# Principles of Different X-ray Phase-Contrast Imaging: A Review
## 2 Methods  
### [PERSON]'s X-ray Microscopy  
[PERSON]'s X-ray microscopy was first introduced by [PERSON] in 1942 [3]. A brief review of the principle of [PERSON]'s phase-contrast microscopy is shown in Figure 1.  
Figure 1 shows that after the ring-shaped illuminating (green) light passes through the sample, part of the light is diffracted by the sample, as indicated in blue. The undiffracted light, which is indicated in red, forms the background on the image plane. Typically, diffracted light has a \(-90^{\circ}\) phase shift compared with undiffracted light. Without the phase ring, the interfered waves show intensities similar to the background; thus, the interference patterns in the detector exhibit low imaging contrast, as shown in Figure 2.  
Figure 1: Sketch of [PERSON]’s phase-contrast microscope. If the phase ring is placed to phase-shift the background light by \(-90^{\circ}\), the undiffracted light constructively interferes with the diffracted light. Then, the contrast of the object on the image plane increases. If the undiffracted light is phase-shifted by \(90^{\circ}\), it destructively interferes with the diffracted light. The contrast also increases, as shown in Figure 2.  
[PERSON]'s X-ray microscope was reported in 1994 by [PERSON] et al. with a Fresnel zone plate (FZP) [4]. The principle is similar to that of visible light except zone plates replace the condenser and object. Their work was performed using 2.4-nm radiation, resulting in a higher-order contrast and one-sixth of the dose than those in the absorption image with the same signal-to-noise ratio. As shown in Figure 1, this method requires that the sample is aligned at the focus of the first zone plate. The detector needs to be aligned at the focus of the second zone plate, similar to traditional optical microscopy. Furthermore, the phase ring needs to be aligned with the annular aperture. Unlike other phase-contrast X-ray imaging techniques, [PERSON]'s phase-contrast microscopy does not require a high-brilliance synchrotron source. It works with a low-brilliance laboratory source. Because this method enhances the contrast of the image with a single shot, [PERSON]'s phase-contrast microscopy brings less dosage to the object [4]. [PERSON] et al. independently derived the expression for image contrast using this method in the X-ray region [18]. By using new phase zone plates and beamline BL24 XU of SPring-8, a 60-nm resolution was achieved. [PERSON] et al. achieved a 50-nm resolution using a copper rotating anode X-ray source [19]. [PERSON] et al. applied [PERSON]'s phase-contrast imaging to a scanning X-ray microscope by simply swapping the detector and source plane in a full-field [PERSON]'s microscope [20]. In 2006, [PERSON] et al. found the halo effect, a bright boundary, at the edge of the object with hard X-ray Zernike microscopy. This effect is well known in optical microscopy [21]. [PERSON] et al. suppressed the halo by applying a beam shaper instead of a condenser [22]. In addition to the halo effect, [PERSON]'s X-ray phase-contrast microscopy suffers from a lower contrast than the absorption images when used on thick samples. However, new techniques for fabricating the FZP allow for 30-nm resolution capability [23]. [PERSON]'s X-ray phase-contrast microscopy (ZXPCM) converts phase modulations into amplitude modulations, resulting in sharper absorption images without numerical phase retrieval [3]. It has been widely applied to biological samples. In 2017, [PERSON] et al. used this method to image cells in polymer scaffolds at a resolution of 150 nm with a commercial source [24]. Their group successfully removed the halo effects by deconvolution with an image filter [24]. In 2017, [PERSON] et al. employed this method with a synchrotron source to image Al-Si microstructures and 2 \(\upmu\)m-diameter polystyrene spheres on a membrane. Both experiments showed that ZXPCM delivers a higher contrast than conventional absorption imaging [25]. In 2020, [PERSON] et al.