Sub-pixel Edge Detection in Diameter Measurement for Single Silicon Crystal

Edge detection plays an important role in diameter measurement for single silicon crystal. However, the high-temperature production process (about 1,450 °C) emits intense infrared and visible lights that will blur the edge and hinder the accurate calculation for the diameter of the crystal ingot. In this paper, the aura phenomenon caused by high-temperature radiation is deliberated and the Sigmoid function is discovered to best fit the luminance distribution along the normal direction of the edge. Thus, a sub-pixel edge detection method based on Sigmoid fitting is proposed for high-temperature objects, such as the single silicon crystal. The method first extracts the coarse edge of the object, then the luminance distribution on the normal direction of the coarse edge is fitted to the Sigmoid function. Mathematical analysis points out the location of the precise sub-pixel edge is closely related to the parameters of the fitted Sigmoid function. Real-world experiments of applying our proposed method and other different methods in the measurement system are performed. Comparison results prove superiority of our proposed method in accuracy and robustness.