Using coherent X-ray ptychography to probe medium-range order.

Characterization of microscopic structural order and in particular medium range order (MRO) in amorphous materials is challenging. A new technique is demonstrated that allows analysis of MRO using X-rays. Diffraction data were collected from a sample consisting of densely packed polystyrene-latex micro-spheres. Ptychography is used to reconstruct the sample transmission function and fluctuation microscopy applied to characterize structural order producing a detailed `fluctuation map' allowing analysis of the sample at two distinct length scales. Independent verification is provided via X-ray diffractometry. Simulations of dense random packing of spheres have also been used to explore the origin of the structural order measured.

Simultaneous X-ray fluorescence and ptychographic microscopy of Cyclotella meneghiniana.

Scanning X-ray fluorescence microscopy (XFM) is a particularly useful method for studying the spatial distribution of trace metals in biological samples. Here we demonstrate the utility of combining coherent diffractive imaging (CDI) with XFM for imaging biological samples to simultaneously produce high-resolution and high-contrast transmission images and quantitative elemental maps. The reconstructed transmission function yields morphological details which contextualise the elemental maps. We report enhancement of the spatial resolution in both the transmission and fluorescence images beyond that of the X-ray optics. The freshwater diatom Cyclotella meneghiniana was imaged to demonstrate the benefits of combining these techniques that have complementary contrast mechanisms.

Nanoscale Fresnel coherent diffraction imaging tomography using ptychography.

We demonstrate Fresnel Coherent Diffractive Imaging (FCDI) tomography in the X-ray regime. The method uses an incident X-ray illumination with known curvature in combination with ptychography to overcome existing problems in diffraction imaging. The resulting tomographic reconstruction represents a 3D map of the specimen's complex refractive index at nano-scale resolution. We use this technique to image a lithographically fabricated glass capillary, in which features down to 70nm are clearly resolved.

Coherence properties of individual femtosecond pulses of an x-ray free-electron laser.

Measurements of the spatial and temporal coherence of single, femtosecond x-ray pulses generated by the first hard x-ray free-electron laser, the Linac Coherent Light Source, are presented. Single-shot measurements were performed at 780 eV x-ray photon energy using apertures containing double pinholes in "diffract-and-destroy" mode. We determined a coherence length of 17 µm in the vertical direction, which is approximately the size of the focused Linac Coherent Light Source beam in the same direction. The analysis of the diffraction patterns produced by the pinholes with the largest separation yields an estimate of the temporal coherence time of 0.55 fs. We find that the total degree of transverse coherence is 56% and that the x-ray pulses are adequately described by two transverse coherent modes in each direction. This leads us to the conclusion that 78% of the total power is contained in the dominant mode.

Ultrafast optical multidimensional spectroscopy without interferometry.

We present here the details of a phase retrieval technique that provides access to multidimensional modalities that are not currently available using existing interferometric techniques. The development of multidimensional optical spectroscopy has facilitated significant insights into electronic processes in physics, chemistry, and biology. The versatility and number of available techniques are, however, significantly limited by the requirement that the detection be interferometric. Many of these techniques are closely related to the vast range of multidimensional NMR spectroscopies, which revolutionized analytical chemistry more than 30 years ago. We focus here on the specific case of two-color multidimensional spectroscopy (analogous to heteronuclear NMR) and discuss the details of an iterative algorithm that recovers the relative phase relationships required to perform the Fourier transformation and find the unique solution for the 2D spectrum. A detailed guide is provided that describes the practical implementation of such algorithms. The effectiveness and accuracy of the phase retrieval process are assessed for simulated one- and two-color experiments. It is also compared with one-color experimental data for which the target phase information has been obtained independently by interferometry. In all the cases, the present algorithm yields results that compare well with the solutions obtained by other means. There are, however, some limitations and potential pitfalls that are identified and discussed. We conclude with a discussion of the potential applications and further advances that may be possible by adopting iterative phase retrieval algorithms of the type discussed here.

Three-dimensional electronic spectroscopy of excitons in asymmetric double quantum wells.

We demonstrate three-dimensional (3D) electronic spectroscopy of excitons in a double quantum well system using a three-dimensional phase retrieval algorithm to obtain the phase information that is lost in the measurement of intensities. By extending the analysis of two-dimensional spectroscopy to three dimensions, contributions from different quantum mechanical pathways can be further separated allowing greater insight into the mechanisms responsible for the observed peaks. By examining different slices of the complete three-dimensional spectrum, not only can the relative amplitudes be determined, but the peak shapes can also be analysed to reveal further details of the interactions with the environment and inhomogeneous broadening. We apply this technique to study the coupling between two coupled quantum wells, 5.7 nm and 8 nm wide, separated by a 4 nm barrier. Coupling between the heavy-hole excitons of each well results in a circular cross-peak indicating no correlation of the inhomogeneous broadening. An additional cross-peak is isolated in the 3D spectrum which is elongated in the diagonal direction indicating correlated inhomogeneous broadening. This is attributed to coupling of the excitons involving the two delocalised light-hole states and the electron state localised on the wide well. The attribution of this peak and the analysis of the peak shapes is supported by numerical simulations of the electron and hole wavefunctions and the three-dimensional spectrum based on a density matrix approach. An additional benefit of extending the phase retrieval algorithm from two to three dimensions is that it becomes substantially more reliable and less susceptible to noise as a result of the more extensive use of a priori information.

Fresnel coherent diffraction tomography.

Tomographic coherent imaging requires the reconstruction of a series of two-dimensional projections of the object. We show that using the solution for the image of one projection as the starting point for the reconstruction of the next projection offers a reliable and rapid approach to the image reconstruction. The method is demonstrated on simulated and experimental data. This technique also simplifies reconstructions using data with curved incident wavefronts.

Use of a complex constraint in coherent diffractive imaging.

We demonstrate use of a complex constraint based on the interaction of x-rays with matter for reconstructing images from coherent X-ray diffraction. We show the complementary information provided by the phase and magnitude of the reconstructed wavefield greatly improves the quality of the resulting estimate of the transmission function of an object without the need for a priori information about the object composition.

Diffractive imaging using partially coherent x rays.

The measured spatial coherence characteristics of the illumination used in a diffractive imaging experiment are incorporated in an algorithm that reconstructs the complex transmission function of an object from experimental x-ray diffraction data using 1.4 keV x rays. Conventional coherent diffractive imaging, which assumes full spatial coherence, is a limiting case of our approach. Even in cases in which the deviation from full spatial coherence is small, we demonstrate a significant improvement in the quality of wave field reconstructions. Our formulation is applicable to x-ray and electron diffraction imaging techniques provided that the spatial coherence properties of the illumination are known or can be measured.

Neutron imaging of laser fusion targets.

Along-term goal of inertial-confinement fusion research is the generation of energy by imploding capsules containing deuterium-tritium fuel. Progress in designing the capsules is aided by accurate imaging of the fusion burn. Penumbral coded-aperture techniques have been used to obtain neutron images that are a direct measurement of the fusion burn region in the capsules.

A coherence approach to phase-contrast microscopy II: experiment.

We report an experimental investigation of the optical transfer functions for an X-ray microscope operated in defocus phase-contrast mode. The results are compared with a theoretical model of partially coherent image formation and are found to be in excellent agreement.

Non-iterative solution of the phase retrieval problem using a single diffraction measurement.

Coherent diffractive imaging is a method by which iterative methods are employed to recover image information about a finite object from its coherent diffraction pattern. We employ methods borrowed from density functional theory to show that an image can be recovered in a single non-iterative step for a finite sample subject to phase-curved illumination. The result also yields a new approach to quantitative x-ray phase-contrast imaging.

Quantitative phase measurement in coherent diffraction imaging.

We demonstrate high spatial resolution phase retrieval of a non-periodic gold nano-structure using the method of Fresnel coherent diffractive imaging. The result is quantitative to better than 10% and does not rely on any a priori knowledge of the sample.

Refractive index profiling of axially symmetric optical fibers: a new technique.

We present a new technique for determining the refractive index profiles of axially symmetric optical fibers based on imaging phase gradients introduced into a transmitted optical field by a fiber sample. An image of the phase gradients within the field is obtained using a new non-interferometric technique based on bright field microscopy. This provides sufficient information to reconstruct the refractive index profile using the inverse Abel transform. The technique is robust, rapid and possesses high spatial resolution and we demonstrate its application to the reconstruction of the refractive index profiles of a single-mode and a multimode optical fiber.

Astigmatic electron diffraction imaging: a novel mode for structure determination.

In a conventional transmission electron microscope, stigmators are used to correct for the effects of axial astigmatism in the diffraction lens. It seems feasible that these same stigmators could also be used to form a series of 'astigmatic' diffraction patterns. It is shown how this series of diffraction patterns could then be used to perform exit-surface wavefunction reconstruction. This has the advantage that the diffraction patterns are not resolution limited by the objective aperture as are images when performing exit-surface wavefunction reconstruction from a focal series. A scheme for carrying out phase reconstruction from a series of astigmatic diffraction patterns in an electron microscope is presented.

Diffraction with wavefront curvature: a path to unique phase recovery.

Modern X-ray optics is able to produce very tightly focused beams. The size of these focused spots is comparable to the scale of large molecules and therefore to the lattice spacing of crystals of these molecules. In this case, the phase of the illuminating beam may vary on the scale of the lattice and conventional diffraction theory needs to be modified. In this paper, coherent diffraction by non-planar beams is considered and it is shown that it is possible to uniquely recover the phase of the diffraction pattern.

Phase retrieval from images in the presence of first-order vortices.

We discuss retrieval of the phase of quantum-mechanical and classical wave fields in the presence of first-order vortices. A practical method of phase retrieval is demonstrated which is robust in the presence of noise. Conditions for the uniqueness of the retrieved phase are discussed and we show that determination of the phase in a given plane requires a series of at least three two-dimensional intensity images at different propagation distances. The method is applicable to a wide range of scenarios such as the imaging of imperfect crystals, quantitative determination of the strength of vortex filaments in high-temperature superconductors, and x-ray and electron holography.

Thermal and cold neutron phase-contrast radiography.

In this paper, we will discuss a phase-contrast imaging method that avoids the complications of interferometry to provide phase contrast in weakly absorbing samples. A transversely coherent neutron beam is used with the traditional radiography scheme. Images taken with this scheme show dramatic intensity variations due to sharp changes in the neutron wave refractive index. With some numerical processing these images may be used to reconstruct a quantitative phase radiograph of specimens imaged with this technique.

An in-vacuum x-ray diffraction microscope for use in the 0.7-2.9 keV range.

A dedicated in-vacuum coherent x-ray diffraction microscope was installed at the 2-ID-B beamline of the Advanced Photon Source for use with 0.7-2.9 keV x-rays. The instrument can accommodate three common implementations of diffractive imaging; plane wave illumination; defocused-probe (Fresnel diffractive imaging) and scanning (ptychography) using either a pinhole, focused or defocused probe. The microscope design includes active feedback to limit motion of the optics with respect to the sample. Upper bounds on the relative optics-to-sample displacement have been measured to be 5.8 nm(v) and 4.4 nm(h) rms/h using capacitance micrometry and 27 nm/h using x-ray point projection imaging. The stability of the measurement platform and in-vacuum operation allows for long exposure times, high signal-to-noise and large dynamic range two-dimensional intensity measurements to be acquired. Finally, we illustrate the microscope's stability with a recent experimental result.

The soft x-ray instrument for materials studies at the linac coherent light source x-ray free-electron laser.

The soft x-ray materials science instrument is the second operational beamline at the linac coherent light source x-ray free electron laser. The instrument operates with a photon energy range of 480-2000 eV and features a grating monochromator as well as bendable refocusing mirrors. A broad range of experimental stations may be installed to study diverse scientific topics such as: ultrafast chemistry, surface science, highly correlated electron systems, matter under extreme conditions, and laboratory astrophysics. Preliminary commissioning results are presented including the first soft x-ray single-shot energy spectrum from a free electron laser.