Effects of incident illumination on in-line phase-contrast imaging

Effects of incident illumination on phase-contrast images obtained by means of free-space propagation are investigated under the "transport-of-intensity" approximation. Analytical expressions for image intensity distribution are derived in the cases of coherent quasi-plane and quasi-spherical incident waves, as well as for spatially incoherent and quasi-homogeneous sources and some other types of sources. Practical methods for measuring the relevant parameters of the incident radiation are discussed together with formulas allowing one to calculate the effect of these parameters on the image intensity distribution. The results are expected to be useful in quantitative in-line imaging, phase retrieval, and tomography with polychromatic and spatially partially coherent radiation. As an application we present a method for simultaneous "automatic" phase retrieval and spatial deconvolution in in-line imaging of homogeneous objects using extended polychromatic x-ray sources.     

Phase-space formulation for phase-contrast x-ray imaging

Phase-space formulation based on the Wigner distribution has been presented for analyzing phase-contrast image formation. Based on the statistical nature and affine canonical covariance of Wigner distributions in the phase space, we show that the partial coherence effects of incident x-ray wave field on image intensity are simply accounted for by a multiplication factor, which is the reduced complex degree of coherence of the incident x-ray wave field. We show especially that with the undulator sources one cannot obtain the phase-contrast intensity by summing over the contributions from all electron positions, since the van Cittert-Zernike theorem fails in general for undulators. We derive a comprehensive formula that quantifies the effects of partial spatial coherence, polychromatic spectrum, body attenuation, imaging-detector resolution, and radiation dose on phase-contrast visibility in clinical imaging. The results of our computer modeling and simulations show how the formula can provide design guidelines and optimal parameters for clinical x-ray phase-contrast imaging systems.     

Phase-space evolution of x-ray coherence in phase-sensitive imaging

X-ray coherence evolution in the imaging process plays a key role for x-ray phase-sensitive imaging. In this work we present a phase-space formulation for the phase-sensitive imaging. The theory is reformulated in terms of the cross-spectral density and associated Wigner distribution. The phase-space formulation enables an explicit and quantitative account of partial coherence effects on phase-sensitive imaging. The presented formulas for x-ray spectral density at the detector can be used for performing accurate phase retrieval and optimizing the phase-contrast visibility. The concept of phase-space shearing length derived from this phase-space formulation clarifies the spatial coherence requirement for phase-sensitive imaging with incoherent sources. The theory has been applied to x-ray Talbot interferometric imaging as well. The peak coherence condition derived reveals new insights into three-grating-based Talbot-interferometric imaging and gratings-based x-ray dark-field imaging.     

Determination of the size and structure of an X-pinch x-ray source from the diffraction pattern produced by microfabricated slits

X-pinch plasma emits subnanosecond bursts of x rays in the 3-10-keV energy range from a small source. As such, it has been used for high-resolution point-projection imaging of small, dense, rapidly changing plasmas as well as for submillimeter-thick biological samples. In addition to the effect of source size on geometric resolution, a small source size can also provide high spatial coherence of x rays, enabling the rays to be used for imaging weakly absorbing objects with excellent spatial resolution by a method called phase-contrast imaging. To determine the source size, we microfabricated gold slits and imaged them in a point-projection radiography configuration. The shape of the shadow image pattern depends on the source size and energy band of the x rays, the shape and material used for the slits, and the geometry of the experiment. Experimental results have been compared with wave-optics calculations of the expected image pattern as a function of all the parameters listed above. For example, assuming a Gaussiansource distribution, an effective source size in 2.5-4.1 A radiation (1 A = 0.1 nm) of 1.2 +/- 0.5 microm (full width at half-maximum) was determined for a 20-microm Mo wire X pinch. Characterization of the size and structure of the x-ray bursts from X pinches by the use of different wire materials and different slit structures is made.     

Miniaturized three-dimensional endoscopic imaging system based on active stereovision

A miniaturized three-dimensional endoscopic imaging system is presented. The system consists of two imaging in channels that can be used to obtain an image from an object of interest and to project as tructured light onto the imaged object to measure the surface topology. The structured light was generated with a collimated monochromatic light source and a holographic binary phase grating. The imaging and projection channels were calibrated by use of a modified pinhole camera. The surface profile was extracted by use of triangulation between the projected feature points and the two channel ofthe endoscope. The imaging system was evaluated in three-dimensional measurements of several objects with known geometries. The results show that surface profiles of the objects with different surfaces and dimensions can be obtained at high accuracy. The in vivo measurements at tissue sites of human skin and an oral cavity demonstrated the potential of the technique for clinical applications.     

Noninterferometric quantitative phase imaging with soft x rays

We demonstrate quantitative noninterferometric x-ray phase-amplitude measurement. We present results from two experimental geometries. The first geometry uses x rays diverging from a point source to produce high-resolution holograms of submicrometer-sized objects. The measured phase of the projected image agrees with the geometrically determined phase to within +/-7%. The second geometry uses a direct imaging microscope setup that allows the formation of a magnified image with a zone-plate lens. Here a direct measure of the object phase is made and agrees with that of the magnified object to better than +/-10%. In both cases the accuracy of the phase is limited by the pixel resolution.     

Role of phase information and eye pursuit in the detection of moving objects in noise

As part of an ongoing study that uses objective image quality measures to optimize medical imaging x-ray fluoroscopy, we investigated two basic features of the detection of moving cylinders that mimic arteries, catheters, and guide wires. First, we compared detection with and without a phase cue consisting of a nearby alternating light and dark square. Depending on object size and velocity, phase cuing improved detection from 1% to 15% and gave an average of 6%, an effect much smaller than the 38% predicted from a Monte Carlo simulation of the ideal observer. Evidently, humans were limited in their ability to incorporate knowledge of the phase cue. Second, we evaluated the effect of eye pursuit of a fixation point that moved with the target. In general, motion at the highest velocity degraded (74%) and enhanced (68%) detection of small and large objects, respectively. With eye pursuit, both effects were substantially reduced in a manner consistent with a reduced retinal velocity. Our data compared favorably with a human observer model that included a spatiotemporal contrast sensitivity response and smooth-pursuit eye movements with a gain of 0.8. These mechanisms of perception are thought to be present in coronary artery x-ray fluoroscopy imaging, where phase information is available from the moving heart and where motion markers are available from x-ray opaque markers incorporated in thin catheters and guide wires.     

High-resolution ab initio three-dimensional x-ray diffraction microscopy

Coherent x-ray diffraction microscopy is a method of imaging nonperiodic isolated objects at resolutions limited, in principle, by only the wavelength and largest scattering angles recorded. We demonstrate x-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the three-dimensional diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a nonperiodic object. We also construct two-dimensional images of thick objects with greatly increased depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution with x-ray undulator radiation and establishes the techniques to be used in atomic-resolution ultrafast imaging at x-ray free-electron laser sources.     

Optical phase retrieval by use of first Born- and Rytov-type approximations

The first Born and Rytov approximations of scattering theory are introduced in their less familiar near-field versions. Two algorithms for phase retrieval based on these approximations are then described. It is shown theoretically and by numerical simulations that, despite the differences in their formulation, the two algorithms deliver fairly similar results when used for optical phase retrieval in the near and intermediate fields. The algorithms are applied to derive explicit solutions to four phase-retrieval problems of practical relevance to quantitative phase-contrast imaging and tomography. An example of successful phase reconstruction by use of the Born-type algorithm with an experimental x-ray image is presented.     

Magnification-type x-ray imaging system: optimum design and image restoration

A magnification-type x-ray imaging system, that is, an x-ray microscope, is evaluated by taking into account the partial coherency of the illumination of the objects. The transfer characteristic proposed in an earlier paper [J. Opt. Soc. Am. A 1, 11 (1984)] is used for the evaluation, and based on the results, an optimum design for a high-resolution x-ray imaging system is discussed. The image restoration method for this system is also shown.     

Theory of quantitative phase-contrast computed tomography

Phase-contrast x-ray computed tomography (CT) is an emerging imaging technique that can be implemented at third-generation synchrotron radiation sources or by using a microfocus x-ray source. Promising results have recently been obtained in materials science and medicine. At the same time, the lack of a mathematical theory comparable with that of conventional CT limits the progress in this field. Such a theory is now suggested, establishing a fundamental relation between the three-dimensional Radon transform of the object function and the two-dimensional Radon transform of the phase-contrast projection. A reconstruction algorithm is derived in the form of a filtered backprojection. The filter function is given in the space and spatial-frequency domains. The theory suggested enables one to quantitatively determine the refractive index of a weakly absorbing medium from x-ray intensity data measured in the near-field region. The results of computer simulations are discussed.     

Cone-beam tomography with a digital camera

We show that x-ray computer tomography algorithms can be applied with minimal alteration to the three-dimensional reconstruction of visible sources. Diffraction and opacity affect visible systems more severely than x-ray systems. For camera-based tomography, diffraction can be neglected for objects within the depth of field. We show that, for convex objects, opacity has the effect of windowing the angular observation range and thus blurring the reconstruction. For concave objects, opacity leads to nonlinearity in the transformation from object to reconstruction and may cause multiple objects to map to the same reconstruction. In x-ray tomography, the contribution of an object point to a line integral is independent of the orientation of the line. In optical tomography, however, a Lambertian assumption may be more realistic. We derive an expression for the blur function (the patch response) for a Lambertian source. We present experimental results showing cone-beam reconstruction of an incoherently illuminated opaque object.     

Imaging phase objects with square-root, Foucault, and Hoffman real filters: a comparison

Methods of imaging phase objects are considered. First the square-root filter is inferred from a definition of fractional-order derivatives given in terms of the integration of a fractional order called the Riemann-Liouville integral. Then we present a comparison of the performance of three frequency-domain real filters: square root, Foucault, and Hoffman. The phase-object imaging method is useful as a phase-shift measurement technique under the condition that the output image intensity is a known function of object phase. For the square-root filter it is the first derivative of the object phase function. The Foucault filter, in spite of its position, gives output image intensities expressed by Hilbert transforms. The output image intensity obtained with the Hoffman filter is not expressed by an analytical formula. The performance of the filters in a 4f imaging system with coherent illumination is simulated by use of VirtualLab 1.0 software.     

X射线同轴相衬成像实验

X射线相衬成像技术对软组织成像时比基于衰减的传统X射线成像技术优势明显,现在亟待发展一套广泛适用的相衬成像理论来指导其发展和临床应用．首先介绍了同轴相衬成像及相位成像的原理,随后根据菲涅耳．基尔霍夫衍射理论,利用数值模拟的方法研究微焦点源的尺寸对图像可见度的影响,最后在数值模拟结果指导下通过实验室直径为50μm的微焦点源X射线成像系统获得了厚度为150μm左右塑料气泡膜的相衬图像．     

Influence of illuminating beyond the object support on Zernike-type phase contrast filtering

A general analysis of the image fill-factor influence on Zemike-type phase contrast filtering is presented. We define image fill factor as the ratio of the object support area over the illuminating area. We first consider binary-phase objects and then generalize to arbitrarily quantized and continuous-phase objects. Numerical simulations are presented for binary- and quadratic-phase objects, where the contrast of the output image is evaluated as a function of the image fill factor, image phase variations, and filter phase. The results obtained show that the image fill factor can significantly modify the contrast and irradiance of the contrasted image.     

Investigation of the Cauchy-Riemann equations for one-dimensional image recovery in intensity interferometry

A method of image recovery using noniterative phase retrieval is proposed and investigated by simulation. This method adapts the Cauchy-Riemann equations to evaluate derivatives of phase based on derivatives of magnitude. The noise sensitivity of the approach is reduced by employing a least-mean-squares fit. This method uses the analytic properties of the Fourier transform of an object, the magnitude of which is measured with an intensity interferometer. The solution exhibits the degree of nonuniqueness expected from root-flipping arguments for the one-dimensional case, but a simple assumption that restricts translational ambiguity also restricts the space of solutions and permits essentially perfect reconstructions for a number of non-symmetric one-dimensional objects of interest. Very good reconstructions are obtained for a large fraction of random objects, within an overall image flip, which may be acceptable in many applications. Results for the retrieved phase and recovered images are presented for some one-dimensional objects and for different noise levels. Extensions to objects of two dimensions are discussed. Requirements for signal-to-noise ratio are derived for intensity interferometry with use of the proposed processing.     

Partially coherent image formation with x-ray microscopes

Image formation with partially coherent radiation is evaluated with the Hopkins formula and then applied to x-ray microscopy. Image characteristics expected from instruments with circular and annular pupils in partially coherent conditions are considered for two-point objects and a knife-edge object. The theoretically expected values for image characteristics that are easy accessible by an experiment, such as the width of a knife edge, are given for various x-ray microscopes.     

Vectorial, high-numerical-aperture study of phase-contrast microscopes

We describe, using a high-numerical-aperture vectorial model, the image formation of phase-contrast microscopes. In particular, imaging of a weak phase object is considered. We show that, partly owing to the fact that phase-contrast microscopes are interference microscopes, their image formation is fundamentally different from that of conventional transmission optical microscopes. Our detailed analysis reveals a number of yet undocumented properties of these microscopes, including that depending on the given configuration, they can exhibit an improved lateral resolution when larger detectors are used in comparison with that obtained for a small detector size. We present numerical examples to explain this phenomenon and discuss our analysis in detail.     

基于图像处理的声相云图评价方法研究

基于图像处理,提出了声相云图评价方法,用于评价声相仪的声源定位误差。分析了声相仪的成像原理,提出将方位角误差和俯仰角误差作为声相云图声源定位误差的评价指标。利用差影法提取声相云图的声源定位成像区域,并经过灰度二值化、腐蚀膨胀和加权平均之后,计算出成像区域中心的像素坐标。在声相仪不同抓拍距离平面内,通过图像标定得到成像区域中心在实际物理空间上的位置坐标,将其与所定位的声源实际位置坐标相比较,计算得到方位角误差和俯仰角误差。实验结果表明,该方法所得方位角和俯仰角与声源实际位置坐标计算所得到的真实值相比,两者差异较小,能够客观地对声相仪的声源定位误差进行评价,且操作简单。