Inverse estimation of the tapered probe-sample shear force of scanning near-field optical microscope

In this paper, the conjugate gradient method of minimization with an adjoint equation is successfully applied to solve the inverse problem in estimating the shear force between the tapered probe and sample during the scanning process of scanning near-field optical microscope (SNOM). While knowing the available deflection at the tapered probe tip, the determination of the interaction shear force is regarded as an inverse vibration problem. In the estimating processes, no prior information on the functional form of the unknown quantity is required. The accuracy of the inverse analysis is examined by using the simulated exact and inexact measurements of deflection at the tapered probe tip. Numerical results show that good estimations on the interaction shear force can be obtained for all the test cases considered in this study.