Contrast-to-gradient method for the evaluation of image resolution in scanning electron microscopy

In a previous study, we proposed the contrast-to-gradient (CG) method to evaluate the image resolution in scanning electron microscopy. The directional CG resolution R(θ) is defined as a weighted harmonic mean of the local resolution RP(x,y;θ) having a specified azimuth angle θ, where RP(x,y;θ) is proportional to the quotient of the threshold contrast divided by the local gradient. The local gradient is calculated from the quadratic function that best fits the local pixel intensities over the region of interest (ROI) of 3×3 or 5×5 pixels in size. The image resolution R(CG) is defined as a geometric mean of the directional resolution R(θ). In this paper we review the characteristics of R(CG)-values, which are intrinsically independent of a black-and-white contrast reversal and of a brightness/contrast change (as long as there is no accompanying saturation/cut-off in the intensity). We also demonstrate the wide range applicability of the CG method for various types of images (such as low-contrast, noise containing, strongly directional, and periodic/non-periodic pattern images as well as ordinary images opposite to the above). As to the encountered problem that the R(CG)-value is slightly overestimated for a rather low-magnification image, we propose a zero-corrected CG method as a prospective solution.