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.

Droplet Coalescence

Two recent PRLs are addressing the issue of how two droplets merge into one.

Kamel Fezzaa and Yujie Wang from Argonne use ultrafast x-ray phase-contrast imaging to take sub-microsecond exposures of droplet coalescence, which is complete in just under a milisecond.

Phys. Rev. Lett. 100, 104501 (2008)

The studied liquid droplets are ~1mm (bar size in the image on the left) in size, and can be seen with <5 micron resolution using phase contrast (as opposed to adsorption contrast) using high energy 13keV x-rays. Fezzaa and Wang cleverly used the hybrid filling pattern of Advanced Photon Source, where each electron bunch produces a short x-ray pulse 472 nanoseconds long used for imaging, with each pulse separated from the next one by 3.6 microseconds. The result is a sub-microsecond “shutter time” defined by the length of each pulse, with consecutive images taken 3.6 microseconds apart.

Of particular interest in this study is the stability of torroidal air bubble formed due to air trapped by the two rapidly coalescing droplet menisci. Fezzaa and Wang show for the first time that the torroidal bubble remains trapped until some 400 microsecond after the droplets start merging.

The second recent paper on this topic of droplet coalescence is by Sara Case and Sid Nagel at University of Chicago. PRL 100, 084503 (2008)

Case and Nagel abandon the visual approach to studies of ultrafast coalescence process, and instead adopt a technique which measures the changes in conductivity across the connection between the two droplets as a function of time. When the droplets begin to coalesce, the effective resistivity is high, since it is defined primarily by the width of the narrow region where the two droplets touch each other. As they coalesce, this resistivity will drop. This technique proves to be especially useful in the timescale range from sub-microsecond to hundreds of microsecond. Case and Nagel observe a cross-over in power-law behavior for R(t) from 1/t for small t to 1/√t at large t, but do not see time-dependent fluctuations in R(t) which would be the signature of the connected menisci repeatedly disconnecting and reconnecting again.

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).

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.