Reconstruction of Kelvin probe force microscopy image with experimentally calibrated point spread function.

A Kelvin probe force microscopy (KPFM) image is sometimes difficult to interpret because it is a blurred representation of the true surface potential (SP) distribution of the materials under test. The reason for the blurring is that KPFM relies on the detection of electrostatic force, which is a long-range force compared to other surface forces. Usually, KPFM imaging model is described as the convolution of the true SP distribution of the sample with an intrinsic point spread function (PSF) of the measurement system. To restore the true SP signals from the blurred ones, the intrinsic PSF of the system is needed. In this work, we present a way to experimentally calibrate the PSF of the KPFM system. Taking the actual probe shape and experimental parameters into consideration, this calibration method leads to a more accurate PSF than the ones obtained from simulations. Moreover, a nonlinear reconstruction algorithm based on total variation (TV) regularization is applied to KPFM measurement to reverse the blurring caused by PSF during KPFM imaging process; as a result, noises are reduced and the fidelity of SP signals is improved.