Dwell Time Algorithm for Large Aperture Optical Element in Magnetorheological Finishing

In order to obtain high precise optical surface by magnetorheological finishing (MRF), an algorithm combined with SBB (Subspace Barzilai and Borwein) and adaptive Tikhonov regulation is proposed to get dwell time distribution based on matrix multiplication. Moreover, double removal functions are introduced to polishing of the circle mirror with spiral path to guarantee the convergence of center area and surface precision of full aperture. Algorithm's simulation shows that the accuracy of the method mentioned above is the same with traditional Lawson-Hanson method, but the computing rate is much faster than the latter. The example calculation of 600 mm circle mirror with main coma surface error presents that the value of peak-valley (PV) value and root mean square (RMS) from 2.712 and 0.461 converges to 0.306 and 0.0199 (=632.8 nm) with the center and full aperture consistent. Therefore, the algorithm in this paper can ensure the convergence accuracy of the surface shape while solving the dwell time distribution effectively and keeping the solution accurate and stable fast. The result provides support to the application of MRF on large aperture optical element.