Atomic force microscope cantilevers as encoder for real-time displacement measurements

We have investigated the use of atomic force microscope (AFM) cantilevers as encoder for real-time high-resolution displacement measurements. Mathematical derivations show that two AFM cantilevers signals are needed for real-time forward and backward displacement measurements in any planar direction and in x- or y-axis direction respectively when two are paired with a 1D sinusoidal grating. Tuning-fork (TF) cantilevers are the best choice among AFM cantilevers for the setup of a multi-cantilever encoder head. During the study an AFM head with up to three TF cantilevers as the encoder has been designed and built. The system was experimentally tested for its performance and feasibility of real-time displacement measurements in x- or y- axis by using two cantilevers. To achieve a correct reading the distance between two cantilever tips is preset in such a way that the two 1D sinusoidal grating position-encoded signals have a quadrature phase shift form. The decoding algorithm is based on directly unwrapping of the phase from the signals in real-time. Cross-correlation filtering and differentiation process of two encoded signals could be applied to suppress the noise and to reduce the offset and tilt of the encoded signals and by this allows a successful implementation of real-time displacement measurements.