Imaging surface analysis: Lateral resolution and its relation to contrast and noise

Abstract

Lateral resolution, also called image resolution, is the most relevant quality parameter of maps and line scans. Therefore well defined procedures for the determination of lateral resolution are required. In the surface analysis community different definitions of lateral resolution are in use and there is no generally accepted method for the determination of lateral resolution which meets the demands of the state-of-the-art in surface analysis. We propose the determination of lateral resolution by imaging of well defined square-wave gratings with finely graded periods. This method enables the real time estimation of lateral resolution and the adjustment of instrument settings with respect to lateral resolution. The effect of noise and contrast on lateral resolution has been analysed by numerically simulated images of square-wave gratings. A new resolution criterion has been developed which is based on the dip-to-noise ratio and takes into account the sampling step width by introducing a “reduced noise”. The contrast transfer function has been introduced and its relation to lateral resolution in the presence of noise was analysed. For that reason an “effective cut-off frequency” was defined which is the reciprocal of the lateral resolution. Normalized values of lateral resolution and their relation to signal-to-noise ratio and sampling step width were given for Gaussian and Lorentzian line spread functions. These values enable the calculation of experimental parameters which are necessary to get a required value of lateral resolution. Finally the successful application of the proposed approach to determine lateral resolution has been demonstrated by ToF-SIMS element mapping of the certified reference material BAM-L200.