Compare Study between Planet Motion and Orbital Motion in CCOS

In order to get a profound understanding of planet motion and orbital motion in CCOS (Computer Controlled Optical Surfacing), a compare study between them was conducted here. The material removals of two motions under the same conditions were simulated and the removal of planet motion was higher than that of orbital motion. The figuring abilities of two motions were also studied through the theory of cut-off frequency and the result showed that planet motion had a higher cut-off frequency. Then two figuring runs which employ the planet motion and the orbital motion were simulated. The convergence rates and polishing times of these two runs were compared and the result showed that planet motion had a higher figuring efficiency. As planet motion has stronger figuring ability and higher figuring efficiency, it’s better to employ planet motion in CCOS to get higher convergence rate and higher accuracy when fabricating high quality mirrors.

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An Elementary Approximation of Dwell Time Algorithm for Ultra-Precision Computer-Controlled Optical Surfacing

Micromachines ◽

10.3390/mi12050471 ◽

2021 ◽

Vol 12 (5) ◽

pp. 471

Author(s):

Yajun Wang ◽

Yunfei Zhang ◽

Renke Kang ◽

Fang Ji

Keyword(s):

Dwell Time ◽

Convergence Rates ◽

Rotational Symmetry ◽

Time Algorithm ◽

Two Dimensions ◽

Efficient Computation ◽

Deconvolution Problem ◽

Ultra Precision ◽

Computer Controlled Optical Surfacing ◽

Computer Controlled

The dwell time algorithm is one of the key technologies that determines the accuracy of a workpiece in the field of ultra-precision computer-controlled optical surfacing. Existing algorithms mainly consider meticulous mathematics theory and high convergence rates, making the computation process more uneven, and the flatness cannot be further improved. In this paper, a reasonable elementary approximation algorithm of dwell time is proposed on the basis of the theoretical requirement of a removal function in the subaperture polishing and single-peak rotational symmetry character of its practical distribution. Then, the algorithm is well discussed with theoretical analysis and numerical simulation in cases of one-dimension and two-dimensions. In contrast to conventional dwell time algorithms, this proposed algorithm transforms superposition and coupling features of the deconvolution problem into an elementary approximation issue of function value. Compared with the conventional methods, it has obvious advantages for improving calculation efficiency and flatness, and is of great significance for the efficient computation of large-aperture optical polishing. The flatness of φ150 mm and φ100 mm workpieces have achieved PVr150 = 0.028 λ and PVcr100 = 0.014 λ respectively.

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Research on the Optimized Tool-Path Planning of Computer Controlled Optical Surfacing

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.399-401.1763 ◽

2011 ◽

Vol 399-401 ◽

pp. 1763-1767

Author(s):

Ri Pan ◽

Wei Yang ◽

Yin Biao Guo ◽

Feng Yang ◽

Dong Xu Zhang

Keyword(s):

Convergence Rate ◽

Processing Time ◽

Tool Path ◽

Tool Path Planning ◽

Tool Paths ◽

High Convergence Rate ◽

Computer Controlled Optical Surfacing ◽

Computer Controlled ◽

Removal Processes ◽

Working Efficiency

Computer controlled optical surfacing (CCOS) is widely used in aspheric optical lenses fabrication because of their high convergence rate on surface based on deterministic removal processes since 1963. As an important part of CCOS techniques, reasonable tool-path would increase the polishing speed, decrease the processing time and then improve the efficiency of polishing. Optimized policy combined with improved Prim algorithm is presented in this paper based on the study of the characteristic of aspheric polishing and the tool-paths in common use. The simulated results show that the length of tool-path is reduced so as to decrease the processing time and increase the working efficiency.

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Stability Analysis of the Nanjung Water Diversion Twin Tunnels based on Convergence Measurement

Indonesian Mining Professionals Journal ◽

10.36986/impj.v1i1.11 ◽

2019 ◽

Vol 1 (1) ◽

pp. 49-60

Author(s):

Simon Heru Prassetyo ◽

Ganda Marihot Simangunsong ◽

Ridho Kresna Wattimena ◽

Made Astawa Rai ◽

Irwandy Arif ◽

...

Keyword(s):

Stability Analysis ◽

Convergence Rate ◽

Critical Strain ◽

Convergence Rates ◽

Strain Analysis ◽

Water Diversion ◽

Tunnel Face ◽

Tunnel Stability ◽

The Stability ◽

Twin Tunnels

This paper focuses on the stability analysis of the Nanjung Water Diversion Twin Tunnels using convergence measurement. The Nanjung Tunnel is horseshoe-shaped in cross-section, 10.2 m x 9.2 m in dimension, and 230 m in length. The location of the tunnel is in Curug Jompong, Margaasih Subdistrict, Bandung. Convergence monitoring was done for 144 days between February 18 and July 11, 2019. The results of the convergence measurement were recorded and plotted into the curves of convergence vs. day and convergence vs. distance from tunnel face. From these plots, the continuity of the convergence and the convergence rate in the tunnel roof and wall were then analyzed. The convergence rates from each tunnel were also compared to empirical values to determine the level of tunnel stability. In general, the trend of convergence rate shows that the Nanjung Tunnel is stable without any indication of instability. Although there was a spike in the convergence rate at several STA in the measured span, that spike was not replicated by the convergence rate in the other measured spans and it was not continuous. The stability of the Nanjung Tunnel is also confirmed from the critical strain analysis, in which most of the STA measured have strain magnitudes located below the critical strain line and are less than 1%.

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A predictable smoothing evolution model for computer-controlled polishing

Journal of the European Optical Society Rapid Publications ◽

10.1186/s41476-020-00145-4 ◽

2020 ◽

Vol 16 (1) ◽

Author(s):

Jing Hou ◽

Pengli Lei ◽

Shiwei Liu ◽

Xianhua Chen ◽

Jian Wang ◽

...

Keyword(s):

Evolution Model ◽

Quantitative Prediction ◽

Theoretical Support ◽

Model Combining ◽

Process Guidance ◽

Dependent Model ◽

Computer Controlled Optical Surfacing ◽

Computer Controlled ◽

Time Dependent Model ◽

Selection Of

AbstractQuantitative prediction of the smoothing of mid-spatial frequency errors (MSFE) is urgently needed to realize process guidance for computer controlled optical surfacing (CCOS) rather than a qualitative analysis of the processing results. Consequently, a predictable time-dependent model combining process parameters and an error decreasing factor (EDF) were presented in this paper. The basic smoothing theory, solution method and modification of this model were expounded separately and verified by experiments. The experimental results show that the theoretical predicted curve agrees well with the actual smoothing effect. The smoothing evolution model provides certain theoretical support and guidance for the quantitative prediction and parameter selection of the smoothing of MSFE.

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Computer-Controlled Optical Surfacing

10.1117/12.958767 ◽

1980 ◽

Cited By ~ 2

Author(s):

Allen H. Greenleaf

Keyword(s):

Computer Controlled Optical Surfacing ◽

Computer Controlled

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Properties of high quality GaP single crystals grown by computer controlled liquid encapsulated Czochralski technique

Applied Physics Letters ◽

10.1063/1.93713 ◽

1982 ◽

Vol 41 (9) ◽

pp. 841-843 ◽

Cited By ~ 3

Author(s):

Y. Kokubun ◽

S. Washizuka ◽

J. Ushizawa ◽

M. Watanabe ◽

T. Fukuda

Keyword(s):

Single Crystals ◽

Czochralski Technique ◽

High Quality ◽

Computer Controlled

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KERNEL CONVERGENCE ESTIMATES FOR DIFFUSIONS WITH CONTINUOUS COEFFICIENTS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024911006619 ◽

2011 ◽

Vol 14 (07) ◽

pp. 979-1004

Author(s):

CLAUDIO ALBANESE

Keyword(s):

Convergence Rate ◽

Convergence Rates ◽

Fourier Transforms ◽

Uniform Continuity ◽

Time Step ◽

Uniform Bounds ◽

Kernel Convergence ◽

Discretization Schemes ◽

A New Technique ◽

Derivatives Of

Bidirectional valuation models are based on numerical methods to obtain kernels of parabolic equations. Here we address the problem of robustness of kernel calculations vis a vis floating point errors from a theoretical standpoint. We are interested in kernels of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step h > 0 in the limit as h → 0. We consider both semidiscrete triangulations with continuous time and explicit Euler schemes with time step so small that the Courant condition is satisfied. We find uniform bounds for the convergence rate as a function of the degree of smoothness. We conjecture these bounds are indeed sharp. The bounds also apply to the time derivatives of the kernel and its first two space derivatives. The proof is constructive and is based on a new technique of path conditioning for Markov chains and a renormalization group argument. We make the simplifying assumption of time-independence and use longitudinal Fourier transforms in the time direction. Convergence rates depend on the degree of smoothness and Hölder differentiability of the coefficients. We find that the fastest convergence rate is of order O(h2) and is achieved if the coefficients have a bounded second derivative. Otherwise, explicit schemes still converge for any degree of Hölder differentiability except that the convergence rate is slower. Hölder continuity itself is not strictly necessary and can be relaxed by an hypothesis of uniform continuity.

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Strong convergence rates of semidiscrete splitting approximations for the stochastic Allen–Cahn equation

IMA Journal of Numerical Analysis ◽

10.1093/imanum/dry052 ◽

2018 ◽

Vol 39 (4) ◽

pp. 2096-2134 ◽

Cited By ~ 11

Author(s):

Charles-Edouard Bréhier ◽

Jianbo Cui ◽

Jialin Hong

Keyword(s):

Convergence Rate ◽

Strong Convergence ◽

Convergence Rates ◽

Numerical Solutions ◽

A Priori Estimates ◽

A Priori ◽

Auxiliary Problem ◽

Splitting Scheme ◽

Cahn Equation ◽

Strong Convergence Rate

Abstract This article analyses an explicit temporal splitting numerical scheme for the stochastic Allen–Cahn equation driven by additive noise in a bounded spatial domain with smooth boundary in dimension $d\leqslant 3$. The splitting strategy is combined with an exponential Euler scheme of an auxiliary problem. When $d=1$ and the driving noise is a space–time white noise we first show some a priori estimates of this splitting scheme. Using the monotonicity of the drift nonlinearity we then prove that under very mild assumptions on the initial data this scheme achieves the optimal strong convergence rate $\mathcal{O}(\delta t^{\frac 14})$. When $d\leqslant 3$ and the driving noise possesses some regularity in space we study exponential integrability properties of the exact and numerical solutions. Finally, in dimension $d=1$, these properties are used to prove that the splitting scheme has a strong convergence rate $\mathcal{O}(\delta t)$.

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