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Accuracy of AFM force distance curves via direct solution of the Euler-Bernoulli equation
3.D. Guo, G. Xie, and J. Luo, Journal of Physics D-Applied Physics 47(1), (2014).
14.It is worth pointing out that this ill-posedeness is a peculiarity of the common single point optic lever detection system used in typical atomic force microscopes. This ill-posedness would exist even in the absence of noise.
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In an effort to improve the accuracy of force-separation curves obtained from atomic force microscope data, we compare force-separation curves computed using two methods to solve the Euler-Bernoulli equation. A recently introduced method using a direct sequential forward solution, Causal Time-Domain Analysis, is compared against a previously introduced Tikhonov Regularization method. Using the direct solution as a benchmark, it is found that the regularization technique is unable to reproduce accurate curve shapes. Using L-curve analysis and adjusting the regularization parameter, λ, to match either the depth or the full width at half maximum of the force curves, the two techniques are contrasted. Matched depths result in full width at half maxima that are off by an average of 27% and matched full width at half maxima produce depths that are off by an average of 109%.
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