An improved gradient-integral method with hybrid iteration for surface measurement of free-form large astronomical mirrors

Due to its excellent performance, free-form large astronomical mirrors are playing an important role in astronomical optical telescope. Compared with traditional simple astronomical mirrors, the manufacture and the testing for such kind of mirrors are more complex and difficult since the influence of surface characteristics. In recent years, a gradient-sensing technique based on fringe reflection (FR) is becoming a powerful tool for free-form large astronomical mirror testing owing to its advantages of high accuracy, fast speed, large dynamic range, etc. As an important part of FR, shape integration based on gradient information straightforwardly affects the accuracy of surface reconstruction. To overcome some problems of the existing shape integration methods, e. g. high-frequency information easily missing in Fourier integral method, a high sampling rate requirement in directly linear least-squares integral method based on Southwell's model, etc., an improved shape-integral algorithm with hybrid iteration for surface reconstruction under sparse sampling considering the features of free-form large astronomical mirrors is proposed in this paper. Simulation results demonstrate the effectiveness of the proposed method.