Performance analysis of quantitative phase retrieval method in Zernike phase contrast X-ray microscopy

Since the invention of Zernike phase contrast method in 1930,it has been widely used in optical microscopy and more recently in X-ray microscopy.Considering the image contrast is a mixture of absorption and phase information,we recently have proposed and demonstrated a method for quantitative phase retrieval in Zernike phase contrast X-ray microscopy.In this contribution,we analyze the performance of this method at different photon energies.Intensity images of PMMA samples are simulated at 2.5 keV and 6.2 keV,respectively,and phase retrieval is performed using the proposed method.The results demonstrate that the proposed phase retrieval method is applicable over a wide energy range.For weakly absorbing features,the optimal photon energy is 2.5 keV,from the point of view of image contrast and accuracy of phase retrieval.On the other hand,in the case of strong absorption objects,a higher photon energy is preferred to reduce the error of phase retrieval.These results can be used as guidelines to perform quantitative phase retrieval in Zernike phase contrast X-ray microscopy with the proposed method.     

Towards tender X‐rays with Zernike phase‐contrast imaging of biological samples at 50 nm resolution

X‐ray microscopy is a commonly used method especially in material science application, where the large penetration depth of X‐rays is necessary for three‐dimensional structural studies of thick specimens with high‐Z elements. In this paper it is shown that full‐field X‐ray microscopy at 6.2 keV can be utilized for imaging of biological specimens with high resolution. A full‐field Zernike phase‐contrast microscope based on diffractive optics is used to study lipid droplet formation in hepatoma cells. It is shown that the contrast of the images is comparable with that of electron microscopy, and even better contrast at tender X‐ray energies between 2.5 keV and 4 keV is expected.     

Enhanced renal image contrast by ethanol fixation in phase‐contrast X‐ray computed tomography

Phase‐contrast X‐ray imaging using a crystal X‐ray interferometer can depict the fine structures of biological objects without the use of a contrast agent. To obtain higher image contrast, fixation techniques have been examined with 100% ethanol and the commonly used 10% formalin, since ethanol causes increased density differences against background due to its physical properties and greater dehydration of soft tissue. Histological comparison was also performed. A phase‐contrast X‐ray system was used, fitted with a two‐crystal X‐ray interferometer at 35 keV X‐ray energy. Fine structures, including cortex, tubules in the medulla, and the vessels of ethanol‐fixed kidney could be visualized more clearly than that of formalin‐fixed tissues. In the optical microscopic images, shrinkage of soft tissue and decreased luminal space were observed in ethanol‐fixed kidney; and this change was significantly shown in the cortex and outer stripe of the outer medulla. The ethanol fixation technique enhances image contrast by approximately 2.7–3.2 times in the cortex and the outer stripe of the outer medulla; the effect of shrinkage and the physical effect of ethanol cause an increment of approximately 78% and 22%, respectively. Thus, the ethanol‐fixation technique enables the image contrast to be enhanced in phase‐contrast X‐ray imaging.     

Image contrast in X‐ray reflection interface microscopy: comparison of data with model calculations and simulations

The contrast mechanism for imaging molecular‐scale features on solid surfaces is described for X‐ray reflection interface microscopy (XRIM) through comparison of experimental images with model calculations and simulated measurements. Images of elementary steps show that image contrast is controlled by changes in the incident angle of the X‐ray beam with respect to the sample surface. Systematic changes in the magnitude and sign of image contrast are asymmetric for angular deviations of the sample from the specular reflection condition. No changes in image contrast are observed when defocusing the condenser or objective lenses. These data are explained with model structure‐factor calculations that reproduce all of the qualitative features observed in the experimental data. These results provide new insights into the image contrast mechanism, including contrast reversal as a function of incident angle, the sensitivity of image contrast to step direction (i.e. up versus down), and the ability to maximize image contrast at almost any scattering condition defined by the vertical momentum transfer, Q_z. The full surface topography can then, in principle, be recovered by a series of images as a function of incident angle at fixed momentum transfer. Inclusion of relevant experimental details shows that the image contrast magnitude is controlled by the intersection of the reciprocal‐space resolution function (i.e. controlled by numerical aperture of the condenser and objective lenses) and the spatially resolved interfacial structure factor of the object being imaged. Together these factors reduce the nominal contrast for a step near the specular reflection condition to a value similar to that observed experimentally. This formalism demonstrates that the XRIM images derive from limited aperture contrast, and explains how non‐zero image contrast can be obtained when imaging a pure phase object corresponding to the interfacial topography.     

3D imaging of a rice pollen grain using transmission X‐ray microscopy

For the first time, the three‐dimensional (3D) ultrastructure of an intact rice pollen cell has been obtained using a full‐field transmission hard X‐ray microscope operated in Zernike phase contrast mode. After reconstruction and segmentation from a series of projection images, complete 3D structural information of a 35 µm rice pollen grain is presented at a resolution of ～100 nm. The reconstruction allows a clear differentiation of various subcellular structures within the rice pollen grain, including aperture, lipid body, mitochondrion, nucleus and vacuole. Furthermore, quantitative information was obtained about the distribution of cytoplasmic organelles and the volume percentage of each kind of organelle. These results demonstrate that transmission X‐ray microscopy can be quite powerful for non‐destructive investigation of 3D structures of whole eukaryotic cells.     

A spatial domain constraint iterative phase retrieval method for the propagation based X ray phase contrast imaging

Based on the propagation X ray phase contrast imaging theory, a spatial domain constraint iterative phase retrieval method is described in detail. This algorithm limits the object spatial domain according to the actual sample size firstly, and modify the image plane data with the actual test data, then the iteration can be terminated until iteration precision or the number of iterations meet the preset requirements. Finally the numerical simulation is made to evaluate the rapid phase retrieval algorithm performance, and a real column fiber material experiment is carried out using a micro focus X ray phase contrast imaging experiment platform, the phase distribution image of the column fiber is calculated out by this algorithm. The results show that this phase retrieval algorithm is effective, and the method has a potential stability and accuracy for X ray phase contrast imaging technology.     

X‐ray spectromicroscopy in soil and environmental sciences

X‐ray microscopy is capable of imaging particles in the nanometer size range directly with sub‐micrometer spatial resolution and can be combined with high spectral resolution for spectromicroscopy studies. Two types of microscopes are common in X‐ray microscopy: the transmission X‐ray microscope and the scanning transmission X‐ray microscope; their set‐ups are explained in this paper. While the former takes high‐resolution images from an object with exposure times of seconds or faster, the latter is very well suited as an analytical instrument for spectromicroscopy. The morphology of clusters or particles from soil and sediment samples has been visualized using a transmission X‐ray microscope. Images are shown from a cryo‐tomography experiment based on X‐ray microscopy images to obtain information about the three‐dimensional structure of clusters of humic substances. The analysis of a stack of images taken with a scanning transmission X‐ray microscope to combine morphology and chemistry within a soil sample is shown. X‐ray fluorescence is a method ideally applicable to the study of elemental distributions and binding states of elements even on a trace level using X‐ray energies above 1 keV.     

Zernike phase contrast in scanning microscopy with X-rays

Scanning X-ray microscopy focuses radiation to a small spot and probes the sample by raster scanning. It allows information to be obtained from secondary signals such as X-ray fluorescence, which yields an elemental mapping of the sample not available in full-field imaging. The analysis and interpretation from these secondary signals can be considerably enhanced if these data are coupled with structural information from transmission imaging. However, absorption often is negligible and phase contrast has not been easily available. Originally introduced with visible light, Zernike phase contrast(1) is a well-established technique in full-field X-ray microscopes for visualization of weakly absorbing samples(2-7). On the basis of reciprocity, we demonstrate the implementation of Zernike phase contrast in scanning X-ray microscopy, revealing structural detail simultaneously with hard-X-ray trace-element measurements. The method is straightforward to implement without significant influence on the resolution of the fluorescence images and delivers complementary information. We show images of biological specimens that clearly demonstrate the advantage of correlating morphology with elemental information.     

Elemental x-ray imaging using Zernike phase contrast

We develop an element-specific x-ray microscopy method by using Zernike phase contrast imaging near absorption edges, where a real part of refractive index changes abruptly. In this method two phase contrast images are subtracted to obtain the target element: one is at the absorption edge of the target element and the other is near the absorption edge. The x-ray exposure required by this method is expected to be significantly lower than that of conventional absorption-based x-ray elemental imaging methods. Numerical calculations confirm the advantages of this highly efficient imaging method.     

Numerical reconstruction of an object image using an X‐ray dynamical diffraction Fraunhofer hologram

A numerical method of reconstruction of an object image using an X‐ray dynamical diffraction Fraunhofer hologram is presented. Analytical approximation methods and numerical methods of iteration are discussed. An example of a reconstruction of an image of a cylindrical beryllium wire is considered. The results of analytical approximation and zero‐order iteration coincide with exact values of the amplitude complex transmission coefficient of the object as predicted by the resolution limit of the scheme, except near the edges of the object. Calculations of the first‐ and second‐order iterations improve the result at the edges of the object. This method can be applied for determination of the complex amplitude transmission coefficient of amplitude as well as phase objects. It can be used in X‐ray microscopy.     

Phase-shifting Zernike phase contrast microscopy for quantitative phase measurement

Zernike phase contrast microscopy is extended and combined with a phase-shifting mechanism to perform quantitative phase measurements of microscopic objects. Dozens of discrete point light sources on a ring are constructed for illumination. For each point light source, three different levels of point-like phase steps are designed, which are alternatively located along a ring on a silica plate to perform phase retardation on the undiffracted (dc) component of the object waves. These three levels of the phase steps are respectively selected by rotating the silica plate. Thus, quantitative evaluation of phase specimens can be performed via phase-shifting mechanism. The proposed method has low "halo" and "shade-off" effects, low coherent noise level, and high lateral resolution due to the improved illumination scheme.     

Artifact Halo Reduction in Phase Contrast Microscopy Using Apodization

A new phase contrast microscopy technique for halo reduction is proposed. This technique is based on an apodization method combined with the Zernike phase contrast method. Although it has been a difficult theoretical problem, the proposed technique achieves halo reduction by considering angles of diffraction and phase differences. The technique utilizes an apodized phase plate consisting of a quarter wave phase shift ring with a 25% transmittance, and a pair of adjacent rings, which have 50% transmittance. This element is placed at the back focal plane of the objective. The result is startling, halo reduced images of phase objects providing enhanced inner details.     

相位互异散斑校正技术研究

相位互异散斑（PDS）是一种新颖的成像技术，可用来克服由于未知相差（如大气扰动）带来的图像退化。利用泽尼克多项式拟合未知扰动造成的相位失真，并用一对图像求得波前相位。从分析相位互异散斑技术的机理出发，使用遗传算法作为迭代算法，基于仿真实验数据验证了该技术的可行性，并在仿真实验中分析影响该技术性能的一些因素，如泽尼克多项式模式和湍流大小的影响等。这些研究结果为探索模糊图像恢复提供了新的途径。     

Stokes参量数字全息法实现相位物体成像

为实现对相位物体的无损检测和成像,克服数字同轴全息相位物体成像技术在消除零级像和孪生像的干扰时存在的系列问题,提出一种基于Stokes参量的新的数字同轴全息技术。该方法区别于传统的利用干涉光场来记录原始像项的数字全息方法,通过测量物参光合成光束的Stokes参量来分别得到这两束光的振幅和相位差,从而准确、唯一地获得原始像项;再利用数字再现即可重构物光的振幅和相位信息。实验中对弱吸收的相位样品进行了测量,得到样品清晰的振幅和相位分布。结果表明,采用该方法对相位物体进行数字全息再现,可以克服传统同轴全息图中零级像和共轭像对相位物体信息的严重干扰,对于提取相位物体的振幅和相位信息是可行和有效的。     

Feasibility study of propagation‐based phase‐contrast X‐ray lung imaging on the Imaging and Medical beamline at the Australian Synchrotron

Propagation‐based phase‐contrast X‐ray imaging (PB‐PCXI) using synchrotron radiation has achieved high‐resolution imaging of the lungs of small animals both in real time and in vivo. Current studies are applying such imaging techniques to lung disease models to aid in diagnosis and treatment development. At the Australian Synchrotron, the Imaging and Medical beamline (IMBL) is well equipped for PB‐PCXI, combining high flux and coherence with a beam size sufficient to image large animals, such as sheep, due to a wiggler source and source‐to‐sample distances of over 137 m. This study aimed to measure the capabilities of PB‐PCXI on IMBL for imaging small animal lungs to study lung disease. The feasibility of combining this technique with computed tomography for three‐dimensional imaging and X‐ray velocimetry for studies of airflow and non‐invasive lung function testing was also investigated. Detailed analysis of the role of the effective source size and sample‐to‐detector distance on lung image contrast was undertaken as well as phase retrieval for sample volume analysis. Results showed that PB‐PCXI of lung phantoms and mouse lungs produced high‐contrast images, with successful computed tomography and velocimetry also being carried out, suggesting that live animal lung imaging will also be feasible at the IMBL.     

An iterative image reconstruction algorithm combined with forward and backward diffusion filtering for in‐line X‐ray phase‐contrast computed tomography

In‐line X‐ray phase‐contrast computed tomography (IL‐PCCT) can reveal fine inner structures for low‐Z materials (e.g. biological soft tissues), and shows high potential to become clinically applicable. Typically, IL‐PCCT utilizes filtered back‐projection (FBP) as the standard reconstruction algorithm. However, the FBP algorithm requires a large amount of projection data, and subsequently a large radiation dose is needed to reconstruct a high‐quality image, which hampers its clinical application in IL‐PCCT. In this study, an iterative reconstruction algorithm for IL‐PCCT was proposed by combining the simultaneous algebraic reconstruction technique (SART) with eight‐neighbour forward and backward (FAB8) diffusion filtering, and the reconstruction was performed using the Shepp–Logan phantom simulation and a real synchrotron IL‐PCCT experiment. The results showed that the proposed algorithm was able to produce high‐quality computed tomography images from few‐view projections while improving the convergence rate of the computed tomography reconstruction, indicating that the proposed algorithm is an effective method of dose reduction for IL‐PCCT.     

Tracking extended mucociliary transport activity of individual deposited particles: longitudinal synchrotron X‐ray imaging in live mice

To assess potential therapies for respiratory diseases in which mucociliary transit (MCT) is impaired, such as cystic fibrosis and primary ciliary dyskinesia, a novel and non‐invasive MCT quantification method has been developed in which the transit rate and behaviour of individual micrometre‐sized deposited particles are measured in live mice using synchrotron phase‐contrast X‐ray imaging. Particle clearance by MCT is known to be a two‐phase process that occurs over a period of minutes to days. Previous studies have assessed MCT in the fast‐clearance phase, ～20 min after marker particle dosing. The aim of this study was to non‐invasively image changes in particle presence and MCT during the slow‐clearance phase, and simultaneously determine whether repeat synchrotron X‐ray imaging of mice was feasible over periods of 3, 9 and 25 h. All mice tolerated the repeat imaging procedure with no adverse effects. Quantitative image analysis revealed that the particle MCT rate and the number of particles present in the airway both decreased with time. This study successfully demonstrated for the first time that longitudinal synchrotron X‐ray imaging studies are possible in live small animals, provided appropriate animal handling techniques are used and care is taken to reduce the delivered radiation dose.     

Object image correction using an X‐ray dynamical diffraction Fraunhofer hologram

Taking into account background correction and using Fourier analysis, a numerical method of an object image correction using an X‐ray dynamical diffraction Fraunhofer hologram is presented. An example of the image correction of a cylindrical beryllium wire is considered. A background correction of second‐order iteration leads to an almost precise reconstruction of the real part of the amplitude transmission coefficient and improves the imaginary part compared with that without a background correction. Using Fourier analysis of the reconstructed transmission coefficient, non‐physical oscillations can be avoided. This method can be applied for the determination of the complex amplitude transmission coefficient of amplitude as well as phase objects, and can be used in X‐ray microscopy.     

Quantitative studies of pyrocarbon‐coated materials using synchrotron radiation

Phase‐contrast imaging provides enhanced image contrast and is important for non‐destructive evaluation of structural materials. In this paper, experimental results on in‐line phase‐contrast imaging using a synchrotron source (ELETTRA, Italy) for objects required in material science applications are discussed. Experiments have been carried out on two types of samples, pyrocarbon‐coated zirconia and pyrocarbon‐coated alumina microspheres. These have applications in both reactor and industrial fields. The phase‐contrast imaging technique is found to be very useful in visualizing and determining the coating thickness of pyrocarbon on zirconia and alumina microspheres. The experiments were carried out at X‐ray energies of 16, 18 and 20 keV and different object‐to‐detector distances. The results describe the contrast values and signal‐to‐noise ratio for both samples. A comprehensive study was carried out to determine the thickness of the pyrocarbon coating on zirconia and alumina microspheres of diameter 500 µm. The advantages of phase‐contrast images are discussed in terms of contrast and resolution, and a comparison is made with absorption images. The results show considerable improvement in contrast with phase‐contrast imaging as compared with absorption radiography.     

Current status of the TwinMic beamline at Elettra: a soft X‐ray transmission and emission microscopy station

The current status of the TwinMic beamline at Elettra synchrotron light source, that hosts the European twin X‐ray microscopy station, is reported. The X‐ray source, provided by a short hybrid undulator with source size and divergence intermediate between bending magnets and conventional undulators, is energy‐tailored using a collimated plane‐grating monochromator. The TwinMic spectromicroscopy experimental station combines scanning and full‐field imaging in a single instrument, with contrast modes such as absorption, differential phase, interference and darkfield. The implementation of coherent diffractive imaging modalities and ptychography is ongoing. Typically, scanning transmission X‐ray microscopy images are simultaneously collected in transmission and differential phase contrast and can be complemented by chemical and elemental analysis using across‐absorption‐edge imaging, X‐ray absorption near‐edge structure or low‐energy X‐ray fluorescence. The lateral resolutions depend on the particular imaging and contrast mode chosen. The TwinMic range of applications covers diverse research fields such as biology, biochemistry, medicine, pharmacology, environment, geochemistry, food, agriculture and materials science. They will be illustrated in the paper with representative results.