Methods of filtering densities reconstructed from line projections

We present details important for practical applications of a new algorithm for filtering densities reconstructed from their line projections. The method is applied to densities reconstructed via the Cormack method from both model projections and 2D angular correlation of positron annihilation radiation spectra in CeIn₃ and ErGa₃. It is shown that this algorithm filters the experimental noise as well as enhances some details of the reconstructed densities, which then reveals their fine features. We also compare this way of filtering with the effects of imposing symmetry conditions on densities reconstructed for cubic systems. PACS 78.70.Bj; 87.59.Fm; 74.25.Jb     

Spatial and spatial-frequency filtering using one-dimensional graded-index lattices with defects

The potential of one-dimensional, periodic, graded-index, isotropic dielectric lattices with defects in multiband spatial and spatial-frequency filtering is studied. It is shown that both narrow- and wide-bandpass filters can be obtained at a proper choice of the number, location, and parameters of the defects placed inside the relatively thin slabs. The peculiarities of achieving multibandness for narrow- and wide-bandpass filters are discussed. Multiband narrow-bandpass filtering is closely related to the transmission features that are associated with Fabry–Pérot resonators with semitransparent planar mirrors. Correspondingly, the observed transmission can be interpreted in terms of the equivalent parameters of such resonators. In particular, it is shown that the resonators filled with an ultralow-index medium can be mimicked, so that defect-mode angle-domain spectrum can be rarefied at large angles of incidence. The obtained results are also expected to be applicable for prediction of the angle-domain behavior of transmission in case of piecewise-homogeneous multilayers.     

蒙特卡罗剂量分布去噪中三维高斯和Savitzky-Golay滤波器的改进与混合

对模拟粒子轨迹数较少模拟时间较短的蒙特卡罗粗糙剂量分布进行三维滤波,可以加速其收敛速度.结合蒙特卡罗剂量分布特征,改进三维高斯和Savitzky-Golay滤波器,建立三维混合滤波方法,并比较并联和级联两种基本混合方式.根据卷积性质,提出用等效卷积核简化混合滤波器结构的方法.结果表明,改进后的高斯和Savitzky-Golay滤波器的整体去噪效果得以增强,混合滤波器进一步降低滤波结果的局部误差,两种混合滤波器都能够大幅度抑制MC粗糙剂量分布中的噪声,级联混合滤波器降噪效果略优于并联混合滤波器.     

Talbot holographic illumination nonscanning (THIN) fluorescence microscopy

Optical sectioning techniques offer the ability to acquire three‐dimensional information from various organ tissues by discriminating between the desired in‐focus and out‐of‐focus (background) signals. Alternative techniques to confocal, such as active structured illumination, exist for fast optically sectioned images, but they require individual axial planes to be imaged consecutively. In this article, an imaging technique (THIN), by utilizing active Talbot illumination in 3D and multiplexed holographic Bragg filters for depth discrimination, is demonstrated for imaging in vivo 3D biopsy without mechanical or optical axial scanning.     

Artificial dielectrics designed as wavelength filters

It is shown that metallic subwavelength surface structures can be used as wavelength filters. The design principle is explained and a simple explanation of the filtering effect is given. Fabrication issues are discussed.     

The Action of Time-Domain Convolution Filters for Solvent Suppression

The theory underlying the use of time-domain convolution techniques for solvent suppression is investigated. It is shown analytically that such techniques produce a line-by-line filtering of the spectrum, provided certain criteria are fulfilled. The nature of the criteria is discussed, along with the restrictions that they imply. The difference between line-by-line and point-by-point filters is stressed. Some practical recommendations are made concerning the use of such filters.     

Nonlinear identification of NMR spin systems by adaptive filtering

In this paper, we present two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. The first method uses a truncated discrete Volterra series to describe the nonlinear relationship between excitation (input) and system response (output). First-, second-, and third-order kernels of this series are estimated employing the least mean square (LMS) algorithm. Three parallel filters can then model the NMR spin system so that its output is no more than simple sum of three convolution products between combinations of the input signal and filters coefficients. It is also shown that the contribution of the Volterra second-order term to the total system response is neglected compared with the contributions of the first- and the third-order terms. In the second identification method, the output signal is related to the input signal through a recursive nonlinear difference equation with constant coefficients. The LMS algorithm is used again to estimate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analyzed and compared. It is shown that our methods permit a simple identification of NMR spin systems. The field of applications of this study is promising in the optimization of NMR signal detection, especially in the cases of low signal-to-noise ratios where optimum signal filtering and analysis must be performed.     

圆柱光子晶体全反射隧穿的梳状滤波特性

研究一维圆柱光子晶体的全反射隧穿的梳状滤波特性,利用传输矩阵法计算光在大于全反射角入射一维圆柱光子晶体的透射率.在透射波中发现全反射隧穿效应,全反射隧穿峰具有优良的梳状滤波特性.得到圆柱光子晶体的全反射隧穿随周期数、模式量子数以及圆柱半径的变化特征,为设计性能优良的梳状光子晶体滤波器提供理论依据.     

基于矢量衍射理论的相位型光瞳滤波器设计

根据矢量衍射理论,提出了一种设计纯相位型光瞳滤波器的新方法根据该方法所设计的滤波器主要应用于采用高数值孔径显微物镜的成像系统对点扩散函数中的指数因子进行二次近似处理后,可以得到超分辨参量与滤波器参量的近似关系式以三区相位型滤波器为例,讨论了该近似关系式的有效性给出一个设计实例,根据所要求的超分辨性能要求设计滤波器.模拟结果表明,该滤波器达到了设计要求,最后利用共焦系统点扩散函数的乘积特性,大大减弱了旁瓣的影响.     

三区位相型三维超分辨光瞳滤波器的优化设计

用Matlab优化工具箱,采用非线性规划,对三区位相型(π-0-π型)光瞳滤波器进行了优化设计。结果显示,所设计的滤波器较好地实现了横向和轴向的三维超分辨,且轴向超分辨能力优于横向。该滤波器结构简单,容易实现。     

A study of the optical transfer function for annular binary filters

The annular binary pupil filters consist of two transparent annuli obstructed by an annular mask. The optical transfer functions for them are analytically derived under paraxial approximation, and three- and two- as well as one-dimensional numerical plots are presented. It is shown that by changing the parameters of transparent regions it is possible to improve the axial resolution whilst the transverse resolution remains unchanged, compared with an annular lens. Results indicate, as is well known, that this kind of filters can be applied to three-dimensional confocal microscopy.     

Narrowband spectral filters on the basis of threadlike metal Si photonic crystals

The scattering of transmitted and evanescent electromagnetic waves by threadlike photonic crystals, made of different materials, is studied theoretically. The reflection and transmission spectra of the waves, the electric vector of which is parallel to the threads, are calculated on the basis of a matrix Riccati equation. The physical reasons for the appearance of transparency peaks in the transmission spectra of threadlike photonic crystals are discussed. It is established that narrowband filters suggested previously and formed by a periodic system of Si threads about 1 μm in diameter and adjusted to a wavelength of 1.5 μm totally lose their filtering capabilities at small deviations (about 5%) from the thread diameter. However, the reflection and transmission spectra of filters containing periodically packed metallized Si threads are stable in the case of such variations in thread size. It is shown that threadlike crystals are an effective discrete mirror for radiation of the near- and mid-IR spectral range. The capabilities of threadlike crystals for filtering homogeneous and inhomogeneous waves are shown.     

Investigation of frequency-selective devices based on a microstrip 2D photonic crystal

The frequency-selective properties of structures based on a 2D microstrip photonic crystal have been investigated theoretically and experimentally. It is shown that various microwave devices, including diplexers, bandpass filters, and double bandpass filters, can be designed based on these structures.     

Spatial Filters on Demand Based on Aperiodic Photonic Crystals

Photonic Crystal spatial filters, apart from stand‐alone spatial filtering function, can also suppress multi‐transverse‐mode operation in laser resonators. Here it is shown that such photonic crystals can be designed by solving the inverse problem: for a given spatial filtering profile. Optimized Photonic Crystal filters were fabricated in photosensitive glass. Experiments have shown that such filters provide a more pronounced filtering effect for total and partial transmissivity conditions.     

The combined effect of spatial compounding and nonlinear filtering on the speckle reduction in ultrasound images

Recently, a spatial compounding ultrasound imaging method was presented that utilizes a conventional 64-element phased array transducer with two unfocused pistons, each placed at one of the sides of the phased array transducer. This method is augmented here by inclusion of nonlinear filtering of the compounded images. The combined effects of the specific spatial compounding and nonlinear filtering on speckle reduction in the generated ultrasound images are studied and evaluated in two stages: First, the image quality is studied when nonlinear filtering is used as part of the spatial compounding. The study is performed by simulations using the Field II program, by processing several B-mode images of a kidney. The second stage compares the results obtained by the simulations to those obtained by in vitro laboratory experiments. Five different compounding strategies and two nonlinear filters, Gaussian and anisotropic diffusion, are investigated and evaluated in terms of image quality parameters-contrast and signal-to-noise ratio. It is shown that the combination of "averaging+nonlinear Gaussian filtering" produces the greatest improvement of image quality. When compared to a conventional phased array imaging system, the spatial compounding method that includes the conventional 64-element phased array transducer with two unfocused pistons, and employs the "averaging+nonlinear Gaussian filtering" strategy, obtains improvement in SNR that has reached 334%. Thus, though this method necessitates a somewhat wider probe, it produces significantly improved images.     

Analysis and optimization of a new photonic crystal filters in near ultraviolet band

Transmission characteristics of one-dimensional (1D) photonic crystals (PCs) heterostructures containing defective are studied using the transfer matrix method. The key is to search the best combination style for different 1D PCs to form heterostructures. It is shown that the non-transmission range over near ultraviolet and visible range can be substantially enlarged and the phenomenon of narrow band PC filter in near ultraviolet can be realized by adjusting the repeat cycle counts of various photonic crystals. The theoretical results on multiple heterostructures containing TiO₂/SiO₂ multilayer films are presented. With a perfect omni-directional and high peak transmission filters for TE modes, this structure opens a promising way to fabricate ultra-narrow band PC filters with wide non-transmission range in near ultraviolet and visible range.     

Construction of Commutative Filters for LES on Unstructured Meshes

A method of constructing discrete filters for large eddy simulation of turbulent flows on unstructured meshes is presented. The commutation error between differentiation and filtering can be made arbitrarily small with these filters. The filtering method is applied to various test cases to demonstrate commutation. An extension to three dimensions and implementation into an unstructured solver for LES are discussed.     

Filtering skill for turbulent signals for a suite of nonlinear and linear extended Kalman filters

The filtering skill for turbulent signals from nature is often limited by errors due to utilizing an imperfect forecast model. In particular, real-time filtering and prediction when very limited or no a posteriori analysis is possible (e.g. spread of pollutants, storm surges, tsunami detection, etc.) introduces a number of additional challenges to the problem. Here, a suite of filters implementing stochastic parameter estimation for mitigating model error through additive and multiplicative bias correction is examined on a nonlinear, exactly solvable, stochastic test model mimicking turbulent signals in regimes ranging from configurations with strongly intermittent, transient instabilities associated with positive finite-time Lyapunov exponents to laminar behavior. Stochastic Parameterization Extended Kalman Filter (SPEKF), used as a benchmark here, involves exact formulas for propagating the mean and covariance of the augmented forecast model including the unresolved parameters. The remaining filters use the same nonlinear forecast model but they introduce model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics of the augmented stochastic forecast model. A comprehensive study of filter performance is carried out in the presence of various moment closure errors which are enhanced by additional model errors due to incorrect parameters inducing additive and multiplicative stochastic biases. The estimation skill of the unresolved stochastic parameters is also discussed and it is shown that the linear tangent filter, despite its popularity, is completely unreliable in many turbulent regimes for both parameter estimation and filtering; moreover, regimes of filter divergence for the linear tangent filter are identified. The results presented here provide useful guidelines for filtering turbulent, high-dimensional, spatially extended systems with more general model errors, as well as for designing more skillful methods for superparameterization of unresolved intermittent processes in complex multi-scale models. They also provide unambiguous benchmarks for the capabilities of linear and nonlinear extended Kalman filters using incorrect statistics on an exactly solvable test bed with rich and realistic dynamics.     

Complex noise suppression using a sparse representation and 3D filtering of images

A novel method for the filtering of images corrupted by complex noise composed of randomly distributed impulses and additive Gaussian noise has been substantiated for the first time. The method consists of three main stages: the detection and filtering of pixels corrupted by impulsive noise, the subsequent image processing to suppress the additive noise based on 3D filtering and a sparse representation of signals in a basis of wavelets, and the concluding image processing procedure to clean the final image of the errors emerged at the previous stages. A physical interpretation of the filtering method under complex noise conditions is given. A filtering block diagram has been developed in accordance with the novel approach. Simulations of the novel image filtering method have shown an advantage of the proposed filtering scheme in terms of generally recognized criteria, such as the structural similarity index measure and the peak signal-to-noise ratio, and when visually comparing the filtered images.     

3D image registration using a fast noniterative algorithm

This note describes the implementation of a three-dimensional (3D) registration algorithm, generalizing a previous 2D version [Alexander, Int J Imaging Systems and Technology 1999;10:242-57]. The algorithm solves an integrated form of linearized image matching equation over a set of 3D rectangular sub-volumes ('patches') in the image domain. This integrated form avoids numerical instabilities due to differentiation of a noisy image over a lattice, and in addition renders the algorithm robustness to noise. Registration is implemented by first convolving the unregistered images with a set of computationally fast [O(N)] filters, providing four bandpass images for each input image, and integrating the image matching equation over the given patch. Each filter and each patch together provide an independent set of constraints on the displacement field derived by solving a set of linear regression equations. Furthermore, the filters are implemented at a variety of spatial scales, enabling registration parameters at one scale to be used as an input approximation for deriving refined values of those parameters at a finer scale of resolution. This hierarchical procedure is necessary to avoid false matches occurring. Both downsampled and oversampled (undecimating) filtering is implemented. Although the former is computationally fast, it lacks the translation invariance of the latter. Oversampling is required for accurate interpolation that is used in intermediate stages of the algorithm to reconstruct the partially registered from the unregistered image. However, downsampling is useful, and computationally efficient, for preliminary stages of registration when large mismatches are present. The 3D registration algorithm was implemented using a 12-parameter affine model for the displacement: u(x) = Ax + b. Linear interpolation was used throughout. Accuracy and timing results for registering various multislice images, obtained by scanning a melon and human volunteers in various stationary positions, is described. The algorithm may be generalized to more general models of the displacement field, and is also well suited to parallel processing.