Description method with automatically configurable Gaussian radial basis function for complex freeform surface

The description of deformable mirror (DM) surface, which is usually a complex freeform surface, affects the measurement speed and accuracy in a real-time interferometric measurement system with a DM as the dynamic compensator. We propose an accurate and fast description method with automatically configurable Gaussian radial basis function. The distribution and shape factors of GRBFs are related to the complexity of the surface with sufficient flexibility to improve the accuracy, and the fitting results are automatically obtained using a traversal optimization algorithm, which can improve the fitting speed by reducing the number of time-consuming calculations. The feasibility is verified by numerical and practical experiment.