## Abstract

Optical smoothing is a very effective method to restrict mid-to-high spatial frequency errors generated by computer-controlled sub-aperture polishing technologies. According to Preston’s equation, pressure distribution is the key factor in describing the smoothing effect of a tool. Although the classic bridging model can solve pressure distribution during the smoothing process, it is only suitable for a tool that consists of a rigid base, compliant interlayer, thin metal plate, and pitch polishing layer. In this paper, a mathematical model applicable for any multi-layer polishing tool is proposed, which helps to calculate the pressure distribution dependent on the thickness of the layer, mid-spatial frequency errors at different periods, and the structures of polishing tools. Based on the model, the pressure distributions and smoothing rates of a rigid tool and a semi-flexible tool are deduced and compared in detail. Validity and improvement in accuracy are verified by comparison with the finite element model. In addition, three groups of experiments using a rigid tool and a semi-flexible tool for smoothing 4 mm and 8 mm period errors generated by magnetorheological finishing are carried out to validate the model. The simulation result of the smoothing rates of the errors after every smoothing process matches well with the experiment results.

© 2019 Optical Society of America

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