High accuracy algorithm for calculating best fitting sphere of high-order aspheric surface

In some applications, one is interested in reconstructing a function f from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we suggest a method for deriving high order approximation to f using a Padé-like method. Namely, we do this by fitting some Fourier coefficients of the approximant to the given Fourier coefficients of f. Given the Fourier series coefficients of a function on a rectangular domain in Rd, assuming the function is piecewise smooth, we approximate the function by piecewise high order spline functions. First, the singularity structure of the function is identified. For example in the 2D case, we find high accuracy approximation to the curves separating between smooth segments of f. Secondly, simultaneously we find the approximations of all the different segments of f. We start by developing and demonstrating a high accuracy algorithm for the 1D case, and we use this algorithm to step up to the multidimensional case.

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High-accuracy self-mixing interferometer based on single high-order orthogonally polarized feedback effects

Optics Express ◽

10.1364/oe.23.016977 ◽

2015 ◽

Vol 23 (13) ◽

pp. 16977 ◽

Cited By ~ 14

Author(s):

Zhaoli Zeng ◽

Xueming Qu ◽

Yidong Tan ◽

Runtao Tan ◽

Shulian Zhang

Keyword(s):

High Accuracy ◽

High Order ◽

Feedback Effects

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Solution for Best Fitting Spherical Curvature Radius and Asphericity of Off-Axis Aspherics of Optical Aspheric Surface Component

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.364-366.499 ◽

2007 ◽

Vol 364-366 ◽

pp. 499-503 ◽

Cited By ~ 2

Author(s):

Guo Jun Dong ◽

Cheng Shun Han ◽

Shen Dong

Keyword(s):

Coordinate System ◽

Axial Symmetry ◽

Curvature Radius ◽

Aspheric Surface ◽

Coordinate Systems ◽

Rectangular Coordinate System ◽

Cylindrical Coordinate ◽

Complex Models ◽

Best Fitting ◽

Spherical Curvature

This study aimed to establish the coordinate transformation between the off-axis aspherics coordinate system σ and the axial symmetry aspherics coordinate system σ by transforming coordinates and present the computation models of asphericity in rectangular coordinate system and cylindrical coordinate system respectively. The asphericity expressions in both coordinate systems were applicable to the comparative sphere calculation of Off-axis aspherics with different figures. We selected an Initiation sphere in view of technology, along with equations in a right coordinate system for certain caliber and structure. Then, by numerical computation, we selected the best fitting sphere and simplifed the complex models by choosing a right coordinate system. At last, the solution for asphericity and the best fitting sphere curvature radius of off-axis aspherics were introduced by examples.

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High‐accuracy absorbing boundary conditions for high‐order parabolic wave equations

The Journal of the Acoustical Society of America ◽

10.1121/1.4785179 ◽

2004 ◽

Vol 116 (4) ◽

pp. 2550-2550

Author(s):

Murthy N. Guddati ◽

A. Homayoun Heidari

Keyword(s):

Boundary Conditions ◽

Wave Equations ◽

High Accuracy ◽

Absorbing Boundary Conditions ◽

High Order ◽

Absorbing Boundary

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High-Accuracy Treecode Based on Pseudoparticle Multipole Method

Symposium - International Astronomical Union ◽

10.1017/s0074180900207250 ◽

2003 ◽

Vol 208 ◽

pp. 305-314 ◽

Cited By ~ 1

Author(s):

Atsushi Kawai ◽

Junichiro Makino

Keyword(s):

Arbitrary Order ◽

Scaling Up ◽

Multipole Expansion ◽

High Accuracy ◽

High Order ◽

Point Mass ◽

Linear Scaling ◽

Multipole Method ◽

Primary Advantage

We invented the pseudoparticle multipole method (P2M2), a method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of P2M2 is that it works on GRAPE. Although the treecode has been implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can calculate forces from point-mass particles only. Thus the calculation cost grows quickly when high accuracy is required. With P2M2, the multipole expansion is expressed by particles, and thus GRAPE can calculate high order terms. Using P2M2, we realized arbitrary-order treecode on MDGRAPE-2. Timing result shows MDGRAPE-2 accelerates the calculation by a factor between 20 (for low accuracy) to 150 (for high accuracy). We parallelized the code so that it runs on MDGRAPE-2 cluster. The calculation speed of the code shows close-to-linear scaling up to 16 processors for N ≳ 106.

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Interferometric measurement of high-order aspheric surface parameter errors based on virtual-real combination iterative algorithm

Optics Express ◽

10.1364/oe.435252 ◽

2021 ◽

Author(s):

Qun Hao ◽

Xin Tao ◽

Yao Hu ◽

Tengfei Li ◽

Weiqian Zhao

Keyword(s):

Iterative Algorithm ◽

High Order ◽

Aspheric Surface ◽

Surface Parameter ◽

Interferometric Measurement

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Research of Probability-Based Tunneling Magnetoresistive Sensor Static Hysteresis Model

Sensors ◽

10.3390/s21227672 ◽

2021 ◽

Vol 21 (22) ◽

pp. 7672

Author(s):

Yutao Li ◽

Liliang Wang ◽

Hao Yu ◽

Zheng Qian

Keyword(s):

Small Volume ◽

High Sensitivity ◽

High Accuracy ◽

High Order ◽

Preisach Model ◽

Hysteresis Model ◽

Broad Application ◽

Magnetoresistive Sensor ◽

Hysteresis Characteristics ◽

Application Prospects

Tunneling magnetoresistive (TMR) sensors have broad application prospects because of their high sensitivity and small volume. However, the inherent hysteresis characteristics of TMR affect its applications in high accuracy scenarios. It is essential to build a model to describe the attributes of hysteresis of TMR accurately. Preisach model is one of the popular models to describe the behavior of inherent hysteresis for TMR, whereas it presents low accuracy in high-order hysteresis reversal curves. Furthermore, the traditional Preisach model has strict congruence constraints, and the amount of data seriously affects the accuracy. This paper proposes a hysteresis model from a probability perspective. This model has the same computational complexity as the classic Preisach model while presenting higher accuracy, especially in high-order hysteresis reversal curves. When measuring a small amount of data, the error of this method is significantly reduced compared with the classical Preisach model. Besides, the proposed model’s congruence in this paper only needs equal vertical chords.

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