Resolution analysis of a volumetric coded aperture X-ray diffraction imaging system.

BACKGROUND: A coded aperture X-ray diffraction (XRD) imaging system can measure the X-ray diffraction form factor from an object in three dimensions -X, Y and Z (depth), broadening the potential application of this technology. However, to optimize XRD systems for specific applications, it is critical to understand how to predict and quantify system performance for each use case. OBJECTIVE: The purpose of this work is to present and validate 3D spatial resolution models for XRD imaging systems with a detector-side coded aperture. METHODS: A fan beam coded aperture XRD system was used to scan 3D printed resolution phantoms placed at various locations throughout the system's field of view. The multiplexed scatter data were reconstructed using a model-based iterative reconstruction algorithm, and the resulting volumetric images were evaluated using multiple resolution criteria to compare against the known phantom resolution. We considered the full width at half max and Sparrow criterion as measures of the resolution and compared our results against analytical resolution models from the literature as well as a new theory for predicting the system resolution based on geometric arguments. RESULTS: We show that our experimental measurements are bounded by the multitude of theoretical resolution predictions, which accurately predict the observed trends and order of magnitude of the spatial and form factor resolutions. However, we find that the expected and observed resolution can vary by approximately a factor of two depending on the choice of metric and model considered. We observe depth resolutions of 7-16 mm and transverse resolutions of 0.6-2 mm for objects throughout the field of view. Furthermore, we observe tradeoffs between the spatial resolution and XRD form factor resolution as a function of sample location. CONCLUSION: The theories evaluated in this study provide a useful framework for estimating the 3D spatial resolution of a detector side coded aperture XRD imaging system. The assumptions and simplifications required by these theories can impact the overall accuracy of describing a particular system, but they also can add to the generalizability of their predictions. Furthermore, understanding the implications of the assumptions behind each theory can help predict performance, as shown by our data's placement between the conservative and idealized theories, and better guide future systems for optimized designs.

Application of machine learning classifiers to X-ray diffraction imaging with medically relevant phantoms.

PURPOSE: Recent studies have demonstrated the ability to rapidly produce large field of view X-ray diffraction (XRD) images, which provide rich new data relevant to the understanding and analysis of disease. However, work has only just begun on developing algorithms that maximize the performance toward decision-making and diagnostic tasks. In this study, we present the implementation of and comparison between rules-based and machine learning (ML) classifiers on XRD images of medically relevant phantoms to explore the potential for increased classification performance. METHODS: Medically relevant phantoms were utilized to provide well-characterized ground-truths for comparing classifier performance. Water and polylactic acid (PLA) plastic were used as surrogates for cancerous and healthy tissue, respectively, and phantoms were created with varying levels of spatial complexity and biologically relevant features for quantitative testing of classifier performance. Our previously developed X-ray scanner was used to acquire co-registered X-ray transmission and diffraction images of the phantoms. For classification algorithms, we explored and compared two rules-based classifiers (cross-correlation, or matched-filter, and linear least-squares unmixing) and two ML classifiers (support vector machines and shallow neural networks). Reference XRD spectra (measured by a commercial diffractometer) were provided to the rules-based algorithms, while 60% of the measured XRD pixels were used for training of the ML algorithms. The area under the receiver operating characteristic curve (AUC) was used as a comparative metric between the classification algorithms, along with the accuracy performance at the midpoint threshold for each classifier. RESULTS: The AUC values for material classification were 0.994 (cross-correlation [CC]), 0.994 (least-squares [LS]), 0.995 (support vector machine [SVM]), and 0.999 (shallow neural network [SNN]). Setting the classification threshold to the midpoint for each classifier resulted in accuracy values of CC = 96.48%, LS = 96.48%, SVM = 97.36%, and SNN = 98.94%. If only considering pixels ±3 mm from water-PLA boundaries (where partial volume effects could occur due to imaging resolution limits), the classification accuracies were CC = 89.32%, LS = 89.32%, SVM = 92.03%, and SNN = 96.79%, demonstrating an even larger improvement produced by the machine-learned algorithms in spatial regions critical for imaging tasks. Classification by transmission data alone produced an AUC of 0.773 and accuracy of 85.45%, well below the performance levels of any of the classifiers applied to XRD image data. CONCLUSIONS: We demonstrated that ML-based classifiers outperformed rules-based approaches in terms of overall classification accuracy and improved the spatially resolved classification performance on XRD images of medical phantoms. In particular, the ML algorithms demonstrated considerably improved performance whenever multiple materials existed in a single voxel. The quantitative performance gains demonstrate an avenue to extract and harness XRD imaging data to improve material analysis for research, industrial, and clinical applications.

X-ray fan beam coded aperture transmission and diffraction imaging for fast material analysis.

X-ray transmission imaging has been used in a variety of applications for high-resolution measurements based on shape and density. Similarly, X-ray diffraction (XRD) imaging has been used widely for molecular structure-based identification of materials. Combining these X-ray methods has the potential to provide high-resolution material identification, exceeding the capabilities of either modality alone. However, XRD imaging methods have been limited in application by their long measurement times and poor spatial resolution, which has generally precluded combined, rapid measurements of X-ray transmission and diffraction. In this work, we present a novel X-ray fan beam coded aperture transmission and diffraction imaging system, developed using commercially available components, for rapid and accurate non-destructive imaging of industrial and biomedical specimens. The imaging system uses a 160 kV Bremsstrahlung X-ray source while achieving a spatial resolution of ≈ 1 × 1 mm2 and a spectral accuracy of > 95% with only 15 s exposures per 150 mm fan beam slice. Applications of this technology are reported in geological imaging, pharmaceutical inspection, and medical diagnosis. The performance of the imaging system indicates improved material differentiation relative to transmission imaging alone at scan times suitable for a variety of industrial and biomedical applications.

Simulation based evaluation of a fan beam coded aperture x-ray diffraction imaging system for biospecimen analysis.

X-ray diffraction (XRD) imaging yields spatially resolved, material-specific information, which can aid medical diagnosis and inform treatment. In this work we used simulations to analyze the utility of fan beam coded aperture XRD imaging for fast, high-resolution scatter imaging of biospecimens for tissue assessment. To evaluate the proposed system's utility in a specific task, we employed a deterministic model to produce simulated data from biologically realistic breast tissue phantoms and model-based reconstruction to recover a spatial map of the XRD signatures throughout the phantoms. We found an XRD spatial resolution of ≈1 mm with a mean reconstructed spectral accuracy of 0.98 ± 0.01 for a simulated 1 × 150 mm2 fan beam operating at 160 kVp, 10 mA, and 4.5 s exposures. A classifier for cancer detection was developed utilizing cross-correlation of XRD spectra against a spectral library, with a receiver operating characteristic curve with an area under the curve value of 0.972. Our results indicated a potential diagnostic modality that could aid in tasks ranging from analysis of ex-vivo pathology biospecimens to intraoperative cancer margin assessment, motivating future work to develop an experimental system while enabling the development of improved algorithms for imaging and tissue analysis-based classification performance.

Single-shot memory-effect video.

Imaging through opaque scattering media is critically important in applications ranging from biological and astronomical imaging to metrology and security. While the random process of scattering in turbid media produces scattered light that appears uninformative to the human eye, a wealth of information is contained in the signal and can be recovered using computational post-processing techniques. Recent studies have shown that statistical correlations present in the scattered light, known as 'memory effects', allow for diffraction-limited imaging through opaque media without detailed knowledge of (or access to) the source or scatterer. However, previous methods require that the object and/or scatterer be static during the measurement. We overcome this limitation by combining traditional memory effect imaging with coded-aperture-based computational imaging techniques, which enables us to realize for the first time single-shot video of arbitrary dynamic scenes through dynamic, opaque media. This has important implications for a wide range of real-world imaging scenarios.

X-ray diffraction tomography with limited projection information.

X-ray diffraction tomography (XDT) records the spatially-resolved X-ray diffraction profile of an extended object. Compared to conventional transmission-based tomography, XDT displays high intrinsic contrast among materials of similar electron density and improves the accuracy in material identification thanks to the molecular structural information carried by diffracted photons. However, due to the weak diffraction signal, a tomographic scan covering the entire object typically requires a synchrotron facility to make the acquisition time more manageable. Imaging applications in medical and industrial settings usually do not require the examination of the entire object. Therefore, a diffraction tomography modality covering only the region of interest (ROI) and subsequent image reconstruction techniques with truncated projections are highly desirable. Here we propose a table-top diffraction tomography system that can resolve the spatially-variant diffraction form factor from internal regions within extended samples. We demonstrate that the interior reconstruction maintains the material contrast while reducing the imaging time by 6 folds. The presented method could accelerate the acquisition of XDT and be applied in portable imaging applications with a reduced radiation dose.

Accuracy assessment and characterization of x-ray coded aperture coherent scatter spectral imaging for breast cancer classification.

Although transmission-based x-ray imaging is the most commonly used imaging approach for breast cancer detection, it exhibits false negative rates higher than 15%. To improve cancer detection accuracy, x-ray coherent scatter computed tomography (CSCT) has been explored to potentially detect cancer with greater consistency. However, the 10-min scan duration of CSCT limits its possible clinical applications. The coded aperture coherent scatter spectral imaging (CACSSI) technique has been shown to reduce scan time through enabling single-angle imaging while providing high detection accuracy. Here, we use Monte Carlo simulations to test analytical optimization studies of the CACSSI technique, specifically for detecting cancer in ex vivo breast samples. An anthropomorphic breast tissue phantom was modeled, a CACSSI imaging system was virtually simulated to image the phantom, a diagnostic voxel classification algorithm was applied to all reconstructed voxels in the phantom, and receiver-operator characteristics analysis of the voxel classification was used to evaluate and characterize the imaging system for a range of parameters that have been optimized in a prior analytical study. The results indicate that CACSSI is able to identify the distribution of cancerous and healthy tissues (i.e., fibroglandular, adipose, or a mix of the two) in tissue samples with a cancerous voxel identification area-under-the-curve of 0.94 through a scan lasting less than 10 s per slice. These results show that coded aperture scatter imaging has the potential to provide scatter images that automatically differentiate cancerous and healthy tissue within ex vivo samples. Furthermore, the results indicate potential CACSSI imaging system configurations for implementation in subsequent imaging development studies.

Snapshot fan beam coded aperture coherent scatter tomography.

We use coherently scattered X-rays to measure the molecular composition of an object throughout its volume. We image a planar slice of the object in a single snapshot by illuminating it with a fan beam and placing a coded aperture between the object and the detectors. We characterize the system and demonstrate a resolution of 13 mm in range and 2 mm in cross-range and a fractional momentum transfer resolution of 15%. In addition, we show that this technique allows a 100x speedup compared to previously-studied pencil beam systems using the same components. Finally, by scanning an object through the beam, we image the full 4-dimensional data cube (3 spatial and 1 material dimension) for complete volumetric molecular imaging.

Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples.

A scatter imaging technique for the differentiation of cancerous and healthy breast tissue in a heterogeneous sample is introduced in this work. Such a technique has potential utility in intraoperative margin assessment during lumpectomy procedures. In this work, we investigate the feasibility of the imaging method for tumor classification using Monte Carlo simulations and physical experiments. The coded aperture coherent scatter spectral imaging technique was used to reconstruct three-dimensional (3-D) images of breast tissue samples acquired through a single-position snapshot acquisition, without rotation as is required in coherent scatter computed tomography. We perform a quantitative assessment of the accuracy of the cancerous voxel classification using Monte Carlo simulations of the imaging system; describe our experimental implementation of coded aperture scatter imaging; show the reconstructed images of the breast tissue samples; and present segmentations of the 3-D images in order to identify the cancerous and healthy tissue in the samples. From the Monte Carlo simulations, we find that coded aperture scatter imaging is able to reconstruct images of the samples and identify the distribution of cancerous and healthy tissues (i.e., fibroglandular, adipose, or a mix of the two) inside them with a cancerous voxel identification sensitivity, specificity, and accuracy of 92.4%, 91.9%, and 92.0%, respectively. From the experimental results, we find that the technique is able to identify cancerous and healthy tissue samples and reconstruct differential coherent scatter cross sections that are highly correlated with those measured by other groups using x-ray diffraction. Coded aperture scatter imaging has the potential to provide scatter images that automatically differentiate cancerous and healthy tissue inside samples within a time on the order of a minute per slice.

Giant all-optical tunable group velocity dispersion in an optical fiber.

We realize a strongly dispersive material with large tunable group velocity dispersion (GVD) in a commercially-available photonic crystal fiber. Specifically, we pump the fiber with a two-frequency pump field that induces an absorbing resonance adjacent to an amplifying resonance via the stimulated Brillouin processes. We demonstrate all-optical control of the GVD by measuring the linear frequency chirp impressed on a 28-nanosecond-duration optical pulse by the medium and find that it is tunable over the range ± 7.8 ns(2)/m. The maximum observed value of the GVD is 10(9) times larger than that in a typical single-mode silica optical fiber. Our observations are in good agreement with a theoretical model of the process.

Structured illumination for tomographic X-ray diffraction imaging.

Tomographic imaging of the molecular structure of an object is important for a variety of applications, ranging from medical and industrial radiography to security screening. X-ray diffraction imaging is the preeminent technique for performing molecular analysis of large volumes. Here we propose and demonstrate a new measurement architecture to improve the source and detector efficiency for diffraction imaging. In comparison with previous techniques, our approach reduces the required overall scan time by 1-2 orders of magnitude, which makes possible real-time scanning of a broad range of materials over a large volume using a table-top setup. This method, which relies on structuring spatially the illumination incident on an object moving relative to the X-ray source, is compatible with existing systems and has the potential to significantly enhance performance in an array of areas, such as medical diagnostic imaging and explosives detection.

Snapshot molecular imaging using coded energy-sensitive detection.

We demonstrate a technique for measuring the range-resolved coherent scatter form factors of different objects from a single snapshot. By illuminating the object with an x-ray pencil beam and placing a coded aperture in front of a linear array of energy-sensitive detector elements, we record the coherently scattered x-rays. This approach yields lateral, range, and momentum transfer resolutions of 1 mm, 5 mm, and 0.2 nm⁻¹, respectively, which is sufficient for the distinguishing a variety of solids and liquids. These results indicate a path toward real-time volumetric molecular imaging for non-destructive examination in a variety of applications, including medical diagnostics, quality inspection, and security detection.

Bunching-induced optical nonlinearity and instability in cold atoms [Invited].

We report a new nonlinear optical process that occurs in a cloud of cold atoms at low-light-levels when the incident optical fields simultaneously polarize, cool, and spatially-organize the atoms. We observe an extremely large effective fifth-order nonlinear susceptibility of χ(5) = 7.6 × 10⁻¹5 (m/V)4, which results in efficient Bragg scattering via six-wave mixing, slow group velocities (∼ c/105), and enhanced atomic coherence times (> 100 µs). In addition, this process is particularly sensitive to the atomic temperatures, and provides a new tool for in-situ monitoring of the atomic momentum distribution in an optical lattice. For sufficiently large light-matter couplings, we observe an optical instability for intensities as low as ∼ 1 mW/cm² in which new, intense beams of light are generated and result in the formation of controllable transverse optical patterns.

Absorption-induced trapping in an anisotropic magneto-optical trap.

We report on a simple anisotropic magneto-optical trap for neutral atoms that produces a large sample of cold atoms confined in a cylindrically-shaped volume with a high aspect ratio (100:1). Due to the large number of trapped atoms, the laser beams that propagate along the optically thick axis of the trap to cool the atoms are substantially attenuated. We demonstrate that the resulting intensity imbalance produces a net force that spatially localizes the atoms. This limits both the trap length and the total number of trapped atoms. Rotating the cooling beams by a small angle relative to the trap axis avoids the problem of attenuation, and atoms can be trapped throughout the entire available trapping volume. Numerical and experimental results are reported that demonstrate the effects of absorption in an anisotropic trap, and a steady-state, line-center optical path length of 55 is measured for a probe beam propagating along the length of the trap.