Coded apertures for faster x-ray scatter imaging
Identifying the material composition of a complex, optically thick object—throughout its volume—is a lofty goal that requires sensitivity to both the microscopic and macroscopic structure of the object. Nevertheless, this task is at the heart of in vivo image-based detection methods that are used in a range of disciplines, including diagnosing cancer in the body and determining the presence of explosives or contraband in luggage.1, 2 By combining the penetrating power of x-rays with their ability to interact with matter at atomic length scales, x-ray diffraction tomography (XRDT) provides an attractive solution for these, and related, problems.
Indeed, x-ray diffraction (XRD) has been considered the ‘gold standard’ for determining the molecular structure of material for more than 100 years. In XRD, the microstructure of a target material is translated into the spectral and/or spatial distribution of the x-rays that it scatters. Proper measurement of this scatter spectrum provides material specificity and image contrast (which are critical for identifying the composition of the material) that far exceed those of conventional transmission-based imaging methods. Although conventional XRD is effective, it is limited as a non-imaging technique to the study of thin, homogeneous samples that have been specially prepared.
Over the past three decades, various approaches have therefore been explored with the aim of transforming XRD into a volumetric imaging technology.3, 4 To accomplish such a technology (e.g., XRDT), the location and deflection angle of the measured x-ray scatter must be determined concurrently. Previous techniques have relied on a combination of spatial and spectral filtering, and have required multiple sequential measurements to recover the scatter spectrum at each voxel in the object.3, 4 A large fraction of the scattered x-ray photons, however, are discarded during this filtering process. XRDT methods therefore necessitate the use of either ultrabright x-ray sources (e.g., a synchrotron) or very long exposure times (typically hours), and this limitation has historically precluded the widespread utility of XRDT in practical applications.
To overcome these limitations, we have developed a new, flexible approach to performing real-time XRDT with off-the-shelf components.5 Rather than filtering the scatter, we place a coded aperture between the object and the detectors (see Figure 1) and intentionally modulate the scatter. This allows us to collect almost half of the available signal. Furthermore, because each scatter location (i.e., object voxel) uniquely projects the coded aperture pattern onto the detector, we can measure multiple voxels at the same time. By increasing throughput and making many parallel multiplexed measurements, we can decrease scan times by orders of magnitude (compared with conventional methods). At the same time, we reduce the entire measurement procedure to the acquisition of a single snapshot measurement. After collecting the signal, we use an iterative, model-based reconstruction algorithm to demultiplex the signal and thus recover the scatter spectrum associated with each voxel independently.6 Once the XRD scatter spectrum at each voxel is known, material identification or classification can be performed.
To demonstrate our coded-aperture XRDT architecture, we first considered a simple pencil-beam geometry in which the incident x-ray beam consists of a single line, as illustrated in Figure 2(a). The goal of this demonstration was to measure the XRD scatter spectrum at each point along the beam by acquiring only a single measurement. The results of these tests—see Figure 2(b)—show that we can perform in vivo liquid identification with our technique (i.e., by accurately recording the scatter spectrum) for a variety of materials.
We can easily extend this 2D (i.e., one spatial dimension and one material dimension) imaging result to higher-dimensional configurations. For example, we have shown that by using our framework with an incident cone beam, we can perform snapshot 4D (i.e., three spatial dimensions and one material dimension) XRDT. To make this 4D measurement possible with a 3D detector (i.e., a 2D array of energy-sensitive pixels), we made use of both the fundamental correlations between the angular and spectral distribution of the scattered x-rays, and of compressed sensing techniques.
To illustrate this capability, which is unique to our coded-aperture architecture, we simulated an 8 × 8 × 8 voxel Shepp-Logan phantom (i.e., a standard test image), with 32 scatter spectral bins at each location. To simulate a tissue sample, we assigned the scatter spectrum at each voxel in the phantom as either empty, or filled with bone, adipose, or muscle. Classification maps of the ground truth and estimated objects are shown in Figure 3. In these maps, each color represents a different material and each 2D image represents a different axial slice of the object. Through this study, we have shown that snapshot 4D imaging is possible, but that tradeoffs exist between imaging speed, compression level, and image quality. The beauty of our approach, however, is that it is flexible and can be optimized to specific tasks.
In summary, we have developed and demonstrated a coded-aperture-based approach to XRDT that makes material identification in 3D, via a single measurement, possible. Our approach is flexible and can be optimized to suit the imaging and detection needs of a particular task. To validate our method, we have presented results from experiments and simulations that span a range of system configurations. Going forward, we will apply our technique to the problems of cancer detection1 and aviation security2 to better understand how it can be further optimized and developed to its full potential.
Joel Greenberg received his BSE from Princeton University in 2005, and his MA and PhD in physics from Duke University in 2008 and 2012, respectively. Since 2014, Joel has been an assistant research professor of electrical and computer engineering at Duke University and a member of the Fitzpatrick Institute for Photonics.
