impossible to apply standard crystallography methods applicable for materials with long-range periodicity. Authors focus on PDF, TEM, EXAFS and other techniques, but also briefly mention newly available coherent x-ray scattering techniques based on phase-retrieval algorithms.