Fast Correction of Astigmatism and Focus in the Scanning Electron Microscope using a GPU-accelerated PC

This work forms part of our ongoing research into enhancing and improving the scanning electron microscope (SEM) and was one of a number of projects undertaken to explore methods for automatic correction of astigmatism once optimum focus has been achieved. This project has centred on smart adjustment of an SEM, Carl Zeiss model 1430VP (manufactured c. 2000), using the instrument’s own control computer fitted with a high-performance graphics card to support the procedure’s computational needs and achieve good speed of operation. No additional computer was required to achieve this. There has been much research into techniques for automatic correction of focus and astigmatism in the SEM, and several different approaches have been explored. Recent advances in computing hardware have made possible compute-intensive procedures that could not previously have been contemplated. Ong et al. have given an excellent summary of early work on correction of focus and astigmatism and reported on the development of a Fourier-based technique that ran on a high-performance workstation separate from the SEM [1]. Our own investigations used as a start-point the methodology of Ong, with the added constraint that the software must run solely on the SEM’s own integrated control computer and must operate faster than most human operators could achieve. Adjustment of focus and correction of astigmatism are vital processes in the operation of an SEM. Both seek to optimize the resolution of the instrument by bringing the scanned electron probe to the smallest possible symmetrical form. We reported on progress towards fast adjustment of focus for the SEM in our earlier paper [2]. Correction of astigmatism in the SEM is significantly more challenging than simple focus adjustment, since it typically entails the iterative adjustment of the currents in two orthogonal stigmator coils, while also making small corrections to the focus setting. When carried out manually, this requires experience and manual dexterity. Many instrumental factors may influence the most appropriate settings for best resolution, and when seeking highest resolution, an operator may need to make several adjustments to the objective lens and stigmator during an operating session. The method chosen is based on an adaptation of the mathematical approach that had been successfully applied to automatic focusing, and makes use of power spectra computed using Fast Fourier Transforms. For astigmatism, spectra are computed from 256 x 256 pixel regions near the centre of the field of view, while the stigmator settings are adjusted in an orderly manner. Whereas for automatic focusing it is sufficient to monitor spectral power as a function of objective lens current, for assessment of astigmatism it is necessary to resolve the spectra in two orthogonal directions corresponding to the axes of the stigmator coils, referred to as X and Y, in order to extract directional information and detect distortion of the focused beam. This is achieved by angular segmentation of the computed spectra. Ong et al [1] have described how parameters can be extracted from the segmented spectra in order to determine the direction and the degree of astigmatism. The algorithm developed first determines the magnitude of any astigmatism in X and Y and evaluates which of these is the greater; this axis is corrected first. Further calculations determine whether the stigmator current for that axis should be increased or decreased. The program makes a small incremental adjustment to the stigmator dependent on the magnitude of the astigmatism found and captures new spectra to determine the outcome. This process is repeated a number of times, during which corrections may be made to either or both axes. As the residual astigmatism falls following these adjustments, the algorithm reduces the size of the corrections made in order to home in more accurately on the optimum setting. Once the astigmatism has been reduced below a threshold determined by the operator, the procedure is stopped. The coding for this project was done using the SEM’s own control PC, with the algorithms described written in Python 3, an interpreted language ideal for rapid development and adaptation, but not optimized for speed. In order to achieve sufficiently fast analysis of SEM data, much use was made of a range of mathematical libraries developed for Python. Further, the PC was fitted with an enhanced graphics card, incorporating a Graphics Processing Unit. GPU technology is available from several manufacturers. While its original purpose was to enhance operations such as advanced gaming, in which the fastest possible graphics performance is sought, other groups have devised Python library routines based on this hardware for digital signal and image processing [3]. These execute at many times the speed of the unaided PC. In this instance, the ability of the GPU to accelerate computation of Fast Fourier Transforms was a major factor in its choice. Correction of astigmatism normally takes place as a part of the focusing procedure required after a change of specimen, or of specimen position. This starts with a preliminary focus procedure, comprising a coarse determination followed by a fine focus run carried out at a magnification of ×500. This phase is described in our earlier report [2] and takes around 10 seconds. Correction of astigmatism is normally run at the higher magnification of ×20,000, using the objective lens setting just determined. The time taken for correction of astigmatism depends on the extent to which the instrument’s residual astigmatism may have changed since the last determination, and the accuracy desired, but can normally be accomplished in around 5 – 10 steps, each lasting about 1 second. The time per step depends on the frame rate employed, the choice of which is a compromise between speed and accuracy, but the settings used have given reliable results in our experiments. Hence, with the focus and astigmatism algorithms running in tandem, it is possible to correct the instrument in under twenty seconds with the specimen in an arbitrary position, although adjustment may take longer if the operator requires an especially detailed check. The search extends over the full practicable range of working distances for the instrument, around 6mm to 20mm, and over the full range of adjustment for astigmatism. Subjective inspection indicated that the results obtained were usually as good as a human operator can achieve, and are sustained at higher magnification settings than those used for the adjustments. Rarely, the procedure may fail and need to be repeated, for example if the field of view does not include sufficient image detail to give satisfactory spectra. This project has successfully demonstrated the feasibility of creating a low-cost system for rapid correction of focus and astigmatism in the SEM. The system shows considerable potential for extension to other kinds of adjustment, for example, SEM electron gun alignment.