applied sciences Review Principles of Different X-ray Phase-Contrast Imaging: A Review Siwei Tao 1,†, Congxiao He 1,†, Xiang Hao 1, Cuifang Kuang 1,2,* and Xu Liu 1,2,* 1 State Key Laboratory of Modern Optical Instrumentation, College of Optical Science and Engineering, Zhejiang University, Hangzhou 310027, China; [email protected] (S.T.); [email protected] (C.H.); [email protected] (X.H.) 2 Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China * Correspondence: [email protected] (C.K.); [email protected] (X.L.) † These authors contributed equally to this work and should be considered co-first authors. Abstract: Numerous advances have been made in X-ray technology in recent years. X-ray imag- ing plays an important role in the nondestructive exploration of the internal structures of objects. However, the contrast of X-ray absorption images remains low, especially for materials with low atomic numbers, such as biological samples. X-ray phase-contrast images have an intrinsically higher contrast than absorption images. In this review, the principles, milestones, and recent progress of X-ray phase-contrast imaging methods are demonstrated. In addition, prospective applications are presented. Keywords: X-ray imaging; phase retrieval 1. Introduction As discovered by Wilhelm Conrad Röntgen, X-rays are electromagnetic waves with −12 −8 wavelengths ranging from approximately 10 to 10 m. The X-ray source, which is usually called an X-ray tube, is a vacuum chamber containing the anode and the cathode. Citation: Tao, S.; He, C.; Hao, X.; When a high current is applied to the cathode, its temperature increases, so electrons Kuang, C.; Liu, X. Principles of are released from it. High potential is applied between the cathode and the anode, so Different X-ray Phase-Contrast the electrons are accelerated towards the anode. These electrons stop suddenly after Imaging: A Review. Appl. Sci. 2021, hitting the anode. The loss of energy is then released in the form of X-ray photons. This 11 , 2971. https://doi.org/10.3390/ is called bremsstrahlung radiation. If the electrons knock out the core electron on the app11072971 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. Received: 13 February 2021 When transmitted through materials, the intensity of the X-ray beam changes owing to Accepted: 18 March 2021 Published: 26 March 2021 the different absorption coefficients of materials, allowing the observation of the internal features of objects using noninvasive X-ray imaging. Publisher’s Note: MDPI stays neutral The absorption images of low-Z materials exhibit poor contrast under X-ray irradia- with regard to jurisdictional claims in tion. Theoretically, phase-contrast X-ray imaging has higher contrast and sensitivity than published maps and institutional affil- conventional absorption imaging. Higher contrast makes the different compositions of an iations. object more distinguishable [1,2]. In this review, we did not differentiate between phase- contrast imaging and phase imaging, as Momose 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 Zernike’s X-ray microscopy [3,4], X-ray holography [5], differential X-ray microscopy [6,7], coherent diffrac- Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. tion microscopy [8], crystal interferometer [9], grating interferometer [10,11], diffraction- This article is an open access article enhanced imaging (DEI) [12], and propagation-based techniques [13]. In Zernike’s X-ray distributed under the terms and microscopy, a phase ring is inserted to phase-shift the undiffracted light so that the light conditions of the Creative Commons that has been phase-shifted by the object constructively or destructively interferes with the Attribution (CC BY) license (https:// undiffracted light, which both increase the contrast. In X-ray holography, a coherent wave creativecommons.org/licenses/by/ passes through an object and forms interference patterns on the photographic plate. After 4.0/). being illuminated by the coherent wave without the object, a pair of twin images appear Appl. Sci. 2021, 11, 2971. https://doi.org/10.3390/app11072971 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, x FOR PEER REVIEW 2 of 23 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 appear at both sides of the photographic plate. Differential X-ray microscopy was per- formed 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 Appl. Sci. 2021, 11, 2971 2 of 22 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 sep- aratedat both into sides a of splitter, the photographic a mirror, plate. and Differential an analyzer X-ray with microscopy two grooves. was performed The splitter by splits the incidentinserting beam a pair into of parallel two coherent and laterally waves. displaced One zoneof the plates waves upstream passes of through the sample. the object while theThe other incident one beam does splits not. into Therefore, zeroth- and after higher-order focusing sphericalon the analyzer, waves after these the zone two waves form diffractionplates. The combinationspatterns that of theshow zeroth-order the contrast in the firstof the zone phase plate andshift. the In first a ordergrating in the interferometer, second zone plate and vice versa interfere with each other and form diffraction patterns. aCoherent grating diffractionis placed imagingdownstream (CDI) isof a lenslessthe object method and thatsplits uses the an incoming iterative algorithm beam into two first- diffractionto retrieve phaseorders. information. These two A crystalbeams interferometer interfere with uses each a crystal other that and is separated form linear periodic fringeinto a splitter,patterns. a mirror, By inserting and an analyzer a second with grating two grooves. downstream The splitter of splits the thefirst incident grating at a certain position,beam into the two diffraction coherent waves. fringes One ofcan the be waves restor passesed from through the the stepping object while readouts the other on the detector one does not. Therefore, after focusing on the analyzer, these two waves form diffraction of the second grating. In DEI, monochromatic X-rays are reflected by a crystal (mono- patterns that show the contrast of the phase shift. In a grating interferometer, a grating is chromator)placed downstream with an of incident the object angle and splits at the the Brag incomingg angle. beam After into two transmission first-diffraction through the ob- ject,orders. the These X-rays two are beams reflected interfere to with the each detector other andby forma second linear crystal periodic (analyzer). fringe patterns. The analyzer is setBy parallel inserting to a secondthe first grating one; downstreamtherefore, the of the inci firstdent grating angles at aof certain the X-rays position, are the slightly off the Braggdiffraction angle fringes due canto refraction be restored fromfrom the the stepping object. readouts By tilting on the the detector analyzer of the half second of the full width grating. In DEI, monochromatic X-rays are reflected by a crystal (monochromator) with atan half incident maximum angle at (FWHM) the Bragg angle. of the After rocking transmission curve throughof itself, the with object, the the intensities X-rays are on the detec- tor,reflected the intensity to the detector of the by arefraction second crystal can (analyzer). be resolved. The analyzer Propagation-based is set parallel to imaging the requires onlyfirst one;the source, therefore, object, the incident and anglesdetector. of the The X-rays phas aree slightlyinformation off the Braggis resolved angle due from to the intensity inrefraction the detector. from the All object. of these By tilting methods the analyzer have their half of advantages the full width and at half disadvantages, maximum which are (FWHM) of the rocking curve of itself, with the intensities on the detector, the intensity of discussed in this review. Many reviews have discussed X-ray phase-contrast imaging [14– the refraction can be resolved. Propagation-based imaging requires only the source, object, 17].and However, detector. The none phase of informationthem discussed is resolved almost from all the phase-contrast intensity in the detector.image methods. All In addi- tion,of these as several methods years have theirhave advantages passed, the and progress disadvantages, and applications which are discussed of these in thismethods need to bereview. updated. Many Hence, reviews this have review discussed examines X-ray phase-contrast most of the imaging reported [14– 17X-ray]. However, phase-contrast im- agingnone oftechniques, them discussed and almost we also all phase-contrastdiscuss some image recent methods. applications. In addition, as several years have passed, the progress and applications of these methods need to be updated. Hence, this review examines most of the reported X-ray phase-contrast imaging techniques, 2.and Methods we also discuss some recent applications. 2.1.2. Methods Zernike’s X-ray Microscopy 2.1. Zernike’sZernike’s X-ray X-ray Microscopy microscopy was first introduced by Zernike in 1942 [3]. A brief re- view Zernike’sof the principle X-ray microscopy of Zernike’s was first phase-co introducedntrast by Zernike microscopy in 1942 [ 3is].