Reducing phase retrieval errors in Fourier analysis of 2-dimensional digital model interferograms

In order to measure the displacements of facets on a growing spherical Cu_2−δSe crystal with sub-nanometre resolution, we investigated the reliability and accuracy of standard method of Fourier analysis of digital laser interferograms. Guided by realistic experimental conditions (two-dimensional (2D) interferograms), starting from 2D model interferograms and using original custom designed Gaussian filtering window and multistage unwrapping procedure of the retrieved phase, we demonstrate for a considerable parameter range the non-negligible inherent phase retrieval error due to non-integer number of fringes within the digital image. Our results indicate an intermediate parameter range where the error is acceptably small. We introduce an algorithm modification that significantly reduces the error, especially for low and high fringe densities. In the experimentally most common case of diagonal fringes the reduced error is an order of magnitude smaller than for nearly one-dimensional case within almost entire parameter space.     

An algorithm for computed tomography image reconstruction from limited-view projections

<正>With the development of the compressive sensing theory,the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology.This paper develops an iterative algorithm for image reconstruction,which can fit most cases.This method gives an image reconstruction flow with the difference image vector,which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough.Then the l_2-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles.The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data.Moreover,all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.     

Few-Projection Tomography. II. Radioastronomical Method CLEAN for Three-Dimensional Problems

The radioastronomical method CLEAN is extended to problems of three-dimensional (3D) tomographic reconstruction. We consider two options, namely, 3D_1D (reconstruction using one-dimensional projections) and 3D_2D (reconstruction based on using two-dimensional projections). Deconvolution with the use of the synthesized beam (equivalent total transfer function) makes it possible to reduce several times the number of aspects in comparison with the conventional approach. We point out the relationship between the maximum level of sidelobes of the synthesized ray constructed for the Gaussian transfer functions and the number of used projections. In the case of 3D_2D -reconstruction, the reconstruction quality similar to that for the 2D_1D case is only achieved if the same number of uniformly distributed projections are used in both cases. The use of one-dimensional projections for the 3D_1D -reconstruction requires doubling of the number of projections. The reconstruction process is illustrated by an example of the three-dimensional model of an optically thin radiating object. We consider the possibilities of using the developed approach in astrotomography and remote sensing based on introducing the transfer functions which determine resolution of the receiving beam patterns and spectrographs, as well as temporal resolution of the sensing profiles. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 5, pp. 367–381, May 2005.     

Maximum entropy image reconstruction from projections

The maximum entropy method is applied to image reconstruction from projections, of which angular view is restricted. The relaxation parameters are introduced to the maximum entropy reconstruction and after iteration the median filtering is implemented. These procedures improve the quality of the reconstructed image from noisy projections.     

少量投影数字全息层析重建实验研究

提出了少量投影数字全息层析重建技术.以具有轴对称结构的光纤和非轴对称结构的石膏头像为实验样本,开展了基于单幅全息图和代数迭代重建算法的层析重建模拟分析及实验研究.模拟分析表明,代数迭代重建算法中的加权因子以及松弛因子对重建图像质量影响显著,因此对加权因子采用非线性加权计算方法,以及通过多次模拟重建结果的比较选择合适的松弛因子.层析重建实验结果表明,无论被测物体是轴对称结构或是非轴对称结构,少量投影数字全息层析重建是可行的,也是有效的.这为下一步针对生物样本内部多层折射率检测和基于单幅层析全息图实现三向实时数字全息层析重建技术研究提供了必要的基础.     

Electron momentum density in Cu<Subscript>0.9</Subscript>Al<Subscript>0.1</Subscript>

A reconstruction technique based on the solution of the Radon transform in terms of Jacobi polynomials is used to obtain the 3D electron momentum density, ϱ(p), from nine high-resolution Compton profiles (CPs) for a Cu_0.9Al_0.1 disordered alloy single crystal. The method was also applied to theoretical CPs computed within the Korringa–Kohn–Rostoker coherent potential approximation (KKR-CPA) first-principles scheme for the same nine orientations of the crystal. The experimental ϱ(p) is in satisfactory agreement with the theoretical ϱ(p), shows most details of the Fermi surface (FS) and exhibits electron correlation effects. We comment on the map of the FS obtained by folding the reconstructed ϱ(p) into the first Brillouin zone, which yields the occupation number density, ϱ(k). A test of the validity of data via a consistency condition (within our reconstruction algorithm) as well as the propagation of experimental noise in the reconstruction of both ϱ(p) and ϱ(k) are investigated. Received: 24 October 2001 / Accepted: 20 January 2002 / Published online: 3 June 2002 RID="*" ID="*"Corresponding author. Fax: +48-71/344-10-29, E-mail: samsel@int.pan.wroc.pl     

基于CT算法的旋转多丝靶二维束剖面测量

介绍了一种用于低能电子束的基于CT算法的二维束剖面测量方法及其初步实验结果.该束剖面测量方法首先利用多丝靶进行旋转获得不同角度下的一维束剖面信息,然后采用CT算法对这些信息进行处理重建出二维束剖面.本文对该束剖面测量方法的原理进行了详细分析,并通过实验初步验证了该束剖面测量方法的可行性.     

Laser-ablation-induced refractive index fields studied using pulsed digital holographic interferometry

Pulsed digital holographic interferometry has been used to investigate the plume and the shock wave generated in the ablation process of a Q-switched Nd-YAG (λ=1064 nm and pulse duration=12 ns) laser pulse on a polycrystalline boron nitride (PCBN) target under atmospheric air pressure. A special setup based on two synchronised wavelengths from the same laser for simultaneous processing and measurement has been used. Digital holograms were recorded for different time delays using collimated laser light (λ=532 nm) passed through the volume along the target. Numerical data of the integrated refractive index field were calculated and presented as phase maps showing the propagation of the shock wave and the plume generated by the process. Radon inversion has been used to estimate the 3D refractive index fields measured from the projections assuming rotational symmetry. The shock wave density has been calculated using the point explosion model and the shock wave condition equation and its behaviour with time at different power densities ranging from 1.4 to 9.1 GW/cm² is presented. Shock front densities have been calculated from the reconstructed refractive index fields using the Gladstone–Dale equation. A comparison of the shock front density calculated from the reconstructed data and that calculated using the point explosion model at different time delays has been done. The comparison shows quite good agreement between the model and the experimental data. Finally the reconstructed refractive index field has been used to estimate the electron number density distribution within the laser-induced plasma. The electron number density behaviour with distance from the target at different power densities and its behaviour with time are shown. The electron number densities are found to be in the order of 10¹⁸ cm^?3 and decay at a rate of 3×10¹⁵ electrons/cm³ ns.     

Optimal wavelet filter for suppression of coherent noise with an application to seismic data

Wavelet analysis is combined with the Karhunen-Loève (KL) transform into an innovative hybrid method for locally filtering coherent noise. In applying our method, the original time series is first decomposed with wavelet transform, the scales more contaminated with noise are reduced by an attenuation factor A_f, and the signal is reconstructed using the inverse wavelet transform. Then the KL transform is applied to the reconstructed signal and the behavior of the first energy modes is analyzed as a function of A_f. The point corresponding to a minimum in the first mode is identified with the maximum extraction of the coherent noise. Our methodology is applied with success to seismic data with the aim of locally extracting the relevant coherent noise, namely the ground roll noise. The procedure can be easily extended to other situations where an undesirable signal is associated with a specific set of energy modes.     

Jet reconstruction in heavy ion collisions

We examine the problem of jet reconstruction at heavy-ion colliders using jet-area-based background subtraction tools as provided by FastJet. We use Monte Carlo simulations with and without quenching to study the performance of several jet algorithms, including the option of filtering, under conditions corresponding to RHIC and LHC collisions. We find that most standard algorithms perform well, though the anti-k _t and filtered Cambridge/Aachen algorithms have clear advantages in terms of the reconstructed p _t offset and dispersion.     

基于峰值信噪比和小波方向特性的图像奇异值去噪技术

提出一种利用小波变换子图像不同的方向特性和峰值信噪比进行奇异值分解的图像去噪算法。由于图像经过小波变换后,低频子图像集中了原图像的大部分能量噪声,故仅作简单维纳滤波;而噪声则主要集中在小波域中的三个不同方向的高频子图中,且系数较小,因此可以利用奇异值分解进行去噪处理,即用较大的奇异值和对应的特征向量重构出去噪图像,然而由于奇异值分解固有的行列方向性,对于高频对角线子图重构出的图像去噪效果不理想,故采取旋转至行列方向后再进行常用的奇异值滤波;最后将去噪后的低频和高频子图进行小波反变换重构出最终的去噪图像,其中重构所需的奇异值个数由图像的峰值信噪比确定。 实验结果表明,该方法在有效去噪的同时较好的保留了原有的高频细节信息。     

Energy bands and electron densities of Li3N

Self-consistent band-structure calculations on the fast ionic conductor lithium nitride are performed by means of the linearized augmented plane wave (LAPW) method within the local density formalism. The corresponding density of states is decomposed into local (inside spheres), partial (l-like) and symmetry (p _x p _y ;p _z ) components from which an only very small covalent contribution to the bonding in Li₃N can be deduced. Electron density maps reveal Li₃N to be highly ionic (near Li⁺ and N^3–). A simple Watson model, although a good first approximation, cannot account for all details. For instance a remarkable non-spherical electrons density is found around N which may explain the high electric field gradient experimentally observed on this site; furthermore a reduced electron density around the Li-sites appears in contrast to a simple supper-possition of N^3– ionic densities. However, calculated x-ray structure factors and difference electron densities are in good qualitative agreement with recent x-ray diffraction experiments.This work has been supported by the Hochschuljubiläumsstiftung der Stadt Wien. All calculations were carried out at the Rechenzentrum der Technischen Universität Wien     

Performance of photorefractive crystals as derived from EPR-based defect studies: application to BaTiO<Subscript>3</Subscript>:Rh and Ba<Subscript>0.77</Subscript>Ca<Subscript>0.23</Subscript>TiO<Subscript>3</Subscript>:Rh

A method is introduced which allows us to predict the performance of a photorefractive material quantitatively using electron paramagnetic resonance (EPR)-based defect studies. This includes the determination of the defect densities and the parameters governing their light-induced charge changes. On this basis the effective trap densities and the photorefractive response times are calculated. All quantities can be determined without theoretical simplifications such as employed in previous approaches to the problem. The method is applied to BaTiO₃ and congruently melting Ba_0.77Ca_0.23TiO₃, both doped with rhodium. The iron defects, present as background contaminations, are fully taken into account. Their influence on the intensity saturating the space charges is calculated on this basis. The complete energy dependences of the absorption cross sections of all optically active Rh and Fe defects are given. PACS 42.70.Nq; 76.30.Mi; 78.40.-q     

An iterative image reconstruction algorithm combined with forward and backward diffusion filtering for in‐line X‐ray phase‐contrast computed tomography

In‐line X‐ray phase‐contrast computed tomography (IL‐PCCT) can reveal fine inner structures for low‐Z materials (e.g. biological soft tissues), and shows high potential to become clinically applicable. Typically, IL‐PCCT utilizes filtered back‐projection (FBP) as the standard reconstruction algorithm. However, the FBP algorithm requires a large amount of projection data, and subsequently a large radiation dose is needed to reconstruct a high‐quality image, which hampers its clinical application in IL‐PCCT. In this study, an iterative reconstruction algorithm for IL‐PCCT was proposed by combining the simultaneous algebraic reconstruction technique (SART) with eight‐neighbour forward and backward (FAB8) diffusion filtering, and the reconstruction was performed using the Shepp–Logan phantom simulation and a real synchrotron IL‐PCCT experiment. The results showed that the proposed algorithm was able to produce high‐quality computed tomography images from few‐view projections while improving the convergence rate of the computed tomography reconstruction, indicating that the proposed algorithm is an effective method of dose reduction for IL‐PCCT.     

Improved Quantum Image Filtering in the Spatial Domain

We investigate the quantum image filtering in spatial domain proposed by Yuan et al. (Int. J. Theor. Phys. 56(8), 2495–2511, 2017). Although the complexity of this algorithm is much better than the classical exhaustive algorithm, there may be a defect in it: the quantum multiplication was replaced by quantum addition. There are two shortcomings: 1) We should know exactly the value of the filter coefficients before each filtering behavior. 2) This method is only suitable for integer filter coefficients but not for decimal filter coefficients. In this paper, an improved version is proposed which takes full advantage of the quantum multiplication and can overcome these two shortcomings. The theoretical analysis indicates that the time complexity is the same as the previous algorithm. So this algorithm is also efficient.     

Improvement of experimental data via consistency conditions

Interdependencies between experimental spectra, representing line or plane projections of electronic densities, are derived from their consistency and symmetry conditions. Some additional relations for plane projections are obtained by treating them as line projections of line projections. The knowledge of these dependencies can be utilised both for an improvement of experimental data and for a verification of various techniques used for correcting for example two-dimensional (or one-dimensional) angular correlation of annihilation radiation spectra and Compton scattering profiles.     

Cone-beam local reconstruction based on a Radon inversion transformation

The local reconstruction from truncated projection data is one area of interest in image reconstruction for computed tomography(CT),which creates the possibility for dose reduction.In this paper,a filtered-backprojection(FBP) algorithm based on the Radon inversion transform is presented to deal with the three-dimensional(3D) local reconstruction in the circular geometry.The algorithm achieves the data filtering in two steps.The first step is the derivative of projections,which acts locally on the data and can thus be carried out accurately even in the presence of data truncation.The second step is the nonlocal Hilbert filtering.The numerical simulations and the real data reconstructions have been conducted to validate the new reconstruction algorithm.Compared with the approximate truncation resistant algorithm for computed tomography(ATRACT),not only it has a comparable ability to restrain truncation artifacts,but also its reconstruction efficiency is improved.It is about twice as fast as that of the ATRACT.Therefore,this work provides a simple and efficient approach for the approximate reconstruction from truncated projections in the circular cone-beam CT.     

Evolution of the electronic structures of NixSiy ordered systems: experimental and theoretical investigations

We study the change of the electronic structures of nickel silicides, Ni₃Si and NiSi₂, as well as nickel and silicon through the evolution of their valence band X-ray photoelectron spectra (v-XPS) both experimentally and theoretically. The experimental spectra are compared to the total and partial densities of states using tight-binding linear muffin-tin orbital method (TB-LMTO) in the atomic sphere approximation (ASA). Good agreement is found between theory and experiment. Received 10 July 2000     

惯性约束聚变中环孔编码图像恢复的改进维纳滤波方法

针对惯性约束聚变(ICF)中环形孔径编码图像的恢复问题提出了一种改进的维纳滤波方法。在传统的维纳滤波方法中,由于原图像和噪声是未知的,故通常是用某一待定常量来代替其中的噪声与信号的谱密度之比。这种近似忽视了信号与噪声本身的信息,从而造成丢失某些关键的细节,难以达到高质量的图像复原效果。在改进的方法中,首先采用传统维纳滤波方法求得初始估值,然后利用该初始值求得原图像及噪声的谱密度估值,进而利用这些新获得的信息构成改进的维纳滤波器对退化图像进行第二次滤波。实验表明,这种改进方法可以克服原方法的不足,突出图像的一些关键细节,提高图像的整体质量。在仿真实验中,恢复图像的均方误差降低了15％以上;在实际惯性约束聚变图像的解码恢复实验中,图像恢复效果亦有显著改善。该方法还可以推广到其他图像恢复的应用中。     

聚束非相干合成孔径激光成像雷达研究

反射层析激光成像雷达只能获得目标的二维轮廓像,不能对平面目标进行成像。报道了聚束模式下的非相干合成孔径激光成像雷达实验,在这种成像模式下,可以对二维平面目标进行图像重构。采用侧视观察的模式获取目标的角度-距离-强度信息,然后通过滤波反投影实现平面目标的图像重建,并进行了计算机仿真,证明了实验结果的正确性。该系统作为非相干合成孔径激光雷达的一种,实现了区别于目标轮廓的二维成像,具有一定的实际意义和使用价值。