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 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.     

Ultra-high-speed phase-sensitive optical coherence reflectometer with a stretched pulse supercontinuum source

We demonstrate an ultra-high-speed phase-sensitive time-wavelength-domain optical coherence reflectometer with a stretched pulse supercontinuum source. A pulsed fiber laser operating at 10 MHz repetition rate was used to generate a pulsed supercontinuum of 30 ps pulse duration by using a nonlinear optical fiber. The supercontinuum pulses are stretched into 70 ns pulses with a highly dispersive fiber. With this stretched pulse source, we have built a phase-sensitive optical coherence reflectometer that measures the spectral interferogram of reflected light. By using the linear relation between the wavelength and the temporal position in a linearly chirped pulse, ultra-high-speed spectrum measurement can be obtained with this method in the time domain. We have demonstrated ultra-high-speed two-dimensional surface profiling for a standard image target and high-speed single-point monitoring for a fixed point under vibrational motion. It is shown that the measurement speed for the position of a single point can be as fast as 2.5 MHz, while the position accuracy can be better than 4.49 nm.     

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.     

On coherence in neutron imaging

The variety of imaging signals in neutron radiography and tomography became quite large compared to the pure absorption and scattering contrast in neutron radiographies and topographies in the early sixties or seventies of the last century. The diversity of absorption based techniques for neutron radiography and tomography is comparable to coherence based imaging techniques such as phase contrast, differential phase contrast, dark field imaging, diffraction enhanced contrast, refraction contrast, ultra small angle scattering contrast, grating interferometry and crystal interferometry, also the spin of the neutron was successfully used for imaging [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11] and [12]. We show which effects (total reflection, diffraction, refraction) contribute to e.g. a step boundary or a phase boundary. Taking this simple object, one can learn to understand the imaging procedure and what is displayed in a radiograph.     

Harmonic spatial coherence imaging: an ultrasonic imaging method based on backscatter coherence

We introduce a harmonic version of the short-lag spatial coherence (SLSC) imaging technique, called harmonic spatial coherence imaging (HSCI). The method is based on the coherence of the second-harmonic backscatter. Because the same signals that are used to construct harmonic B-mode images are also used to construct HSCI images, the benefits obtained with harmonic imaging are also obtained with HSCI. Harmonic imaging has been the primary tool for suppressing clutter in diagnostic ultrasound imaging, however secondharmonic echoes are not necessarily immune to the effects of clutter. HSCI and SLSC imaging are less sensitive to clutter because clutter has low spatial coherence. HSCI shows favorable imaging characteristics such as improved contrast-to-noise ratio (CNR), improved speckle SNR, and better delineation of borders and other structures compared with fundamental and harmonic B-mode imaging. CNRs of up to 1.9 were obtained from in vivo imaging of human cardiac tissue with HSCI, compared with 0.6, 0.9, and 1.5 in fundamental B-mode, harmonic B-mode, and SLSC imaging, respectively. In vivo experiments in human liver tissue demonstrated SNRs of up to 3.4 for HSCI compared with 1.9 for harmonic B-mode. Nonlinear simulations of a heart chamber model were consistent with the in vivo experiments.     

Phase coherence imaging of grained materials

Ultrasound detection and evaluation of flaws in materials showing structural noise (austenitic steels, titanium alloys, composites, etc.) is difficult because of the low flaw-to-grain noise ratio. Much research has been performed looking for methods to improve flaw detection in grained materials. Many approaches require a cumbersome tuning process to select the correct parameter values or to use iterative techniques. In this work, the technique of phase coherence imaging is proposed to improve the flaw-to-grain noise ratio. The technique weights the output of a conventional beamformer with a coherence factor obtained from the aperture data phase dispersion. It can be simply implemented in real-time and it operates automatically, without needing any parameter adjustment. This paper presents the theoretical basis of phase coherence imaging to reduce grain noise, as well as experimental results that confirm the expected performance.     

Three-dimensional coherence imaging in the Fresnel domain

We show that three-dimensional incoherent primary sources can be reconstructed from finite-aperture Fresnel-zone mutual intensity measurements by means of coordinate and Fourier transformation. The spatial bandpass and impulse response for three-dimensional imaging that result from use of this approach are derived. The transverse and longitudinal resolutions are evaluated as functions of aperture size and source distance. The longitudinal resolution of three-dimensional coherence imaging falls inversely with the square of the source distance in both the Fresnel and Fraunhofer zones. We experimentally measure the three-dimensional point-spread function by using a rotational shear interferometer.     

Estimation of longitudinal resolution in optical coherence imaging

The spectral shape of a source is of prime importance in optical coherence imaging because it determines several aspects of image quality, especially longitudinal resolution. Wide spectral bandwidth, which provides short coherence length, is sought to obtain high-resolution imaging. To estimate longitudinal resolution, the spectral shape of a source is usually assumed to be Gaussian, although the spectra of real sources are typically non-Gaussian. We discuss the limit of this assumption regarding the estimation of longitudinal resolution. To this end, we also investigate how coherence length is related to longitudinal resolution through the evaluation of different definitions of the coherence length. To demonstrate our purpose, the coherence length for several theoretical and real spectral shapes of sources having the same spectral bandwidth and central wavelength is computed. The reliability of coherence length computations toward the estimation of longitudinal resolution is discussed.     

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.     

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.     

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.     

Cancellation of coherent artifacts in optical coherence tomography imaging

Coherent artifacts in optical coherence tomography (OCT) images can severely degrade image quality by introducing false targets if no targets are present at the artifact locations. Coherent artifacts can also add constructively or destructively to the targets that are present at the artifact locations. This constructive or destructive interference will result in cancellation of the true targets or in display of incorrect echo amplitudes of the targets. We introduce the use of a nonlinear deconvolution algorithm, CLEAN, to cancel coherent artifacts in OCT images of extracted human teeth. The results show that CLEAN can reduce the coherent artifacts to the noise background, sharpen the air-enamel and enamel-dentin interfaces, and improve the image contrast.     

Determining elastic properties of skin by measuring surface waves from an impulse mechanical stimulus using phase-sensitive optical coherence tomography

The mechanical properties of skin are important tissue parameters that are useful for understanding skin patho-physiology, which can aid disease diagnosis and treatment. This paper presents an innovative method that employs phase-sensitive spectral-domain optical coherence tomography (PhS-OCT) to characterize the biomechanical properties of skin by measuring surface waves induced by short impulses from a home-made shaker. Experiments are carried out on single and double-layer agar–agar phantoms, of different concentrations and thickness, and on in vivo human skin, at the forearm and the palm. For each experiment, the surface wave phase-velocity dispersion curves were calculated, from which the elasticity of each layer of the sample was determined. It is demonstrated that the experimental results agree well with previous work. This study provides a novel combination of PhS-OCT technology with a simple and an inexpensive mechanical impulse surface wave stimulation that can be used to non-invasively evaluate the mechanical properties of skin in vivo, and may offer potential use in clinical situations.     

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.     

MVDR-based coherence weighting for high-frame-rate adaptive imaging

Some success has been demonstrated in the extensive studies of adaptive imaging, but these approaches are generally not suitable for high-frame-rate (HFR) imaging where broad transmit beams are required. In this study, we propose an effective adaptive imaging method suitable for HFR imaging based on coherence-factor (CF) weighting and the minimum-variance-distortionless-response (MVDR) method. The CF is an index of focusing quality estimated from receive-channel data in which the amplitude of each image pixel is weighted by the corresponding CF so as to reduce the unwanted sidelobes. Direct implementation of CF weighting in HFR imaging does not provide satisfactory results because the broad transmit beams required for HFR imaging reduce the accuracy of CF calculations. In this study, we alleviated this problem by applying the MVDR method. We test the proposed method with the synthetic transmit aperture method where only 8 firings are required to form an image. Both simulations and clinical breast imaging data were used, and the proposed method enhanced the mean contrast by around 4.6 dB and the mean contrast-to-noise ratio by around 20%. The results demonstrate that the proposed method is effective at improving the image quality.     

Adaptive imaging using the generalized coherence factor

Sound-velocity inhomogeneities degrade both spatial and contrast resolutions. This paper proposes a new adaptive imaging technique that uses the generalized coherence factor (GCF) to reduce the focusing errors resulting from the sound-velocity inhomogeneities. The GCF is derived from the spatial spectrum of the received aperture data after proper receive delays have been applied. It is defined as the ratio of the spectral energy within a prespecified low-frequency range to the total energy. It is demonstrated that the low-frequency component of the spectrum corresponds to the coherent portion of the received data, and that the high-frequency component corresponds to the incoherent portion. Hence, the GCF reduces to the coherence factor defined in the literature if the prespecified low-frequency range is restricted to DC only. In addition, the GCF is also an index of the focusing quality and can be used as a weighting factor for the reconstructed image. The efficacy of the GCF technique is demonstrated for focusing errors resulting from the sound-velocity inhomogeneities. Simulations and real ultrasound data are used to evaluate the efficacy of the proposed GCF technique. The characteristics of the GCF, including the effects of the signal-to-noise ratio and the number of channels, are also discussed. The GCF technique also is compared with the correlation-based technique and the parallel adaptive receive compensation algorithm; the improvement in image quality obtained with the proposed technique rivals that of the latter technique. In the presence of a displaced phase screen, this proposed technique also outperforms the correlation-based technique. Computational complexity and implementation issues also are addressed.     

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 prediction of chaotic time series

We report on improved phase-space prediction of chaotic time series. We propose a new neighbour-searching strategy which corrects phase-space distortion arising from noise, finite sampling time and limited data length. We further establish a robust fitting algorithm which combines phase-space transformation, weighted regression and singular value decomposition least squares to construct a local linear prediction function. The scaling laws of prediction error in the presence of noise with various parameters are discussed. The method provides a practical iterated prediction approach with relatively high prediction performance. The prediction algorithm is tested on maps (Logistic, Hénon and Ikeda), finite flows (Rössler and Lorenz) and a laser experimental time series, and is shown to give a prediction time up to or longer than five times the Lyapunov time. The improved algorithm also gives a reliable prediction when using only a short training set and in the presence of small noise.