Microscale 3-D Rotation Estimation Based on Deflected Defocused Feature Extraction

In micro-electromechanical systems (MEMSs), measuring 3-D rotation presents challenges such as an unclear rotation center and poor orthogonality. Microvision-based rotation estimation is limited by a shallow imaging depth of field, leading to a narrow measurement range and low precision. This article introduces a novel method called deflected defocused feature extraction (DFE) to address these issues and enable accurate microscale rotation estimation. DFE extends the measurement range from 0.03 to 0.92 rad while achieving a precision of 0.1179 mrad for out-of-plane angles. The edge defocus model incorporating deflection angle is derived based on microscopic imaging principles. A general circular array is fabricated and a robust defocus control point extraction method is proposed. Finally, 3-D angular displacement measurement is accomplished via homography matrix decomposition. Experimental results demonstrate a resolution of 0.17, 0.17, and 0.0087 mrad for the three axes. The range-to-resolution ratios are found to be $10^{4}$ , $10^{4}$ , and $10^{6}$ .