位相复原技术在光学成像质量测评中的应用

对于大口径或特殊波段成像的光学系统,采用常规测试手段难以实现对光学系统成像质量的评估。而光学系统波像差是表征光学系统成像质量的重要指标之一。本文基于信息光学基础理论采用傅立叶变换和迭代算法通过对光学成像系统星点图像（光强点扩散函数PSF）计算分析,从而实现对光学成像系统位相的复原获得波像差信息。本文论述了有关的理论依据和分析计算公式;并研制了位相复原分析计算软件。通过计算机仿真与误差分析论证了研制的位相复原计算方法的正确性,复原误差小于5%。提出了在实际应用中采用此方法时减少复原误差的一种途径。通过实际采集的光学系统星点图像的位相复原实验验证了位相复原分析软件的适用性。此方法为非常规光学成像系统波相差的评估工作提供了新途径。     

Application of sensitive,high‐resolution imaging at a commercial lab‐based X‐ray micro‐CT system using propagation‐based phase retrieval

Several dedicated commercial lab‐based micro‐computed tomography (μCT) systems exist, which provide high‐resolution images of samples, with the capability to also deliver in‐line phase contrast. X‐ray phase contrast is particularly beneficial when visualizing very small features and weakly absorbing samples. The raw measured projections will include both phase and absorption effects. Extending our previous work that addressed the optimization of experimental conditions at the commercial ZEISS Xradia 500 Versa system, single‐distance phase‐contrast imaging is demonstrated on complex biological and material samples. From data captured at this system, we demonstrate extraction of the phase signal or the correction of the mixed image for the phase shift, and show how this procedure increases the contrast and removes artefacts. These high‐quality images, measured without the use of a synchrotron X‐ray source, demonstrate that highly sensitive, micrometre‐resolution imaging of 3D volumes is widely accessible using commercially advanced laboratory devices.     

Three‐dimensional imaging of whole mouse models: comparing nondestructive X‐ray phase‐contrast micro‐CT with cryotome‐based planar epi‐illumination imaging

In this study, we compare two evolving techniques for obtaining high‐resolution 3D anatomical data of a mouse specimen. On the one hand, we investigate cryotome‐based planar epi‐illumination imaging (cryo‐imaging). On the other hand, we examine X‐ray phase‐contrast micro‐computed tomography (micro‐CT) using synchrotron radiation. Cryo‐imaging is a technique in which an electron multiplying charge coupled camera takes images of a cryo‐frozen specimen during the sectioning process. Subsequent image alignment and virtual stacking result in volumetric data. X‐ray phase‐contrast imaging is based on the minute refraction of X‐rays inside the specimen and features higher soft‐tissue contrast than conventional, attenuation‐based micro‐CT. To explore the potential of both techniques for studying whole mouse disease models, one mouse specimen was imaged using both techniques. Obtained data are compared visually and quantitatively, specifically with regard to the visibility of fine anatomical details. Internal structure of the mouse specimen is visible in great detail with both techniques and the study shows in particular that soft‐tissue contrast is strongly enhanced in the X‐ray phase images compared to the attenuation‐based images. This identifies phase‐contrast micro‐CT as a powerful tool for the study of small animal disease models.     

Registration of phase‐contrast images in propagation‐based X‐ray phase tomography

X‐ray phase tomography aims at reconstructing the 3D electron density distribution of an object. It offers enhanced sensitivity compared to attenuation‐based X‐ray absorption tomography. In propagation‐based methods, phase contrast is achieved by letting the beam propagate after interaction with the object. The phase shift is then retrieved at each projection angle, and subsequently used in tomographic reconstruction to obtain the refractive index decrement distribution, which is proportional to the electron density. Accurate phase retrieval is achieved by combining images at different propagation distances. For reconstructions of good quality, the phase‐contrast images recorded at different distances need to be accurately aligned. In this work, we characterise the artefacts related to misalignment of the phase‐contrast images, and investigate the use of different registration algorithms for aligning in‐line phase‐contrast images. The characterisation of artefacts is done by a simulation study and comparison with experimental data. Loss in resolution due to vibrations is found to be comparable to attenuation‐based computed tomography. Further, it is shown that registration of phase‐contrast images is nontrivial due to the difference in contrast between the different images, and the often periodical artefacts present in the phase‐contrast images if multilayer X‐ray optics are used. To address this, we compared two registration algorithms for aligning phase‐contrast images acquired by magnified X‐ray nanotomography: one based on cross‐correlation and one based on mutual information. We found that the mutual information‐based registration algorithm was more robust than a correlation‐based method.     

Visualization of water drying in porous materials by X‐ray phase contrast imaging

We present in this study results from X‐ray tomographic microscopy with synchrotron radiation performed both in attenuation and phase contrast modes on a limestone sample during two stages of water drying. No contrast agent was used in order to increase the X‐ray attenuation by water. We show that only by using the phase contrast mode it is possible to achieve enough water content change resolution to investigate the drying process at the pore‐scale. We performed 3D image analysis of the time‐differential phase contrast tomogram. We show by the results of such analysis that it is possible to obtain a reliable characterization of the spatial redistribution of water in the resolved pore system in agreement with what expected from the theory of drying in porous media and from measurements performed with other approaches. We thus show the potential of X‐ray phase contrast imaging for pore‐scale investigations of reactive water transport processes which cannot be imaged by adding a contrast agent for exploiting the standard attenuation contrast imaging mode.     

Quantification of micrometre-sized porosity in quasicrystals using coherent synchrotron radiation imaging

The ability to image phase distributions with high spatial resolution is a key capability of microscopy systems. Consequently, the development and use of phase microscopy has been an important aspect of microscopy research and development. Most phase microscopy is based on a form of interference. Some phase imaging techniques, such as differential interference microscopy or phase microscopy, have a low coherence requirement, which enables high‐resolution imaging but in effect prevents the acquisition of quantitative phase information. These techniques are therefore used mainly for phase visualization. On the other hand, interference microscopy and holography are able to yield quantitative phase measurements but cannot offer the highest resolution. A new approach to phase microscopy, quantitative phase‐amplitude microscopy (QPAM) has recently been proposed that relies on observing the manner in which intensity images change with small defocuses and using these intensity changes to recover the phase. The method is easily understood when an object is thin, meaning its thickness is much less than the depth of field of the imaging system. However, in practice, objects will not often be thin, leading to the question of what precisely is being measured when QPAM is applied to a thick object. The optical transfer function formalism previously developed uses three‐dimensional (3D) optical transfer functions under the Born approximation. In this paper we use the 3D optical transfer function approach of Streibl not for the analysis of 3D imaging methods, such as tomography, but rather for the problem of analysing 2D phase images of thick objects. We go on to test the theoretical predictions experimentally. The two are found to be in excellent agreement and we show that the 3D imaging properties of QPAM can be reliably predicted using the optical transfer function formalism.     

Simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object

We demonstrate simultaneous phase and amplitude extraction from a single defocused image of a homogeneous object. Subject to the assumptions explicitly stated in the derivation, the algorithm solves the twin‐image problem of in‐line holography and is capable of analysing data obtained using X‐ray microscopy, electron microscopy, neutron microscopy or visible‐light microscopy, especially as they relate to defocus and point projection methods. Our simple, robust, non‐iterative and computationally efficient method is applied to data obtained using an X‐ray phase contrast ultramicroscope.     

Imaging of cochlear tissue with a grating interferometer and hard X‐rays

This article addresses an important current development in medical and biological imaging: the possibility of imaging soft tissue at resolutions in the micron range using hard X‐rays. Challenging environments, including the cochlea, require the imaging of soft tissue structure surrounded by bone. We demonstrate that cochlear soft tissue structures can be imaged with hard X‐ray phase contrast. Furthermore, we show that only a thin slice of the tissue is required to introduce a large phase shift. It is likely that the phase contrast image of the soft tissue structures is sufficient to image the structures even if surrounded by bone. For the present set of experiments, structures with low‐absorption contrast have been visualized using in‐line phase contrast imaging and a grating interferometer. The experiments have been performed at the Advanced Photon Source at Argonne National Laboratories, a third generation source of synchrotron radiation. The source provides highly coherent X‐ray radiation with high‐photon flux (>10¹² photons/s) at high‐photon energies (5–70 keV). Radiographic and light microscopy images of the gerbil cochlear slice samples were compared. It has been determined that a 20‐μm thick tissue slice induces a phase shift between 1/3π and 2/3π. Microsc. Res. Tech., 2009. © 2009 Wiley‐Liss, Inc.     

Quantitative X-ray projection microscopy: phase-contrast and multi-spectral imaging

We outline a new approach to X‐ray projection microscopy in a scanning electron microscope (SEM), which exploits phase contrast to boost the quality and information content of images. These developments have been made possible by the combination of a high‐brightness field‐emission gun (FEG)‐based SEM, direct detection CCD technology and new phase retrieval algorithms. Using this approach we have been able to obtain spatial resolution of < 0.2 µm and have demonstrated novel features such as: (i) phase‐contrast enhanced visibility of high spatial frequency image features (e.g. edges and boundaries) over a wide energy range; (ii) energy‐resolved imaging to simultaneously produce multiple quasi‐monochromatic images using broad‐band polychromatic illumination; (iii) easy implementation of microtomography; (iv) rapid and robust phase/amplitude‐retrieval algorithms to enable new real‐time and quantitative modes of microscopic imaging. These algorithms can also be applied successfully to recover object–plane information from intermediate‐field images, unlocking the potentially greater contrast and resolution of the intermediate‐field regime. Widespread applications are envisaged for fields such as materials science, biological and biomedical research and microelectronics device inspection. Some illustrative examples are presented. The quantitative methods described here are also very relevant to projection microscopy using other sources of radiation, such as visible light and electrons.     

Investigation of inner ear anatomy in mouse using X‐ray phase contrast tomography

A thorough understanding of inner ear anatomy is important for investigators. However, investigation of the mouse inner ear is difficult due to the limitations of imaging techniques. X‐ray phase contrast tomography increases contrast 100–1,000 times compared with conventional X‐ray imaging. This study aimed to investigate inner ear anatomy in a fresh post‐mortem mouse using X‐ray phase contrast tomography and to provide a comprehensive atlas of microstructures with less tissue deformation. All experiments were performed in accordance with our institution's guidelines on the care and use of laboratory animals. A fresh mouse cadaver was scanned immediately after sacrifice using an inline phase contrast tomography system. Slice images were reconstructed using a filtered back‐projection (FBP) algorithm. Standardized axial and coronal planes were adjusted with a multi‐planar reconstruction method. Some three‐dimensional (3D) objects were reconstructed by surface rendering. The characteristic features of microstructures, including otoconia masses of the saccular and utricular maculae, superior and inferior macula cribrosae, single canal, modiolus, and osseous spiral lamina, were described in detail. Spatial positions and relationships of the vestibular structures were exhibited in 3D views. This study investigated mouse inner ear anatomy and provided a standardized presentation of microstructures. In particular, otoconia masses were visualized in their natural status without contrast for the first time. The comprehensive anatomy atlas presented in this study provides an excellent reference for morphology studies of the inner ear.     

Condenser‐free contrast methods for transmitted‐light microscopy

Phase contrast microscopy allows the study of highly transparent yet detail‐rich specimens by producing intensity contrast from phase objects within the sample. Presented here is a generalized phase contrast illumination schema in which condenser optics are entirely abrogated, yielding a condenser‐free yet highly effective method of obtaining phase contrast in transmitted‐light microscopy. A ring of light emitting diodes (LEDs) is positioned within the light‐path such that observation of the objective back focal plane places the illuminating ring in appropriate conjunction with the phase ring. It is demonstrated that true Zernike phase contrast is obtained, whose geometry can be flexibly manipulated to provide an arbitrary working distance between illuminator and sample. Condenser‐free phase contrast is demonstrated across a range of magnifications (4–100×), numerical apertures (0.13–1.65NA) and conventional phase positions. Also demonstrated is condenser‐free darkfield microscopy as well as combinatorial contrast including Rheinberg illumination and simultaneous, colour‐contrasted, brightfield, darkfield and Zernike phase contrast. By providing enhanced and arbitrary working space above the preparation, a range of concurrent imaging and electrophysiological techniques will be technically facilitated. Condenser‐free phase contrast is demonstrated in conjunction with scanning ion conductance microscopy (SICM), using a notched ring to admit the scanned probe. The compact, versatile LED illumination schema will further lend itself to novel next‐generation transmitted‐light microscopy designs. The condenser‐free illumination method, using rings of independent or radially‐scanned emitters, may be exploited in future in other electromagnetic wavebands, including X‐rays or the infrared.     

Maximum pixel spectrum: a new tool for detecting and recovering rare, unanticipated features from spectrum image data cubes

A new software tool, the maximum pixel spectrum, detects rare events within a spectrum image data cube, such as that generated with electron‐excited energy‐dispersive X‐ray spectrometry in a scanning electron microscope. The maximum pixel spectrum is a member of a class of ‘derived spectra’ that are constructed from the spectrum image data cube. Similar to a conventional spectrum, a derived spectrum is a linear array of intensity vs. channel index that corresponds to photon energy. A derived spectrum has the principal characteristics of a real spectrum so that X‐ray peaks can be recognized. A common example of a derived spectrum is the summation spectrum, which is a linear array in which the summation of all pixels within each energy plane gives the intensity value for that channel. The summation spectrum is sensitive to the dominant features of the data cube. The maximum pixel spectrum is constructed by selecting the maximum pixel value within each X‐ray energy plane, ignoring the remaining pixels. Peaks corresponding to highly localized trace constituents or foreign contaminants, even those that are confined to one pixel of the image, can be seen at a glance when the maximum pixel spectrum is compared with the summation spectrum.     

Quantitative phase-amplitude microscopy I: optical microscopy

In this paper, the application of a new optical microscopy method (quantitative phase‐amplitude microscopy) to biological imaging is explored, and the issue of resolution and image quality is examined. The paper begins by presenting a theoretical analysis of the method using the optical transfer function formalism of Streibl (1985 ). The effect of coherence on the formation of the phase image is explored, and it is shown that the resolution of the method is not compromised over that of a conventional bright‐field image. It is shown that the signal‐to‐noise ratio of the phase recovery, however, does depend on the degree of coherence in the illumination. Streibl (1985) notes that partially coherent image formation is a non‐linear process because of the intermingling of amplitude and phase information. The work presented here shows that the quantitative phase‐amplitude microscopy method acts to linearize the image formation process, and that the phase and amplitude information is properly described using a transfer function analysis. The theoretical conclusions are tested experimentally using an optical microscope and the theoretical deductions are confirmed. Samples for microscopy influence both the phase and amplitude of the light wave and it is demonstrated that the new phase recovery method can separate the amplitude and phase information, something not possible using traditional phase microscopy. In the case of a coherent wave, knowledge of the phase and amplitude constitutes complete information that can be used to emulate other forms of microscopy. This capacity is demonstrated by recovering the phase of a sample and using the data to emulate a differential interference contrast image.     

基于ZEMAX用户自定义操作数的波前编码成像系统优化设计

针对目前波前编码成像系统中相位板的设计工作量大且未能考虑除相位板外其它光学元件像差的问题,提出了两种基于常用光学设计软件ZEMAX的优化设计方法:使用ZPL宏指令编写用户自定义操作数,优化点扩散函数的能量集中度和一致性,实现了旋转对称型相位板的设计,以斯托列尔比不小于0.8为衡量标准,设计结果使景深扩展到传统光学系统的5.5倍;使用在外部定义和编译的C程序编写用户自定义操作数,优化调制传递函数的离焦不变性,实现了奇对称型相位板的设计;以MTF离焦不变性为衡量标准,设计结果使景深扩展到传统光学系统的12.5倍,而同等条件下的三次方相位板只能使景深扩展到传统光学系统的10.1倍。得到的实验结果说明本文所述设计方法是方便而有效的。     

Evidence of multimicrometric coherent γ′ precipitates in a hot‐forged γ–γ′ nickel‐based superalloy

This paper demonstrates the existence of large γ’ precipitates (several micrometres in diameter) that are coherent with their surrounding matrix grain in a commercial γ–γ’ nickel‐based superalloy. The use of combined energy dispersive X‐ray spectrometry and electron backscattered diffraction (EBSD) analyses allowed for revealing that surprising feature, which was then confirmed by transmission electron microscopy (TEM). Coherency for such large second‐phase particles is supported by a very low crystal lattice misfit between the two phases, which was confirmed thanks to X‐ray diffractograms and TEM selected area electron diffraction patterns. Dynamic recrystallization of polycrystalline γ–γ’ nickel‐based superalloys has been extensively studied in terms of mechanisms and kinetics. As in many materials with low stacking fault energy, under forging conditions, the main softening mechanism is discontinuous dynamic recrystallization. This mechanism occurs with preferential nucleation on the grain boundaries of the deformed matrix. The latter is then being consumed by the growth of the newly formed grains of low energy and by nucleation that keeps generating new grains. In the case of sub‐solvus forging, large γ’ particles usually pin the migrating boundaries and thus limit grain growth to a size which is determined by the distribution of second‐phase particles, in good agreement with the Smith–Zener model. Under particular circumstances, the driving force associated with the difference in stored energy between the growing grains and the matrix can be large enough that the pinning forces can be overcome, and some grains can then reach much larger grain sizes. In the latter exceptional case, some intragranular primary γ’ particles can be observed, although they are almost exclusively located on grain boundaries and triple junctions otherwise. In both cases, primary precipitates have no special orientation relationship with the surrounding matrix grain(s). This paper demonstrates the existence of high fractions of large γ’ precipitate (several micrometres in diameter) that are coherent with their surrounding matrix grain, in a commercial γ–γ’ nickel‐based superalloy. Such a configuration is very surprising, because there is apparently no reason for the coherency of such particles.     

Software image alignment for X-ray microtomography with submicrometre resolution using a SEM-based X-ray microscope

Improved X-ray sources and optics now enable X-ray imaging resolution down to ∼50 nm for laboratory-based X-ray microscopy systems. This offers the potential for submicrometre resolution in tomography; however, achieving this resolution presents challenges due to system stability. We describe the use of software methods to enable submicrometre resolution of approximately 560 nm. This is a very high resolution for a modest laboratory-based point-projection X-ray tomography system. The hardware is based on a scanning electron microscope, and benefits from inline X-ray phase contrast to improve visibility of fine features. Improving the resolution achievable with the system enables it to be used to address a greater range of samples.     

Contact X‐ray microscopy of living cells by using LiF crystal as imaging detector

In this paper, the use of lithium fluoride (LiF) as imaging radiation detector to analyse living cells by single‐shot soft X‐ray contact microscopy is presented. High resolved X‐ray images on LiF of cyanobacterium Leptolyngbya VRUC135, two unicellular microalgae of the genus Chlamydomonas and mouse macrophage cells (line RAW 264.7) have been obtained utilizing X‐ray radiation in the water window energy range from a laser plasma source. The used method is based on loading of the samples, the cell suspension, in a special holder where they are in close contact with a LiF crystal solid‐state X‐ray imaging detector. After exposure and sample removal, the images stored in LiF by the soft X‐ray contact microscopy technique are read by an optical microscope in fluorescence mode. The clear image of the mucilaginous sheath the structure of the filamentous Leptolyngbya and the visible nucleolus in the macrophage cells image, are noteworthiness results. The peculiarities of the used X‐ray radiation and of the LiF imaging detector allow obtaining images in absorption contrast revealing the internal structures of the investigated samples at high spatial resolution. Moreover, the wide dynamic range of the LiF imaging detector contributes to obtain high‐quality images. In particular, we demonstrate that this peculiar characteristic of LiF detector allows enhancing the contrast and reveal details even when they were obscured by a nonuniform stray light.     

Comparative analysis of isolated cellular organelles by means of soft X-ray contact microscopy with laser-plasma source and transmission electron microscopy

Soft X‐ray contact microscopy (SXCM) is, at present, a useful tool for the examination at submicrometre resolution of biological systems maintained in their natural hydrated conditions. Among current X‐ray‐generating devices, laser‐plasma sources are now easily available and, owing to their pulse nature, offer the opportunity to observe living biological samples before radiation damage occurs, even if the resolution achievable is not as high as with synchrotron‐produced X‐rays. To assess the potential of laser‐plasma source SXCM in the study of cellular organelles, we applied it for the analysis of chloroplasts extracted from spinach leaves and mitochondria isolated from bovine heart and liver. X‐ray radiation was generated by a nanosecond laser‐plasma source, produced by a single shot excimer XeCl laser focused onto an yttrium target. The images obtained with SXCM were then compared with those produced by transmission electron microscopy observation of the same samples prepared with negative staining, a technique requiring no chemical fixation, in order to facilitate their interpretation and test the applicability of SXCM imaging.     

Shack-Hartmann wave front measurements in cortical tissue for deconvolution of large three-dimensional mosaic transmitted light brightfield micrographs

We present a novel approach for deconvolution of 3D image stacks of cortical tissue taken by mosaic/optical‐sectioning technology, using a transmitted light brightfield microscope. Mosaic/optical‐sectioning offers the possibility of imaging large volumes (e.g. from cortical sections) on a millimetre scale at sub‐micrometre resolution. However, a blurred contribution from out‐of‐focus light results in an image quality that usually prohibits 3D quantitative analysis. Such quantitative analysis is only possible after deblurring by deconvolution. The resulting image quality is strongly dependent on how accurate the point spread function used for deconvolution resembles the properties of the imaging system. Since direct measurement of the true point spread function is laborious and modelled point spread functions usually deviate from measured ones, we present a method of optimizing the microscope until it meets almost ideal imaging conditions. These conditions are validated by measuring the aberration function of the microscope and tissue using a Shack‐Hartmann sensor. The analysis shows that cortical tissue from rat brains embedded in Mowiol and imaged by an oil‐immersion objective can be regarded as having a homogeneous index of refraction. In addition, the amount of spherical aberration that is caused by the optics or the specimen is relatively low. Consequently the image formation is simplified to refraction between the embedding and immersion medium and to 3D diffraction at the finite entrance pupil of the objective. The resulting model point spread function is applied to the image stacks by linear or iterative deconvolution algorithms. For the presented dataset of large 3D images the linear approach proves to be superior. The linear deconvolution yields a significant improvement in signal‐to‐noise ratio and resolution. This novel approach allows a quantitative analysis of the cortical image stacks such as the reconstruction of biocytin‐stained neuronal dendrites and axons.