Measurement and correction of TEM image distortion using arbitrary samples.

We have developed a method to quantitatively measure image distortion, one of the five Seidel aberrations, in transmission electron microscopes without using a standard sample with a known structure. Displacements of small local segments in an image due to image distortion of the intermediate and projection lens system are first measured by comparing images taken before and after a given shift at the first image plane of the objective lens. Then, the sum of the second partial derivatives, or the Laplacian, of the displacement field is measured, and the radial and azimuthal distortion parameters are determined from the measured results. We confirmed using numerically distorted images that the proposed method can measure the image distortion within a relative error ratio of 0.04 for a wide range of distortion amount from 0.1% to 5.0%. The distortion measurement and correction were confirmed to work correctly by using the experimental images, and the iterative measurement and correction procedure could reduce the distortion to a level where the average image displacement was < 0.05 pixels.