Objective As a new optical machining technology, magnetorheological finishing has many advantages, such as high machining certainty, stable convergence efficiency, controllable edge effect, small subsurface damage layer, so it has a wide range of applications in the field of high-precision optical machining. According to the principle of magnetorheological finishing, high-precision machining process requires stable removal function and accurate dwell time distribution of each dwell point. However, the actual machining process is often affected by various kinds of errors, which makes the actual machining results deviate from the ideal results. In the field of high-precision machining, small errors will also have a great impact on the surface accuracy and the errors of each frequency band, and even lead to the non-convergence of the surface errors. With its continuous development, aspherical optics have the advantages of correcting aberrations, improving image quality and reducing system weight, so it has been widely used. However, the surface of aspherical optical components is complicated, and the manufacturing process is more difficult than that of spherical optical components. In the existing research, the machining of aspherical optical elements by magnetorheological finishing is realized through the cyclic process of inspection and machining, but there are problems such as the uncertainty of surface accuracy and the uncontrollable mid-spatial error.

Methods The processing method based on uncertainty error can increase the certainty of the processing process, optimize the process flow, and effectively suppress the mid-spatial error. Therefore, in order to realize the high-precision machining of optical elements, the uncertainty error method is adopted, and the ideal surface accuracy can be obtained in the actual machining process. The feasibility of the scheme is verified by simulation processing, experimental verification and error compensation on the aspherical surface.

Results and Discussions  The magnetorheological finishing experiment of #B is carried out under uncertainty error. According to the experimental results, the surface error RMS value increases from 15.432 7 nm (Fig.10(a)) to 19.317 nm (Fig.11(g)), and the uncertainty error of surface error RMS value is controlled at 3.884 3 nm after machining compared with the predicted result before machining. The mid-spatial error RMS value increases from 10.262 nm (Fig.10(b)) to 13.282 nm (Fig.11(h)), and the uncertainty error of the mid-spatial error RMS value is controlled at 3.02 nm. The experimental results show that the method based on uncertainty error not only effectively converges the surface error, but also reasonably restrains the mid-spatial error. It provides theoretical support for surface error and mid-spatial error suppression in magnetorheological finishing. This method has important practical value for realizing high-precision magnetorheological machining of optical components.

Conclusions The uncertainty theory in magnetorheological finishing is analyzed, and the removal function uncertainty error and position uncertainty error are specifically analyzed, and the process flow of magnetorheological finishing under the uncertainty error is summarized. On this basis, two off-axis aspheric mirrors are used to verify the process. The errors in the magnetorheological finishing of off-axis aspherical surface #A are analyzed in detail to determine the uncertainty in the machining of off-axis aspherical surface #B, so as to guide the machining of off-axis aspherical surface #B. The experimental results show that the surface accuracy and mid-spatial error of the off-axis aspherical surface #B meet the engineering requirements. On the basis of uncertainty analysis, the process flow is optimized, and the surface error convergence is achieved and the mid-spatial error is suppressed by means of uncertainty.