Large-scale fast dwell time algorithm for complex structure phase optical elements based on magnetorheological polishing

Abstract

Due to the characteristics of large depth, small period and high steepness, phase optical elements with complex structure need to use a small size removal function in magnetorheological processing, and use very small line spacing and step size values when planning the polishing path，so the dwell time matrix is very large, and the dwell time calculation speed is slow; besides, because of the complicated phase optical profile, it is difficult to achieve high-precision convergence of the dwell time. This paper proposes a fast and high-precision numerical iterative dwell time algorithm for complex structure phase optical elements. this paper proposes the concept of the dwell point matrix, which realizes the methods of the FFT convolution multi-core parallel algorithm to calculate the dwell time in the entire iterative calculation process. Also, to achieve high-precision convergence of the dwell time calculation, this paper proposes a calculation rule based on machine dynamic performance matching, when calculating the dwell time, the speed, acceleration, and speed smoothness of the machine were matched with the performance of the magnetorheological machine, which improves the stability of the machine. A large-diameter Continuous Phase Plate (CPP) is processed on a magnetorheological machine. The shape of the CPP contains a random structure of various periods. The initial RMS = 228.07nm, the CPP data matrix size is 2424 × 2424, and the line spacing is 0.6mm, the dwell time is calculated using the algorithm described in this article, the entire calculation process takes only 4.2 seconds, the calculation speed is about 3 times faster than the traditional iterative methods, the CPP residual error RMS converges to 10.2nm; After the CPP processing is completed, the CPP actual residual error RMS is reduced from the original 228.07nm to 15.6nm, and its convergence rate is 93.1%, which shows that the algorithm has high calculation efficiency and convergence accuracy.