Compact sensor for measuring two-dimensional tilt using a two-dimensional transmission grating and the Talbot effect

Abstract

This paper proposes a tilt sensor that measures the small two-dimensional tilt of a plane reflective object using the Talbot effect. It is an extension of a previously proposed one-dimensional tilt sensor. The light beam reflected from the object impinges on a hexagonal grating, and the intensity of the diffracted wave is detected on an image sensor located at a Talbot distance from the grating. The diffraction intensity displaces due to the tilt of the object. The displacement is calculated by the Fourier transform method to obtain the two-dimensional tilt. This sensor is very simple and compact. The principle of the sensor is explained for a grating with a general pattern. An experiment using a hexagonal grating shows its validity. Discussions are given for making it more practical.