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Inverse calculation of the tip–sample interaction force in atomic force microscopy by the conjugate gradient method

An inverse vibration problem based on the conjugate gradient method is presented for estimating the unknown tip–sample interaction force with an atomic force microscope (AFM) by using the measured cantilever displacement. No prior information on the functional form of the unknown quality is required beforehand. The accuracy of the inverse analysis is examined using simulated exact and inexact measurements of the displacement. Numerical results show that an excellent estimate of the tip–sample interaction force by an AFM can be obtained within 1 s of CPU time with a Pentium III-450 MHz PC.