Imaging Breast Microcalcifications Using Dark-Field Signal in Propagation-Based Phase-Contrast Tomography.

Breast microcalcifications are an important primary radiological indicator of breast cancer. However, microcalcification classification and diagnosis may be still challenging for radiologists due to limitations of the standard 2D mammography technique, including spatial and contrast resolution. In this study, we propose an approach to improve the detection of microcalcifications in propagation-based phase-contrast X-ray computed tomography of breast tissues. Five fresh mastectomies containing microcalcifications were scanned at different X-ray energies and radiation doses using synchrotron radiation. Both bright-field (i.e. conventional phase-retrieved images) and dark-field images were extracted from the same data sets using different image processing methods. A quantitative analysis was performed in terms of visibility and contrast-to-noise ratio of microcalcifications. The results show that while the signal-to-noise and the contrast-to-noise ratios are lower, the visibility of the microcalcifications is more than two times higher in the dark-field images compared to the bright-field images. Dark-field images have also provided more accurate information about the size and shape of the microcalcifications.

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons, Part II: Differential Holographic Tomography.

It has been argued that in atomic-resolution transmission electron microscopy (TEM) of sparse weakly scattering structures, such as small biological molecules, multiple electron scattering usually has only a small effect, while the in-molecule Fresnel diffraction can be significant due to the intrinsically shallow depth of focus. These facts suggest that the three-dimensional reconstruction of such structures from defocus image series collected at multiple rotational orientations of a molecule can be effectively performed for each atom separately, using the incoherent first Born approximation. The corresponding reconstruction method, termed here Differential Holographic Tomography, is developed theoretically and demonstrated computationally on several numerical models of biological molecules. It is shown that the method is capable of accurate reconstruction of the locations of atoms in a molecule from TEM data collected at a small number of random orientations of the molecule, with one or more defocus images per orientation. Possible applications to cryogenic electron microscopy and other areas are briefly discussed.

Relative roles of multiple scattering and Fresnel diffraction in the imaging of small molecules using electrons.

The relative roles of multiple electron scattering and in-molecule Fresnel diffraction in atomic-resolution transmission electron microscopy of small molecules are discussed. It is argued that, while multiple scattering tends to have only a moderate effect, the in-molecule Fresnel diffraction can be significant due to the shallow depth of focus in high-resolution electron microscopy. When the depth of focus is smaller than the size of molecule along the trajectory of the electrons, the projection approximation breaks down and pairs of images at orientations of the molecule rotated by 180 degrees are not the same. Put another way, it matters which way the electrons traverse the specimen. In such cases, diffraction tomography based on the first Born or first Rytov approximation represents a more suitable method for the reconstruction of the three-dimensional distribution of the electrostatic potential, compared to conventional computed tomography which intrinsically relies on the validity of the projection approximation. A simplified method for diffraction tomography based on the approximation of Fresnel diffraction by the transport of intensity equation is proposed and tested on numerically simulated examples.

Dark-field signal extraction in propagation-based phase-contrast imaging.

A method for extracting the dark-field signal in propagation-based phase-contrast imaging is proposed. In the case of objects consisting predominantly of a single material, or several different materials with similar ratios of the real decrement to the imaginary part of the complex refractive index, the proposed method requires a single image for extraction of the dark-field signal in two-dimensional projection imaging. In the case of three-dimensional tomographic imaging, the method needs only one image to be collected at each projection angle. Initial examples using simulated and experimental data indicate that this method can improve visualization of small sharp features inside a larger object, e.g. the visualization of microcalcifications in propagation-based x-ray breast cancer imaging. It is suggested that the proposed approach may be useful in other forms of biomedical imaging, where it can help one to obtain additional small-angle scattering information without increasing the radiation dose to the sample.

Propagation-based x-ray phase-contrast tomography of mastectomy samples using synchrotron radiation.

PURPOSE: Propagation-based phase-contrast computed tomography (PB-CT) is a method for three-dimensional x-ray imaging that utilizes refraction, as well as absorption, of x rays in the tissues to increase the signal-to-noise ratio (SNR) in the resultant images, in comparison with equivalent conventional absorption-only x-ray tomography (CT). Importantly, the higher SNR is achieved without sacrificing spatial resolution or increasing the radiation dose delivered to the imaged tissues. The present work has been carried out in the context of the current development of a breast CT imaging facility at the Australian Synchrotron. METHODS: Seven unfixed complete mastectomy samples with and without breast cancer lesions have been imaged using absorption-only CT and PB-CT techniques under controlled experimental conditions. The radiation doses delivered to the mastectomy samples during the scans were comparable to those approved for mammographic screening. Physical characteristics of the reconstructed images, such as spatial resolution and SNR, have been measured and compared with the results of the radiological quality assessment of the complete absorption CT and PB-CT image stacks. RESULTS: Despite the presence of some image artefacts, the PB-CT images have outperformed comparable absorption CT images collected at the same radiation dose, in terms of both the measured objective image characteristics and the radiological image scores. The outcomes of these experiments are shown to be consistent with predictions of the theory of PB-CT imaging and previous reported experimental studies of this imaging modality. CONCLUSIONS: The results presented in this paper demonstrate that PB-CT holds a high potential for improving on the quality and diagnostic value of images obtained using existing medical x-ray technologies, such as mammography and digital breast tomosynthesis (DBT). If implemented at suitable synchrotron imaging facilities, PB-CT can be used to complement existing imaging modalities, leading to more accurate breast cancer diagnosis.

Optimization of propagation-based x-ray phase-contrast tomography for breast cancer imaging.

The aim of this study was to optimise the experimental protocol and data analysis for in-vivo breast cancer x-ray imaging. Results are presented of the experiment at the SYRMEP beamline of Elettra Synchrotron using the propagation-based phase-contrast mammographic tomography method, which incorporates not only absorption, but also x-ray phase information. In this study the images of breast tissue samples, of a size corresponding to a full human breast, with radiologically acceptable x-ray doses were obtained, and the degree of improvement of the image quality (from the diagnostic point of view) achievable using propagation-based phase-contrast image acquisition protocols with proper incorporation of x-ray phase retrieval into the reconstruction pipeline was investigated. Parameters such as the x-ray energy, sample-to-detector distance and data processing methods were tested, evaluated and optimized with respect to the estimated diagnostic value using a mastectomy sample with a malignant lesion. The results of quantitative evaluation of images were obtained by means of radiological assessment carried out by 13 experienced specialists. A comparative analysis was performed between the x-ray and the histological images of the specimen. The results of the analysis indicate that, within the investigated range of parameters, both the objective image quality characteristics and the subjective radiological scores of propagation-based phase-contrast images of breast tissues monotonically increase with the strength of phase contrast which in turn is directly proportional to the product of the radiation wavelength and the sample-to-detector distance. The outcomes of this study serve to define the practical imaging conditions and the CT reconstruction procedures appropriate for low-dose phase-contrast mammographic imaging of live patients at specially designed synchrotron beamlines.

Precise and Accurate Measurements of Strong-Field Photoionization and a Transferable Laser Intensity Calibration Standard.

Ionization of atoms and molecules in strong laser fields is a fundamental process in many fields of research, especially in the emerging field of attosecond science. So far, demonstrably accurate data have only been acquired for atomic hydrogen (H), a species that is accessible to few investigators. Here, we present measurements of the ionization yield for argon, krypton, and xenon with percent-level accuracy, calibrated using H, in a laser regime widely used in attosecond science. We derive a transferable calibration standard for laser peak intensity, accurate to 1.3%, that is based on a simple reference curve. In addition, our measurements provide a much needed benchmark for testing models of ionization in noble-gas atoms, such as the widely employed single-active electron approximation.

High-order harmonic generation from a dual-gas, multi-jet array with individual gas jet control.

We present a gas jet array for use in high-order harmonic generation experiments. Precise control of the pressure in each individual gas jet has allowed a thorough investigation into mechanisms contributing to the selective enhancement observed in the harmonic spectra produced by dual-gas, multi-jet arrays. Our results reveal that in our case, the dominant enhancement mechanism is the result of a compression of the harmonic-producing gas jet due to the presence of other gas jets in the array. The individual control of the gas jets in the array also provides a promising method for enhancing the harmonic yield by precise tailoring of the length and pressure gradient of the interaction region.

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.

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.

Coherent Vibronic Coupling in Light-Harvesting Complexes from Photosynthetic Marine Algae.

Observations of long-lived coherences in photosynthetic light-harvesting complexes utilize short pulses with broad spectral bandwidths to coherently excite multiple transitions and coherent superpositions. In order to identify the role that such quantum effects might play in efficient energy transfer, however, an alternative approach is required. We have developed a technique for two-color photon echo spectroscopy to selectively excite the pathway of interest and measure its evolution in the absence of any other excitation. We use this technique to excite a coherence pathway in phycocyanin-645 from cryptophyte algae and measure the dynamics of this coherence. A decoherence time of 500 fs was measured, and clear signatures for strong coupling between the electronic states and phonon modes were observed, allowing coherent coupling between otherwise nonresonant transitions. This provides detailed experimental evidence of the long-lived coherences and the nature of the quantum mechanical interactions between electronic states and phonon modes in phycocyanin-645 from cryptophyte marine algae.

Extreme ultraviolet interferometer using high-order harmonic generation from successive sources.

We present a new interferometer technique whereby multiple extreme ultraviolet light pulses are generated at different positions within a single laser focus (i.e., from successive sources) with a highly controllable time delay. The interferometer technique is tested with two generating media to create two extreme ultraviolet light pulses with a time delay between them. The delay is found to be a consequence of the Gouy phase shift. Ultimately the apparatus is capable of accessing unprecedented time scales by allowing stable and repeatable delays as small as 100 zs.

Experimental ionization of atomic hydrogen with few-cycle pulses.

We present experimental data on strong-field ionization of atomic hydrogen by few-cycle laser pulses. We obtain quantitative agreement at the 10% level between the data and an ab initio simulation over a wide range of laser intensities and electron energies.

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.

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.

A new approach for structure analysis of two-dimensional membrane protein crystals using X-ray powder diffraction data.

The application of powder diffraction methods to problems in structural biology is generally regarded as intractable because of the large number of unresolved, overlapping X-ray reflections. Here, we use information about unit cell lattice parameters, space group transformations, and chemical composition as a priori information in a bootstrap process that resolves the ambiguities associated with overlapping reflections. The measured ratios of reflections that can be resolved experimentally are used to refine the position, the shape, and the orientation of low-resolution molecular structures within the unit cell, in leading to the resolution of the overlapping reflections. The molecular model is then made progressively more sophisticated as additional diffraction information is included in the analysis. We apply our method to the recovery of the structure of the bacteriorhodopsin molecule (bR) to a resolution of 7 Å using experimental data obtained from two-dimensional purple membrane crystals. The approach can be used to determine the structure factors directly or to provide reliable low-resolution phase information that can be refined further by the conventional methods of protein crystallography.

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.

Non-iterative imaging of inhomogeneous cold atom clouds using phase retrieval from a single diffraction measurement.

We demonstrate a new imaging technique for cold atom clouds based on phase retrieval from a single diffraction measurement. Most single-shot diffractive imaging methods for cold atoms assume a monomorphic object to extract the column density. The method described here allows quantitative imaging of an inhomogeneous cloud, enabling recovery of either the atomic density or the refractive index, provided the other is known. Using ideas borrowed from density functional theory, we calculate the approximate paraxial diffracted intensity derivative from the measured diffracted intensity distribution and use it to solve the Transport of Intensity Equation (TIE) for the phase of the wave at the detector plane. Back-propagation to the object plane yields the object exit surface wave and then provides a quantitative measurement of either the atomic column density or refractive index. Images of homogeneous clouds showed good quantitative agreement with conventional techniques. An inhomogeneous cloud was created using a cascade electromagnetically induced transparency scheme and images of both phase and amplitude parts of refractive index across the cloud were separately retrieved, showing good agreement with theoretical results.

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.

Noninterferometric two-dimensional fourier-transform spectroscopy of multilevel systems.

We demonstrate a technique that determines the phase of the photon-echo emission from spectrally resolved intensity data without requiring phase-stabilized input pulses. The full complex polarization of the emission is determined from spectral intensity measurements. The validity of this technique is demonstrated using simulated data, and is then applied to the analysis of two-color data obtained from the light-harvesting molecule lycopene.