Calibration of scanning electron microscope using a multi-image non-linear minimization process

Abstract

In this paper, a novel approach of SEM calibration based on non-linear minimization process is presented. The SEM calibration for the intrinsic parameters are achieved by an iterative non-linear optimization algorithm which minimize the registration error between the current estimated position of the pattern and its observed position. The calibration can be achieved by one image and multiple images of calibration pattern. Perspective and parallel projection models are addressed in this approach. The experimental results show the efficiency and accuracy of the proposed method. I. INTRODUCTIONScanning electron microscope (SEM) is an electron microscope where a focused beam of electrons is used to scan the surface of a specimen. This is an essential instrument to display, measure and manipulate the micro and nanostructure with a micrometers or nanometers accuracy. When the task requires the computation of metric information from the acquired 2D images, the calibration of the SEM is an important issue to be considered.Since the structure of a scanning electron microscope is very different from the structure of an optical microscope, it became apparent that novel image analysis, geometrical projection models and calibration processes would be necessary in order to extract accurate information from the SEM images. In earlier studies, photogrammetric analysis of SEM has been considered by several authors [1],[6]. The projection model relates a three-dimensional (3D) point on a specimen in the observed space to its projection in the two-dimensional (2D) image. Previous studies consider that at low magnification, perspective projection model can be applied because the observed area and electron beam sweep angle are both large. At higher magnification, the center of projection is usually regarded at infinity so the parallel projection model is assumed. However, the practical limit between the choice of perspective projection and parallel projection model is not clear. Some experiments [4], [16] show that parallel projection is assumed at magnification of 1000× and higher. [9] have concluded that the use of parallel projection depends on the desired accuracy for the calculation of position of a point on the specimen. Another important issue in calibration is distortion, which contains spatial distortion (static distortion) and time-dependent drift (temporally-varying distortion). The drift is mainly due to the accumulation of electrons on the surface of the observed 1 Le Cui is with Université Rennes 1,

Three-dimensional visual tracking and pose estimation in Scanning Electron Microscopes

“…With these parameters, the posture of the object in the camera coordinate frame or in the world coordinate frame can be then recovered. It should be noted that, in SEM vision, the motion along the depth direction can not be observed by measuring the sample scale since the parallel projection model is applied [10]. In this case, the estimation of the position along the depth direction and the partial posture on other axes should be performed separately.…”

“…It remains that two major aspects of image formation within a SEM have to be considered for proper visual tracking. The former is that, from a geometrical aspect, a SEM obey to a parallel projection model [10], [11]. A consequence is that a motion along the depth direction is not observable and, thus, depth can not be estimated from the observation of geometric features.…”

Characterization of Model-Based Visual Tracking Techniques for MOEMS Using a New Block Set for MATLAB/Simulink

“…The predominant noise on the Z coordinate can be explained by the fact that the focal distance is considerably higher than the size of the sensor, and the pinhole projection model becomes close to a parallel one, thus, it is more difficult to estimate the depth coordinate. The problem of depth coordinate estimation with long focal distance has also been established for SEM environments where assumption of parallel beams is close to reality [19] [20].…”

Accurate 3D-Positioning in a SEM Through Robot Calibration

“…Indeed, a distortion-free parallel projection model (affine camera) may be used for description of image formation in SEM [1]. SEM image is formed by gathering the electrons reflected from the surface of the sample.…”