A novel method for measurement of angular displacement in one or two dimensions for arbitrarily shaped objects is presented. The method is based on Fourier transforming the scattered field from a single laser beam that illuminates the target. The angular distribution of the light field at the target is linearly mapped onto an array image sensor placed in the Fourier plane. Measuring this displacement facilitates the determination of the angular displacement. It is demonstrated both theoretically and experimentally that the angular displacement sensor is insensitive to object shape, target distance and any longitudinal or transverse movement of the target, if the image sensor is placed in the Fourier plane. A straightforward procedure to place the image sensor in the Fourier plane is presented here. Theoretically and experimentally, it is shown that the method has a resolution of 0.3 mdeg for small angular displacements, and methods for further improvement in resolution are discussed. No special surface treatment is required for surfaces having irregularities of the order of or larger than the wavelength of the incident light. It is shown that this is the case for most surfaces of practical interest. Furthermore, it is shown that robust, non-contact optical systems for industrial applications can be produced.
Journal of Optics, 1998, Vol 29, Issue 3, p. 115-120