# Principles of Different X-ray Phase-Contrast Imaging: A Review
## 1 Introduction  
As discovered by [PERSON], X-rays are electromagnetic waves with wavelengths ranging from approximately \(10^{-12}\) to \(10^{-8}\) m. The X-ray source, which is usually called an X-ray tube, is a vacuum chamber containing the anode and the cathode. When a high current is applied to the cathode, its temperature increases, so electrons are released from it. High potential is applied between the cathode and the anode, so the electrons are accelerated towards the anode. These electrons stop suddenly after hitting the anode. The loss of energy is then released in the form of X-ray photons. This is called bremsstrahlung radiation. If the electrons knock out the core electron on the anode, the valence electron falls to fill the core-shell. During this transition, the loss of energy is released in the form of X-ray photons, which is the characteristic radiation. When transmitted through materials, the intensity of the X-ray beam changes owing to the different absorption coefficients of materials, allowing the observation of the internal features of objects using noninvasive X-ray imaging. The absorption images of low-Z materials exhibit poor contrast under X-ray irradiation. Theoretically, phase-contrast X-ray imaging has higher contrast and sensitivity than conventional absorption imaging. Higher contrast makes the different compositions of an object more distinguishable [1; 2]. In this review, we did not differentiate between phase-contrast imaging and phase imaging, as [PERSON] did in a previous review [2]. Instead, we refer to all X-ray imaging that contains phase information as X-ray phase imaging. The main streams of X-ray phase imaging include but are not limited to [PERSON]'s X-ray microscopy [3; 4], X-ray holography [5], differential X-ray microscopy [6; 7], coherent diffraction microscopy [8], crystal interferometer [9], grating interferometer [10; 11], diffraction-enhanced imaging (DEI) [12], and propagation-based techniques [13]. In [PERSON]'s X-ray microscopy, a phase ring is inserted to phase-shift the undiffracted light so that the light that has been phase-shifted by the object constructively or destructively interferes with the undiffracted light, which both increase the contrast. In X-ray holography, a coherent wave passes through an object and forms interference patterns on the photographic plate. After being illuminated by the coherent wave without the object, a pair of twin images appearat both sides of the photographic plate. Differential X-ray microscopy was performed by inserting a pair of parallel and laterally displaced zone plates upstream of the sample. The incident beam splits into zeroth- and higher-order spherical waves after the zone plates. The combinations of the zeroth-order in the first zone plate and the first order in the second zone plate and vice versa interfere with each other and form diffraction patterns. Coherent diffraction imaging (CDI) is a lensless method that uses an iterative algorithm to retrieve phase information. A crystal interferometer uses a crystal that is separated into a splitter, a mirror, and an analyzer with two grooves. The splitter splits the incident beam into two coherent waves. One of the waves passes through the object while the other one does not. Therefore, after focusing on the analyzer, these two waves form diffraction patterns that show the contrast of the phase shift. In a grating interferometer, a grating is placed downstream of the object and splits the incoming beam into two first-diffraction orders. These two beams interfere with each other and form linear periodic fringe patterns. By inserting a second grating downstream of the first grating at a certain position, the diffraction fringes can be restored from the stepping readouts on the detector of the second grating. In DEI, monochromatic X-rays are reflected by a crystal (monochromator) with an incident angle at the Bragg angle. After transmission through the object, the X-rays are reflected to the detector by a second crystal (analyzer).