Aspherical Measurement Error Decoupling Technology Based on Global Optimal Fitting of Full-Aperture Surface Shape Features and Local Measurement Errors

Aspheric optical elements are essential in high-end manufacturing and scientific research. As precision demands increase, the coupling of surface features and measurement errors during high-asphericity and high steepness element measurement based on annular subaperture stitching limits high-precision measurement development. The traditional overlapping-region based subaperture stitching method suffers from two major issues: the error of the first subaperture, which serves as the reference, cannot be decoupled, and the error accumulation. To solve the error coupling problem, this paper proposes an aspherical measurement error decoupling technology based on global optimal fitting of full-aperture surface shape features and local measurement errors. The method uses fullaperture circular and subaperture annular Zernike polynomials to build a global optimization model, where the former represents surface features and the latter describes subaperture errors. By integrating these polynomials to create a global optimization function and solving for Zernike coefficients, error decoupling and enhanced accuracy can be achieved. Furthermore, processing errors globally can avoid error accumulation in the traditional method and reduce the number of subapertures for higher measurement efficiency. Simulation and experimental validations are demonstrated in this paper. The simulation shows effective fitting of Zernike polynomial coefficients and error decoupling. Experiments shows that the achievement of error decoupling in measurement of high-asphericity and high steepness elements with the proposed method, and the PVr accuracy of measurement is improved by nearly 30% compared to traditional methods. The proposed method offers a practical solution for high-precision measurement of high-asphericity and high steepness element measurement.