X-rays interact with matter in two primary processes: Photoelectric Absorption and Compton Scatter. More on x-ray interaction with matter is presented here. In the current context, three types of x-ray imaging technologies which are based on the processes above will be presented:
X-ray Transmission Imaging
X-ray Transmission imaging, also known as Projection Imaging, utilizes the Photoelectric absorption process of x-ray interaction with matter. When a beam of x-rays travels through material, some of the x-ray photons will hit inner shell electrons of atoms which are then fully absorbed (stopped) while other x-ray photons will continue to propagate through the material. The fraction of x-ray photons which gets absorbed when traveling through some material depends on the x-ray energy, the density (and atomic number) of material and its thickness. A simplified x-ray attenuation process is as follows:
An x-ray beam of intensity I enters some material. Think of this intensity as the number of x-ray photons in the beam.
The x-ray beam intensity is exponentially attenuated as it travels through the material. The x-ray attenuation depends primarily on three factors:
Attenuation Coefficient (a). Materials with higher attenuation coefficient results in more x-ray attenuation. Materials with higher density and higher atomic number generally have higher attenuation coefficient.
Thickness of material (x). X-rays attenuate more as they propagate through material.
Energy of the x-ray beam. The attenuation coefficient is inversely correlated with the energy of the x-ray beam; the higher the energy the lower the attenuation coefficient.
X-ray Attenuation. Illustrating x-ray attenuation through material with Photoelectric Absorption process.
Putting it all together using the simplified exponential attenuation model above, when an x-ray beam of intensity I travels through material of thickness x and with an x-ray attenuation coefficient of a, the beam is attenuated such that its intensity after it exits the material is equal to I exp(-xa).
X-ray Half Value Layer (HVL) for Lead and Concrete, for common x-ray tube energies in mm (inch).
X-ray attenuation in material is often measured by a measure called the Half Value Layer (HVL), which represents the thickness of material required to attenuate an x-ray beam by a factor of two—hence Half Value. Based on presentation above, we expect that the HVL be smaller for denser material. That is, less material is needed to attenuation an x-ray beam by a factor of 2. Inversely, we expect the HVL to increase with energy. That is, more material is needed to attenuate a higher energy x-ray beam by a factor of 2.
Here we present HVL for two materials commonly used in x-ray shielding: Lead and Concrete. Clearly, Lead is a strong absorber for x-rays and hence it takes much less of it to attenuate x-rays by a factor of two compared to Concrete. As discussed above, a single HVL will attenuate an x-ray beam by a factor of 2; two HVL will result in twice the attenuation (factor of 4), while 3 HVLs will attenuate the same beam by a factor of 8. Hence, the overall attenuation factor can be calculated as A = 2^(HVL), that is the 2 to the power of number HVLs.
For example, 0.3 mm of Lead will attenuate an x-ray beam with peak energy of 150 keV by a factor of 2, and a 3.0 mm of Lead will attenuate the same x-ray beam of a factor of 2^10 = 1024. On the other hand, 22.32 mm and 223.2 mm of Concrete are required to achieve a factor of 2 and 1024 attenuation, respectively.
Hence, an x-ray transmission image represents a shadowgraph of inspected objects where denser and thicker material attenuate x-rays more than lighter and thinner material. Metallic objects generally have higher x-ray attenuation coefficients than lower density organic materials. Hence, in x-ray Transmission imaging, metallic objects, such as guns and knives, appear with higher contrast relative to lower density organics, such as explosives, drugs, cash, and people.
Given x-rays must travel through an inspected object in x-ray Transmission imaging, x-ray detectors must be placed on the far-side of the inspected object to intercept x-rays which passed through the object and generate the shadowgraph.
To scan faster, the x-ray beam is typically formed (collimated) to cover an extended portion of the inspected object. It is common to collimate the x-ray beam into a one-dimensional (thin plane) form usually referred to as a Fan-Beam, or a two-dimensional form, such as a circle or rectangle, usually referred to as a Cone-Beam. Many small detectors, typically hundreds or thousands, are organized in a one or two-dimensional array to match the shape of the x-ray beam. These detectors are spatially-multiplexed to simultaneously capture the incident x-ray beam to produce an image. This is an important distinction compared to x-ray scatter imaging as will be discussed later.
Based on the space-multiplexing principle used in x-ray Transmission image formation, the size of each detector in the detector array is key for determining the system imaging resolution. That is, the smaller each detector the higher the resolution. Granted, smaller detectors implies more are needed to cover the required detector area, which adds cost and complexity to the overall system. Further, smaller detectors capture fewer x-rays and hence are more susceptible to photon starvation, which leads to lower Signal to Noise Ratio (SNR) which negatively impacts image quality.
X-ray Scatter Imaging
X-ray Scatter imaging utilizes the Compton Scattering process of x-ray interaction with matter. When a beam of x-rays travels through material, some of the x-ray photons will hit outer shell electrons of atoms which are then scattered (deflected). The probability of Compton scatter is generally proportional to the amount of Hydrogen atoms in the material. Hence, Organic material generally results in more Compton scatter than metallic materials.
As shown in the illustration, when an x-ray source (SRC) puts out an x-ray beam, it interacts with an object generating Compton Scatter which travels in all directions relative to the point of scatter. The energy of scattered photons is inversely dependent on the scatter angle. Hence, x-ray photons which scatter in the forward direction have higher energies than those scattered in the backward direction.
Compton scatter is detected by placing detectors at various locations relative to the source of x-rays and the location where scatter occurs:
Back-scatter. Detectors can be placed near the x-ray source to detect x-rays scattered in the backward direction. This type of scatter is often referred to as Backscatter—Bx for short.
Side-scatter. Similar to backscatter, detectors can be placed to the side of the scattering object to detect x-rays which scatter to the side and hence referred to as Side-scatter—Sx for short.
Forward-scatter. Similarly, detectors can be placed after the scattering object to detect x-rays which scatter forward and hence referred to as Forward-scatter—Fx for short.
Transmission. X-ray photons which are not scattered or absorbed continue to travel forward, along a straight line, and can be detected by a detector located behind the scanned object.
X-ray Scatter and Transmission imaging. Detectors can be placed at different locations relative to an inspected object to capture transmitted and scattered x-rays simultaneously.
In x-ray scatter imaging in general, it is key to know where the interrogating x-ray beam is pointing at precisely. Hence, the interrogating x-ray beam is formed into a narrow pencil beam, similar to a laser pointer, and then used to scan the inspected object. That is, an x-ray pencil beam is directed at a point in the inspected object for a short period of time (Dwell Time) and scattered x-rays are collected , then the pencil beam is moved to the next point and scattered x-rays are collected again, and so on until the entire object is scanned. As one would expect, the interrogating x-ray pencil beam must move very fast to inspect a large-sized object, such as a car or a truck. Hence, in typical x-ray scatter imaging applications, an interrogating x-ray pencil beam dwell time on a given point is in the order of few micro-seconds.
Unlike x-ray Transmission imaging, detectors used in scatter imaging often do not have spatial sensitivity. That is, a detector is unable to localize where on its surface a scattered x-ray photon hit. Instead, spatial location is determined by knowing where the interrogating x-ray pencil beam is pointing at any point in time. Hence, detectors are temporally-multiplexed. In contrast, x-ray transmission detectors are spatially-multiplexed as was discussed earlier.
Based on the time-multiplexing principle used in x-ray scatter image formation, detector size does not determine the imaging resolution of the system. Instead, imaging resolution is determined by
Size (cross-section) of the interrogating pencil beam;
Dwell Time; and
Temporal response of detectors—how fast the detectors are.
As with any imaging system, there’s always a tradeoff between imaging resolution and signal to noise ratio (SNR), whereas reducing the pencil-beam size increases resolution, it reduces the number of x-ray photons detected and hence reduces SNR. Same applies to dwell time; shorter dwell-time improves imaging resolution (causes less image blurring), but it also reduces SNR.
X-ray photons scattered with different angles reveal different properties of the inspected material. Further, adding detectors does not increase the x-ray dose. Hence, a single imaging system may contain a combination of Back-scatter, Side-scatter, Forward-scatter and Transmission detectors all positioned to detect different x-rays generated from the same interrogating x-ray beam. Images presented by these various detectors provide complimentary information for the inspected object hence improving the overall system detection performance.
Computed Tomography (CT) Imaging
A third x-ray imaging technology widely used in non-intrusive inspection is Computed Tomography. This imaging technology uses mathematical computations to create sections of the objects scanned, hence the name Computed Tomography, CT for short.
CT images are typically collected by mounting an x-ray source and x-ray detectors on opposite sides of a rotating gantry then creating images as follows:
The x-ray source emits an x-ray beam, which penetrates an object to be inspected, such as a piece of luggage. The x-ray beam is attenuated as it passes through the inspected object due to the Photoelectric Absorption process, and the resulting x-ray beam is captured by the detectors positioned on the opposite side of the inspected object generating a Transmission (Projection) image. Such a Transmission image is typically referred to as a View.
The gantry where the x-ray source and detectors are mounted is rotated around the inspected objects and the process above is repeated to collect views from all 360 degrees around the inspected object.
A reconstruction algorithm is processes the views above to generate a 3-dimensional section through the inspected object.
X-Ray Computed Tomography. X-ray source and detectors placed on opposite sides of the inspected object. X-ray views are collected from multiple angle and then mathematically reconstructed.
The x-ray projection of a point onto the detectors across multiple views takes a sinusoidal form. In the case of multiple points, the projection across views appears like multiple sinusoidal waves overlaid on top of each other. Hence, the projected views from multiple angles are generally called Sinograms.
To perform tomographic reconstruction, views from around the inspected object are needed. Hence, instead of rotating a source and detectors around an object, the object can rotate while the source and detectors are stationary. Alternatively, multiple sources and detectors can be configured around the inspected object hence alleviating the need for rotation. Instead of multiple sources, an x-ray source with a large anode may also be used where the electron beam is steered over the anode to generate x-rays from multiple locations around the inspected object. The CT configurations with multiple x-ray sources or with a steered electron beam are less common due to cost and complexity.
When performing tomographic reconstruction, collecting more views covering 360 around around the inspected object generally improves the imaging performance. However, it is also possible to perform limited-angle tomographic reconstruction where sparse angles covering 360 degrees or less are used generally at the expense of degraded imaging performance.
In CT imaging, the process starts with x-ray projection (Transmission) imaging from multiple views. In each view, x-rays move from the x-ray focal-spot, through the inspected object, to reach the detector array. This process is referred as the Forward Projection (or forward model). The reconstruction is based on reversing this process to calculate the density of the inspected object, given the projection views, hence referred to as the Back Projection (or inverse model). There are generally 3 categories of tomographic reconstruction algorithms which attempt to solve to build an inverse model to reconstruct the scanned object:
Direct. The x-ray beam is traced back, using line projections, from each detector position to the focal-spot. Since x-rays travel in straight lines from focal-spot to detectors to create the views, the inverse model is typically based on the Radon Transform. These methods are fast as the reconstruction is performed only one time with a closed-form solution. This is different than iterative methods below.
Iterative. The inverse model may be under-constrained. That is, measurements (views) are not sufficient to solve for all the densities of the reconstructed object, especially when correcting for imaging artifacts. To solve this under-constrained problem, an iterative algorithms starts with a back-projection to estimate the densities of the scanned object, then follows with a forward projection to mathematically project the estimated densities on the detectors. This pair of steps: back projection followed by forward projection completes one iteration. A second iteration is then applied where the difference (error) between actual views and forward projections is calculated, and the back-projection is adjusted to reduce this difference. The iterations are repeated until the error is below some threshold. Iterative methods generally result in improved reconstruction at the expense of computational time.
Deep Learning Methods. These are relatively newer methods which use Deep Learning techniques for reconstruction which are becoming more widely used especially in low-dose CT imaging systems to correct for artifacts caused by the low photon counts in low-dose CT.
Some of the common imaging artifacts stemming from the mathematical reconstruction include:
Metal artifacts. Metallic objects (high density) attenuate x-rays more (Photoelectric Absorption) and when reconstructed can result in streaks around the edges of the metallic regions which appear like star artifacts.
Beam hardening artifacts. as an x-ray beam passes through material, the lower-energy x-rays are absorbed at a higher rate compared to higher-energy ones, hence the mean-energy of the x-ray beam gets higher (or harder). Beam-hardening as a function of material density and thickness is difficult to model in forward and back projection equations. Beam hardening artifacts reduce the calculated densities of objects. For example, a sphere made of uniform material would appear to have lower densities in the center compared to the peripheries.
Computed Tomography imaging is generally higher dose than Transmission and Scatter imaging. further, CT imaging is generally restricted to imaging smaller objects as increasing the size and weight of a rotating gantry becomes impractical.
X-ray Imaging: Comparative Summary
A deep analysis of the x-ray imaging technologies is beyond the current scope. Rather, the goal here is to empower the reader with a reasonable level of understanding to perform tradeoff analysis of the different technologies with respect to a given application. If you have more questions on these or other technologies not covered herein, let us know—we can help.
The figure below provides a high-level comparison of the underlying imaging formation method for the main three x-ray imaging technologies discussed herein:
X-ray imaging comparison. High-level comparison of key components of x-ray CT, Transmission and Scatter imaging techniques.
The photoelectric absorption process is key for x-ray Transmission Imaging, where a beam of x-ray photons are attenuated while traveling through the matter. As one would expect, the photoelectric absorption depends on the density and thickness of material the x-ray beam is going through. That is, denser, and/or thicker material causes higher attenuation of x-rays than lower density or thinner material. More discussion on x-ray Transmission imaging will follow.
Key metric comparison. Comparison of the key performance metrics between x-ray CT, Transmission and Scatter imaging.
Finally, there are some practical limitations on the usable energies and type of objects inspected in different x-ray imaging technologies.
Energy. Most of the CT applications use energies of 160 keV or less as the overall weight and complexity become impractical. For scatter, most applications use energies of 225 keV or less. Energies up to 450 keV are also used in scatter imaging, though uncommon. Finally, energies up to 7.5 MeV are commonly used in x-ray transmission applications. Energies up to 450 keV are usually referred to as low-energy, while those higher than 450 keV are referred to as high-energy.
Application. Given the energy and size limitations, most CT imaging systems are suitable for inspecting small items such as bags, parcels, and small pallets. Scatter imaging has no size limitation and can virtually scan objects of any size. Transmission imaging must have detectors on the far side of an inspected object and hence size limitations apply. Transmission scanners which can accommodate large trucks are common.
The energy ranges and applicable objects sizes for x-ray CT, Transmission, and Scatter imaging are summarized in the figure below.
Energy and applications. Comparing the applications and usable energies for different x-ray imaging technologies.