Simulation of partially coherent image formation in a compact soft X-ray microscope

In this paper, we describe a numerical method of simulating two-dimensional images in a compact soft X-ray microscope using partially coherent illumination considerations. The work was motivated by recent test object images obtained by the latest generation in-house compact soft X-ray microscope, which showed diffraction-like artifacts not observed previously. The numerical model approximates the condenser zone plate as a secondary incoherent source represented by individually coherent but mutually incoherent source points, each giving rise to a separate image. A final image is obtained by adding up all the individual source point contributions. The results are compared with the microscope images and show qualitative agreement, indicating that the observed effects are caused by partially coherent illumination.     

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.     

Holographic methods in microscopy

Holography can be used to record, on a flat photographic plate, information about a three-dimensional object. In conventional microscopy a thin slice of an object is observed in focus and recorded. By combining microscopy and holography it is possible to encode, on the same flat record, all the depth information in a three-dimensional microscopic object, not just a single infocus section. Any section of the three-dimensional object may be subsequently reconstructed and brought into focus by using a suitable viewing system to decode the hologram. Arrangements for doing this are described. It is shown that in order to achieve the highest resolution imagery of a three-dimensional object, reversed wave reconstruction is necessary. As holograms are made and reconstructed using a coherent laser light source, holographic microscopes are easily adapted for interferometry and an example of this is described. The differences between coherent and conventional imagery are briefly considered. The coherence of the illumination gives rise to the problems of coherent noise and speckle. Coherent noise is due to stray reflections in the optical system and can be reduced by using as few surfaces as possible or by using holographic lenses. A speckle reduction technique employing a new type of holographic optical element is described and its application to the stereomicroscopy of fossil ostracods considered.     

Characterization of JEOL 2100F Lorentz-TEM for low-magnification electron holography and magnetic imaging

We present results that characterize the performance and capabilities of the JEOL 2100F-LM electron microscope to carry out holography and quantitative magnetic imaging. We find the microscope is well-suited for studies of magnetic materials, or for semi-conductor dopant profiling, where a large hologram width ( approximately 1 microm) and fine fringe spacing ( approximately 1.5 nm) are obtained with good contrast ( approximately 20%). We present, as well, measurements of the spherical aberration coefficient Cs=(108.7+/-9.6)mm and minimum achievable focal step delta f=(87.6+/-1.4)nm for the specially designed long-focal-length objective lens of this microscope. Further, we detail experiments to accurately measure the optical parameters of the imaging system typical of conventional holography setup in a transmission electron microscope. The role played by astigmatic illumination in the hologram formation is also assessed with a wave-optical model, which we present and discuss. The measurements obtained for our microscope are used to simulate realistic holograms, which we compare directly to experimental holograms finding good agreement. These results indicate the usefulness of measuring these optical parameters to guide the optimization of the experimental setup for a given microscope, and to provide an additional degree of practical experimental possibility.     

Probe retrieval in ptychographic coherent diffractive imaging

Ptychography is a coherent diffractive imaging method that uses multiple diffraction patterns obtained through the scan of a localized illumination on the specimen. Until recently, reconstruction algorithms for ptychographic datasets needed the a priori knowledge of the incident illumination. A new reconstruction procedure that retrieves both the specimen's image and the illumination profile was recently demonstrated with hard X-ray data. We present here the algorithm in greater details and illustrate its practical applicability with a visible light dataset. Improvements in the quality of the reconstruction are shown and compared to previous reconstruction techniques. Implications for future applications with other types of radiation are discussed.     

部分相干系统标准物体成像的计算机模拟

本文研究了部分相干条件下,不同相干度对标准物体象场分布的影响。表明了照明条件与部分相干光学系统成象之间有着十分密切的关系。基于H.H.Hopkins的部分相干成象理论,在IBM-PC/XT个人计算机上,建立了模拟部分相干条件下,一维标准物体成象的FORTRAN程序,从而为部分相干光学系统(微缩、显微系统等)的设计评价和最佳照明条件的选择,提供了可靠的途径;从对象差光学系统的计算表明,标准物体的象场强度分布,很灵敏地反映了光学系统的品质,它可以做为部分相干条件下,实际光学系统的质量判据。     

谱域OCT系统设计与实验研究

光学相干层析成像（Optical Coherence Tomography,OCT）是一种非侵入、非接触的新型光学成像技术,利用生物组织的后向散射光与参考光之间的弱相干实现结构成像,具有高灵敏度、高分辨率、成像速度快等特点。本文设计了一套基于LabVIEW软件平台下的谱域OCT成像系统,并对系统进行了测试与实验研究,验证了系统的可靠性与准确性。     

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.     

Linear versus non-linear structural information limit in high-resolution transmission electron microscopy

A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has different effects on the transfer of the linear and non-linear terms, such that the non-linear imaging contributions are damped less than the linear imaging contributions at high spatial frequencies. This will be important when coherent aberrations such as spherical aberration and defocus are reduced.     

A formula for the image intensity of phase objects in Zernike mode

I present an analytical expression for the image intensity of a phase object visualized in Zernike phase contrast mode. The formula is valid for periodic and non-periodic weak and strong objects, and accounts for the effects of finite illumination. The expression provided is intended as a generalization of the standard reference formula given in the Born and Wolf [Principles of Optics, sixth ed., Pergamon Press, New York, 1980, p. 427] textbook as well as of the formalism employed to evaluate imaging doses in Zernike mode [M. Malac, M. Beleggia, R. Egerton, Y. Zhu, Ultramicroscopy 108 (2008) 126]. I illustrate the usefulness of the improved expression by means of three examples: a sinusoidal phase grating, a Gaussian object, and a phase step. The optimal Zernike phase angle yielding maximum image contrast is found to be object-dependent and not necessarily equal to pi/2. Phase plate optimization criteria are derived and presented for two of the examples considered.     

Spatial incoherence in phase retrieval based on focus variation

We investigate the effect of spatial incoherence on two methods of phase retrieval based on focus variation: the transport of intensity equation and iterative wave function reconstruction. Spatial incoherence provides an upper bound on the defocus step size which should be used in each case. The requirement that phase information manifests itself in sufficient variation in the defocused images provides a lower bound on the defocus step size which should be used in each case. The scaling of these upper and lower bounds with object size and imaging resolution differs in such a way that, given the spatial incoherence properties of the source, for sufficiently low resolutions neither technique can retrieve phase information. The regions of applicability of the two techniques are discussed.     

Image sharpness and contrast transfer in coherent confocal microscopy

Confocal microscopes provide clear, thin optical sections with little disturbance from regions of the specimen that are not in focus. In addition, they appear to provide somewhat greater lateral and axial image resolution than with non-confocal microscope optics. To address the question of resolution and contrast transfer of light microscopes, a new test slide that enables the direct measurement of the contrast transfer characteristics (CTC) of microscope optics at the highest numerical aperature has been developed. With this new test slide, the performance of a confocal scanning laser microscope operating in the confocal reflection mode and the non-confocal transmission mode was examined. The CTC curves show that the confocal instrument maintains exceptionally high contrast (up to twice that with non-confocal optics) as the dimension of the object approaches the diffraction limit of resolution; at these dimensions, image detail is lost with non-confocal microscopes owing to a progressive loss of image contrast. Furthermore, we have calculated theoretical CTC curves by modelling the confocal and non-confocal imaging modes using discrete Fourier analysis. The close agreement between the theoretical and experimental CTC curves supports the earlier prediction that the coherent confocal and the incoherent non-confocal imaging mode have the same limit of resolution (defined here as the inverse of the spatial frequency at which the contrast transfer converges to zero). The apparently greater image resolution of the coherent confocal optics is a consequence of the improved contrast transfer at spacings which are close to the resolution limit.     

Electronic interface systems for goals of spectral domain optical coherence tomography

A setup for visualizing the internal structure of media, which partially scatter radiation, using the spectral domain optical coherence tomography (OCT) method is described. The special complex of electron interface systems, ensuring the operating speed of the spectral domain OCT system at a level of 10000 A-scans (longitudinal scans along the depth) per second, high dynamic imaging range, and complete suppression of coherent noise peculiar to the spectral method has been designed to eliminate artifacts characteristic of this method.     

Resolution in nonlinear laser scanning microscopy

The lateral and depth resolution of nonlinear microscopy was studied systematically. Nonlinear microscopy can be classified into several categories depending on the coherence properties of the process that generates the imaging signal from the illuminating light, on whether a single- or a two-beam geometry is used, and whether the optical setup is Type I or Type II. An evaluation of the imaging equations shows that (i) lateral and depth resolution improve with increasing nonlinearity, (ii) the differences between coherent and incoherent imaging diminish, and (iii) nonlinear imaging allows depth discrimination in Type I microscopy.     

大视场主动光学成像系统的成像研究

从主动光学成像系统的照明模型出发,研究了大视场情况下目标和景物的成像性质,分析了传输介质对照明和成像光束的衰减作用,得出了光学成像系统像面照度的计算公式,并对其衬比传递特性和视场大小对成像的影响进行了详细的分析,得出了小视场近似的条件,其结果可用于主动光学成像系统的设计、图像分析和目标识别.     

Influence of the elliptical illumination on acquisition and correction of coherent aberrations in high-resolution electron holography

In high-resolution off-axis electron holography, the interpretable lateral resolution is extended up to the information limit of the electron microscope by means of a correcting phase plate in Fourier space. A plane illuminating electron wave is generally assumed. However, in order to improve spatial coherence, which is essential for holography, the object under investigation is illuminated with an elliptically shaped electron source. This special illumination imposes a variation of beam directions over the field of view. Therefore, due to the interaction of beam tilt and coherent wave aberration, the effective aberrations vary over the field of view yielding a loss of isoplanicity. Consequently, in the past the aberrations were only corrected successfully for a small part of the field of view. However, a thorough analysis of the holographic imaging process shows that the imaging artifacts introduced by the elliptical illumination can be corrected under reconstruction by means of a phase curvature, which models the illuminating wave front. Applied in real space, this phase curvature is seamlessly incorporated into the correction process for coherent wave aberration resulting in an improvement of interpretable lateral resolution up to the information limit for the whole field of view.     

Flatness and distortion measurements in semiconductor manufacturing

In semiconductor manufacturing processes as currently employed, a 100% error-free mask pattern transfer into the resist layer of a silicon wafer is impossible. It is essentially limited by in-plane and out-of-plane deformations of the mask and wafer substrates. Another limitation is given by the non-error-free transfer system itself, resulting in distortions of the printed wafer pattern.Applied parallel coherent optical interference measurement methods for mask and wafer flatness, as well as for the detection of local distortions of imaging systems of lithographic printers, are presented in this paper.     

应用多个非球面优化鱼眼镜头的方法

对于鱼眼镜头一类光学系统,其超大视场的物点对于光学系统的成像,是符合平面对称光学系统的成像规律的。应用LU发展的平面对称光学系统的波像差理论,研究如何在鱼眼镜头光学系统中应用非球面对成像系统进行优化设计。首先,通过计算各个光学面的非球面系数对超大视场光学系统波像差的影响,找到受非球面系数变化影响最大的几个光学面;然后,以这几个面的非球面系数为变量,以光学系统调制传递函数作为评价函数,应用自适应归一化实数编码遗传算法,优化设计鱼眼镜头光学系统;最后,通过实例验证了所提出方法的有效性。所提出的方法可以有效地确定一个或多个最佳非球面的位置,对优化设计鱼眼镜头系统具有指导意义。