Stephen Petretti, summer semester 2018
The manipulation of X-Rays has been proven useful in many applications such as in thin film characterization in material analysis, and in radiology to study the anatomy of the human body. By studying the effect of scattering of a coherent beam upon interaction with a specimen, one can determine certain material information regarding the crystal structure and chemical composition, as well as the macroscopic composition of heterogeneous objects. However, there are many factors which can cause an unwanted scattering of X-rays and may be detrimental to the identification and characterization of a specimen. This can cause undesirable data being detected or an overlap of signals and thus, leading to incorrect conclusions.
Controlling the the propagation of incident, reflected, and transmitted X-Rays waves through a specimen greatly improves the quality and reliability of the data being measured by means of simple elimination and/or reduction methods. The main focus of this article is not about detailing the physical characteristics and generation of different types of X-Rays, but rather, how these are manipulated in situ into allowing detection of specific ranges of parametric values of particular interest such as angle of incidence/reflectance, coherency, and beam energy, which can lead to the proper identification of the object at hand.
Scattering of X-Rays:
X-Ray scattering can be caused by a number of factors attributed to both the atmospheric conditions of the media where the rays pass through, as well as the material properties of the specimen. Collectively, these factors produce variations in the energy strength, beam direction, and wavelength, contributing to varying degrees of attenuation caused fundamentally by electronic or photonic interactions.
In material characterization, methods utilizing X-Rays beam incidence serve as a non-destructive testing technique to reveal information about the material according to the type of scattering produced.
When a coherent beam consisting of homogenous rays falls upon a material, the scattering phenomena occurs in function to the state of the atomic structure of the material. For any sort of reflectance to occur, the wavelength of the rays must be in the same order of magnitude as the interatomic spacing of a crystal structure. For this reason, X-Rays are of particular use in X-Ray Diffraction material analysis (XRD). Briefly said, in this technique a monochromatic beam of X-Rays is reflected by diffracting upon interacting with the first few atomic layers of a materials surface. Described by Braggs law:
where the intensity of the diffracted rays is dependent on the spacing between atoms d, angle of incidence θ, and wavelength of the beam λ. With this equation one can determine such properties like the crystal orientation in metals, and the crystallization ratios in polymers.
For amorphous materials, the interatomic spacing is widely dispersed and can be orientated in any way, as opposed to the discrete values found in crystal structures. Due to this, it is possible for the intensity of the diffracted beam to be of similar value across a full range of angles of incidence.
In radiology, X-Rays are widely used to assist in the non-invasive imaging of in vitro features mostly for clinical analysis and medical intervention. In this application, the scattered X-Rays of interest are not reflected back towards a detector, such as they are in the characterization of crystalline materials, but are also capable of passing through matter into a detector. The underlying principle is when the primary beam interacts with anatomy of different densities, the higher density matter will attenuate the X-Rays to a greater magnitude. There is also scattering produced solely upon passing through a heterogeneous object with inclusions of different densities.
The scattered beam then exposes an image receptor resulting in darker and lighter areas, which for example may correspond to soft tissue and bone, respectively, due to their different densities. Although this application of X-Rays is known by many, fundamentally it can also be applied to other objects as well, such as the identification of concrete and steel in construction engineering. The phenomena of of scattering and absorption can be visualized in Figure 1. Here we have coherent X-Rays inflecting an object. Then, as the matter they’re interacting with changes density, they lose intensity due to absorption and scattering. This may occur many times throughout the material (represented by the darker circle in the object) until it finally reaches the detector. Depending on the quantity of scattered X-Rays, or rather, a highly heterogeneous object, poor image contrast may occur.
|Figure 1. Scattering and absorption of X-Rays passing through an object onto a detector.|
Scattering reduction methods
A collimator consists of essentially a grid or structure which regulates the properties of the incident beam. In some X-Ray sources like those for example in XRD equipment, these devices may be employed to filter out scattered X-Rays in order to allow only the rays parallel to the direction of the collimation grid to pass through. There are several ways to create collimation either by physical interactions, or by satisfying an optical law.
|Figure 2. X-Rays are either absorbed by the walls of a collimator, or are linear enough no pass through to the detector.|
Slits or pinholes
This method is the most widely applied as a primary mean to reduce directional scattering at the source by taking advantage of geometric conditions. Figure 2 demonstrates a beam of scattered X-Rays passing through a slit collimator. A beam passing sufficiently parallel through the slits, or pinholes if it is grated, would be transmitted through to the detector. If a ray has a large enough angle of incidence upon the collimator, this would then be come into contact with it and thus filtered out by X-Ray absorbent material such as lead or tungsten.
More scattered X-Rays can be filtered by either reducing the spacing dbetween two adjacent slits, or by elongating the trajectory they have to travel to reach the detector L. Both of these modifications reduce the incident angle necessary for a ray to be transmitted through, resulting in a reduced range of angles among rays detected, and greater coherency. However, a disadvantage is a great reduction in the quantity of rays being transmitted, causing an increase in radiation time to achieve a useful image.
The scattering of wavelengths in neutron and X-Ray optics can be regulated by monochromatic filtering through a high quality crystal, which in principle allows only a certain range of wavelengths to be filtered through. The use of a single high quality monocrystal operates through the diffraction process (Figure 3) according to Braggs law. This same principle is used in XRD analysis to scan materials and collect the diffraction patterns of crystals that satisfy Braggs condition.
Crystal monocromation as well as XRD analysis function off of Braggs Condition. This occurs when the wavelength of the incoming X-Ray beam is similar to the spacing between the atomic layers of a crystalline material. When the beam penetrates the material, it will be reflected off the atomic layers and constructive interference may occur as observed in Figure 4. If there are two rays having different wavelength or are not coherent, upon reflection the waves will not be in phase and cancel each other out, and thus filtering undesirable wavelengths.
|Figure 3. Monocrystals are used to filter the wavelength of X-Rays that satisfy Braggs Condition.||Figure 4. Braggs condition leading to Braggs law. Two beams are reflected off of atomic layers of a crystalline material. When they possess the same wavelength, the reflected signal is intensified due to constructive interference. The opposite occurs with different wavelengths.|
Bucky plotter grid
A Bucky Potter grid is a device based on the principles of a geometric collimator that is widely used in radiology. However, instead of being at the X-Ray source, this device is usually positioned between the patient and the detector in order to reduce the quantity of rays that have been scattered by anatomy. The result is increased image resolution and higher contrast.
Contrast, sharpness, and magnification of an X-Ray image are not only caused by scattering upon interaction with an object, but also the relative positions of the X-Ray source and the detector from the object, as well as other geometric factors like beam cross sectional area.  An appropriate analogy would be the workings of a DSLR camera focusing on objects of different distances.
In normal operation, the beam cross section coming out of a source is not always a point source, but rather an area called the focal spot size, located at point ‘A’ in Figure 5. Considering that a large source area is made up of infinite point sources, the difference in beam propagation between two point sources on opposite sides of the focal spot size will converge at a point ‘B’ and thus the sharpness will be at a maximum. The distance AB is known as the source object distance (SOD) and is good practice to place the object as close as possible to this point to enhance the image’s resolution. The interaction of the rays with the edges of an object can include additional scattering due to diffraction, this also includes the edges of objects of different densities.
Beyond the SOD, one would have the object detector distance (ODD) between ‘BC’ and the two point beams here start to diverge, and still increase their spot size, magnifying the image. In the area where both of the beams intersect, an umbra is created which is essentially brighter due to the added intensities of the point beams in this example. Outside of this, the penumbra, is usually an image of less intensity and has a more visible unsharpness. Increasing the ODD allows scattered X-Rays to have greater angle of incidence into a Bucky Potter grid and thus, reduces scattered Rays and increases contrast. The ODD needs to be properly adjusted to balance the sharpness and contrast of an image for best results.
|Figure 5. Effect of the focal spot size on beam propagation and sharpness in radiology.|
Cone beam computed tomography (CT scanning) is a useful method for examining large, solid objects and internal features by allowing the 3D construction of stacked 2D images. Since mechanical duration and resilience have increasing industrial implications, the widespread implementation of novel technologies in CT scanning a being limited due to degraded image quality versus the time to scan an object due to scattering effects. An example would include the strong scattering from large scale samples of iron or aluminum, which lead to artifacts such as cupping, streaks, and reduction in contrast.
Several techniques have been developed to diagnose these insufficiencies in order to create scatter correction methods which can be implemented into the post-processing of a scanned CT-volume, such as Beam Hole Arrays and the more widely known, Beam Stop Arrays.
Beam hole array
A beam hole array (BHA) is an indirect method to sample primary X-Ray signals from the total signal, and is an extension of the more widely known Beam stop array (BSA) technique. In this method, a sheet of X-Ray absorbing material with an array of pinholes and a detector on the opposite side is scanned, such as can be observed in Figure 6A. The rays that travel through the pinholes produce a conic beam due to scattering effects that can be detected onto a pixelated array. The stronger primary beams directly irradiate the detector and produce a larger signal, while the secondary, scattered beams are less strong. The gradient in signal strength upon the detector is also visualized in Figure 6A.
A second scan is performed without the metal sheet in which the unrestricted scattering of the beam is then detected. The difference in measured signal from the primary and secondary scans are plotted with respect to their respective locations on a grid. Using these plotted values, image forming algorithms in post-processing can utilize this to produce a final, better quality image.
|Figure 5. Schematic of: A. Beam hole array, and B. Beam stop array. Both techniques consist of a point source (top), either a pinhole grid or a small object grid (middle), and a pixel detector (bottom). Dotted lines indicate the direction of the transmitted or stopped primary beam. The gradient on the detector indicates signal strength (darker) of the incident beam.|
Beam stop array
Utilizing the same methodology as beam hole arrays, one can say the material of the X-Ray absorbing array is now inverted, thus having solid cylindrical material arranged in a spaced grid. Just like an object in the sun, these cylinders produce a shadow over the pixelated detector. However, due to scattering phenomena, a perfect shadow isn’t formed. A gradient of the signal strength of this configuration can also be visualized in Figure 6B. Once again, a secondary scan is made without the grid. These scans are then compared and plotted onto a grid showing the scattering magnitude respective of the location from the center of origin.
Simulation of scattering
Simulation tools can aid the development of radiographic systems, machinery, processing techniques, and even help in modifying experimental conditions in order to achieve higher quality imagery.
X-Ray simulation software are capable of modeling realistic radiographic setups whenever accurate inputs of the system are taken into account. Many works have been published to understand and quantify these scattering effects of X-Rays using using the photon transport equation by employing several approaches such as using build up factors, and Monte Carlo simulations. One example of software capable of this is aRTist, developed by the Bundesanstalt für Materialforschung und –prüfung.
Monte Carlo methods for modeling photon propagation, or X-Ray propagation, utilizes statistical probability distributions to describe photon transport and varying degrees of randomness in its trajectory and angle of deflection in scattering phenomena. In radiology, Monte Carlo simulations are employed to study the amount of peripheral dose the patient will receive due to scattering. In materials science, it is employed to study the depth of penetration of X-Rays in relation to the photons energy, for which, the nature of the secondary electronic emission can be determined.
Mainly, aside from computational factors, the dissimilarities between computed scatter results from reality lie in the accurate representation of ambient scatter and photon noise, as well as geometric positioning inaccuracies between the model and the experimental setup.
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