Elliptic Arc Fitting for the Shape Control System of Silicon Single Crystal Growth

Pengliang Li,Ding Liu

doi:10.1109/access.2020.2972612

Abstract

In the vision-based shape control system of silicon single crystal (SSC) growth, shape parameters are used as the control variables to make the grown SSC approximate to a perfect cylinder. A highlight halo at the junction of the solid crystal and the liquid crysta is a distinctive feature that reflects the current shape of SSC, and the edge of the captured halo is an elliptic arc that consistently changes with the shape of the halo. To estimate the shape parameters through the elliptic arc, we propose a two-side (TS) constraint method to fit the elliptic arc. Firstly, the error correction parameter is introduced into the second-order polynomial model to make the model more robust in the case of noise disturbing, and the resultant non-convex TS constraint model is constructed. Then, two weighted functions, which give the data out of TS constraint a small weight coefficient to resist the large level noise disturbing, are brought into the TS constraint optimization problem tactfully. Simulation and real SSC data examples show that the proposed method can obtain the elliptic arc parameters effectively.

Highlights

In the industrial silicon single crystal (SSC) control system, automatic measurement sensors are used for collecting the pattern features of SSC
It is worth highlighting two aspects of the proposed method here: 1) We introduce the error correct parameter into the second-order polynomial model, which is more robust in the case of noise disturbing
For the purpose of comparison, the Hough transform (HT) [8], the Bayesian method [9], and the direct least square fitting (DLSF) method [18] are implemented on the same data

Summary

INTRODUCTION

In the industrial silicon single crystal (SSC) control system, automatic measurement sensors are used for collecting the pattern features of SSC. The parameters of the fitted ellipse on the image plane uniformly change with the shape parameters of the current crystal slice. The elliptic halo parameters of SSC are estimated by fitting a set of edge points that are only distributed on part of the ellipse. In noisy environment, the performance of the existing algorithms will be affected To address this problem, this paper develops a twoside (TS) constraint method, which belongs to the algebraic method. This paper develops a twoside (TS) constraint method, which belongs to the algebraic method It is worth highlighting two aspects of the proposed method here: 1) We introduce the error correct parameter into the second-order polynomial model, which is more robust in the case of noise disturbing.

PROBLEM FORMULATION

SIMULATION AND EXPERIMENTAL RESULTS

EXPERIMENT 1

EXPERIMENT 2

EXPERIMENT 3

CONCLUSION AND FUTURE WORKS