On the convergence of the lp ‐norm algorithm for polynomial perceptron having different error signal distributions

Abstract

The convergence property of the l_p ‐norm algorithm for polynomial‐perceptron having different error signal distributions will be analyzed in this paper. To see the effect of error signal on the convergence rate, two types of activation functions are considered in the analysis: one is of a linear type and the other is of a sigmoidal type. Different activation functions yield different ranges of output signal and, in turn, yield different error signal distributions. Linear activation function causes the error signal to be distributed in an uncertain way, while sigmoidal activation function causes it to be distributed in a tightly bounded region. Based on this difference the convergence property of the l_p ‐norm algorithm, 1 ≤ p ≤ 2, is investigated in this paper. Expressions of average learning gains are obtained in terms of the power metric p, the error probability, and the upper bound of the error signal distribution. Analytic results indicate that it is of particular value in using the l_p ‐norm algorithm for the perceptron using sigmoidal activation functions. Computer simulation of an adaptive equalizer using this algorithm confirms the theoretical analysis.     

Importance of Initial Distribution for Iterative Calculation of Quantized Diffractive Elements

Abstract

The significance of the initial distribution for three iterative calculation techniques of diffractive elements; simulated annealing, direct binary search, and Fourier transform algorithm, is investigated. Depending on the initial distributions, convergence problems may occur. Techniques to calculate special initial distributions for the three methods are described: these significantly improve the capabilities of the iterative techniques.     

Design and analysis of a diffractive optical filter for use in an optoelectronic error-diffusion neural network

The design, fabrication, experimental characterization, and system-performance analysis of a diffractive optical implementation of an error-diffusion filter for use in digital image halftoning is reported. A diffractive optical filter was fabricated as an eight-level phase element that diffuses the quantization error nonuniformly in both the weighting and the spatial dimensions, according to a prescribed algorithm. Ten identical diffractive elements were fabricated on ten different wafers and subsequently characterized experimentally. A detailed error analysis including both fabrication and instrumentation errors was carried out to quantify the performance of the fabrication process as well as the expected system performance of the filters. Halftone system performance was evaluated by use of the experimental filter's performance and both quantitative and qualitative performance metrics. The results of this analysis demonstrate that multiple identical copies of a diffractive optical filter can be produced with sufficient accuracy that no loss in the halftoning system performance results.     

Optimization design of diffractive phase elements for beam shaping

An improved approach called the weighted YG algorithm for the design of the diffractive phase element (DPE) that implements beam shaping in the fractional Fourier transform domain and free space is presented. Modeling designs of the DPE are carried out for several fractional orders and different parameters of the beam for optimally converting a Gaussian profile into a uniform beam. We found that our algorithm can improve the beam shaping effect, reduce the error function, and increase uniformity of light intensity.     

Diffractive optics at the surface of light-emitting/receiving semiconductor components

Abstract

Semiconductor components that emit or receive light can use diffractive surface structures to increase the functionality and reduce the number of additional optical components needed in the system. The diffractive structure couples the light out of, or into, the semiconductor material; it splits the light and directs it into one focus or several foci at any desired position. Further, the diffractive optics can be designed so that the function of the device is largely insensitive to the polarization of the light. In this survey, we briefly discuss design and fabrication issues, and show simulated and measured results, for a few different types of components.     

Diffractive elements designed to suppress unwanted zeroth order due to surface depth error

Abstract

We consider a design approach to reduce unwanted zero-order intensity due to profile depth error in diffractive elements. Our method is based on addition of local bias phase to a binary element phase, leading to the introduction of a third phase level. We show theoretically and experimentally that gratings obtained with such modifications are more tolerant to profile depth error than conventionally designed binary or multilevel elements, thus reducing the appearance of unwanted zero order.     

Superresolution and increased depth of focus: An inverse problem of vector diffraction

Abstract

Using vector diffraction theory, we have addressed the issue of finding the pupil function when the rate of decay of the intensity in the vicinity of the Gaussian focus along the optical axis is prescribed. The problem posed here reduces to a Fredholm integral equation, which is then solved to obtain the pupil function. We show that the diffraction integrals, as formulated by Wolf, are invariant if they are expressed in terms of the zth (the direction of the optical axis) component of the unit normal to the aberrated wave front. This makes it possible to obtain the pupil function from the solution of the Fredholm integral equation. We present results for lenses with high numerical aperture and show that the depth of focus is significantly increased without any loss of transmitted energy. Results further indicate that the FWHM of the primary lobe is significantly narrower than the clear aperture.     

FFBP算法在合成孔径声纳成像中的应用

时域合成孔径成像算法可以更好地适应多子阵造成的方位向采样不均匀问题,并且具有存储空间小、并行处理方便的优点。但精确时域算法运算量非常大,快速分块反向传播投影（Fast Factorized Back Projection,FFBP）成像算法则可以大大降低成像计算量。详细分析了FFBP声程误差的距离效应、孔径合并策略和图像分裂策略、成像的计算量等关键问题,并给出了仿真和实测数据成像结果。通过对仿真和实测成像结果的分析表明：FFBP算法可以提高计算效率,适用于实时合成孔径声纳成像系统。     

Effect of electrospark deposited surface layers on bond strength of titanium–porcelain

Abstract

Casting of titanium can be successfully used in prosthodontic applications, but it demands special machines and protection gas to avoid oxidation of the metal. The aims of this study are to investigate the bond compatibility between porcelain and titanium using three-point bending, oxide adherence and thermal expansion tests, and to compare the results with those of a conventional titanium–porcelain system. Titanium alloy surfaces were modified with Nb, YG8 and silicon electrode by electrospark surface modification process. The effect of electrospark surface depositing (ESD) layers on bond strength of titanium to porcelain was evaluated comparatively. Some reasons about bond strength of titanium to porcelain were discussed. Results indicate that ESD modified layer prepared in atmosphere using Si electrode can obtain the strongest bonding to porcelain. The ESD modified layer show metallurgical bond to Ti substrate. In addition, the facts that rough surface can help to improve physic bond, similar nature can also help to chemical link and compact ESD layer represent good high temperature oxidation resistance are the reasons that enhance good bond strength of titanium to porcelain.     

Fringe Variation and Visibility in Speckle-shearing Interferometry

Abstract

Frequency spectra are analysed for two typical speckle-shearing interference recording methods; using a single aperture speckle-shearing camera (SASSC) and a double-aperture speckle-shearing camera (DASSC) to show the fringe variation due to the displacement involved in differentiation. Speckle statistics are then made for the filtering system to show the fringe-contrast variation resulting from the object deformation and the aperture of the filtering-image system.     

True beam smoothing in the fractional fourier transform domain

Abstract

The design of a diffractive optical element (DOE) for true beam smoothing in the fractional Fourier transform domain is described. Based on the Fresnel integrals, the intensity distribution on the output plane is calculated accurately and the discretization error of the spherical phase factor is avoided. The ‘fine design' of the DOE for true beam smoothing is completed with the sampling interval chosen as half of the traditional sampling interval. Simulation results show that the intensity at any point on the output plane fully meets the required demands, not just those sampling points used in the optimization.     

Noise reduction using mean shift algorithm for estimating 3D shape

Abstract

The technique to estimate the three-dimensional (3D) geometry of an object from a sequence of images obtained at different focus settings is called shape from focus (SFF). In SFF, the measure of focus — sharpness — is the crucial part for final 3D shape estimation. However, it is difficult to compute accurate and precise focus value because of the noise presence during the image acquisition by imaging system. Various noise filters can be employed to tackle this problem, but they also remove the sharpness information in addition to the noise. In this paper, we propose a method based on mean shift algorithm to remove noise introduced by the imaging process while minimising loss of edges. We test the algorithm in the presence of Gaussian noise and impulse noise. Experimental results show that the proposed algorithm based on the mean shift algorithm provides better results than the traditional focus measures in the presence of the above mentioned two types of noise.     

Achromatic fan-out diffractive system for white-light free-space optical interconnects

Abstract

A simple and versatile white-light fan-out diffractive system based on the achromatization of the fractional Talbot effect is proposed. This achromatic configuration is able to interconnect a single polychromatic point source with a 2-D array of optoelectronic microdevices with low residual chromatic aberration even for white light. The whole broadband beamsplitter system is formed by two simple diffractive optical elements, a periodic diffractive lenslet array and a diffractive lens, that are made with a direct laser writing technique giving high light efficiency. The focal amplitude distribution corresponding to the lenslet array produces, by free-space propagation, self-replicas with different density of light points. These patterns, in conjunction with the achromatization process carried out by the additional diffractive lens, are, in short, the key to achieving a set of undistorted white-light spots at the output plane with high uniformity and variable separation between them. Experimental results are also shown.     

改进的多子阵双站合成孔径声纳成像算法

在常规单站SAS系统中,多子阵技术是提高测绘率的一个有效方法,针对发射站固定的双站SAS模型,多子阵技术同样可以用来解决测绘率与降空间采样率的矛盾,但是当"停-走-停"假设不再成立时,将引入相位误差项,降低双站SAS的成像质量,针对该问题在原有多子阵逐点成像算法的基础上,研究了发射站固定的双站SAS基阵运动引起的相位误差,提出了多子阵双站合成孔径声纳带相位补偿的逐点成像算法,在建立多子阵双站SAS数学模型的同时,形成了新的多子阵双站SAS系统方案设计。并给出了改进的波束形成逐点算法和仿真实验。改进的逐点算法并未改进运算量大小,新方法能够改善成像效果,仿真实验验证了该方法的有效性。多子阵双站合成孔径声纳成像的逐线算法有待进一步研究。     

Multi-wavelength optical pickup with diffractive optical elements

Abstract

A novel, to our knowledge, multi-wavelength diffractive optical pickup is presented. The pickup enables multi-focus imaging and increases the data transfer rate considerably. Parallel reading of two or more memory layers is possible. The different spots can be controlled independently. The optical pickup consists of different diffractive optical elements (DOEs). The measured full-width at half-maximum (FWHM) spot intensity for the DOE-pickup is 0.76 μm—close to the diffraction limited predicted value of 0.71 μm—indicating good optical performance. The measured highest diffraction efficiencies of the realized DOEs are about 92%.     

Modelling correlation between hot working parameters and flow stress of IN625 alloy using neural network

Abstract

In this work, an optimum multilayer perceptron neural network is developed to model the correlation between hot working parameters (temperature, strain rate and strain) and flow stress of IN625 alloy. Three variations of standard back propagation algorithm (Broyden, Fletcher, Goldfarb and Shanno quasi-Newton, Levenberg–Marquardt and Bayesian) are applied to train the model. The results show that, in this case, the best performance, minimum error and shortest converging time are achieved by the Levenberg–Marquardt training algorithm. Comparing the predicted values and the experimental values reveals that a well trained network is capable of accurately calculating the flow stress of the alloy as a function of the processing parameters. Sensitivity analysis revealed that temperature has the largest effect on the flow stress of the alloy being in good agreement with the metallurgical fundamentals.     

Self-adaptive stress analysis based on stress convergence

A new algorithm for self-adaptive stress analysis is presented. The algorithm is based on h-convergence and uses the measured stress convergence rate as an error indicator. A theoretical relation between stress convergence rate and pointwise error of stresses is derived for both the 1-D and 2-D case. Some examples are presented to illustrate the behaviour of the algorithm.     

Rigorous electromagnetic design of finite-aperture diffractive optical elements by use of an iterative optimization algorithm

We propose a rigorous electromagnetic design of two-dimensional and finite-aperture diffractive optical elements (DOEs) that employs an effective iterative optimization algorithm in conjunction with a rigorous electromagnetic computational model: the finite-difference time-domain method. The iterative optimization process, the finite-difference time-domain method, and the angular spectrum propagation method are discussed in detail. Without any approximation based on the scalar theory, the algorithm can produce rigorous design results, both numerical and graphical, with fast convergence, reasonable computational cost, and good design quality. Using our iterative algorithm, we designed a diffractive cylindrical lens and a 1-to-2-beam fanner for normal-incidence TE-mode illumination, thus showing that the optimization algorithm is valid and competent for rigorously designing diffractive optical elements. Concerning the problem of fabrication, we also evaluated the performance of the DOE when the DOE profile is discrete.     

The focus of light—linear polarization breaks the rotational symmetry of the focal spot

Abstract

We experimentally demonstrate for the first time that a linearly polarized beam is focused to an asymmetric spot when using a high-numerical aperture focusing system. This asymmetry was predicted by Richards and Wolf in 1959 and can only be measured when a polarization-insensitive sensor is placed in the focal region. We used a specially modified photodiode in a knife-edge-type set-up to obtain highly resolved images of the total electric energy density distribution at the focus. The results are in good agreement with the predictions of a vectorial focusing theory.     

Elastic Collision Studies in Caesium/noble Gas Systems Using Two-pulse Echoes

Abstract

Measurements are presented of the collisional relaxation of two-pulse echoes on the 455 nm and 459 nm D-lines of atomic caesium perturbed by low pressures of He, Ar and Xe using the echo-polarisation rotation technique, with interpulse times up to approximately 200 ns. The line broadening constants are measured to about 3% and show significant discrepancies with line profile measurements. For τ ? 100ns there is evidence for the diffractive velocity-changing aspects of the collisions. The mean collisional velocity changes and the cross-sections for diffractive velocity-changing collisions are estimated from the data. The results are found to be insensitive to variations of axial magnetic fields and optical densities.