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A schematic of an atomic force microscope. The cantilever is attached to a vertical positioner. The cantilever deflection is sensed, and a feedback controller moves the positioner to maintain a constant deflection.
The block diagram model of the AFM, where , , , model the cantilever, piezoelectric positioner, controller, and the deflection transducer, respectively. and are the cantilever deflection and transducer noise, respectively. models the sample topography. represents a combination of positioner, cantilever, and transducer dynamics. The cantilever has a high resonant frequency and is assumed to be a constant over the frequency region of interest. Hence is a scaled version of the sample topography.
(a) , , and are the weights used for designing the optimal controller . is a function of controller states. is the proposed signal to estimate the sample profile. (b) The block diagram in (a) can be redrawn as shown in (b). is the generalized positioner transfer function which is used in the optimal control scheme.
(a) Experimental data shows that significantly superior images are obtained by using the proposed imaging signal compared with using the control effort as the sample topography estimate. (b) Experimental data shows that the proposed signal gives an accurate image of sine wave topography. The control signal, becomes attenuated and incurs significant phase lag from the sample profile. (c) The experimental frequency response of the control effort to sample topography. (d) The experimental frequency response of the estimate to sample topography.
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