Simultaneous detection of translational and angular displacements of micromachined elements

An astigmatic detection system is constructed with a modified digital-versatile-disk optical head. This system, with a detecting spot of ∼1μm, can simultaneously measure the vertical displacements and two-dimensional angular tilts of micromachined elements. It can detect thermal vibrations of microfabricated cantilevers with noise levels of 1.3pmHz−1∕2 for the linear displacement and of 3.2nradHz−1∕2 for angular displacements over a frequency range from 1to800kHz. The detecting frequency can even reach beyond 100MHz if high-speed electronic devices are adopted. Further optimization of the system will broaden its applications in diverse technological fields.