Combining gradient ascent search and support vector machines for effective autofocus of a field emission–scanning electron microscope

Summary Autofocus is an important issue in electron microscopy, particularly at high magnification. It consists in searching for sharp image of a specimen, that is corresponding to the peak of focus. The paper presents a machine learning solution to this issue. From seven focus measures, support vector machines fitting is used to compute the peak with an initial guess obtained from a gradient ascent search, that is search in the direction of higher gradient of focus. The solution is implemented on a Carl Zeiss Auriga FE‐SEM with a three benchmark specimen and magnification ranging from x300 to x160 000. Based on regularized nonlinear least squares optimization, the solution overtakes the literature nonregularized search and Fibonacci search methods: accuracy improvement ranges from 1.25 to 8 times, fidelity improvement ranges from 1.6 to 28 times, and speed improvement ranges from 1.5 to 4 times. Moreover, the solution is practical by requiring only an off‐line easy automatic train with cross‐validation of the support vector machines. Lay description Autofocus is an interesting facility for scanning electron microscopes, particularly at high magnification where the depth‐of‐field is very short. If it is useful for the analysis of specimens from two‐dimensional (2D) images, it becomes essential for the robotic handling of specimens by enabling their depth estimation. In the future it will enable the achievement of high‐resolution reconstruction of 3D images from several 2D images obtained by rotating the specimen. New scanning electron microscopes are equipped with autofocus facility but their performance can be improved. Autofocus consists in searching for sharp image of a sample, that is corresponding to the peak of focus. The paper presents a machine learning solution to this issue. From seven focus measures, support vector machines regression is used to compute the peak with an initial guess obtained from a gradient ascent search, that is search in the direction of higher gradient of focus. It is applied to a Carl Zeiss Auriga FE‐SEM with three benchmark specimens (a gold‐coated gripper over 20‐μm polymere balls on an aluminium substrate, tin‐on‐carbon test specimen with 5‐ to 30‐μm particle, gold‐on‐carbon test specimen with 5 to 150 nm particles) and magnification ranging from x300 to x160 000. Based on regularized nonlinear least squares optimization, the solution overtakes the literature nonregularized search and Fibonacci search methods: accuracy i