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.     

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.     

X-ray omni microscopy

The science of wave‐field phase retrieval and phase measurement is sufficiently mature to permit the routine reconstruction, over a given plane, of the complex wave‐function associated with certain coherent forward‐propagating scalar wave‐fields. This reconstruction gives total knowledge of the information that has been encoded in the complex wave‐field by passage through a sample of interest. Such total knowledge is powerful, because it permits the emulation in software of the subsequent action of an infinite variety of coherent imaging systems. Such ‘virtual optics’, in which software forms a natural extension of the ‘hardware optics’ in an imaging system, may be useful in contexts such as quantitative atom and X‐ray imaging, in which optical elements such as beam‐splitters and lenses can be realized in software rather than optical hardware. Here, we develop the requisite theory to describe such hybrid virtual‐physical imaging systems, which we term ‘omni optics’ because of their infinite flexibility. We then give an experimental demonstration of these ideas by showing that a lensless X‐ray point projection microscope can, when equipped with the appropriate software, emulate an infinite variety of optical imaging systems including those which yield interferograms, Zernike phase contrast, Schlieren imaging and diffraction‐enhanced imaging.     

Quantitative phase-amplitude microscopy II: differential interference contrast imaging for biological TEM

Although phase contrast microscopy is widespread in optical microscopy, it has not been as widely adopted in transmission electron microscopy (TEM), which has therefore to a large extent relied on staining techniques to yield sufficient contrast. Those methods of phase contrast that are used in biological electron microscopy have been limited by factors such as the need for small phase shifts in very thin samples, the requirement for difficult experimental conditions, or the use of complex data analysis methods. We here demonstrate a simple method for quantitative TEM phase microscopy that is suitable for large phase shifts and requires only two images. We present a TEM phase image of unstained Radula sp. (liverwort spore). We show how the image may be transformed into the differential interference contrast image format familiar from optical microscopy. The phase images contain features not visible with the other imaging modalities. The resulting technique should permit phase contrast TEM to be performed almost as readily as phase contrast optical microscopy.     

Linear phase imaging using differential interference contrast microscopy

We propose an extension to Nomarski differential interference contrast microscopy that enables isotropic linear phase imaging. The method combines phase shifting, two directions of shear and Fourier‐space integration using a modified spiral phase transform. We simulated the method using a phantom object with spatially varying amplitude and phase. Simulated results show good agreement between the final phase image and the object phase, and demonstrate resistance to imaging noise.     

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.     

微分相衬干涉显微镜定量测量表面形貌

改进了用于定量测量样品表面形貌的微分相衬干涉显微镜系统,对系统中由Nomarski棱镜引起的相位差β的消零工作提出了一种新的方法,实验证明是有效可靠的,并且对样品表面三维形貌重构、截面轮廓比对及系统的测量精度进行了实验研究.     

Reconstruction of the complex reflectance function in acoustic microscopy

We describe the theory and practical implementation of an iterative computer algorithm (an extension of the Gerchberg Saxton algorithm, originally developed for electron microscopy) for enabling an estimate of the complex reflectance function of a material to be reconstructed from measured values of only the magnitude of the response of an acoustic microscope (i.e. without the phase of the transducer voltage). Results are presented for eight materials measured with a spherical lens (at 320 MHz) and five with a cylindrical line-focus lens (at 210 and 228 MHz).     

Automated noninvasive epithelial cell counting in phase contrast microscopy images with automated parameter selection

Cell counting is commonly used to determine proliferation rates in cell cultures and for adherent cells it is often a ‘destructive’ process requiring disruption of the cell monolayer resulting in the inability to follow cell growth longitudinally. This process is time consuming and utilises significant resource. In this study a relatively inexpensive, rapid and widely applicable phase contrast microscopy‐based technique has been developed that emulates the contrast changes taking place when bright field microscope images of epithelial cell cultures are defocused. Processing of the resulting images produces an image that can be segmented using a global threshold; the number of cells is then deduced from the number of segmented regions and these cell counts can be used to generate growth curves. The parameters of this method were tuned using the discrete mereotopological relations between ground truth and processed images. Cell count accuracy was improved using linear discriminant analysis to identify spurious noise regions for removal. The proposed cell counting technique was validated by comparing the results with a manual count of cells in images, and subsequently applied to generate growth curves for oral keratinocyte cultures supplemented with a range of concentrations of foetal calf serum. The approach developed has broad applicability and utility for researchers with standard laboratory imaging equipment.     

Improving DIC microscopy with polarization modulation

It is demonstrated experimentally, as well as analytically, that when the polarization of the light incident upon the first Nomarski–Wollaston prism in a differential interference contrast (DIC) light microscope is switched by 90°, image highlights are changed into shadows and vice versa. Using an inexpensive ferroelectric liquid-crystal modulator, which is easily installed in the microscope, this switching can be done at 30 frames s⁻¹, synchronized to the camera. Subtraction of alternate digitized frames generates a stream of images in which contrast is doubled, compared with conventional video-enhanced DIC, while image defects and noise tend to cancel. Subtraction of alternate images is carried out efficiently by frame buffer operations and amounts to massively parallel synchronous detection. The new method eliminates the problems inherent in obtaining a separate background image, as required by current video-enhanced DIC practice, without loss of resolution.     

Quantitative analysis of backscattered-electron contrast in scanning electron microscopy

Backscattered-electron scanning electron microscopy (BSE-SEM) imaging is a valuable technique for materials characterisation because it provides information about the homogeneity of the material in the analysed specimen and is therefore an important technique in modern electron microscopy. However, the information contained in BSE-SEM images is up to now rarely quantitatively evaluated. The main challenge of quantitative BSE-SEM imaging is to relate the measured BSE intensity to the backscattering coefficient η and the (average) atomic number Z to derive chemical information from the BSE-SEM image. We propose a quantitative BSE-SEM method, which is based on the comparison of Monte–Carlo (MC) simulated and measured BSE intensities acquired from wedge-shaped electron-transparent specimens with known thickness profile. The new method also includes measures to improve and validate the agreement of the MC simulations with experimental data. Two different challenging samples (ZnS/Zn(O_xS_1–x)/ZnO/Si-multilayer and PTB7/PC₇₁BM-multilayer systems) are quantitatively analysed, which demonstrates the validity of the proposed method and emphasises the importance of realistic MC simulations for quantitative BSE-SEM analysis. Moreover, MC simulations can be used to optimise the imaging parameters (electron energy, detection-angle range) in advance to avoid tedious experimental trial and error optimisation. Under optimised imaging conditions pre-determined by MC simulations, the BSE-SEM technique is capable of distinguishing materials with small composition differences.     

Imaging of semiconducting polymer blend systems using environmental scanning electron microscopy and environmental scanning transmission electron microscopy

This study has investigated the potential of environmental electron microscopy techniques for studying the structure of polymer‐based electronic devices. Polymer blend systems composed of F8BT and PFB were examined. Excellent contrast, both topographical and compositional, can be achieved using both conventional environmental scanning electron microscopy (ESEM) and a transmission detector giving an environmental scanning transmission electron microscope (ESTEM) configuration. Controllable charging effects present in the ESEM were observed, giving rise to a novel voltage contrast. This shows the potential of such contrast to provide excellent images of phase structure and charge distributions.     

Diabetes screening by telecentric digital holographic microscopy

Diabetes is currently the world's fastest growing chronic disease and it is caused by deficient production of insulin by the endocrine pancreas or by abnormal insulin action in peripheral tissues. This results in persistent hyperglycaemia that over time may produce chronic diabetic complications. Determination of glycated haemoglobin level is currently the gold standard method to evaluate and control sustained hyperglycaemia in diabetic people. This measurement is currently made by high‐performance liquid chromatography, which is a complex chemical process that requires the extraction of blood from the antecubital vein. To reduce the complexity of that measurement, we propose a fully‐optical technique that is based in the fact that there are changes in the optical properties of erythrocytes due to the presence of glucose‐derived adducts in the haemoglobin molecule. To evaluate these changes, we propose to perform quantitative phase maps of erythrocytes by using telecentric digital holographic microscopy. Our experiments show that telecentric digital holographic microscopy allows detecting, almost in real time and from a single drop of blood, significant differences between erythrocytes of diabetic patients and healthy patients. Besides, our phase measurements are well correlated with the values of glycated haemoglobin and the blood glucose values.     

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.     

Phase‐retrieved pupil function and coherent transfer function in confocal microscopy

This work reports on the retrieval of the pupil function and coherent transfer function of a coherent reflection type confocal microscope from simulated measurements of the intensity point spread function. Two phase retrieval algorithms are presented in this vein, which incorporate the multiple pupil dependence of image formation in confocal microscopy. Verification of the algorithms follows by numerical simulations.     

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.     

Multimodal microscopy by digital image processing

A matching algorithm is proposed for aligning microscope images obtained using different modalities, making use of cross-correlations of outputs from Prewitt's edge filter. Brightfield, phase contrast and differential interference contrast microscope images of algal and bacterial cells from an experimental, high-rate algal pond are used for illustration. The information content of multimodal images is explored using principal components analysis and colour displays, and an image which represents optical thickness is constructed digitally.     

Quantitative theory of ideal phase-contrast microscopy,taking object width into account

In ‘ideal’ phase-contrast microscopy all the direct light and none of the diffracted light is influenced by the phase plate in the back focal plane of the objective. Contrary to almost all previous work, it appears that the intensity of an ideal phase-contrast image is affected not only by the transmittance and retardation of the object and of the phase plate, but also by the width of the specimen (or total width of multiple specimens) relative to the microscopic field. Equations and computer code are presented with which the intensity of such images can be calculated. Previously published equations are special cases, and implicitly or explictly assume either that the object is of negligible width, or occupies precisely half the microscopic field. The absolute brightness of an image in ideal central dark-field microscopy is a function of the object retardation, but the intensity of the image relative to the background is a function only of the width of the object(s) relative to the field. The equations give results for ideal phase-contrast microscopy identical with those of a computer program simulating microscopic imaging. The program can in addition take into account non-ideal factors including a finite width of phase plate, finite objective aperture, deviations from best focus, glare, primary spherical aberration and obliquity of the coherent illumination.