Photogrammetric calibration of a scanning electron microscope

Abstract

Since the invention of the SEM (Scanning Electron Microscope), researchers have used 2-dimensional measurements on micrographs. Stereo-pairs of micrographs are used to some extent for limited 3-dimensional analyses. This is done primarily for qualitative analyses. With the growing need for serious quantitative investigations, more attention is presently drawn to statistically sound metric calibration of the SEM. A procedure of analytical calibration of SEM developed in the Ohio State University department of Geodetic Science is discussed. The concept of system calibration is used. This procedure used advanced photogrammetric self-calibration techniques to solve for the tilt and rotation angles, also magnification and systematic distortion parameters which define the trajectory of light rays and electron beams in the SEM system. Utilizing multiple micrographs made of a diffraction-granting replica calibration standard tilted at angles up to 45°, with four 90° differential rotation angles for each tilt, hundreds of photogrammetric comparator measurements made on each micrograph were combined in a least-squares adjustment, which determines the calibration parameters and their variances and covariances. The sample test SEM (Materials Analysis Co. Model 700) was calibrated separately for magnifications of 2000 ×, 5000 ×, and 10,000 ×. In addition to an affine deformation plus radial and tangential distortions, as found in other photographic systems, a new “spiral” distortion was mathematically modelled which accounted for more than 300 μm of systematic distortion at photo scale for each image throughout the format of the micrographs.