Analysis of force-deconvolution methods in frequency-modulation atomic force microscopy

In frequency-modulation atomic force microscopy the direct observable is the frequency shift of an oscillating cantilever in a force field. This frequency shift is not a direct measure of the actual force, and thus, to obtain the force, deconvolution methods are necessary. Two prominent methods proposed by Sader and Jarvis (Sader-Jarvis method) and Giessibl (matrix method) are investigated with respect to the deconvolution quality. Both methods show a nontrivial dependence of the deconvolution quality on the oscillation amplitude. The matrix method exhibits spikelike features originating from a numerical artifact. By interpolation of the data, the spikelike features can be circumvented. The Sader-Jarvis method has a continuous amplitude dependence showing two minima and one maximum, which is an inherent property of the deconvolution algorithm. The optimal deconvolution depends on the ratio of the amplitude and the characteristic decay length of the force for the Sader-Jarvis method. However, the matrix method generally provides the higher deconvolution quality.