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.     

Phase-space reconstruction of focused x-ray fields

We apply the method of phase-space tomography to reconstruct x-ray beams focused using a compound refractive lens. We show that it is possible to decouple the effect of aberrations in the optical system from the field and hence measure both them and the original field. We recover the complex coherence function and find that it is consistent with expectations.     

Noninterferometric phase-contrast images obtained with incoherent x-ray sources

We report on what are believed to be the first full-scale images obtained with the coded aperture concept, which uses conventional x-ray sources without the need to collimate/aperture their output. We discuss the differences in the underpinning physical principles with respect to other methods, and explain why these might lead to a more efficient use of the source. In particular, we discuss how the evaluation of the first imaging system provided promising indications on the method's potential to detect details invisible to conventional absorption methods, use an increased average x-ray energy, and reduce exposure times-all important aspects with regards to real-world implementations.     

Coherence-contrast x-ray imaging based on x-ray interferometry

Coherence-contrast x-ray imaging--which detects changes in the degree of coherence caused by the placement of a sample in an x-ray interferometer--was developed for biomedical applications. Because the technique's sensitivity depends on the density gradient in the sample, it is particularly suitable for observing biomedical samples with large density differences, such as samples that include both biological soft tissue and bone. A measurement principle and method of this technique are described, and a fine coherence-contrast image of a mouse leg is given as an example result.     

Phase-space distributions for high-frequency fields

The Wigner distribution function and various windowed Fourier transforms are examples of phase-space distributions that are used, among other things, to formalize the link between ray and wave optics. It is well known that, in the limit of high frequencies, these distributions become localized for simple wave fields and therefore that the localization can be used to define the associated ray families. This localized form is characterized here for both the Wigner distribution function and a Gaussian windowed Fourier transform. Aside from the greater understanding of the distributions themselves, these results promise a clearer intuition of phase-space-based methods for optical modeling. In particular, regardless of the context, the geometric construction that is presented for estimating the Wigner distribution function gives a valuable appreciation of its highly structured and sometimes surprising form.     

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.     

Grazing-incidence hyperboloid-hyperboloid designs for wide-field x-ray imaging applications

The classical Wolter type I grazing-incidence x-ray telescope consists of a paraboloidal primary mirror and a confocal hyperboloidal secondary mirror. This design exhibits stigmatic imaging on-axis but suffers from coma, astigmatism, field curvature, and higher-order aberrations such as oblique spherical aberration. Wolter-Schwarzschild designs have been developed that strictly satisfy the Abbe sine condition and thus exhibit no spherical aberration or coma. However, for wide-field applications such as the solar x-ray imager (SXI), there is little merit in a design with stigmatic imaging on-axis. Instead, one needs to optimize some area-weighted-average measure of resolution over the desired operational field of view. This has traditionally been accomplished by mere despacing of the focal plane of the classical Wolter type I telescope. Here we present and evaluate in detail a family of hyperboloid-hyperboloid grazing-incidence x-ray telescope designs whose wide-field performance is much improved over that of an optimally despaced Wolter type I and even somewhat improved over that of an optimally despaced Wolter-Schwarzschild design.     

X-ray phase-contrast imaging: transmission functions separable in Cartesian coordinates

In-line, x-ray phase-contrast imaging is responsive to both phase changes and absorption as the x radiation traverses a body. Expressions are derived for phase-contrast imaging of objects having transmission functions separable in Cartesian coordinates. Starting from the Fresnel-Kirchhoff integral formula for image formation, an expression is found for the phase-contrast image produced by an x-ray source with nonvanishing dimensions. This expression is evaluated in limiting cases where the source-to-object distance is large, where the source acts as a point source, and where the weak phase approximation is valid. The integral expression for the image is evaluated for objects with simple geometrical shapes, showing the influence of the source dimensions on the visibility of phase-contrast features. The expressions derived here are evaluated for cases where the magnification is substantially greater than one as would be employed in biological imaging. Experiments are reported using the in-line phase-contrast imaging method with a microfocus x-ray source and a CCD camera.     

Phase-space measurements of micro-optical objects

The phase-space measurement of micro-optical objects with submillimeter dimensions is reported for the first time to our knowledge. The experimental data were compared with simulated results from interferometric measurements and were found to be in good agreement.     

High-resolution x-ray imaging of extended lasing plasmas

An x-ray imaging system with a bent focusing crystal was used for time-resolved one-dimensional imaging of a long plasma column of highly ionized aluminum. This scheme uses a focusing geometry with a spherically bent crystal and a slit on the Rowland circle. Alternative schemes of x-ray monochromatic imaging are briefly discussed. The homogeneity of the up to 40-mm-long laser-generated plasma column was studied with a temporal resolution of 100 ps. The potential spatial resolution of the instrument is 90 mum or better. Monochromatic images taken on the resonance Healpha line of Al XII characterize the homogeneity of a plasma generated to study a recombination x-ray laser scheme, giving an amplified spontaneous emission in AlXI.     

Application of a plastic scintillating fiber array for low-energy x-ray imaging

Interest in digital imaging has led to the development of new detectors in the form of large-area displays. Most of the recent improvements are based on charge-coupled devices, a:Si photodiodes arrays, and so on. Some of these photodetectors must be coupled to scintillating screens to convert the ionizing radiation into light. Fiber-optic screens offer an advantage for achieving this interface because the length (thickness) of the interaction medium does not contribute too much to the degradation of the spatial resolution. We discuss the possibility of using a plastic scintillating fiber (PSF) array for x-ray detection and imaging in the 10-keV range. Modulation-transfer-function (MTF) measurements of the PSF array are compared with the optics MTF of the imaging system (without the sample); cross talk in the fiber array is negligible, even though the fiber array thickness is 20 mm. The optimal thickness of the array is estimated experimentally.     

CdTe quantum dots and polymer nanocomposites for x-ray scintillation and imaging

Investigations are reported on the x-ray scintillation and imaging application of CdTe quantum dots (QDs) and their polymer nanocomposites. Aqueous CdTe QDs with emissions ranging between 510 and 680 nm were prepared and incorporated into polyvinyl alcohol or polymethyl methacrylate polymer matrices. The x-ray luminescent properties were evaluated and a resolution of 5 lines∕mm was obtained from the nanocomposite films. Additionally, the fast decay time, nonafterglow, and superior spectral match to conventional charge coupled devices, show that CdTe QD nanocomposites have high promise for x-ray imaging applications.     

Compensation of the inherent wave front curvature in digital holographic coherent microscopy for quantitative phase-contrast imaging

An approach is proposed for removing the wavefront curvature introduced by the microscope imaging objective in digital holography, which otherwise hinders the phase contrast imaging at reconstruction planes. The unwanted curvature is compensated by evaluating a correcting wave front at the hologram plane with no need for knowledge of the optial parameters, focal length of the imaging lens, or distances in the setup. Most importantly it is shown that a correction effect can be obtained at all reconstruction planes. Three different methods have been applied to evaluate the correction wave front and the methods are discussed in detail. The proposed approach is demonstrated by applying digital holography as a method of coherent microscopy for imaging amplitude and phase contrast of microstructures.     

Phase-space representation of iterative design processes

A large variety of design optimization methods have been proposed in recent years. Comparison of the relative performance of each method is a difficult task, and attempts to do so are often based on a limited number of numerical experiments. Recently, a ‘basins of attraction’ construction has been proposed as a graphical tool for investigating global performance of iterative design optimization methods, and as a basis for comparison of different methods. The phase-space representation presented in this paper is a companion to the basins of attraction construction. Basins of attraction reveal the relationship between starting design and final outcome of the solution process; the phase-space construction reveals that nature of the paths connecting the starting design and final outcome. The two constructions complement one another in summarizing the performance of design optimization processes. Both constructions are demonstrated in this paper, applied to the optimal design of an elastic grillage structure using Newton's method and the stress ratio method.     

Phase-space interpretation of deterministic phase retrieval

Deterministic phase retrieval is reinterpreted in terms of phase-space optics. A novel derivation of the transport-of-intensity equation is presented based on the Wigner distribution function and the ambiguity function. The phase retrieval problem is formulated as estimating the local first-order moment of the Wigner function from intensity information. A comparison with phase-space tomography suggests a generalization of deterministic phase retrieval that provides larger flexibility for signal recovery. In addition, one particular numerical implementation of generalized deterministic phase retrieval is presented. Simulated intensity data are used to validate the method.     

Wavelet-based image enhancement in x-ray imaging and tomography

We consider an application of the wavelet transform to image processing in x-ray imaging and three-dimensional (3-D) tomography aimed at industrial inspection. Our experimental setup works in two operational modes-digital radiography and 3-D cone-beam tomographic data acquisition. Although the x-ray images measured have a large dynamic range and good spatial resolution, their noise properties and contrast are often not optimal. To enhance the images, we suggest applying digital image processing by using wavelet-based algorithms and consider the wavelet-based multiscale edge representation in the framework of the Mallat and Zhong approach [IEEE Trans. Pattern Anal. Mach. Intell. 14, 710 (1992)]. A contrast-enhancement method by use of equalization of the multiscale edges is suggested. Several denoising algorithms based on modifying the modulus and the phase of the multiscale gradients and several contrast-enhancement techniques applying linear and nonlinear multiscale edge stretching are described and compared by use of experimental data. We propose the use of a filter bank of wavelet-based reconstruction filters for the filtered-backprojection reconstruction algorithm. Experimental results show a considerable increase in the performance of the whole x-ray imaging system for both radiographic and tomographic modes in the case of the application of the wavelet-based image-processing algorithms.