Multiple linear regression analysis of the overlay accuracy model

The multiple linear regression method was used to analyze the overlay accuracy model and study the feasibility of using linear methods to solve parameters of nonlinear overlay equations. The methods of analysis include changing the number of sample points to derive the least sample number required for solving the accurate estimated parameter values. Besides, different high-order lens distortion parameters were ignored, and only the various modes of low-order parameters were regressed to compare their effects on the overlay analysis results. The findings indicate that given a sufficient number of sample points, the usage of multiple linear regression analysis to solve the high-order nonlinear overlay accuracy model containing seventh-order lens distortion parameters is feasible. When the estimated values of low-order overlay distortion parameters are far greater than those of high-order lens distortion parameters, excellent overlay improvement can still be obtained even if the high-order lens distortion parameters are ignored. When the overlay at the four corners of image field obviously exceeds that near the center of image field, it is found, through simulation, that the seventh-order parameters overlay model established in this paper has to be corrected by high-order lens distortion parameters to significantly improve the overlay accuracy.