Object-wave reconstruction by carbon film-based Zernike- and Hilbert-phase plate microscopy: a theoretical study not restricted to weak-phase objects

Transmission electron microscopy phase-contrast images taken by amorphous carbon film-based phase plates are affected by the scattering of electrons within the carbon film causing a modification of the image-wave function. Moreover, image artefacts are produced by non-centrosymmetric phase plate designs such as the Hilbert-phase plate. Various methods are presented to correct phase-contrast images with respect to the scattering of electrons and image artefacts induced by phase plates. The proposed techniques are not restricted to weak-phase objects and linear image formation. Phase-contrast images corrected by the presented methods correspond to those taken by an ideal centrosymmetric, matter-free phase plate and are suitable for object-wave reconstruction.     

Defocusing microscopy

Transparent objects (phase objects) are not visible in a standard brightfield optical microscope. In order to see such objects the most used technique is phase-contrast microscopy. In phase-contrast microscopy the contrast observed is proportional to the optical path difference introduced by the object. If the index of refraction is uniform, phase-contrast microscopy then yields a measure of the thickness profile of phase objects. We show that by slightly defocusing an optical microscope operating in brightfield, phase objects become visible. We modeled such an effect and show that the image contrast of a phase object is proportional to the amount of defocusing and proportional to the two-dimensional Laplacian of the optical path difference introduced by the object. For uniform index of refraction, defocusing microscopy then yields a measure of the curvature profile of phase objects. We extended our previous model for thin objects to thick objects. To check our theoretical model, we use as phase objects polystyrene spherical caps and compare their curvature radii obtained by defocusing microscopy (DM) to those obtained with atomic force microscopy (AFM). We also show that for thick curved phase objects one can reconstruct their thickness profiles from DM images. We illustrate the utility of defocusing microscopy in biological systems to study cell motility. In particular, we visualize and quantitatively measure real-time cytoskeleton curvature fluctuations of macrophages (a cell of the innate immune system). The study of such fluctuations might be important for a better understanding of the engulfment process of pathogens during phagocytosis.     

Measurement of the width of thin,cylindrical, transparent objects by phase contrast light microscopy6

Measurement of the width of a thin, cylindrical, transparent object by phase contrast light microscopy has been frustrated by the absence of an established relationship between the true width of the object and its apparent width in the phase contrast image. We have solved this problem by devising a simple method by which individual glass fibres may be measured using both phase contrast light microscopy and electron microscopy. Using this method we have constructed calibration curves relating the diameter measured by phase contrast microscopy to the real diameter of the fibres. These curves are linear in the range 0.10-2.5 μm real diameter, with slopes close to unity and intercepts of about 0.2 μm. Thus widths of such objects are overestimated. The precise value of the intercept is related to the overall numerical aperture of the optical system. Each calibration curve permits the true width of a cylindrical object to be estimated by phase contrast microscopy with an accuracy of better than ±0.05 μm. We have found that greater precision is obtained by taking measurements of light micrographs subjectively using a microcomparator rather than objectively using a microdensitometer.     

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.     

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.     

High-resolution cell outline segmentation and tracking from phase-contrast microscopy images

Accurate extraction of cell outlines from microscopy images is essential for analysing the dynamics of migrating cells. Phase-contrast microscopy is one of the most common and convenient imaging modalities for observing cell motility because it does not require exogenous labelling and uses only moderate light levels with generally negligible phototoxicity effects. Automatic extraction and tracking of high-resolution cell outlines from phase-contrast images, however, is difficult due to complex and non-uniform edge intensity. We present a novel image-processing method based on refined level-set segmentation for accurate extraction of cell outlines from high-resolution phase-contrast images. The algorithm is validated on synthetic images of defined noise levels and applied to real image sequences of polarizing and persistently migrating keratocyte cells. We demonstrate that the algorithm is able to reliably reveal fine features in the cell edge dynamics.     

Video microscopic image processing facilitates the evaluation of light microscopic autoradiography at high magnification

Light microscopic autoradiographs of H-thymidine labelled unstained semithin sections of Xenopus laevis embryonic nuclei were examined with conventional Nomarski differential interference contrast, phase-contrast and video microscopy. Whereas at low magnification it was possible to obtain a photograph of the nuclear structure and the silver grains in one focal plain, at high magnification, with small depths of focus, a satisfactory image was not attainable. Therefore, we stored the images of the two different focus levels with a digital image processing system and combined both images by an arithmetic operation. This video microscopic technique allows the use of high magnification light microscopy with oil immersion objectives and the application of additional electronic contrast enhancing methods for an adequate and rapid analysis of light microscopic autoradiographs.     

Axial Phase-Darkfield-Contrast (APDC), a new technique for variable optical contrasting in light microscopy

Axial phase-darkfield-contrast (APDC) has been developed as an illumination technique in light microscopy which promises significant improvements and a higher variability in imaging of several transparent 'problem specimens'. With this method, a phase contrast image is optically superimposed on an axial darkfield image so that a partial image based on the principal zeroth order maximum (phase contrast) interferes with an image, which is based on the secondary maxima (axial darkfield). The background brightness and character of the resulting image can be continuously modulated from a phase contrast-dominated to a darkfield-dominated character. In order to achieve this illumination mode, normal objectives for phase contrast have to be fitted with an additional central light stopper needed for axial (central) darkfield illumination. In corresponding condenser light masks, a small perforation has to be added in the centre of the phase contrast providing light annulus. These light modulating elements are properly aligned when the central perforation is congruent with the objective's light stop and the light annulus is conjugate with the phase ring. The breadth of the condenser light annulus and thus the intensity of the phase contrast partial image can be regulated with the aperture diaphragm. Additional contrast effects can be achieved when both illuminating light components are filtered at different colours. In this technique, the axial resolution (depth of field) is significantly enhanced and the specimen's three-dimensional appearance is accentuated with improved clarity as well as fine details at the given resolution limit. Typical artefacts associated with phase contrast and darkfield illumination are reduced in our methods.     

φFLIM: a new method to avoid aliasing in frequency-domain fluorescence lifetime imaging microscopy

In conventional wide‐field frequency‐domain fluorescence lifetime imaging microscopy (FLIM), excitation light is intensity‐modulated at megahertz frequencies. Emitted fluorescence is recorded by a CCD camera through an image intensifier, which is modulated at the same frequency. From images recorded at various phase differences between excitation and intensifier gain modulation, the phase and modulation depth of the emitted light is obtained. The fluorescence lifetime is determined from the delay and the decrease in modulation depth of the emission relative to the excitation. A minimum of three images is required, but in this case measurements become susceptible to aliasing caused by the presence of higher harmonics. Taking more images to avoid this is not always possible owing to phototoxicity or movement. A method is introduced, φFLIM, requiring only three recordings that is not susceptible to aliasing. The phase difference between the excitation and the intensifier is scanned over the entire 360° range following a predefined phase profile, during which the image produced by the intensifier is integrated onto the CCD camera, yielding a single image. Three different images are produced following this procedure, each with a different phase profile. Measurements were performed with a conventional wide‐field frequency‐domain FLIM system based on an acousto‐optic modulator for modulation of the excitation and a microchannel‐plate image intensifier coupled to a CCD camera for the detection. By analysis of the harmonic content of measured signals it was found that the third harmonic was effectively the highest present. Using the conventional method with three recordings, phase errors due to aliasing of up to ± 29° and modulation depth errors of up to 30% were found. Errors in lifetimes of YFP‐transfected HeLa cells were as high as 100%. With φFLIM, using the same specimen and settings, systematic errors due to aliasing did not occur.     

Optimizing phase contrast in transmission electron microscopy with an electrostatic (Boersch) phase plate

Imaging of weak amplitude and phase objects, such as unstained vitrified biological samples, by conventional transmission electron microscopy (TEM) suffers from poor object contrast since the amplitude and phase of the scattered electron wave change only very little. In phase contrast light microscopy the imaging of weak phase objects is greatly enhanced by the use of a quarter-wave phase plate, which produces high signal contrast by shifting the phase of the scattered light. An analogous quarter-wave plate for the electron microscope, designed as an electrostatic einzel lens, was proposed by Boersch in 1947 but the small dimensions of the device have impeded its realization up to now. We here present the first fabrication and application of a miniaturized electrostatic einzel lens driven as TEM quarter-wave phase plate. Phase modulation is generated by the electrostatic field confined to the inside of a microstructured ring electrode. This field affects the phase velocity of the unscattered part of the electron wave. By varying its strength the phase shift of the primary beam can be adjusted to pi/2, producing strong phase contrast independent of spatial frequency. The phase plate proves to be mechanically stable and does not impair image quality, in particular it does not reduce the high-resolution signal. The expected residual lens effect of the einzel lens is minimal. Our microlens is supported by conducting rods arranged in a threefold symmetry. This particular geometry provides optimized single-sideband signal transfer for spatial frequencies otherwise obstructed by the supporting rods.     

Laser scanning phase modulation microscope

We describe the concept and first implementation of an innovative new instrument for quantitative light microscopy. Currently, it provides selective imaging of optical path differences due to birefringence; with further development, it is also possible to selectively image several optical properties, including refractive path differences, optical rotation, and linear and circular dichroism, all with diffraction-limited resolution. An image consists of a 512×512 element array, with each pixel displaying one of 256 grey levels, linearly proportional to the specific optical property being observed. Additionally, conventional brightfield and polarized light microscopy are available, with the accompanying advantages of laser scanning and digital image processing. The microscope consists of three subsystems, representing three distinct technologies. The laser scanning subsystem moves a focused, microspot across the specimen; the output of a photodetector is an electric signal corresponding to a scanned image. The image display subsystem digitizes this signal and displays it as an image on a video monitor. When used in conjunction with a phase modulation feedback loop, the image formed is of the specimen's birefringent retardation or other selected optical property. The digitized images are also available for computer enhancement.     

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.     

Segmentation and tracking of live cells in phase-contrast images using directional gradient vector flow for snakes

Cell shape is an important characteristic of the physiological state of a cell and is used as a primary read-out of cell behaviour in various assays. Automated accurate segmentation of cells in microscopy images is hence of large practical importance in cell biology. We report a simple algorithm for automated cell segmentation in high-magnification phase-contrast images, which takes advantage of the characteristic directionality of the local image intensity gradient at cellular boundaries due to the 'halo-effect'. We employ a two-step algorithm in which a gradient vector flow (GVF) field is first used to direct active contours to an approximate cell boundary. A directional GVF (DGVF) field is then calculated by considering only edges for which the image intensity gradient is directed outwards with respect to the approximate cell contour. Subsequently, the DGVF field is used to refine the cell contour, by directing active contours to edges with the desired gradient directionality. This method allows us to accurately segment cells in an image series, as well as follow the dynamics of cell shape over time in an automated fashion.     

基于并行共聚焦显微系统的物方差动轴向测量

差动共聚焦显微成像技术可以获得很高的轴向测量精度,然而已有的差动共聚焦测量技术主要适用于激光扫描共聚焦,还不能满足微纳加工过程中对工件进行非接触式的在线、在位测量的要求。本文在分析差动共聚焦显微成像系统能够实现轴向测量原理的基础上,提出了适用于并行共聚焦技术的轴向测量方法。该方法利用均匀白光照明,在像方只需要使用一台相机做探测器,在物方通过移动载物台分别对样品在焦前和焦后两次成像,根据预先刻度好的差动曲线就可以得出物体表面的高度。理论模拟与实验结果均表明,该方法可以实现高精度的轴向测量,对500nm的台阶样品测量的平均误差为2.9nm,相对误差为0.58%。该方法简单、廉价、测量精度高,可以用于普通显微镜,易于实现样品的三维快速形貌还原与测量。     

数字全息术用于光学元件表面缺陷形貌测量

利用像面数字全息显微术对光学元件表面缺陷的三维形貌测量进行了理论及实验研究。设计并搭建了相应光路系统记录全息图,采用角谱算法数值重建物光场,通过相位修正消除了系统误差引入的波前畸变,获得了经过待测光学元件表面缺陷调制的物光相位分布,并根据建立的相位分布与表面缺陷面形的关系模型计算得到缺陷三维形貌。实验以多个划痕和麻点等常见表面缺陷作为测量对象,分别获得了它们的三维形貌,以其中一条实际宽度为35μm、深度为270nm的划痕为例,测量得到该划痕的宽度为35.21μm,平均深度为267.6nm,与真实值相比,横向测量误差为0.6%,纵向测量误差为0.9%。实验结果证实该测量方法是有效、可靠的,能够准确测量光学元件表面缺陷的三维形貌,因而有助于判断光学元件损伤程度以及分析缺陷对系统波前的影响,对保障高功率激光装置的安全正常运行有重要意义。     

基于微分干涉相衬的相位分析法研究

通过对微分干涉相衬显微定量测量方法进行研究,提出了一种更有效的相位分析法。即在不对双光束干涉光路进行改造或处理的前提下,通过对光学成像进行处理而得到理想的结果。即把图像中的光强信号转变成相位信号,并通过维纳滤波对噪声进行了消除,最后获得表面微观形貌定量参数。     

Calculation of the object edge position after its projection in a spatially noninvariant coherent optical system

Specific features of half-plane image formation in a spatially noninvariant (aberration-free) coherent optical system of the 2F–2F telecentric type with a limited aperture of the projection objective (in the absence of the spatial frequency filter) are studied. The dependence of the light intensity behavior at a point corresponding to the half-plane edge in the image on the object position is found in an analytical form on the basis of approximating the Fresnel functions by analytical functions. As the half-plane approaches the boundary of the field of vision of the system determined by the objective aperture diameter, the light intensity is demonstrated to deviate significantly from that in the case of the axial position of the half-plane, which may lead to noticeable measurement errors in inspecting the geometric parameters of objects by the projection method in transmitted light.     

Zernike filter based on orientational optical nonlinearity of liquid crystalline systems

Visualization of the phase object with the use of a phase-contrast scheme incorporating a nonlinear Zernike filter was carried out. A liquid crystal or liquid crystalline polymer doped with azobenzene dye inducing orientational optical nonlinearity was used as the filter. Inversion of the image contrast depending on the angle of incidence of the light beam on a nematic liquid crystal cell was implemented.     

On the accuracy of microinterferometric measurements of optical-path differences by means of the half-shade method

Using a shearing double-refracting interference microscope with a half-shade eyepiece, the accuracy of optical-path-difference measurements has been examined. For the half-shade elements, birefringent strips with phase difference equal to 180°, 110° and 20° as well as a half-wave plate with a narrow slit, cemented between two glass plates, were used. It is known that different relative intensities of the background inside and outside the half-shade strip introduce a subjective error in the correct visual assessment of the matching point of the interference image of the object under examination. Applying test objects made of thin strips of dielectric evaporated in vacuum onto glass slides, it has been demonstrated that this error depends upon the optical-path difference and image size of the object being measured, as well as upon the half-shade phase difference. For a small half-shade phase difference the error is practically imperceptible and for the half-shade strip giving half-wave retardation it attains maximum values. In the case of homogeneous objects, the images of which are as large as 1.5–2° in the field of view of the microscope, this error does not usually produce inaccuracies greater than ± λ/100 in optical-path-difference measurements. Using the half-shade strip with a diaphragm which masks the misleading background and enables an observer to see the matched image areas only, the optical-path difference can be measured with accuracy ± 0.003λ or better.