New Computed Tomography Algorithm of Electrostatic Force Microscopy Based on the Singular Value Decomposition Combined with the Discrete Fourier Transform

A new algorithm for three dimensional electrostatic force microscopy, which deduces the charge distribution in a sample from a horizontal distribution of a gradient of electrostatic force measured above the sample surface, was proposed. One dimensional horizontal distribution of the electrostatic force gradient was transformed into frequency space and the singular value decomposition was performed. Very small singular values were removed and then the inverse matrix was calculated. This method was more tolerant of noise than the conjugate gradient method. Even with 0.1% noise in the distribution of force gradient, the charge even in the fourth layer can be reconstructed.