Diffusion filtration for the evaluation of MEMs surface

MEMs surfaces are one type of typical structured surface. For this type of surfaces the accuracy of the geometrical feature (line width, step height etc.) are generally more important than roughness. For the exaction of these geometrical features, traditional convolution based filtration techniques are lack of the ability to preserve the feature with high accuracy. In this paper, a Partial Differential Equation (PDE) based nonlinear diffusion filter is proposed for the filtration of structured surface. In this model, the filtration procedure can be seen as a nonlinear heat equation, which describes the distribution of heat (or variation in temperature) in a given region over time. By choosing a proper diffusivity function, which is a nonnegative monotonically decreasing function in respect of the gradient of the surface, the diffusion process will take place mainly in the interior regions/feature (line, step, etc.) of the surface, and it will not affect the region boundaries. A wavelet based regularization method is introduced into the diffusion procedure, which can help to decrease the measurement outliers’ influence. Experimental work using simulated and practical measurement surface data shows that, the proposed filter can separate the geometrical feature (especially the line and step) from roughness and measurement noise and outliers with ideal edge preserving property.