<p>Galvanometer-based laser processing systems are crucial tools in modern precision manufacturing. To effectively enhance the processing accuracy of galvanometer systems and meet the precision requirements of diverse processing tasks, an error compensation method based on ordinary Kriging interpolation for generating a Compensation value extension look-up table is proposed. First, the transmission characteristics of the optomechanical chain components are analyzed, and a ray transfer model is established to simulate the distribution patterns of errors. Second, a circular grid array measurement method is employed to obtain compensation values, and a correction look-up table is constructed. Finally, the error compensation for any position within the grid is rapidly achieved using bilinear interpolation. To validate the effectiveness of the proposed method, comparative experiments are conducted. The experimental results show that this method can reduce the maximum error by 96.44% in the 100 mm² range of galvanometer processing. Further investigation revealed that the maximum error decreased as the processing area was reduced, the nonlinear relationship between the two is effectively described using a polynomial model, therefore, a machining range optimization search method is presented, providing an effective method for determining the scanning range of processing systems to meet different precision requirements. The proposed compensation method offered an effective solution to address the issue of insufficient processing accuracy caused by galvanometer scanning errors in laser processing systems.</p>