The use of circular optical grating for measuring angular rotation of mirrors

This paper explores the feasible use of circular optical grating for measuring the rotation of mirrors that are commonly found in micro-systems. Both theoretical and experimental results show that distortion of the circular grating that is projected onto the mirror surface is a simple function of the angular rotation of the mirror. The circular grating may readily be generated using a standard Michelson interferometer or an LCD projector. Through manipulating the distance between the interferometer and the mirror surface, the diameter of the optical grating may be varied. Furthermore, the additional use of a converging lens enables a significant reduction in the size of the grating: with simple laboratory facility, small circular grating of about 400µm is achieved for use on micro-systems. With the use of more sophisticated optical elements, the angular rotation of even smaller micro-mirrors may be measured.