Research Progress of Grating-Based X-Ray Phase-Contrast Imaging and Key Devices

Abstract

X-ray phase-contrast imaging presents a significant advancement in the field of X-ray imaging, surpassing traditional X-ray absorption imaging in detecting hydrogen substances. It effectively addresses the limitations of the latter in providing contrast for imaging weakly absorbing objects, thereby opening up vast potential applications in biomedical research, materials science, and industrial inspection. This article initially explores the fundamental principles of X-ray phase-contrast imaging and several prevalent imaging techniques. Notably, imaging devices such as grating-based Talbot–Lau interferometers emerge as the most promising in phase-contrast imaging due to their exceptional compatibility and imaging quality. Furthermore, this article introduces key parameters for assessing the quality of grating phase-contrast imaging, specifically image noise and sensitivity, along with their calculation methods. These insights are valuable for optimizing grating-based phase-contrast imaging devices. Lastly, this article examines potential applications and advancements in the key components of X-ray phase-contrast imaging while addressing current challenges and future directions in its technological development. This article aims to provide insights and inspiration for scholars interested in this field.

1. Introduction

X-ray phase-contrast imaging is currently a prominent area of research in the field of X-ray imaging. This technique leverages the principle of generating varying contrast levels based on differences in the refractive index of the sample materials, which is fundamentally different from traditional X-ray absorption imaging. The latter relies on variations in the absorption coefficient or thickness across different parts of the object to achieve a specific level of contrast. Notably, in regions with significant density variations at the external edges or within the object, phase-contrast imaging can produce substantial contrast enhancement, facilitating the acquisition of more detailed structural information without compromising the integrity of the sample [1]. Consequently, X-ray phase-contrast imaging holds vast potential applications in various fields, including biology, medicine, physics, chemistry, and polymer materials. This imaging technique primarily captures information regarding the internal refractive index (or electron density) of an object, while absorption imaging focuses on differences in absorption coefficients or thickness. The information obtained from both techniques is complementary. Essentially, X-ray phase-contrast imaging technology measures the micro-arc level refractive angle produced by X-rays as they pass through an object [2], enabling the acquisition of phase information about its internal structure. Therefore, X-ray phase-contrast imaging enhances our understanding of internal structural information beyond what absorption imaging can provide, presenting immense potential value. The energy of X-rays is inversely related to the refraction angle they produce when passing through an object; higher-energy X-rays generate smaller refraction angles. Objects composed of elements with lower atomic numbers, such as carbon, hydrogen, and oxygen, exhibit weaker absorption of low-energy X-rays. In contrast, objects made of elements with higher atomic numbers tend to absorb low-energy X-rays almost completely. As a result, the imaging effect of phase-contrast images is more pronounced for objects composed of light elements compared to those made of heavy elements.

This article serves as a research reference for scholars in the field of X-ray imaging. and offers new inspiration for experts in this domain. Its aim is to help researchers understand the fundamental principles, key devices, and future development trends of X-ray phase-contrast imaging. Firstly, this article introduces the basic physical quantity closely related to the physical mechanism of X-ray phase-contrast imaging—the refractive index. It analyzes the factors that influence the refractive index of objects within the X-ray spectrum, as well as the quantitative relationship and calculation methods between the refractive angle and phase shift. Secondly, it discusses six commonly used methods for achieving X-ray phase-contrast imaging and outlines their future development trends. Next, this article presents the performance indicators of phase-contrast imaging and the primary factors that affect imaging quality. Finally, it details the key components and fabrication techniques of the X-ray phase-contrast imaging system, including the manufacturing methods for X-ray phase gratings, absorption gratings, and structured anode X-ray sources. This article concludes with a summary of the current challenges and future prospects of X-ray phase-contrast imaging methods.

2. Materials and Methods

After X-ray irradiation of the sample, absorption, scattering, and refraction phenomena occur within the internal substances of the sample. The X-rays emitted from the sample carry information about its internal structure along their path, resulting in a specific contrast. X-ray imaging is a technique that utilizes this contrast information to characterize the distribution and structure of internal substances within the sample. The phenomena generated by the interaction between X-rays and matter can be represented in the refractive index formula of the material. In the X-ray wavelength range, the refractive index of a substance is complex; therefore, it is referred to as the complex refractive index, typically expressed in the following form:

$$n=1-\delta +i\beta$$

(1)

where δ represents the attenuation of the reduction in the refractive index, which is related to the phase of the object, and its typical value is in the order of micro radians, while the imaginary part β is related to the absorption of the object. The calculation formulae [3] of δ and β are, respectively, as follows:

$$\delta ={\displaystyle \frac{\lambda \phi }{2\pi }}={\displaystyle \frac{r_e{\lambda }^2}{2\pi }}{\displaystyle \sum _j{N}_j{f}_{1,j}}$$

(2)

$$\beta ={\displaystyle \frac{\lambda \mu }{4\pi }}={\displaystyle \frac{r_e{\lambda }^2}{2\pi }}{\displaystyle \sum _j{N}_j{f}_{2,j}}$$

(3)

where $r_e$ is the classical electron radius, $\lambda$ is the wavelength of the incident light, $N_j$ is the atomic density of type j atoms (number of atoms per unit volume), and $f_{1,j}$ and $f_{2,j}$ are the real part and the image part of their atomic scattering factor in the forward direction, respectively. If the photon energy of the incident X-ray radiation lies considerably above the absorption edges, It can be approximated that $f_{1,j}=Z_j$, where $Z_j$ represents the total number of electrons in the atom, and the sum in Equation (2) then describes the electron density inside the sample.

The X-ray will be absorbed through the object, and the change in its intensity meets the Beer–Lambert law, that is

$$I_1=I_0\exp \left(-\mu t\right),$$

(4)

where $I_0$, $I_1$, $\mu$, and t are the light intensity before incident on the object, the light intensity after exiting the object, the linear attenuation coefficient of the object, and the thickness of the object, respectively.

The X-ray will also refract after passing through the object. The calculation formula of its refraction angle α is usually written as follows [4,5]:

$$\alpha ={\displaystyle \frac{1}{k}}{\displaystyle \frac{\partial \varphi \left(x,y,z\right)}{\partial x}}$$

(5)

where x refers to the direction of vertical X-ray propagation, and ϕ (x, y, z) refers to the phase shift in X-ray after passing through the object, which can be generally written as follows:

$$\varphi \left(x,y,z\right)=k{\displaystyle \underset{L}{\int }\delta \left(x,y,z\right)}dl$$

(6)

where L is the propagation path of the X-ray and k is the wave vector.

3. X-Ray Phase-Contrast Imaging Method

The primary methods for implementing X-ray phase-contrast imaging include crystal interferometers, propagation-based X-ray phase-contrast imaging, diffraction enhancement, and grating-based phase-contrast imaging methods [6]. Among these, grating-based phase imaging systems are currently the mainstream research direction in phase-contrast imaging due to their high imaging quality and ease of large-scale market promotion. The grating-based phase-contrast imaging methods primarily consist of the single-grating phase-contrast imaging method, the Talbot–Lau interferometer, the inverse geometry Talbot–Lau interferometer, and the dual-phase grating interferometer. Specifically, the Talbot–Lau interferometer has gained popularity in application research for X-ray phase-contrast imaging under ordinary laboratory conditions. Its advantages include compatibility with conventional X-ray sources, the ability to simultaneously recover three signals—absorption, phase-contrast, and scattering—and a relatively large imaging field of view. The single-grating phase-contrast imaging system features a simple structure and is capable of recovering three signals in a single exposure, resulting in a short exposure time. However, it has relatively low signal sensitivity and suboptimal imaging quality. The inverse geometry Talbot–Lau interferometer offers a simple system structure and high light utilization efficiency, making it particularly suitable for large-scale promotion and application. It represents a promising future direction for grating phase-contrast imaging. The main challenge hindering its widespread adoption is the immature fabrication process of small-period microstructure anode targets and the need for advancements in the technology of structured light sources. Recently proposed, the dual-phase grating interferometer utilizes two phase gratings to effectively create a small-period structured light source, thereby overcoming the manufacturing challenges associated with small-period structured light sources. The resulting images have a large fringe period and can be directly detected by a flat-panel detector, eliminating the limitations imposed by the analysis grating on the imaging field of view. This approach serves as a compromise solution for optimizing the grating phase-contrast imaging system. However, challenges such as complex structure, low light utilization efficiency, and limited field of view remain. The advantages and disadvantages of various phase contrast imaging methods are compared in

Table 1. Comparison of several phase-contrast imaging methods.

Methods	Source	Spatial Coherence Requirements	Characteristic	Light Utilization Rate	Imaging Quality	Signal-to-Noise Ratio (SNR)
Crystal interferometer	Synchrotron radiation	High	High sensitivity, small field of view	Low	excellent	-
Propagation-based X-ray phase-contrast imaging	Synchrotron radiation, Microfocus X-ray tube	High	Simple structure, insensitive to boundary features, unable to quantify phase information	High	good	∝1/E2
Diffraction-enhanced imaging	Synchrotron radiation,	High	High precision and sensitivity requirements for motion	Low	excellent	∝1/E
Talbot–Lau interferometer	Synchrotron radiation, X-ray tube	Low	Complex structure, high sensitivity	High	excellent	∝1/E2
Dual-phase grating interferometer	Synchrotron radiation, X-ray tube	Low	Complex structure, high sensitivity	Low	excellent	∝1/E2
Inverse Talbot–Lau interferometer	Synchrotron radiation, X-ray tube	Low	Simple structure and high sensitivity	High	excellent	∝1/E2
Single-grating X-ray imaging	Synchrotron radiation, Microfocus X-ray tube	High	Fast imaging	Low	good	-
Wave-front coding phase-contrast imaging	Synchrotron radiation, X-ray tube	Low	Fast imaging	Low	good	∝1/E

.

3.1. Crystal Interferometer

As early as the 1960s, BONSE U et al. proposed the use of a crystal interferometer to detect the phase change in X-rays after they pass through an object [7], as illustrated in Figure 1. They created two grooves in a single crystal of silicon, forming three diffraction planes: S, M, and A. When an X-ray beam strikes the diffraction plane S, it is divided into two diffracted beams due to Bragg diffraction. As these beams continue to propagate, they reach the second diffraction plane M, where they are further split by diffraction, each generating two new beams. Two of these beams converge on the third diffraction plane A. One beam is designated as the reference light, while the other serves as the non-reference light, creating interference fringes on plane A. If a sample is positioned in the path of the non-reference light, it modulates the phase of the light wave, thereby imprinting the sample’s internal structural information onto the modulated light. The light exiting plane A, after interacting with the sample, is a superposition of the reference and modulated beams. Since the period of the interference fringes formed by this superposition closely matches the spacing between the Bragg diffraction planes in the crystal, it cannot be directly distinguished by a detector. However, the third diffraction plane A magnifies the fringe period, enabling the interference fringe image to be detected by detector D. After passing through plane A, two in-phase beams emerge, allowing the detector to receive the intensity distribution of either beam. Subsequently, Fourier analysis is applied to the obtained interference patterns, and by weighted summation of different patterns, the phase shift in the X-rays as they pass through the object can be determined, ultimately yielding a phase-contrast image of the sample.

When conducting phase measurements on a sample using a crystal interferometer, it is essential to position the sample within one of the interferometer’s optical paths. This configuration creates a specific optical path difference between the two paths, causing the interference fringes to deform and shift in response to variations in the optical path difference, thereby making it highly sensitive to phase changes. In the crystal interferometer, the diffraction effect of X-rays only allows light with specific wavelengths to be diffracted, effectively functioning as a filter. Due to the stringent requirements for crystal collimation and mechanical stability, an interferometer constructed from a single crystal can meet the demands for high stability. However, the limited size of the crystal results in a narrow field of view, typically measuring 3 cm × 3 cm. In 2001, A. Momose and colleagues developed an X-ray interferometer that relied solely on two crystals. The linear displacement between the two crystals within this interferometer does not affect the interference field, and interference fringes can be generated by adjusting the rotation axes of the crystals. This crystal-separated interferometer can utilize the plane wave of synchrotron radiation to achieve a broader field of view, extending up to 5 cm × 20 cm, while still requiring nanometer-level stability.

The crystal interferometer requires precise control over distance, parallelism, and system stability across the three diffraction planes. This demand presents considerable processing challenges and complicates the separation of the sample’s absorption and phase information. Additionally, due to its fundamental principles, the interferometer has a narrow imaging field of view and a low utilization rate of X-rays under laboratory light source conditions, which impedes the imaging of large-scale objects. These inherent limitations significantly restrict its broader application.

3.2. Propagation-Based X-Ray Phase-Contrast Imaging

Propagation-based X-ray phase-contrast imaging [8], also referred to as coaxial holographic phase-contrast imaging, employs X-ray diffraction in the Fresnel near-field region to achieve phase-contrast imaging. When a uniform coherent light wave traverses a sample with a non-uniform cross-section, the intensity of the light remains constant while the wavefront experiences distortion. After propagating a certain distance, the distorted wavefront overlaps with the undistorted wavefront, resulting in an interference effect. Consequently, after passing through a thin layer of weakly absorbing and weakly phase-shifting samples and propagating freely for a specified distance, the X-ray can convert phase change information into modulated intensity information, which is ultimately displayed on the image plane.

Figure 2 illustrates the schematic diagram of the experimental setup for X-ray propagation-based X-ray phase-contrast imaging. The propagation-based X-ray phase-contrast imaging system primarily consists of a spatially coherent light source and a detector, with the sample to be measured positioned between them. Since the X-rays incident on the object must exhibit a certain degree of spatial coherence, the light source is typically either synchrotron radiation or an X-ray micro-focal spot light source. In propagation-based X-ray phase-contrast imaging, an appropriate distance between the object and the detector is essential for optimal imaging, typically exceeding several tens of centimeters to achieve superior phase-contrast effects. However, this distance cannot be excessively long; according to wave optics theory, propagation-based X-ray phase-contrast imaging yields ideal results only within the Fresnel imaging region. As the distance increases, the system transitions into the holographic imaging region, where light wave diffraction becomes too pronounced, resulting in blurred details [9,10]. For a specific spatial frequency, $f_x$, the optimal imaging position is $z=1/(2\lambda f_x^2)$, where λ represents the wavelength of the incident light. There are many spatial frequencies present within the object, so the optimal position is only relative. The upper limit of the spatial frequency is associated with the maximum sampling frequency determined by the Nyquist criterion, which is given by $f_{\max }=1/2p_s$, where $p_s$ is the pixel size of the detector.

For the propagation-based X-ray phase-contrast imaging system illuminated by parallel light, the light intensity distribution of the image obtained on the image plane is

$$I(x,y)=\exp [-\mu (x,y)]\left(1-{\displaystyle \frac{\lambda z}{2\pi }}{\nabla }^2\varphi (x,y)\right).$$

(7)

From the formula above, it is evident that the diffraction intensity distribution in the Fresnel near-field region is directly proportional to the Laplacian transform (${\nabla }^2\varphi$) of the phase change. However, the intensity distribution map obtained on the image plane does not directly represent the two-dimensional distribution of the phase change. Instead, the information regarding the phase change is conveyed indirectly through enhanced edge contrast. In a propagation-based X-ray phase-contrast imaging system illuminated by cone beam light, the light intensity incident on the detector surface can be calculated based on Fresnel diffraction theory, as described in the referenced literature.

$$\begin{array}{c}I=I_0/M^2\left\{1+{\displaystyle \frac{R_2}{kM}}{\nabla }_{x,y}^2\varphi \left(x,y;R_1,k\right)\right\}\\ =I_0/M^2\left\{1-2\pi {\displaystyle \frac{r_e{R}_2}{k^{2}M}}{\nabla }_{x,y}^2{\displaystyle \int \rho \left(x,y,z\right)dz}\right\}\end{array}$$

(8)

Here, $I_0$, M, $R_2$, and $\rho \left(x,y,z\right)$ represent the light intensity incident on the object, the system magnification, the distance from the object to the detector, and the electron density of the object, respectively. Various methods exist for recovering the phase-contrast signal in coaxial imaging. For instance, iterative algorithms can be employed to calculate the phase from images captured at different positions [11], or the phase can be determined through calculations based on the intensity transmission equation [12].

Propagation-based X-ray phase-contrast imaging requires high spatial coherence from the light source, typically necessitating a spot size of less than 20 μm. While synchrotron radiation light sources satisfy these criteria due to their high coherence and flux, their widespread adoption is limited. Although laboratory microfocus light sources can meet the demands of propagation-based X-ray phase-contrast imaging, their low light flux results in extended exposure times and a diminished signal-to-noise ratio. Furthermore, the information obtained through coaxial phase imaging is directly proportional to the second derivative of the phase shift, complicating the quantitative calculation of the phase shift and rendering it unsuitable for quantitative detection.

3.3. Diffraction-Enhanced Imaging

When X-rays strike a crystal at the Bragg angle, the intensity of the reflected X-rays reaches a peak due to Bragg diffraction [13,14,15]. However, when the deviation $\Delta \theta$ between the incident angle and the Bragg angle exceeds the micro-radian level, the intensity of the X-rays reflected by the crystal decreases rapidly. The curve that illustrates the variation in light intensity reflectivity with the incident angle of X-rays is referred to as the “rocking curve”, as shown in Figure 3a. The diffraction enhancement method takes advantage of the sensitivity of the crystal’s diffracted X-ray intensity to the incident angle, allowing for the extraction of the refraction angle of X-rays passing through an object. Figure 3b presents a schematic of the diffraction enhancement method setup. When the sample is irradiated with quasi-parallel light, monochromated by a double flat crystal monochromator, some deflections occur. This light then impinges on the analytical crystal positioned behind it, which screens out light from various angles. The screened light, upon emission, is received and recorded by a detector, forming an image. The contrast of the image captured by the detector depends on the width of the deviation angle in the analytical crystal’s rocking curve, its position on the curve, and the deviation angle of the X-rays after traversing the sample. Specifically, when the angle between the incident light and the analytical crystal aligns with the peak position of the rocking curve (θ₂ position in Figure 3a), the X-rays that pass directly through the sample without deflection are diffracted by the analytical crystal, exhibiting the highest intensity. Conversely, other X-rays that deviate from the original incident direction yield lower diffraction intensities. Consequently, the image captured by the detector reflects absorption imaging.

When adjusting the angle between the analytical crystal and the incident light to align with the waist of the rocking curve (positions θ₁ and θ₃ in Figure 3a), the slope of the rocking curve reaches its maximum. Minor changes in the incident angle can induce sharp fluctuations in reflectivity, facilitating the acquisition of phase images with optimal contrast enhancement. At this point, the image captured by the detector corresponds to the phase image. Conversely, when the angle is adjusted to align with the tail of the rocking curve (position θ₄ in Figure 3a), only the most intense refracted or scattered X-rays are visible in the image, resulting in a dark field image captured by the detector. The diffraction-enhanced imaging method directly records the gradient information (▽ϕ) of the phase change in the quasi-plane wave after it passes through the sample, selecting the angle of the incident light based on the Bragg diffraction principle of the analytical crystal. Consequently, this method is highly sensitive to phase changes in the object, making it easy to differentiate between absorption images, phase-contrast images, and dark field images. Figure 4a–c illustrate the apparent absorption image, phase-contrast image, and dark field image of mice, respectively, obtained using the diffraction enhancement method. Due to the edge enhancement effect of the phase-contrast image, it is clearer than the absorption image, providing significant advantages.

The diffraction-enhanced imaging method relies on highly collimated and high-brightness synchrotron radiation, which makes it challenging to conduct imaging in standard laboratory settings. Furthermore, the spot size of synchrotron radiation typically ranges from millimeters to centimeters, limiting its application to the imaging of large-scale objects. This requirement for scanning significantly extends the imaging time, rendering it unsuitable for imaging live animals. Consequently, this imaging method cannot be directly applied in medical clinical diagnosis and is not conducive to large-scale promotion and application.

3.4. Grating-Based Phase-Contrast Imaging Method

3.4.1. Talbot–Lau Interferometer

The earliest device to achieve X-ray phase-contrast imaging using gratings was the Talbot interferometer, as illustrated in Figure 5a [17,18]. The Talbot interferometer operates on the principle that a monochromatic, parallel beam of X-rays is incident vertically upon a phase grating. Due to the Talbot effect, a self-image of the phase grating emerges at a specific Talbot distance behind it, exhibiting periodic variations in light intensity. When an object is introduced into the optical path, the intensity at corresponding positions in the self-image diminishes and shifts due to the object’s absorption, refraction, and scattering effects. Given that the period of the phase grating and its self-image is exceedingly short (typically measured in micrometers), which is smaller than the detector’s pixel size, detecting changes in the self-image with the detector becomes challenging. Consequently, an absorbing grating with the same period as the self-image must be positioned at the location of the self-image to monitor these changes, thereby enabling the detector to capture its intensity distribution. The phase information changes recorded by the grating interferometer correlate with the object’s phase gradient (▽ϕ), allowing for the quantitative recovery of the object’s phase information from the variations induced by the self-image.

However, the Talbot interferometer requires spatially coherent X-rays and can only utilize synchrotron radiation or micro-focal X-ray sources for imaging. The structure of synchrotron radiation is complex, and micro-focal X-ray sources exhibit low flux, which hinders the market adoption and application of grating phase-contrast imaging systems. In 2006, Pfeiffer et al. ingeniously incorporated the Lau effect into the Talbot interferometer, thereby developing the Talbot–Lau interferometer based on the original interferometer [19]. The schematic diagram of this interferometer is depicted in Figure 5b, where G2 and D represent the absorption grating and detector, respectively. The Talbot–Lau interferometer integrates an absorption grating G0 (also known as the source grating) into the Talbot interferometer. This grating divides the wave field of the large focal spot X-ray source S at the absorption grating into numerous sub-wave sources, generating a series of partially coherent line light sources. Consequently, each line light source meets the spatial coherence requirements for self-imaging by phase grating G1 and fulfills the conditions for Talbot interference. Each line light source forms its own set of self-imaging fringe patterns downstream of the phase grating. Given the incoherence among these line light sources, the total light intensity on the self-imaging plane equals the sum of the intensities of each self-image. When these self-images are precisely staggered by an integer multiple of the period, the contrast of the superimposed fringes is significantly enhanced, demonstrating the Lau effect. Due to the combination of the large focal spot X-ray source and the source grating, which can produce high-brightness spatially coherent light, the Talbot–Lau interferometer can achieve high imaging quality even with laboratory X-ray sources, thereby eliminating the reliance on synchrotron radiation sources. Consequently, upon its introduction, the Talbot–Lau interferometer garnered extensive research and attention, becoming the most widely utilized X-ray phase-contrast imaging system today.

In the Talbot–Lau interferometer, the position of the fringes with the highest contrast generated by the phase grating is related to both the period of the phase grating and the wavelength of the light. This relationship is determined by the fractional Talbot order P [20], expressed as follows:

$$p={\displaystyle \frac{\lambda z_2}{M{p}_1^2}}=\left\{\begin{array}{l}(2n-1)/8,\begin{array}{cc}& \begin{array}{ccc}\pi & \mathit{phase}& \mathit{Grating}\end{array}\end{array}\\ (2n-1)/2,\begin{array}{cc}& \begin{array}{ccc}\pi /2& \mathit{phase}& \mathit{Grating}\end{array}\end{array}\end{array}\right.$$

(9)

where $\lambda$ is the wavelength of X-ray, $z_2$ is the distance from G1 to G2, $p_1$ is the period of G1, n is an integer, M is the system magnification, and its expression is $M=\left(z_1+z_2\right)/z_1$, and $z_1$ is the distance from G0 to G1. For phase gratings with different phase differences, the period $p_2$ of the imaging fringes is also different.

$$p_2=\left\{\begin{array}{cccc}0.5M{P}_1,\hfill & \hfill \pi & \hfill \mathit{phase}& \hfill \mathit{Grating}\\ M{P}_1,\hfill & \hfill \pi /2& \hfill \mathit{phase}& \hfill \mathit{Grating}\end{array}\right.$$

(10)

The image of each wavelet source divided by the absorption grating G0 to the phase grating should meet the condition of mutual reinforcement, namely the Lau condition.

$$p_0={\displaystyle \frac{z_1}{z_2}}{p}_2$$

(11)

The fundamental parameters of the Talbot–Lau interference imaging system can be determined using Formulas (9)–(11), facilitating the design and construction of an interferometer. In this interferometer system, the information recorded by the detector does not directly correspond to the phase of the object. Therefore, it is essential to employ an appropriate phase retrieval algorithm to compute the phase. The simplest phase retrieval algorithm is the Moire fringe spectrum analysis method, which leverages the periodic or angular mismatch between the self-imaging of the phase grating and the absorption grating (i.e., a small angle exists between the two) to generate large-period Moire fringes. Subsequently, the Fourier transform method is utilized to separate the spectra of the object’s absorption, refraction, and scattering signals from the large-period Moire fringe spectrum [21,22,23]. Finally, the corresponding information can be extracted by performing an inverse Fourier transform on these spectra. While the Fourier spectrum analysis method offers rapid imaging speed, its signal sensitivity is low and prone to artifacts. An improved method is reported in references [24,25], which involves using two images of the object for the Fourier transform. This approach mitigates artifacts caused by zero-frequency aliasing. However, the imaging quality remains constrained by the method, and the signal sensitivity cannot be enhanced.

The phase shift method is a widely used technique for phase retrieval, recognized for its excellent imaging quality and sensitivity to signals. In the absence of an object in the system, the phase grating or absorption grating is laterally shifted in a direction perpendicular to the optical axis, moving a distance of 1/N of the grating period (where N is an integer) with each shift. The detector then captures an image, and this process is repeated until a total of N images are recorded. During this time, the light intensity detected by each pixel varies with the relative position of the two gratings, resulting in the phase shift curve shown as the blue curve in Figure 6. When an object is introduced into the optical path, repeating the aforementioned steps produces the phase shift curve depicted as the red curve in Figure 6. By analyzing the phase difference Δϕ between the two-phase shift curves, one can apply the corresponding phase recovery algorithm to ascertain the object’s phase, scattering properties, and other details, thereby facilitating the separation of the object’s absorption, phase, and dark field images. Typically, the phase shift curve resembles a sine wave, and its mathematical expression can be formulated as follows:

$$I(n,m,i)=a_0\left(n,m\right)+a_1\left(n,m\right)\cos \left({\displaystyle \frac{2\pi }{N}}i+\varphi \left(n,m\right)\right) ,i=0,1\cdots N-1$$

(12)

where n and m represent the row and column positions of the detector pixels, respectively, i denotes the step number, and $a_0\left(n,m\right)$, $a_1\left(n,m\right)$, and $\varphi \left(n,m\right)$ represent the average light intensity, amplitude, and initial phase of the phase shift curve, respectively.

$$a_0\left(n,m\right)={\displaystyle \sum _{i=0}^{N-1}I(n,m,i)}$$

(13)

$$\phi \left(n,m\right)=\arctan \left(-{\displaystyle \frac{{\displaystyle \sum _{i=0}^{N-1}I\left(n,m,i\right)\sin (2\pi \frac{i}{N})}}{{\displaystyle \sum _{i=0}^{N-1}I\left(n,m,i\right)\cos \left(2\pi \frac{i}{N}\right)}}}\right)$$

(14)

$$a_1\left(n,m\right)={\displaystyle \frac{2}{N}}\sqrt{{\left({\displaystyle \sum _{i=0}^{N-1}I\left(n,m,i\right)\sin \left(2\pi \frac{i}{N}\right)}\right)}^2+{\left({\displaystyle \sum _{i=0}^{N-1}I\left(n,m,i\right)\cos \left(2\pi \frac{i}{N}\right)}\right)}^2}$$

(15)

Finally, after deducting the background influence, the absorption information $T\left(n,m\right)$, phase information $\Delta \varphi \left(n,m\right)$, and scattering information $V\left(n,m\right)$ of the object can be obtained using the following formula:

$$T\left(n,m\right)={\displaystyle \frac{a_0^o\left(n,m\right)}{a_0^r\left(n,m\right)}}$$

(16)

$$\Delta \varphi \left(n,m\right)={\varphi }^o\left(n,m\right)-{\varphi }^r\left(n,m\right)$$

(17)

$$V={\displaystyle \frac{a_1^o{a}_0^r}{a_1^r{a}_0^o}}$$

(18)

Superscripts “o” and “r” in Equations (16)–(18) denote information with and without objects, respectively.

Due to factors such as system stability and the repetitive accuracy of the stepper motor, the phase-shift method employed for image capture may result in misalignment between the grating positions of the background and sample images. This misalignment inevitably leads to errors and artifacts during subsequent information recovery, thereby compromising image quality. To enhance step accuracy, Miao et al. introduced an electromagnetic phase-stepping method in 2013. This method utilizes a magnetic field to control the position of electron bombardment on the target, enabling motion scanning of the light source [26]. Consequently, it facilitates phase-contrast imaging without mechanical displacement, offering distinct advantages over traditional phase-shifting methods in terms of imaging speed and phase-shifting accuracy. However, this method presents a challenge; as the phase-shift curve is altered, the object’s position also changes, which may affect the recovered signal. An alternative approach involves capturing an image of the object at the point of maximum slope on the phase-shift curve, then rotating the object by 180° and capturing another image. With just two images of the object, the “back projection” algorithm can calculate the object’s phase-contrast and absorption information, significantly reducing exposure time and the dose received by the object [27,28]. Another approach involves the specific design of the analysis grating structure, which facilitates the formation of a phase shift curve among four adjacent pixels of the detector. In this case, phase shifting is unnecessary; simply capturing an image of the object suffices, and the radiation dose received by the object is comparable to that of traditional absorption imaging [29,30]. Furthermore, the phase-contrast signal of the object was restored by an algorithm, even in scenarios where the positions of the phase shifts are completely disordered [31,32,33]. This method entails calculating the eigenvalues and eigenvectors of the image sequence and selecting the eigenvector with the largest eigenvalue to recover the object’s information. It demonstrates excellent resistance to noise. Although these methods represent advancements over the phase-shift technique, they still do not improve the dose utilization efficiency of the Talbot interferometer.

Utilizing the phase-shift method to extract phase information provides several advantages, including high angular sensitivity and spatial resolution. However, the requirement to scan and capture multiple images (at least three) results in extended data acquisition times, which in turn leads to low temporal resolution and limited compatibility with the data acquisition processes of three-dimensional tomography. Furthermore, multiple exposures inevitably increase the radiation dose received by the sample, thereby constraining the wider application of grating interferometers.

3.4.2. Dual-Phase Grating Interferometer

In the Talbot–Lau interferometer, the imaging field of view is primarily limited by the size of the absorption grating closest to the detector. To expand the imaging field of view, researchers often resort to splicing absorption gratings [34] or scanning the sample [35,36]. However, the absorption grating obstructs half of the X-rays incident on the detector, thereby affecting the dose utilization rate. To address these challenges, researchers have introduced a dual-phase grating interferometer, as illustrated in Figure 7a [37,38].

The dual-phase grating interferometer consists of a micro-focus light source S, two phase gratings G1 and G2, and a detector D. The first phase grating G1 modulates the phase of the incident X-rays. Thanks to the Talbot effect, an intensity distribution is generated at a specific distance behind G1, serving as a virtual structural illumination source for the second phase grating G2. This, in turn, produces a large periodic stripe pattern on the detector plane. Since the stripe period generated on the detector plane is sufficiently large—typically in the hundreds of microns—there is no need to place an absorption grating in front of the detector. This configuration allows the detector to directly image the stripes without the necessity of an additional absorption grating. By eliminating the limitations imposed by an absorption grating, the dual-phase grating system enhances X-ray utilization and ensures that the field of view is not constrained by grating size. Figure 7b displays the absorption image, phase-contrast image, and dark-field image of a seahorse obtained using the dual-phase grating interferometer, demonstrating high image quality.

According to Fresnel diffraction theory, the light field distribution on the imaging surface of the dual-phase grating interferometer illuminated by monochromatic light can be expressed by the following formula [40,41,42]:

$$U\left(x_3\right)=A{\displaystyle \sum _{n=-\infty }^{+\infty }{\displaystyle \sum _{m=-\infty }^{+\infty }{a}_n{b}_m\exp \left(-j\pi p{n}^2\right)\exp \left[-j\pi \frac{\lambda z_3}{M_2}{\left(\frac{n}{M_1{p}_1}+\frac{m}{p_2}\right)}^2\right]\exp \left[j2\pi \frac{x_3}{M_2}\left(\frac{n}{M_1{p}_1}+\frac{m}{p_2}\right)\right]}}$$

(19)

where A is the phase constant, $a_n$ and $b_m$ are the coefficients of the Fourier series of the phase grating G1 and G2, respectively, $x_3$ is the coordinates on the detector plane, $p_1$ and $p_2$ are the periods of G1 and G2, respectively, and the expressions of $p$, $M_1$ and $M_2$ are, respectively,

$$p={\displaystyle \frac{\lambda z_2}{M_1{p}_1^2}}$$

(20)

$$M_1={\displaystyle \frac{z_1+z_2}{z_1}}$$

(21)

$$M_2={\displaystyle \frac{z_1+z_2+z_3}{z_1+z_2}}$$

(22)

where $z_1$, $z_2$, and $z_3$ represent the distances from S to G1, G1 to G2, and G2 to the detector, respectively. When both gratings are π-phase gratings, it is only necessary to analyze the period and phase relationship of the interference fringes formed between the positive and negative first-order and positive and negative third-order diffraction of the phase grating. This allows for determining the optimal imaging fringe period and contrast conditions for the dual π-phase grating interferometer [43].

$$p_3={\displaystyle \frac{1}{2}}{\displaystyle \frac{L{p}_1{p}_2}{z_1{p}_2-\left(z_1+z_2\right)p_1}}$$

(23)

$$\left\{\begin{array}{l}{\displaystyle \frac{\lambda z_3}{M_2}}\left({\displaystyle \frac{1}{p_2^2}}-{\displaystyle \frac{1}{M_1{p}_1{p}_2}}\right)={\displaystyle \frac{2h_1-1}{8}}\\ {\displaystyle \frac{\lambda z_3}{M_2}}\left({\displaystyle \frac{1}{M_1^2{p}_1^2}}-{\displaystyle \frac{1}{M_1{p}_1{p}_1}}\right)+p={\displaystyle \frac{2h_2-1}{8}}\end{array}\right.$$

(24)

where L denotes the total length of the system, h₁ and h₂ are integers. When both gratings are π/2-phase gratings, the optimal imaging fringe period and contrast conditions can be obtained by analyzing the interference fringe period and phase relationship between the positive and negative first-order and zero-order diffraction of the phase grating.

$$p_3={\displaystyle \frac{L{p}_1{p}_2}{z_1{p}_2-\left(z_1+z_2\right)p_1}}$$

(25)

$$\left\{\begin{array}{l}{\displaystyle \frac{\lambda z_3}{M_2}}\left({\displaystyle \frac{1}{M_1^2{p}_1^2}}-{\displaystyle \frac{1}{M_1{p}_1{p}_2}}\right)+p={\displaystyle \frac{2h_1+1}{2}}\\ {\displaystyle \frac{\lambda z_3}{M_2}}\left({\displaystyle \frac{1}{p_2^2}}-{\displaystyle \frac{1}{M_1{p}_1{p}_2}}\right)={\displaystyle \frac{2h_2+1}{2}}\end{array}\right.$$

(26)

where h₁ and h₂ are integers. It is worth noting that whether or not the imaging fringe period of the dual π-phase grating interferometer is twice as long as that under monochromatic illumination when illuminated by polychromatic light requires a comprehensive consideration of whether the system parameters meet the optimal contrast conditions, as expressed in Equation (23). Many properties of the dual-phase grating interferometer and the Talbot–Lau interferometer are closely related. For instance, as one of the phase grating periods approaches infinity, the fringe period, source grating period, and contrast optimization conditions of the dual-phase grating interferometer can be transformed into those of the corresponding Talbot–Lau interferometer. However, the dual-phase grating interferometer has a longer system length, lower light flux utilization efficiency, and reduced sensitivity.

3.4.3. Inverse Talbot–Lau Interferometer

In 2009, an inverse geometry Talbot–Lau system was proposed by T. Donath and colleagues [44]. This innovative system eliminates the need for an absorption grating. Refer to Figure 8 for its structural diagram, where Figure 8a illustrates the configuration of the inverse Talbot–Lau interferometer, and Figure 8b depicts the standard Talbot–Lau interferometer. The primary distinction between the two systems lies in the positioning of the phase grating G1; one is located closer to the light source, while the other is situated nearer to the detector. Due to the proximity of the phase grating in the inverse geometry Talbot–Lau interferometer to the light source, it provides higher imaging magnification than the standard Talbot–Lau interferometer, facilitating self-imaging with enhanced magnification. The coherence length of this system is comparable to the pixel size of current large-area X-ray detectors. When the period of self-imaging of phase grating G1 exceeds the pixel size of the detector, its self-image can be directly captured by the detector, thereby eliminating the need for an absorption grating. This significantly enhances the utilization rate of rays, consequently reducing the radiation dose received by the sample. In 2011, Momose from Japan conducted further research on the inverse Talbot–Lau imaging method, theoretically demonstrating its feasibility and performing a preliminary verification test [45]. In 2014, Morimoto from Osaka University in Japan published experimental results on inverse Talbot–Lau phase-contrast imaging [46]. Zhu Peiping from China conducted theoretical research on this imaging technique and proposed the angle signal theory [47], providing system parameters for the inverse Talbot–Lau phase-contrast imaging system used in breast diagnostics. These studies collectively illustrate the feasibility of inverse Talbot–Lau phase-contrast imaging from various perspectives. The inverse Talbot–Lau system addresses the challenges associated with manufacturing large-area, high-efficiency absorption gratings, simplifies the structure of the X-ray phase-contrast imaging system, and further reduces the complexities involved in its production. Due to its simplified structure and diminished manufacturing challenges, this system has significantly contributed to the advancement and widespread adoption of X-ray phase-contrast imaging technology. This is particularly beneficial for enhancing the application of X-ray phase-contrast imaging in biomedicine and clinical settings, representing a promising future direction for grating phase-contrast imaging.

3.4.4. Single-Grating X-Ray Imaging

In 2008, the phase and scattering information of an object were successfully extracted by Han Wen and colleagues using the Fourier transform method with a single-grating system [48,49,50]. A more straightforward imaging system structure and reduced exposure time were utilized in this approach, requiring only a single exposure in contrast to the traditional Talbot–Lau interferometer imaging method. The X-ray imaging system consists of an X-ray source, an absorption grating, and a detector, as illustrated in Figure 9. The object to be measured is positioned between the grating and the source. The single-grating X-ray radiation emitted by the source is irradiated onto the target object. Due to variations in the refractive index within the object, the wavefront of the X-rays passing through will deform as the internal structure of the object changes. The transmitted X-rays carry information about the object’s internal structure, and their intensity is modulated by the periodic grating structure before being received and processed by the detector. The phase and scattering information of the X-ray image is subsequently extracted through data processing. However, because the Fourier transform method is employed to extract phase-contrast and dark-field information, some high-frequency data are lost, resulting in a decrease in resolution and the introduction of Moire artifacts, which diminish the image’s signal-to-noise ratio (SNR) [51,52]. In 2018, Lee H.W. and colleagues effectively suppressed the Moire artifacts by employing a rotating grating method, achieving promising results in their experiments. However, the image signal-to-noise ratio (SNR) of single grating imaging is low, resulting in poor quality. Therefore, the extraction methods for phase contrast and dark field information need further optimization to enhance the SNR. Optimizing the extraction method for phase-contrast and dark-field information, along with enhancing the SNR, has become a central focus of research in X-ray single-grating imaging systems.

3.4.5. X-Ray Phase-Contrast Imaging Based on Wave-Front Coding

In 2007, A. Olivo and colleagues from the University of London introduced a phase-contrast imaging method based on wavefront coding [53], referred to as the coded aperture method or edge illumination method [54]. This non-coherent imaging technique [55,56] utilizes standard X-ray tubes to achieve image quality comparable to that obtained under synchrotron radiation source conditions. The schematic diagram of the experimental setup is illustrated in Figure 10. The experimental configuration consists of an X-ray source, two absorption gratings (G1 and G2), and a detector. The working principle is as follows: when the thin beam of X-rays passes through the first grating (G1) and strikes the edge of the transparent portion of the second grating (G2), the presence of an object in the optical path causes the X-rays to refract. This refraction enhances or diminishes the light at the edge of the transparent section of G2, thereby producing the phase contrast of the object. The essence of this imaging method lies in fine beam imaging. After passing through G1, the X-rays become narrower, resulting in each detector pixel receiving less information about the object, which is akin to reducing the pixel size of the detector. Consequently, the finer the beam, the more pronounced the phase-contrast effect.

In 2012, MUNRO R.T. et al. successfully separated phase-contrast signals from absorption signals using their system [57]. The process of signal recovery involves capturing two images of the objects. First, an image is taken, followed by a movement of the grating (G1 or G2) along the direction perpendicular to the optical axis by half a grating period, after which the second image is captured. By utilizing these two images, the extraction and recovery of phase-contrast signals can be accomplished. In 2014, Endrizzi M. et al. employed incoherent systems to capture three images of breast samples, successfully restoring three types of images: absorption, refraction, and scattering [58]. This method offers a rapid imaging speed; however, the use of two absorption gratings in the imaging system results in a relatively low light utilization rate.

4. Primary Performance Indexes of X-Ray Grating Phase-Contrast Imaging

4.1. Variance of Signal

The Talbot–Lau interferometer is currently the leading device for phase-contrast imaging. A smaller variance in the recovered signal indicates lower system noise and a higher signal-to-noise ratio. The following sections introduce the primary factors that affect absorption, phase-contrast, and scattering image noise. The results are presented in

Table 2. Some factors that affect absorption, phase-contrast, and scattering signals of the sample [59].

Signal Type	With Sample	Without Sample
${\left({\displaystyle \frac{{\sigma }_T}{T}}\right)}^2$	${\displaystyle \frac{f_1^r}{N{a}_0^r}}\left(1+{\displaystyle \frac{f_1^o}{T{f}_1^r}}\right)$	${\displaystyle \frac{2f_1^r}{N{a}_0^r}}$
${\left({\sigma }_{DP}\right)}^2$	${\displaystyle \frac{f_1^r}{2{\pi }^2{v}^{r^2}N{a}_0^r}}\left(1+{\displaystyle \frac{f_1^o}{f_1^{r}T{V}^2}}\right)$	${\displaystyle \frac{f_1^r}{{\pi }^2{v}^{r^2}N{a}_0^r}}$
${\left({\displaystyle \frac{{\sigma }_V}{V}}\right)}^2$	${\displaystyle \frac{f_1^r}{v^{r^2}N{a}_0^r}}\left[v^{r^2}\left(1+{\displaystyle \frac{f_1^o}{f_1^{r}T}}\right)+2\left(1+{\displaystyle \frac{f_1^o}{f_1^{r}T{V}^2}}\right)\right]$	${\displaystyle \frac{2f_1^r}{v^{r^2}N{a}_0^r}}\left(v^{r^2}+2\right)$

:

${\sigma }_T$, ${\sigma }_{DP}$, and ${\sigma }_V$ are the standard deviations of the recovered absorption, phase-contrast, and scattering signals, respectively, and T and V are the absorption and scattering signals, respectively. ν is the contrast of the phase shift curve, N is the number of phase shift steps, $a_0$ is the average number of photons with N times of phase shift, and the superscript “o” and “r”, respectively, indicate the case with or without samples. $f_1$ is the proportional coefficient between the variance ${\sigma }_I^2$ of detector output light intensity and the average light intensity $\overline{I}$, and the relationship between the three is as follows:

$${\sigma }_I^2=f_1\stackrel{-}{I}$$

(27)

The simulation and experimental curves depicting the relative standard deviation of absorption, phase-contrast, and scattering signals as a function of average light intensity in the phase shift curve are illustrated in Figure 11. The blue circle represents the experimental data obtained from the source grating without a sample, utilizing a duty cycle (the ratio of the width of the light transmission section to the period) of 0.3. The blue curve corresponds to the simulation results. The green cross indicates the experimental data collected using a 5 mm thick aluminum plate as a sample, also with a source grating featuring a duty cycle of 0.3. The green short line represents the corresponding simulation curve. The red box illustrates the experimental data measured with the source grating without a sample, employing a duty cycle of 50%, while the red dotted line denotes the associated simulation curve. The relative uncertainties in T, DP, and V were measured for a tube voltage of 50 kV as a function of the mean intensity $a_0^r$, in the background case with v^r = 0.23 (round markers), in the background case with v^r = 0.16 (square markers), and within the 5 mm aluminum plate (T = 0.27 and V = 0.55) with a visibility v^r = 0.23 (cross markers). Each phase stepping series was performed over one period of G0 for a total of 12 phase steps, and the exposure time was set to 6.7 s for each raw image. For each situation, the quantitative estimations of the model are indicated with solid lines (dotted line and dashed lines).

It can be observed from the comparison between the red box and the blue circle in Figure 11 that a higher contrast in the phase shift curve corresponds to reduced noise in both the phase-contrast signal and the scattered signal. Additionally, utilizing a source grating with a small duty cycle can enhance the contrast of the phase shift curve. The comparison between the blue circle and the green cross indicates that the noise levels of absorption, phase-contrast, and scattering signals increase with the introduction of the object. This increase in noise occurs because the light intensity received by the detector diminishes when the object is present. Therefore, to minimize noise and improve the signal-to-noise ratio, it is essential to enhance both the contrast of the phase shift curve and the X-ray luminous flux of the system as much as possible. The primary factors influencing the contrast of the phase shift curve in the system include the spectrum, the duty cycle of the source grating, the transmittance of the source grating, and the duty cycle of the phase grating. When employing a phase grating with a duty cycle of 70%, the contrast of the phase shift curve in the Talbot–Lau interferometer can exceed 50% at a voltage range of 40–45 kVp [60]. Figure 12 illustrates the variation in contrast of the phase shift curve generated by a 4 μm periodic phase grating, considering both the duty cycle of the source grating (a) and the transmittance of the X-ray absorption component of the source grating (b) at a voltage of 40 kVp. As shown in Figure 12, an increase in the duty cycle of the source grating (i.e., a larger duty cycle of the light-transmitting portion) or an enhancement in the transmissivity of the opaque section results in a decrease in the contrast of the phase shift curve.

4.2. Sensitivity of the System

In the grating-based, X-ray phase-contrast imaging system, sensitivity is defined as the fringe phase shift induced by the unit refraction angle of X-rays passing through the object, as follows:

$$S={\displaystyle \frac{1}{2\pi }}{\displaystyle \frac{\Delta \varphi }{\alpha }}$$

(28)

where S represents the sensitivity of the system, α denotes the refraction angle produced by X-rays passing through the object, and Δϕ signifies the corresponding fringe phase shift. When the object is positioned between the source grating and the phase grating, the sensitivity of the Talbot–Lau interferometer can be derived from geometric relationships as follows:

$$S={\displaystyle \frac{z_s}{p_0}}$$

(29)

where $z_s$ indicates the distance between the object and the source grating, and $p_0$ represents the period of the source grating. Equation (27) demonstrates that when the object is positioned between the source grating and the phase grating, the closer the object is to the phase grating, or the smaller the period of the source grating, the greater the system’s sensitivity.

When the object is positioned between the phase grating and the analysis grating, the sensitivity of the Talbot–Lau interferometer is defined as follows:

$$S={\displaystyle \frac{z_D}{p_2}}$$

(30)

where $z_D$ represents the distance between the object and the analysis grating, and $p_2$ denotes the period of the analysis grating. Equation (28) indicates that when the object is positioned between the phase grating and the analysis grating, the system’s sensitivity increases as the object approaches the phase grating or as the period of the analysis grating decreases. The experimental results, which illustrate the relationship between the phase shift induced by the object and its position, were obtained using the Talbot–Lau interferometer and are presented in Figure 13. These findings demonstrate that as the object moves closer to the phase grating G1, the fringe phase shift increases, resulting in a more sensitive system, which is consistent with the theoretical analysis.

In the grating-based, X-ray phase-contrast imaging system, sensitivity is defined as the fringe phase shift induced by the unit refraction angle of X-rays passing through the object. Specifically, for a two-phase grating interferometer, the variation in sensitivity with the object’s position closely resembles that of the Talbot–Lau interferometer [62,63]. In other words, the closer the object is to the phase grating, the greater the system’s sensitivity. The qualitative experimental results are illustrated in Figure 14, where the numbers “1, 2, 3, …” in Figure 13a correspond to “position 1, position 2, position 3, …” in Figure 13b, indicating the object’s position.

5. Important Applications of X-Ray Grating Interferometer

The grating interferometer can simultaneously capture absorption, phase-contrast, and scattering images of the measured object. This capability allows for a clearer and more distinct diagnosis of signal characteristics compared to traditional imaging methods, leading to significant applications in medical clinical diagnosis.

5.1. Application of X-Ray Phase-Contrast Imaging

In the hard X-ray band, the phase factor of substances composed of light elements is over three orders of magnitude greater than the absorption factor. This results in phase-contrast images that are richer in detail compared to absorption images. X-ray phase-contrast imaging technology captures internal information of an object by detecting changes in phase after X-rays pass through the material, thereby revealing more intricate details than traditional X-ray absorption imaging. Consequently, X-ray phase-contrast imaging technology provides significant advantages in detecting the structures of light element substances, demonstrating high application value in the fields of biomedical research and clinical medical diagnosis, particularly in the early detection of cancer.

Grating-based phase-contrast imaging has proven to be effective in medical clinical diagnosis, particularly in the detection and accurate characterization of various subtypes of renal cell carcinoma (RCC). Existing clinical imaging methods have limitations that are critical for the treatment and prognosis of RCC. Literature reports indicate that grating-based X-ray phase-contrast computed tomography (gbPC-CT) holds significant potential for visualizing and characterizing human RCC subtypes. A comparison was made between the results of 23 formalin-fixed isolated human kidney specimens using gbPC-CT, absorbed CT (abCT), clinical CT (clinCT), and 3T MRI. The findings demonstrate that grating-based phase-contrast CT exhibits strong visual consistency with the results of hematoxylin and eosin (HE) staining. GbPC-CT can clearly distinguish between large and small tumor nodules (**), as well as low signal areas, and it can diffuse intratumoral bleeding (indicated by the arrow), a fatty region (indicated by the arrowhead), and a large vessel at the bottom of the slice, as shown in Figure 15B. The meaning of the markings: the tumor nodules (**), diffuse intratumoral bleedings (arrow) and a fatty area (arrowhead). GbPC-CT (B) demonstrated superior visualization of tumor boundaries and various tumor nodules (**) compared to abCT (C) and clinical CT (F), which could only detect fat (arrowhead) and soft tissue (area of hyperdensity). GbPC-CT imaging (A) provided a clearer depiction of tumor components, such as intratumoral bleeding, than MRI images (D and E), which were affected by susceptibility artifacts.

Table 3. Detection of different tumor components in gbPC-CT, abCT, clinCT, and MRI compared with histopathologic findings.

Signal Type	gbPC-CT/Histo	abCT/Histo	clinCT/Histo	MRI/Histo
Fibrous strands	15/15	0/15	0/15	4/15
Pseudocapsule	8/9	0/ 9	0/9	6/9
Calcification	9/17	17/17	4/17	*
Microbleeding	10/11	0/11	0/ 11	*
Diffuse hemorrhage	5/5	3/5	2/5	5/5
Hyalinization	6/8	6/8	2/8	6/8
Necrosis	2/3	0/3	0/3	1/3

* Small susceptibility artifacts in susceptibility weighted images (SWI) in 17 samples.

presents a comparison of the detection and pathological characteristics of various tumor components, including fibrous strands, pseudocapsules, calcifications, microbleeding, diffuse hemorrhage, hyalinization, and necrosis, using grating phase imaging (gbPC-CT), abCT, clinCT, and MRI. The results indicate that gbPC-CT demonstrates high sensitivity for detecting soft tissue components. It has a strong detection rate for fibrous bundles, pseudocapsules, microbleeds, diffuse hemorrhage, and other components, significantly outperforming abCT, clinCT, and MRI. However, gbPC-CT exhibits a low detection rate for necrosis and hyalinization, while clinCT shows the lowest sensitivity overall.

When a patient’s fingers are affected by rheumatoid arthritis, the cartilage in the finger joints can become thinner or may even completely disappear, leading to joint deformation and significant pain for the patient. Therefore, early diagnosis and intervention for rheumatoid arthritis are crucial to prevent further deterioration of the condition. Figure 16a–c illustrate the absorption, scattering, and phase-contrast images of the finger joint restored using a Talbot–Lau interferometer, while Figure 16d presents the corresponding MRI image [66]. The white arrow in Figure 15C indicates the cartilage in the finger joint. In Figure 16d, the cartilage appears white, whereas in Figure 15A,B, the cartilage is not visible. Consequently, by obtaining the phase-contrast image of the finger joint using a Talbot–Lau interferometer and measuring the cartilage thickness, it is possible to determine whether the patient has early-stage rheumatoid arthritis.

The Talbot–Lau interferometer can be utilized to obtain clear images of the trachea in small animals [67], as illustrated in Figure 16. Figure 17a–c display the absorption, phase-contrast, and scattering images of rats, respectively. The arrow in Figure 17b points to the trachea, which is not visible in the other two contrast mechanisms, thereby highlighting the unique advantages of phase-contrast imaging for visualizing weakly absorbing materials. Furthermore, the area indicated by the arrow in the scattering image of Figure 17c represents the lung of a mouse, emphasizing that scattering images provide distinct morphological details and are unaffected by surrounding bones. This underscores the significant potential of scattering information in the diagnosis of lung diseases.

5.2. Application of X-Ray Scattering Image

X-ray scattering images, also known as X-ray dark-field images, are produced using a grating-based X-ray phase-contrast system. These images reveal disease information that is not detectable through absorption imaging during clinical examinations of the human lungs and chest, offering a novel technological approach for medical diagnosis.

By comparing the contrast ratio of the phase shift curve of the Talbot–Lau interferometer with and without sample objects, the ultra-small angle scattering image of X-rays, commonly referred to as the scattering image, can be calculated. The numerous alveoli in the lungs create a vast number of interfaces with air. As X-rays traverse these interfaces, they undergo multiple refractions, causing the propagation direction of the X-rays to spread within a narrow angular range after emission. This phenomenon results in a decrease in the contrast of the phase shift curve. In 2017, Scherer K. and colleagues employed the Talbot–Lau interferometer to conduct imaging tests on mouse lungs [68], confirming that the scattering signals from mouse lungs were highly sensitive, while those from other tissues were significantly weaker. This sensitivity enables the diagnosis of small pulmonary nodules. Through the diagnosis of eight mice with lung tumors, it was found that the scattering image could detect at least 92% more tumors than the absorption image. In 2021, Willer K applied the Talbot–Lau interferometer in clinical practice to image the lungs of a long-term smoker. The absorption image of his lungs (Figure 18A) showed no evident signs of structural damage, and the dark-field values of most regions of his lungs (Figure 18B) were comparable to those of healthy lungs. However, the affected areas of his lungs appeared dark, which was attributed to a reduction in air–tissue interfaces, decreased small-angle scattering, and consequently, a significant decrease in signal. These findings suggest that dark-field imaging plays a crucial role in the clinical diagnosis of lung structural injuries.

By utilizing the ratio r of absorption to scattering information, one can effectively differentiate between two types of calcifications in the breast: calcium oxalate dihydrate and calcium carbonate [70]. Figure 18A depicts an isolated breast sample, where the red circle marks calcium phosphate and the blue circle denotes calcium oxalate dihydrate. Figure 18B illustrates the distribution of r-values for the corresponding calcifications. Evidently, Figure 19b shows a distinct boundary between the r-values of their two calcifications, enabling the identification of their type based on the r-value.

6. Key Components of the Grating-Based X-Ray Phase-Contrast Imaging

Grating-based X-ray phase-contrast imaging is one of the most promising techniques in this field, demonstrating significant market potential. It currently represents the leading method for phase-contrast imaging. In a grating-based phase-contrast imaging system, X-ray grating and spatially coherent light source are the two most critical components. The source grating, G0, and the analysis grating, G2, are both absorption gratings, while grating G1 functions as a phase grating. The generation of spatially coherent light can be achieved using either a structured anode X-ray source or a combination of a large focal spot X-ray source and a source grating.

6.1. X-Ray Phase Grating

An X-ray phase grating is an optical component that periodically modulates the phase of X-rays. For the X-ray phase grating to produce self-imaging with a specific contrast, the transverse coherence length of the X-rays at the phase grating must be comparable to the period of the phase grating. Typically, the transverse coherence length of X-rays generated by a microfocus X-ray source is in the submicron range, while the period of the phase grating is in the micron range. Since the phase grating directly limits the system’s field of view, larger samples necessitate a greater area of the phase grating. Common materials used to generate phase shifts in the phase grating include silicon, gold, and nickel [72,73]. According to Formula (1), at the same X-ray energy, a higher atomic number of the phase-shifting material results in a smaller required material thickness and a lower aspect ratio requirement for the phase grating. For example, under X-ray illumination with an energy of 28 keV, silicon requires a thickness of 36 μm to achieve a π phase shift, whereas gold only requires 5.4 μm. Reduced material thickness contributes to a lower aspect ratio, thereby facilitating the fabrication of the grating.

Currently, the technology for manufacturing X-ray phase gratings is relatively mature, enabling the production of phase gratings with good uniformity. There are several methods for fabricating phase gratings: LIGA (lithography, electrodeposition, and replication), DRIE (Deep Reactive Ion Etching), and Wet Chemical Etching.

LIGA technology was developed in the 1980s to produce high-aspect-ratio micro-nano devices, offering advantages such as high aspect ratio and good sidewall steepness. Currently, it has the capability to create micro-nano structures with an aspect ratio exceeding 100 through exposure and development on photoresist. The technical process is illustrated in Figure 20.

DRIE can create microstructures with steep sidewalls and high aspect ratios in materials such as silicon, which falls under the category of dry etching. When etching silicon substrates using this technology, the etching gas (such as sulfur hexafluoride) simultaneously etches both the grooves and the sidewalls of the substrate material. Consequently, after a certain period of etching, it is essential to introduce a protective gas (such as octafluorocyclobutane) to form a protective film on the surface of the sidewalls, thereby reducing corrosion from the etching gas. Subsequently, the etching gas continues to further etch the grooves downward for a specified duration, while the protective gas safeguards the newly exposed sidewalls. Through this continuous cycle of “Etching-Passivation-Etching”, microstructures with high aspect ratios can be achieved [75], as illustrated in Figure 21a,b.

High-aspect-ratio phase gratings can also be fabricated using wet etching. The fabrication process consists of several steps. The first step involves the creation of electrodes. Initially, a layer of silicon nitride is deposited on the front side of the silicon wafer. This is followed by transferring the mask pattern onto the silicon nitride using photolithography, and then plating a layer of aluminum on the opposite side of the silicon to serve as a transparent electrode. The second step involves etching the tip on the front side of the silicon wafer using a potassium hydroxide solution with a concentration of approximately 10%. Subsequently, a voltage is applied across the silicon wafer, and the backside is illuminated with a tungsten halogen lamp. This illumination generates electron–hole pairs on the backside of the silicon due to light exposure, and the holes migrate toward the tip on the front side of the silicon wafer under the influence of an external electric field. Guided by the holes, the etching solution, hydrofluoric acid, continuously corrodes the tip, while the sidewalls remain largely uncorroded, thereby producing the grating structure. As illustrated in Figure 21c, a phase grating with a period of 3 microns and a depth of 150 microns is achieved through wet etching.

6.2. X-Ray Absorption Grating

The X-ray absorption grating is a component that periodically modulates the amplitude of X-rays. To optimize X-ray absorption, a thicker absorption material is necessary. Due to the small grating period, the absorption grating exhibits a high aspect ratio, typically ranging from tens to hundreds. The primary fabrication methods for X-ray absorption gratings include LIGA, atomic layer deposition, micro-casting, nanoparticle filling, and all-metal stacking molding. The fabrication process of an X-ray absorption grating using the LIGA method is similar to that of a phase grating; however, it requires the plating of a thicker absorption material. Additionally, LIGA technology heavily depends on synchrotron radiation light sources and specialized mask plates. Given the limited availability of synchrotron radiation light sources, along with the high operational and maintenance costs and the lengthy fabrication time required for high-precision, high-aspect-ratio gratings, the production costs are prohibitively high, making mass production unfeasible. The atomic layer deposition (ALD) method involves depositing a layer of iridium of the desired thickness onto the sidewalls of a prefabricated grating structure, which serves as the X-ray absorption layer, thereby creating the absorption grating, as illustrated in Figure 22. Compared to the method of first fabricating electrodes followed by electroplating, the ALD method excels in uniformity and thickness control. However, it is particularly advantageous for the fabrication of small-period gratings (e.g., less than 1 μm) with high aspect ratios. For gratings with larger periods, the ALD process requires extended time, and iridium is an expensive material, resulting in a high overall cost.

Another method for fabricating absorption gratings is micro-casting [78]. This technique employs bismuth, a metal recognized for its low cost, low melting point, and high atomic number, as the X-ray absorbing material. To fabricate an absorption grating using micro-casting, it is first necessary to prefabricate the grating structure, as depicted in Figure 23. To facilitate the smooth entry of liquid bismuth into the grating grooves, the sidewalls of these grooves must be oxidized, thereby enhancing the wettability between the bismuth and the groove sidewalls.

Subsequently, the bismuth and the grating structure are placed in a high-temperature, high-pressure furnace, where a vacuum is created to expel as much air as possible from the grating grooves, thereby increasing the bismuth filling rate. The bismuth is heated to its liquid state, and the grating structure is immersed in the molten bismuth to initiate the filling process. During this process, nitrogen or argon gas is introduced into the high-temperature, high-pressure furnace to elevate the internal pressure, while the bismuth is continuously stirred to ensure optimal flow into the grooves. Upon completion, the grating structure is separated from the liquid bismuth, any excess bismuth on the surface is removed, the heat source is turned off, and the structure is extracted from the furnace once its temperature has cooled to room temperature. The literature indicates that an absorption grating with a 3 μm period and a 150 μm depth can be fabricated using the micro-casting method, as illustrated in Figure 23a. Besides absorbing X-rays, the micro-casting method can also be employed to incorporate fluorescent materials, such as cesium iodide, to create an X-ray conversion screen with analytical grating capabilities, as illustrated in Figure 23b. This analytical grating conversion screen offers two significant advantages. Firstly, for analytical gratings that rely on heavy metals to absorb X-rays, increased X-ray energy can lead to incomplete absorption, which adversely affects the contrast of the phase–shift curve. In contrast, conversion screens equipped with analytical gratings do not encounter this problem, as areas not filled with fluorescent materials do not emit visible light and thus remain undetected by the detector. Conversely, areas filled with fluorescent materials can convert X-rays into visible light, thereby enhancing the contrast of the phase–shift curve. Furthermore, because the fluorescent material is separated by silicon sidewalls, the visible light produced in adjacent grooves does not interfere with one another, significantly improving the system’s resolution. When the conversion screen depicted in Figure 23b is coupled with a CCD featuring a pixel size of 13.5 μm through panel coupling, a resolution of 20 lp/mm is achieved, as demonstrated in Figure 23c.

In recent years, novel methods for manufacturing absorption gratings have emerged. These methods involve stacking two types of metal films, such as aluminum and tantalum or aluminum and silver, which exhibit significant differences in X-ray absorptivity. The upper and lower ends of the stacked structure are then secured using molds. After curing and molding, the structure is sliced, resulting in the creation of an all-metal absorption grating. This process, known as the film stacking method, has been described in various ways in the literature, as illustrated in Figure 24. A team from Tokyo University utilizes solder to cure the film stacking structure [80], while a team from Shenzhen University heats and cures the fixed stacking structure in a vacuum high-temperature furnace. This heating process causes the metals of the two different materials to interdiffuse at their contact surfaces, forming a robust composite [81]. Ultimately, the cured membrane stacking structure is cut to a specific thickness as required, thus producing the absorption grating. Theoretically, this method of fabricating gratings through film stacking can produce absorption gratings with an infinitely high aspect ratio, making it highly suitable for mass production of hard X-ray absorption gratings. This approach not only reduces the production costs and difficulties associated with X-ray absorption gratings but also lends itself to large-scale market promotion.

6.3. Spatial Coherent Structured X-Ray Source

In Talbot–Lau, inverse Talbot–Lau, or two-phase grating interferometers, high-throughput spatially coherent structured light is essential. This light is typically provided by a source grating coupled with a large focal spot X-ray tube. However, there are two significant disadvantages associated with using the source grating. First, the opaque regions of the source grating necessitate complete absorption of X-rays by the imaging system. However, for cone beam X-rays, this requirement cannot be met due to the effects of energy and divergence. Second, the high aspect ratio of the source grating permits only small-angle X-rays emitted by the light source to pass through, while large-angle X-rays are partially absorbed by the source grating. This not only impacts the imaging field of view but also diminishes the quality of the transmitted coherent light.

To address these issues, in 2007, Professor Guo from Shenzhen University proposed a novel X-ray source. By fabricating a microstructure on the surface of the anode target, a line emitter array structure was created, resulting in an X-ray source with a structured anode. The emitted X-rays exhibit spatial coherence, thereby eliminating the need for a source grating. In 2011, a type of X-ray source developed using this approach was reported in the literature [81,82]. The periodic structure on the anode target surface was fabricated through mechanical processing. The microstructure of the anode target is depicted in Figure 25a, with a periodicity of 42 μm. Electrons are incident on the structured anode from top to bottom. The electrons bombarding the target surface generate spatially coherent X-rays, while those striking the grooves produce X-rays that are absorbed by the anode target itself. The intensity distribution of the generated X-rays is illustrated in Figure 25b. Although there is potential for further optimization of the uniformity of the generated X-rays, distinct stripe-structured light can still be observed, confirming the feasibility of utilizing a structured anode to create a spatially coherent structured light source.

Fabricating micron-scale, small-period microstructures through mechanical processing presents significant challenges. Consequently, the fabrication of structured anode X-ray sources with periods of several microns necessitates higher precision in reactive ion etching and sputtering filling processes. In 2014, Naoki Morimoto from Japan employed a transmission-type microstructure anode target X-ray light source, as illustrated in Figure 26. This method involves etching grooves with periodic structures on a commercial polycrystalline conductive diamond substrate using reactive ion etching technology. Subsequently, copper (Cu) is utilized as the anode material to fill the grooves through a sputtering process, resulting in a transmission-type multi-microstrip structured anode target. The width of the Cu microstrip on the anode target surface measures 1 μm, while the period of the strip microstructure is 3 μm. This multi-microstrip anode target is employed to construct a compact Talbot interferometer system, which includes an X-ray source, grating, and detector, thereby enabling the acquisition of absorption, phase, and dark-field information.

In 2019, American scholar Zan Guibin published the results of design optimization for a microstructure anode X-ray source intended for hard X-rays. He conducted parameter design and spectral calculations for microstructure anode targets composed of tungsten (W), molybdenum (Mo), and copper (Cu) materials, providing a theoretical foundation for the development of a hard X-ray microstructure anode target X-ray source [84]. In 2021, additional research reported on a microstructure anode X-ray source for hard X-rays, as illustrated in Figure 27 [85]. The fabrication method for its anode target is similar to the approach proposed by Morimoto, which involves etching a groove array structure onto a diamond substrate and subsequently filling the grooves with metal tungsten strips. When the electrons emitted by the cathode filament are subjected to an electric field, they bombard the microstructure anode at high speeds, generating spatially coherent structured X-rays.

Spatially coherent X-ray sources are highly significant for simplifying the structure of grating imaging systems while providing high-throughput, high-contrast spatially coherent X-rays. By substituting the source grating with a micro-structured target, these sources circumvent the limitations imposed by the source grating on the emittance of spatially coherent X-rays, thereby significantly enhancing the imaging field of view. They serve as an ideal light source for grating interferometers. In the development of spatially coherent X-ray sources, it is essential to explore production processes and control costs to provide technical support for the large-scale promotion and application of grating interferometers.

6.4. The Groundbreaking Efforts of Our Team

The grating-based phase-contrast imaging system offers high imaging quality and exceptional application potential. However, its widespread market adoption requires bold innovations from industry researchers in the craftsmanship and cost control of essential components. Our team conducted extensive research on key devices for grating-based phase-contrast imaging, including absorption gratings and a spatially coherent anode-structured target X-ray source. In this field, we have proposed numerous groundbreaking and beneficial initiatives. For example, we developed a low-cost production method for large-area gratings by introducing a micro-casting technique during the fabrication process (as illustrated in Figure 23). Additionally, we proposed a production scheme for all-metal gratings (as illustrated in Figure 24), facilitating the low-cost mass production of high-energy X-ray gratings. Furthermore, we designed and successfully fabricated a structured anode X-ray tube (as illustrated in Figure 25), which simplifies the structure of the grating phase-contrast imaging system and presents promising prospects. Moving forward, our team remains dedicated to the low-cost manufacturing and promotion of grating phase-contrast imaging systems.

7. Conclusions and Prospects

Grating-based phase-contrast imaging is an X-ray phase-contrast imaging technology that is well suited for large-scale applications, particularly in the field of clinical medical diagnosis. Its primary research focus is on system integration and simplification. Its clinical effectiveness has already been demonstrated in various areas, including the detection of articular cartilage thickness, examination of breast calcifications, and screening for lung nodules and tumors. However, there remains potential for further clinical applications that are yet to be developed and validated. In the case of the Talbot–Lau interferometer, the extensive use of gratings in its design necessitates further advancements in dose control and signal sensitivity, highlighting the need for breakthroughs in both methodology and device manufacturing technology.

In terms of methodology, several areas present opportunities for breakthroughs. Firstly, advancing research on new theories and methods for X-ray phase-contrast imaging is essential. For instance, in the Talbot–Lau interferometer, we typically assume that X-rays refract after passing through an object. However, in coaxial imaging, we must consider why X-rays diffract after passing through an object. Can this phenomenon be explained by the same theory? Addressing this question may lead to a deeper understanding of the mechanisms underlying X-ray phase-contrast imaging, potentially resulting in new methods to enhance signal quality. Secondly, employing a more compact inverse geometry Talbot–Lau interferometer system could improve the utilization rate of X-rays. However, this necessitates the use of a source grating with a shorter period, thereby increasing the production demands on the source grating.

In terms of device fabrication, significant advancements can be made in two areas: light sources and gratings. Firstly, the development of an X-ray source with high brightness and high spatial coherence can reduce imaging time and minimize the impact of vibrations. High coherence enhances image clarity and reduces blur, thereby emphasizing weak phase-contrast signals. Spatially coherent X-ray sources, which do not require a source grating, provide higher brightness, improved contrast, and a wider field of view. These sources function as high-quality spatially coherent light sources for grating interferometer systems, specifically designed to align with the parameters of both the Talbot and inverse Talbot systems. Secondly, for the Talbot system, there is a need to further develop conversion screen technologies that feature large surface areas, excellent uniformity, and effective analytical grating capabilities. This advancement will reduce reliance on analytical gratings, simplify the system’s structure, and enhance signal extraction capabilities. Analytical grating conversion screens can minimize visible light diffusion within the screen while maintaining high light output efficiency, thereby improving resolution. Theoretically, these screens can produce 100% contrast fringes for incident X-rays, which enhances the contrast of the phase–shift curve and reduces detection signal noise. Thirdly, there is a pressing need for innovative, high-quality, and cost-effective manufacturing processes for gratings. In fields such as bioengineering and clinical medicine, there is a substantial demand for hard X-ray gratings that offer extensive imaging fields and high aspect ratios. This highlights the necessity for economical manufacturing techniques that can produce high-quality hard X-ray gratings. A novel manufacturing process for absorption gratings, such as metal film stacking, is particularly well suited for the production of large-area, high-quality X-ray absorption gratings.