Atomic Force Microscope (AFM) Cantilevers as Encoder for Real-Time Displacement Measurements

This thesis proposes that atomic force microscope (AFM) cantilevers be used as encoder for real-time high-resolution displacement measurements.

It first focuses on the displacement decoding mathematics. From the mathematical derivation it is found that four AFM cantilever signals are needed when a 2D sinusoidal grating is paired as a reference for real-time forward and backward displacement measurements in any planar direction, and two AFM cantilevers signals are needed when a 1D sinusoidal grating is paired as the reference for real-time forward and backward displacement measurements in x- or y-axis direction. Furthermore it demonstrates that so far a tuning fork (TF) cantilever is the best choice among AFM cantilevers for multi cantilevers to be integrated into a compact encoder head.

An AFM with one TF cantilever has been designed and built. The performance and feasibility of one TF cantilever used as encoder for real-time forward or backward displacement measurement has been investigated and experimentally tested. The decoding principle is based on direct count of integer periods plus calculation of two fractional parts of such periods standing at the beginning and at the actual position in the encoded signal corresponding to a given path of displacement. To ensure accurate implementation of this decoding process, a cross-correlation technique has been employed to filter a 1D grating encoded signal in real time. A half sinusoidal waveform template is proved to be very efficient and correct to filter 1D any waveform grating encoded signal by cross- correlating with it.

Finally an AFM head with three TF cantilevers as the encoder has been designed and built. It has been experimentally tested for its performance and feasibility of real-time forward and backward displacement measurements in x- or y- axis by using two cantilevers, if the distance between two cantilever tips in the AFM head is preset by a special piezo in such that two 1D sinusoidal grating position-encoded signals have a quadrature phase shift. By directly unwrapping the phase between two encoded signals, forward and backward displacements can be detected and measured in real time. Cross-correlation filtering and differentiation process of two encoded signals are found very successful to guarantee the implementation of real-time displacement measurements by suppressing noise and reducing the offset and tilt of the encoded signals.