Abstract: Since the middle of the 1990s, X-ray phase imaging including phase tomography has been attracting increasing attention. The advantage of X-ray phase imaging is that an extremely high sensitivity is achieved for weak-absorbing materials, such as biological soft tissues, which generate a poor contrast by conventional methods. Medical and biological imaging is the main target of X-ray phase imaging, and several trials using synchrotron radiation sources and laboratory sources have been made. Measuring and controlling the X-ray phase are also significant for X-ray microscopy with a high spatial resolution, and innovative techniques are attracting intense interest. The progress of X-ray phase imaging is supported by the developments in X-ray sources such as third-generation synchrotron radiation sources, optical elements, and image detectors. This article describes the advantages of using X-ray phase information and reviews various techniques studied for X-ray phase imaging.

Abstract: A novel swept-laser-based Fourier-domain optical coherence tomography system using an electro-optic phase modulator was demonstrated. The imaging range was doubled by cancellation of the mirror image. The elimination of low-frequency noises resulting from dc and autocorrelation terms increased the sensitivity by 20 dB.

Abstract: X ray radiography and tomography are important tools in medicine as well as in life science and materials science. Not long ago an approach called in-line holography based on simple propagation became possible using partially coherent synchrotron beams like the ones available at the European Synchrotron Radiation Facility (ESRF). Theoretical and experimental work by Cloetens et al. [Appl. Phys. Lett 75, 2912 (1999)] have shown that quantitative retrieval of the optical phase, from a set of radiographs taken at different sample-to-detector distances, is feasible. Mathematically speaking we are dealing with a direct method based on linearization in order to solve an inverse nonlinear problem. The phase retrieval can be combined with classical tomography in order to obtain a three-dimensional representation of the object’s electron density (holotomography). In order to optimize the image contrast for the numerical phase retrieval process, we have carried out calculations resulting in an optimized choice of v...

Abstract: Phase retrieval is the key to quantitative x-ray phase-contrast imaging. To retrieve the phase image of an x-ray wave field, in general one needs multiple phase-contrast images. We have made a new observation of phase-attenuation duality for soft tissues, and we show how only a single phase-contrast image is needed for successful phase retrieval based on this duality. The phase-retrieval formula based on a single phase-contrast image of inhomogeneous soft tissue is derived and presented. We show the striking enhancement of the tissue contrast in simulated phase images that this new approach produces.

Abstract: Phase retrieval algorithms based on 4-f system for optical image encryption are compared in respect of the image retrieval quality and the convergence. Simulation results show that enlarging the searching space can decrypt the image with extremely high quality, while employing the searching strategy of modifying both the phase-distributions in the input and the frequency planes can result in much faster convergence for the algorithm.

Abstract: We present a detailed derivation of the phase-retrieval formula based on the phase-attenuation duality that we recently proposed in previous brief communication. We have incorporated the effects of x-ray source coherence and detector resolution into the phase-retrieval formula as well. Since only a single image is needed for performing the phase retrieval by means of this new approach, we point out the great advantages of this new approach for implementation of phase tomography. We combine our phase-retrieval formula with the Feldkamp-Davis-Kresss (FDK) cone-beam reconstruction algorithm to provide a three-dimensional phase tomography formula for soft tissue objects of relatively small sizes, such as small animals or human breast. For large objects we briefly show how to apply Katsevich’s cone-beam reconstruction formula to the helical phase tomography as well.

Abstract: Recent studies have demonstrated that the phase recovery from a single fringe pattern with closed fringes can be properly performed if the modulo 2π fringe orientation is estimated. For example, the fringe pattern in quadrature can be efficiently obtained in terms of the orientational phase spatial operator using fast Fourier transformations and a spiral phase spectral operator in the Fourier space. The computation of the modulo 2π fringe orientation, however, is by far the most difficult task in the global process of phase recovery. For this reason we propose the demodulation of fringe patterns with closed fringes through the computation of the modulo 2π fringe orientation using an orientational vector-field-regularized estimator. As we will show, the phase recovery from a single pattern can be performed in an efficient manner using this estimator, provided that it requires one to solve locally in the fringe pattern a simple linear system to optimize a regularized cost function. We present simulated and real experiments applying the proposed methodology.

Abstract: We introduce a novel method for retrieving the phase from a spectral shearing interferogram, based on wavelet-transform technique. We demonstrate with both theoretical and experimental data that this technique provides an alternative and reliable technique for phase retrieval, particularly for highly structured pulse spectra.

Abstract: An extension of the far-field x-ray diffraction theory is presented by the introduction of a distorted object for calculation of coherent diffraction patterns in the near-field Fresnel regime. It embeds a Fresnel-zone construction on an original object to form a phase-chirped distorted object, which is then Fourier transformed to form a diffraction image. This approach extends the applicability of Fourier-based iterative phasing algorithms into the near-field holographic regime where phase retrieval had been difficult. Simulated numerical examples of this near-field phase retrieval approach indicate its potential applications in high-resolution structural investigations of noncrystalline materials.

Abstract: We examined the range of shape factor of the Gabor wavelet in the analysis of spectral phase retrieval with an interferogram. We demonstrated that for the pulses with moderate high order phase the accuracy of the retrieved phase is insensitive to the shaping factor in the range of 1∼20. Both simulated ideal Gaussian spectrum and actual non-Gaussian spectrum are applied in the analysis.

Abstract: Generally, the reconstruction of an object image from its diffraction field requires both the amplitude and the phase information of this field. We systematically investigated the effects of using only the real part, the imaginary part, or the phase information of the diffraction field to reconstruct the original image for both the binary and the gray-level images. We show that the phase information can yield a better result of image retrieval than the real or imaginary part and that the recovered image from the phase information is satisfactory especially for binary input. On the basis of this idea, a new technique of image encryption and watermarking by use of only one delivered image-the phase map of the diffraction field of the original image-through double random-phase encoding is proposed and verified by computer simulations with phase-shifting interferometry. This method can greatly cut down the communication load and is suitable for Internet transmission.

Abstract: The method presented extracts the demodulated phase from only one fringe pattern. Locally, this method approaches the fringe pattern morphology with the help of a mathematical model. The degree of similarity between the mathematical model and the real fringe is estimated by minimizing a correlation function. To use an optimization process, we have chosen a polynomial form such as a mathematical model. However, the use of a polynomial form induces an identification procedure with the purpose of retrieving the demodulated phase. This method, polynomial modulated phase correlation, is tested on several examples. Its performance, in terms of speed and precision, is presented on very noised fringe patterns.

Abstract: There is a retraction (October 2006) associated with this Article. Please click here to view. The observation of the detailed atomic arrangement within nanostructures has previously required the use of an electron microscope for imaging. The development of diffractive (lensless) imaging in X-ray science and electron microscopy using ab initio phase retrieval provides a promising tool for nanostructural characterization. We show that it is possible experimentally to reconstruct the atomic-resolution complex image (exit-face wavefunction) of a small particle lying on a thin carbon substrate from its electron microdiffraction pattern alone. We use a modified iterative charge-flipping algorithm and an estimate of the complex substrate image is subtracted at each iteration. The diffraction pattern is recorded using a parallel beam with a diameter of ∼50 nm, illuminating a gold nanoparticle of ∼13.6 nm diameter. Prior knowledge of the boundary of the object is not required. The method has the advantage that the reconstructed exit-face wavefunction is free of the aberrations of the objective lens normally used in the microscope, whereas resolution is limited only by thermal vibration and noise.

Abstract: Analytical expressions to describe the phase gradient of monochromatic light by means of the three-dimensional intensity distribution are derived. With these formulas it is shown that the two-dimensional phase gradient in a plane can be completely determined from noninterferometric intensity measurements if the light propagates strictly in one direction. The analytical expressions are verified by means of numerical investigations on simulated speckle fields, and the results are discussed with respect to common deterministic phase retrieval approaches.

Abstract: At the NEUTRA facility (SINQ), a great variety of objects was investigated with phase contrast radiography, for instance metal foams and casted objects. The phase contrast effect is now well understood and great efforts are made to improve the existing set-up and to exploit all the possibilities offered by this technique. The tomography facility ANTARES at the FRM-II in Garching was designed to perform phase contrast measurements with neutrons as a matter of routine. A big goal is to do quantitative phase contrast radiography and the step towards phase contrast tomography. By performing phase retrieval for every slice of a tomographic data set, it becomes possible to assign every voxel the imaginary (attenuation coefficient) and the real part of the refractive index. This allows the separation of materials, which could not be separated hitherto in conventional tomographies.

Abstract: In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image By avoiding the use of a lens the resolution is limited, in principle, only by the largest scattering angles recorded However, the imaging task is shifted from the experiment to the computer, and the algorithm's ability to recover meaningful images in the presence of noise and limited prior knowledge may produce aberrations in the reconstructed image We analyze the low order aberrations produced by our phase retrieval algorithms We present two methods to improve the accuracy and stability of reconstructions

Abstract: The phase of an electron wave, which has traveled through a magnetic sample, is modified by the magnetic and electrostatic potentials of the material. The ability to reconstruct this phase is a powerful method for quantitatively studying the magnetic structure of the sample. Recently, the ``transport-of-intensity'' equation (TIE) has been applied to phase reconstruction using Lorentz transmission electron microscopy (LTEM) data. For magnetic analyses, it is important to separate the influence of the electrostatic potential on the electron wave. In this paper, an energy-dependent TIE analysis is presented in order to differentiate the magnetic and electrostatic contributions. This approach is developed using ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ and Co patterned films in which the contribution of the electrostatic potential is significant compared to that of the magnetic potential. A good fit to theory is obtained, showing that the contribution of the electrostatic potential to the phase is dependent on the energy of the electrons, namely the applied accelerating voltage, while that of the magnetic potential is not. The energy-dependent analysis shows that neglecting the contribution of the electrostatic potential in continuous films of constant thickness can be reasonable. For patterned materials, this methodology determines which features in Fresnel and Foucault contrast LTEM images originate from the magnetic potential and can remove the electrostatic contribution in order to enable a quantitative reconstruction of the magnetic structure. In addition, the different magnetic samples are used to explain the sensitivity limits of the TIE methodology in respect to quantitative measurements of magnetic properties.

Abstract: We propose phase retrieval from three or more interferograms corresponding to different tilts of an object wavefront. The algorithm uses the information contained in the interferogram differences to reduce the problem to phase shifting. Three interferograms is the minimum for restoring the phase over most of the image. Four or more interferograms are needed to restore the phase over the whole image. The method works with images including open and closed fringes in any combination.

Abstract: In coherent X-ray diffraction microscopy the diffraction pattern generated by a sample illuminated with coherent x-rays is recorded, and a computer algorithm recovers the unmeasured phases to synthesize an image. By avoiding the use of a lens the resolution is limited, in principle, only by the largest scattering angles recorded. However, the imaging task is shifted from the experiment to the computer, and the algorithm's ability to recover meaningful images in the presence of noise and limited prior knowledge may produce aberrations in the reconstructed image. We analyze the low order aberrations produced by our phase retrieval algorithms. We present two methods to improve the accuracy and stability of reconstructions.

Abstract: The problem of recovering a complex signal from the magnitudes of any number of its fractional Fourier transforms at any set of fractional orders is addressed. This problem corresponds to the problem of phase retrieval from the transverse intensity profiles of an optical field at arbitrary locations in an optical system involving arbitrary concatenations of lenses and sections of free space. The dependence of the results on the number of orders, their spread, and the noise is investigated. Generally, increasing the number of orders improves the results, but with diminishing return beyond a certain point. Selecting the measurement planes such that their fractional orders are well separated or spread as much as possible also leads to better results.

Abstract: Phase retrieval can be useful in the measurement of optical surfaces and systems. It distinguishes itself through the simplicity of the experimental apparatus, just a detector array which collects light near a focal plane. Aspherics can be measured without null optics. The challenging part of the method is the estimation of the wavefront from the near-focus intensity measurements to reconstruct the wavefront.

Abstract: A local histogram-data-orientated filtering algorithm is proposed to remove noise from the deformation phase map obtained by a phase stepping electronic speckle pattern interferometry (ESPI). The proposed filter can successfully eliminate any speckle-generated residues of a real dislocation free map. Since the filtered result is totally free from any phase inconsistency, a simple unwrapping rule, like Macy's method, can be applied for the correct phase retrieval. The motivation and theory of the proposed method is described. A simulated noisy wrapped map is employed to detail its implementation. An intercomparison of the present study and two well-known methods is performed to present the performance of the proposed method. In addition, several ESPI experiments are conducted to provide successful filtering of practical phase maps and to prove the effectiveness of the proposed method.

Abstract: A three-frame phase-shifting algorithm with a constant but unknown phase shift is proposed. The algorithm is based on background-intensity removal prior to phase retrieval to eliminate an undetermined factor in a fringe pattern. The proposed method is validated on three-dimensional profilometry by fringe projection and on deformation measurement by means of digital speckle shearing interferometry. For a fringe pattern with slow-varying background intensity, the background removal is achieved in the frequency domain. For a speckle pattern, a background removal technique is integrated with the three-frame algorithm. In this process, manual intervention is minimal, and high computational speed is achieved. In addition, high-frequency phase signals would not be removed in the noise-reduction process as is the case in the bandpass-filtering technique. Accuracy of the method is discussed.

Abstract: The paper presents a new approach to the radia- tion pattern reconstruction from near-field amplitude only measurement over a two planar scanning surfaces. This new method for antenna pattern reconstruction is based on the global optimization PSO (Particle Swarm Optimiza- tion). The paper presents appropriate phaseless measure- ment requirements and phase retrieval algorithm together with a brief description of the particle swarm optimization method. In order to examine the methodologies developed in this paper, phaseless measurement results for two diffe- rent antennas are presented and compared to results obtai- ned by a complex measurement (amplitude and phase).

Abstract: New alignment methods of millimeter-wave transmission lines for Electron Cyclotron resonance Heating are proposed and evaluated on a high power level. These methods are based on the measured data of infrared images on the target, which is irradiated by the high power millimeter-waves at several positions. The first and second moments and retrieved phase obtained from these data are used to determine the propagation direction of the millimeter-wave beam along the waveguide axis. It is demonstrated that these methods have sufficient resolution to discriminate 0.1 deg., which is required to restrict the transmission loss below 1% over the 100 GHz range.

Abstract: Received 12 April 2005; published 10 August 2005A scheme in which a velocity drive serves as an interferometer and phase shifter in nuclear resonantscattering experiments is presented, and a straightforward algorithm for phase determination is developed. Theexperimental feasibility of the concept is demonstrated for nuclear forward scattering by an -iron foil fordifferent directions of the hyperfine field. It is also shown that the obtained phase information can be used forthe reconstruction of the energy spectrum.DOI: 10.1103/PhysRevB.72.081402 PACS number s : 42.30.Rx, 42.25.Hz, 76.80. y

Abstract: There is provided an electron microscopic method capable of realizing a high resolution based on the principle of the phase retrieval method. An electron microscope (10) using the method is a device dedicated to the phase retrieval method in which hardware (incident system (100), a sample system (200), a detection system (300), a computer system (400)) and software (constriction condition, optimization method) are formed into a unitary block. The intensity distribution and the phase distribution of the support slit (210) are given as a real space constriction condition. The detection system (300) includes a course system having an objective lens (310) and a course detector (320) and a fine system has a fine detector (330). The course image is acquired by electrically turning on the objective lens. After acquiring the diffraction pattern by electrically turning off the objective lens, the fine image is reconfigured by the phase retrieval method using the obtained course image and diffraction pattern.