Calibration of projector lens distortions.

The distortions introduced into high-resolution transmission electron microscope (HRTEM) images by the projector lens system are an important source of systematic error for quantitative displacement and strain determination. Using geometric phase analysis of images of perfect crystals, we measured these errors for two different transmission electron microscopes. Local magnification varies by as much as 5%, and rotation can reach 2 degrees across a typical image. Our experimental results are compared with theory, and optical pincushion and spiral distortion coefficients are determined. A method for calibrating and removing these distortions is presented that enables quantification to 0.1% strain and 0.1 degrees rotation across the whole field of view. This calibration is also critical for the accurate measurement of local lattice parameters from HRTEM images.