Image blur analysis for the subpixel-level measurement of in-plane vibration parameters of MEMS resonators

Abstract

The objective of this work is to develop a reliable image processing technique to measure the vibration parameters on every part of MEMS resonators using microscopic images of the vibrating devices. Images of resonators vibrating in high frequencies are characterized by the blurs whose point spread functions (PSFs) are expressed in a parametric form with two parameters - vibration orientation and magnitude. We find it necessary to use the reference image (image of the still object) when analyzing the blur image, to achieve a subpixel-level accuracy. The orientation of the vibration is identified by applying the Radon transform on the difference between the reference image and the blur image. A blur image is usually modeled as a convolution of the PSF of the vibration with the reference image and added noise terms, assuming uniform vibration across the view. The vibration magnitude could then be recovered by using a minimum mean-squared error (MMSE) estimator to find the optimal PSF with the identified orientation. However, in real images only parts of the image belong to the vibrating object and the vibration may not be uniform over all parts of it. To overcome that problem, we use local optimization with a mean of weighted squared errors (MWSE) as the cost function instead of MSE. Indeed, it is capable of suppressing non-vibrating high-frequency components of the image. Sensitivity analysis and experiments on real images have been performed.