D. Van Dyck

Holotomography: Quantitative phase tomography with micrometer resolution using hard synchrotron radiation x rays

Because the refractive index for hard x rays is slightly different from unity, the optical phase of a beam is affected by transmission through an object. Phase images can be obtained with extreme instrumental simplicity by simple propagation provided the beam is coherent. But, unlike absorption, the phase is not simply related to image brightness. A holographic reconstruction procedure combining images taken at different distances from the specimen was developed. It results in quantitative phase mapping and, through association with three-dimensional reconstruction, in holotomography, the complete three-dimensional mapping of the density in a sample. This tool in the characterization of materials at the micrometer scale is uniquely suited to samples with low absorption contrast and radiation-sensitive systems.

Maximum-likelihood estimation of Rician distribution parameters

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR.

Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy

Abstract This paper deals with image reconstruction in high-resolution transmission electron microscopy (HRTEM) via focus variation. This technique aims at the reconstruction of the complex-valued electron wave at the exit plane of the specimen including correction for the aberrations of the microscope, with a focal series of HRTEM images as input. The general case with linear and non-linear contributions to the images is considered, requiring recursive optimization of the wave function, which is obtained by a non-linear least-squares fit to the measured image intensities. Based upon the pioneering work of Kirkland (1984) in this field, we discuss the following improvements. In the first place, a solution of the maximum-likelihood (MAL) equations for image reconstruction is derived in which the - for HRTEM inherent - coupling between the wave function and its complex conjugate is accounted for. Secondly, it is outlined how optimum convergence for the MAL solution is obtained. Thirdly, a computationally efficient implementation of the recursive algorithm to solve the MAL equations is presented. The algorithm is based on a factorization of the spatial coherence envelope, and on focal integration approach for the temporal coherence envelope in the transmission-cross-coefficient. The convergence behavior of this algorithm is studied using simulated focal series as input.

Estimation of the Noise in Magnitude MR Images

Magnitude magnetic resonance data are Rician distributed. In this note a new method is proposed to estimate the image noise variance for this type of data distribution. The method is based on a double image acquisition, thereby exploiting the knowledge of the Rice distribution moments.

Focal-series reconstruction in HRTEM: simulation studies on non-periodic objects

Abstract The reliability of focal-series reconstruction algorithms for the retrieval of the wavefunction at the exit plane of the object (exit-plane wavefunction) is investigated for the case of non-periodic object features. Simulated high-resolution electron microscope images of an abrupt GaAs/AlAs interface and of an edge dislocation in GaAs are chosen as test cases. The reconstruction schemes employed for the retrieval of the exit-plane wavefunction are the so-called “paraboloid method” (PAM) and the “maximum likelihood” method (MAL) which have been developed to application stage within the framework of the BRITE-EURAM project No. 3322. Special attention is given to the convergence behavior of the algorithms in the presence of noise and under highly non-linear imaging conditions.

Watershed-based segmentation of 3D MR data for volume quantization

The aim of this work is the development of a semiautomatic segmentation technique for efficient and accurate volume quantization of Magnetic Resonance (MR) data. The proposed technique uses a 3D variant of Vincent and Soilles immersion-based watershed algorithm that is applied to the gradient magnitude of the MR data and that produces small volume primitives. The known drawback of the watershed algorithm, oversegmentation, is strongly reduced by a priori application of a 3D adaptive anisotropic diffusion filter to the MR data. Furthermore, oversegmentation is a posteriori reduced by properly merging small volume primitives that have similar gray level distributions. The outcome of the proceeding image processing steps is presented to the user for manual segmentation. Through selection of volume primitives, the user quickly segments of first slice, which contains the object of interest. Afterwards, the subsequent slices are automatically segmented by extrapolation. Segmentation results are contingently manually corrected. The proposed segmentation technique is tested on phantom objects, where segmentation errors less than 2% are observed. In addition, the technique is demonstrated on 3D MR data of the mouse head from which the cerebellum is extracted. Volumes of the mouse cerebellum and the mouse brains in toto are calculated.

A simple intuitive theory for electron diffraction

Abstract It is shown that the dynamical diffraction can simply be described in real space using the property that electrons are trapped in the electrostatic potential of the atomic columns. Due to this channelling effect, the electron diffraction can be highly dynamical inside each column, and at the same time retain a one-to-one relationship with the crystal structure. This description does not require the crystal to be periodic. Influence of adjacent columns can be treated using a perturbation theory. If the crystal is sufficiently thin, i.e. of the order of 10 nm, and the accelerating voltage is not too high (e.g. 100–300 keV), the motion of the electrons is almost perfectly periodic with depth. The theory shows how the depth periodicity is related to the mass/thickness of the column which allows the exit wavefunction to be parametrized in a simple analytical form. These results open perspectives to solve the inverse problem of how to derive the projected structure of the object from the exit wavefunction.

Quantitative atomic resolution mapping using high-angle annular dark field scanning transmission electron microscopy

A model-based method is proposed to relatively quantify the chemical composition of atomic columns using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images. The method is based on a quantification of the total intensity of the scattered electrons for the individual atomic columns using statistical parameter estimation theory. In order to apply this theory, a model is required describing the image contrast of the HAADF STEM images. Therefore, a simple, effective incoherent model has been assumed which takes the probe intensity profile into account. The scattered intensities can then be estimated by fitting this model to an experimental HAADF STEM image. These estimates are used as a performance measure to distinguish between different atomic column types and to identify the nature of unknown columns with good accuracy and precision using statistical hypothesis testing. The reliability of the method is supported by means of simulated HAADF STEM images as well as a combination of experimental images and electron energy-loss spectra. It is experimentally shown that statistically meaningful information on the composition of individual columns can be obtained even if the difference in averaged atomic number Z is only 3. Using this method, quantitative mapping at atomic resolution using HAADF STEM images only has become possible without the need of simultaneously recorded electron energy loss spectra.

Wavelet correlation signatures for color texture characterization

In the last decade, multiscale techniques for gray-level texture analysis have been intensively used. In this paper, we aim to extend these techniques to color images. We introduce wavelet energy-correlation signatures and we derive the transformation of these signatures upon linear color space transformations. Experiments are conducted on a set of 30 natural colored texture images in which color and gray-level texture classification performances are compared. It is demonstrated that the wavelet correlation features contain more information than the intensity or the energy features of each color plane separately. The influence of image representation in color space is evaluated.

Wave function reconstruction in HRTEM: the parabola method

Abstract The non-linear parabola method for wave function reconstruction in HRTEM is presented in detail. It consists of an iterative procedure in which the linear and non-linear contributions to HRTEM images of a defocus series are optimally separated which will allow to benefit from a fast linear reconstruction scheme in which the non-linear contribution is corrected for in a self-consistent way. The method has proven to be a fast and workable algorithm for quantitative wave function reconstruction with direct resolution improvement. Results are shown for wave function reconstruction on experimentally acquired defocus series for a 200 keV FEG-TEM with a point-to-point resolution of 0.24 nm. In the reconstructed wave functions the resolution could clearly be enhanced up to 0.14 nm.