# State-of-the-Art Research on Loess Microstructure Based on X-ray Computer Tomography
## 2 The Development History of CT Technology
### The Detection Principle of CT Technology  
Computerized Tomography technology, often referred to simply as CT, is a technique that utilizes an X-ray source to rotate around the object under test and collect information on the attenuation of the rays to reconstruct two-dimensional or three-dimensional images of the object. Compared to traditional radiographic imaging techniques, CT technology can image a specific slice of an object being tested, effectively avoiding interference from other tissue structures. This capability provides clearer images of the internal structure. Additionally, CT technology is highly sensitive when identifying material density and atomic number, making it widely applicable in the field of non-destructive testing. The X-rays emitted by the signal source of a CT device follow a specific equation when they penetrate an object:  
\[I=I_{0}\exp(-\mu_{m}\rho x) \tag{2}\]  
In Formula (2), \(I_{0}\) is the initial X-ray intensity before the material is penetrated (ev/m\({}^{2}\cdot\)s); I is the X-ray intensity after penetrating the material (ev/m\({}^{2}\cdot\)s); \(\mu_{m}\) is the mass attenuation coefficient of the material (cm\({}^{2}\)/g); \(\rho\) is the density of the material (g/cm\({}^{3}\)); and \(x\) is the length that the incident X-ray travels through the material (cm). Under normal circumstances, the absorption characteristics of a substance to X-rays can be described by the per unit mass attenuation coefficient, which is closely related to the wavelength of the incident X-rays. For X-rays of a specific wavelength, the wavelength remains constant. Therefore, the per unit mass attenuation coefficient can be combined with the density of the substance to derive the per unit volume attenuation coefficient (\(\mu\)) as follows:  
\[\mu=\mu_{m}\rho \tag{3}\]  
Under computer control, the X-ray tube S and the detector D rotate around the center of rotation O. For each rotation position \(\beta\), a certain detector receives the projection data \(P(\beta,\alpha)\) that penetrates the measured material as follows:  
\[P(\beta,\alpha)=\int_{(\beta,\alpha)}f(x,y)dl=\int_{(\beta,\alpha)}f(r,\varphi )dl \tag{4}\]  
In Formula (4), \(\beta\) is the position parameter on the line, representing the distance from the origin along the line to a certain point, and \(\alpha\) is the angular parameter, representing the rotation angle of the line relative to the \(x\)-axis. \(P(\beta,\alpha)\) is a function concerning position \(\beta\) and angle \(\alpha\). The equation above represents the Radon transform, where CT images are generated from a multitude of projection data to determine the density distribution function \(f(x,y)\) of the material under examination. In actual scanning, it is necessary to calibrate and normalize \(P(\beta,\alpha)\)[27] to eliminate the non-uniformity of various detectors and obtain absolute measurement values. This is achieved by performing a pre-scan of the air and a standard water film:\[P=\frac{P-P_{A}-P_{W}}{P_{W}} \tag{5}\]  
In Formula (5), \(P\) represents the preprocessed projection data; \(P_{A}\) is the projection value from the air scan; and \(P_{B}\) is the projection value from scanning a standard water film. There are numerous methods for reconstructing images, with the commonly used Convolution Back Projection (CBP) method, the calculation formula for which is the following:  
\[P(\beta,\alpha)=\int_{0}^{2\pi}\frac{1}{L^{2}}P(\beta,\alpha)g(\alpha)d\beta \tag{6}\]  
where function g (\(\alpha\)) is the convolution kernel function. The design of this function aims to minimize the artifacts caused by detector spacing while sacrificing some density resolution, thereby reducing the computational differences between central and peripheral back projections [28]. In Equation (4), \(f(x,y)\) corresponds to the X-ray absorption coefficient of the point being examined, commonly referred to as the CT number (\(H\) value).