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.     

Quantitative phase retrieval in X‐ray Zernike phase contrast microscopy

In recent years, increasing attention has been devoted to X‐ray phase contrast imaging, since it can provide high‐contrast images by using phase variations. Among the different existing techniques, Zernike phase contrast microscopy is one of the most popular phase‐sensitive techniques for investigating the fine structure of the sample at high spatial resolution. In X‐ray Zernike phase contrast microscopy, the image contrast is indeed a mixture of absorption and phase contrast. Therefore, this technique just provides qualitative information on the object, which makes the interpretation of the image difficult. In this contribution, an approach is proposed for quantitative phase retrieval in X‐ray Zernike phase contrast microscopy. By shifting the phase of the direct light by π/2 and 3π/2, two images of the same object are measured successively. The phase information of the object can then be quantitatively retrieved by a proper combination of the measured images. Numerical experiments were carried out and the results confirmed the feasibility of the proposed method. It is expected that the proposed method will find widespread applications in biology, materials science and so on.     

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.     

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.     

Compact Zernike phase contrast x-ray microscopy using a single-element optic

We demonstrate Zernike phase contrast in a compact soft x-ray microscope using a single-element optic. The optic is a combined imaging zone plate and a Zernike phase plate and does not require any additional alignment or components. Contrast is increased and inversed in an image of a test object using the Zernike zone plate. This type of optic may be implemented into any existing x-ray microscope where phase contrast is of interest.     

Zernike apodized photon sieves for high-resolution phase-contrast x-ray microscopy

We present a type of diffractive lens, Zernike apodized photon sieves (ZAPS), used as the objective for high spatial resolution and high phase-contrast imaging of weakly absorbing materials in x rays. The structure of ZAPS is based on the combination of two concepts: apodized photon sieves and Zernike phase contrast. The ZAPS is a single optic that integrates the appropriate ±π/2 rad phase shift through selective zone placement shifts in an apodized photon sieve. Analysis of the focusing properties of the apodized photon sieve in terms of point-spread function show that the sidelobes have been significantly suppressed at the expense of slightly widening the width of the main lobe. In combination with synchrotron light sources, ZAPS offers new opportunities for high-resolution phase-contrast x-ray microscopy in the physical and life sciences.     

Halo Reduction Technique in Phase Contrast Microscopy

A new phase contrast microscopy technique has been developed which achieves halo reduction by applying an apodization to the Zernike phase contrast method. In this technique, a new apodized phase plate is placed at the back focal plane of the objective. This plate consists of a quarter wave phase shift ring conjugated of the illuminating aperture, which has a 25#x0025; transmittance, and a pair of adjacent rings having 50#x0025; transmittance. The developed technique yields the highest resolution images without a bluish hue effect ever achieved in phase contrast microscopy.This paper was originally presented at the 2nd International Conference on Optical Design and Fabrication, ODF2000 which was held on November 15-17, 2000 at the International Conference Center, Tokyo, Waseda University, Japan.     

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.     

Elemental x-ray imaging using Zernike phase contras

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.     

透明体的光学定量测量

综述了使用光学方法测量透明体的方法。介绍了两种常用的光学方法——相衬法和微分干涉相衬法。在 2 0世纪 80年代 ,一般认为相衬法和微分干涉相衬法只适用于定性观察而不能实现定量测量 ,主要是因为在其成像原理中的非线性因素的影响。但是对于微分干涉相衬法 ,最近国内外出现了几种定量测量的方法 ,本文对这几种方法进行了总结和比较。     

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.     

Penetrating view of nano-structures in Aleochara verna spermatheca and flagellum by hard X-ray microscopy

A penetrating view of the three-dimensional nanostructure of female spermatheca and male flagellum in the species Aleochara verna is obtained with 100-nm resolution using a hard X-ray microscope, which provides a fast noninvasive imaging technology for insect morphology. Through introducing Zernike phase contrast and heavy metal staining, images taken at 8 keV displayed sufficient contrast for observing nanoscale fine structures, such as the spermatheca cochleate duct and the subapex of the flagellum, which have some implications for the study of the sperm transfer process and genital evolution in insects. This work shows that both the spatial resolution and the contrast characteristic of hard X-ray microscopy are quite promising for insect morphology studies and, particularly, provide an attractive alternative to the destructive techniques used for investigating internal soft tissues.     

A method for fringe normalization by Zernike polynomial

A new approach for fringe normalization by Zernike polynomial fitting to cancel background illumination in an interferogram is proposed. With this method, background illumination can be suppressed, high frequency noise is immunized and the contrast is improved by normalization. The main idea for this paper is to use the Zernike polynomial fitting interferogram to cancel background illumination; the high frequency noise is then filtered by a Wiener filter. Finally, the paper uses the method of local region contrast modulation to enhance fringe contrast. This method can overcome the problem of the non-uniformity illumination of fringe patterns resulting from the marginal reflection of optical components and a non-uniformity light source     

基于三片曲面反射镜的离轴投影成像系统

采用调制传递函数和波前像差分析方法,设计了基于偶次非球面反射镜和Zernike自由曲面反射镜构成的放大倍数为80,相对孔径为2.8的三个离轴投影成像系统.其中第一片反射镜M1表面为凹面用于减小第二片反射镜的尺寸及获得高的对比度,而第二片反射镜M2和第三片反射镜M3表面为凸面用于校正系统像差及获得更短的投影距离.经软件设计与分析,三系统中基于三片Zernike自由曲面反射镜的成像系统光学性能最好,调制传递函数实现60lp/mm时60%以上,畸变小于2.0%.与其它文献相比,基于三片Zernike自由曲面反射镜系统可以更好地消除像差,缩短系统厚度,增大系统的可视角与相对孔径.     

不同对比度下自适应的自动调焦新算法

针对大多数自动调焦函数不能克服对比度变化引起的调焦曲线失去理想特性、陷入局部极小值甚至失去单峰性等问题,介绍了Zernike正交矩,分析了各阶Zernike矩的调焦函数曲线并且提出了一种新的基于Zernike正交矩的自动调焦算法,定义了此算法的公式.与几种常用自动调焦函数在不同对比度条件下进行了调焦效果的比较分析,验证了通过调整各阶Zernike矩的权重系数、可以灵活变换调焦公式,能够适应不同对比度下的调焦过程.实验比较了基于Zernike正交矩的自动调焦算法应用于完全对称型物体和非对称型物体时焦效果的差别,证明了该算法应用于圆形或球状等完全对称型的物体时调焦效果较好.     

What spatial light modulators can do for optical microscopy

With the availability of high‐resolution miniature spatial light modulators (SLMs) new methods in optical microscopy have become feasible. The SLMs discussed in this review consist of miniature liquid crystal displays with micron‐sized pixels that can modulate the phase and/or amplitude of an optical wavefront. In microscopy they can be used to control and shape the sample illumination, or they can act as spatial Fourier filters in the imaging path. Some of these applications are reviewed in this article. One of them, called spiral phase contrast, generates isotropic edge enhancement of thin phase samples or spiral‐shaped interference fringes for thicker phase samples, which can be used to reconstruct the phase topography from a single on‐axis interferogram. If SLMs are used for both illumination control and spatial Fourier filtering, this combination for instance allows for the generalization of the Zernike phase contrast principle. The new SLM‐based approach improves the effective resolution and avoids some shortcomings and artifacts of the traditional method. The main advantage of SLMs in microscopy is their flexibility, as one can realize various operation modes in the same setup, without the need for changing any hardware components, simply by electronically switching the phase pattern displayed on the SLMs.     

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.     

基于三片曲面反射镜的离轴投影成像系统

采用调制传递函数和波前像差分析方法,设计了基于偶次非球面反射镜和Zernike自由曲面反射镜构成的放大倍数为80,相对孔径为2.8的三个离轴投影成像系统.其中第一片反射镜M₁表面为凹面用于减小第二片反射镜的尺寸及获得高的对比度,而第二片反射镜M₂和第三片反射镜M₃表面为凸面用于校正系统像差及获得更短的投影距离.经软件设计与分析,三系统中基于三片Zernike自由曲面反射镜的成像系统光学性能最好,调制传递函数实现60 lp/mm 时60%以上,畸变小于2.0%.与其它文献相比,基于三片Zernike自由曲面反射镜系统可以更好地消除像差,缩短系统厚度,增大系统的可视角与相对孔径.     

Wavelet processing and digital interferometric contrast to improve reconstructions from X‐ray Gabor holograms

In this work, the application of an undecimated wavelet transformation together with digital interferometric contrast to improve the resulting reconstructions in a digital hard X‐ray Gabor holographic microscope is shown. Specifically, the starlet transform is used together with digital Zernike contrast. With this contrast, the results show that only a small set of scales from the hologram are, in effect, useful, and it is possible to enhance the details of the reconstruction.     

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.