Magnification-continuous static calibration model of a scanning-electron microscope

We present a new calibration model of both static distortion and projection for a scanning-electron microscope (SEM). The proposed calibration model depends continuously on the magnification factor. State-of-the-art methods have proposed models to solve the static distortion and projection model but for a discrete set of low and high magnifications: at low magnifications, existing models assume static distortion and perspective projection. At high magnifications, existing models assume an orthogonal projection without presence of static distortion. However, a magnification-continuous model which defines continuous switch from low to high magnifications has not yet been proposed. We propose a magnification-continuous static calibration model of the SEM. The static distortion and intrinsics of the projection matrix are modeled by partial differential equations (PDEs) with respect to magnification. The approach is applied with success to the JEOL-JSM 820 in a secondary electron imaging mode for magnification ranging from 100× to 10k×. The final RMS reprojection error is about 0.9 pixels. This result together with two application-based experiments: the consistent measurements of the bending of a cantilever and a 3-D reconstruction of a nano-ball emphasize the relevance of the proposed approach.