Mathematical model for optical smoothing prediction of high-spatial-frequency surface errors

Pravin K. Mehta; Paul B. Reid

doi:10.1117/12.363825

28 September 1999 Mathematical model for optical smoothing prediction of high-spatial-frequency surface errors

Pravin K. Mehta, Paul B. Reid

Proceedings Volume 3786, Optomechanical Engineering and Vibration Control; (1999) https://doi.org/10.1117/12.363825
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

This paper describes a mathematical model, called the Bridging model, for predicting the smoothing of high spatial frequency surface errors in optical surfaces during polishing processes, which use large flexible polishing laps. The mathematical model is developed in two stages. First, the Kirchoff flat plate equation, which is modified to include the effect of shear flexibility of the lap and compressive stiffness of the pitch, is solved for lap pressure distribution over a surface error feature represented by a sinusoidal spectrum. This pressure distribution is used as an input to the Preston's equation for material removal rate. The resulting equation is then solved for material removal and surface error smoothing predictions. Available data from a laboratory test and a real optics fabrication program are compared with analytical predictions of the mathematical model. Good correlation is obtained between the two.

Citation Download Citation

Pravin K. Mehta and Paul B. Reid "Mathematical model for optical smoothing prediction of high-spatial-frequency surface errors", Proc. SPIE 3786, Optomechanical Engineering and Vibration Control, (28 September 1999); https://doi.org/10.1117/12.363825

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