A new sample-profile estimation signal in dynamic-mode atomic force microscopy

In this paper, a design scheme is proposed that separates the issues of sample-profile estimation and amplitude regulation in dynamic-mode atomic force microscopy. In current AFM, the control signal for amplitude regulation is also used as the estimate for the sample-profile. Therefore, the sample profile estimation signal is accurate as long as the sample-profile signal perceived by the cantilever is well within the bandwidth of the control transfer function. In the proposed design scheme, maintaining a constant amplitude while scanning at high bandwidth does not impose limitations on the reconstruction of the sample topography. In fact, we analytically prove that the sample-profile signal estimation problem can be solved independently of the control design scheme for amplitude regulation. Therefore, accurate sample-profile estimations can be obtained even at frequencies near and beyond the closed-loop control bandwidths. However, we show that the robustness of estimation does depend on the control design for regulation and in fact, the robustness of estimation is described by the closed-loop sensitivity transfer function. The independence of the profile-estimation problem from the control design is another salient distinguishing characteristic of this work. The estimation bandwidths by this new scheme are improved significantly over commonly used signals. Comparison with the existing methods of using the control signal as the image is provided. The experimental results corroborate the theoretical development.