Abstract
Electron microscopes, which are indispensable to the research and development of materials, pose some problems in their focus adjustment. Detection of defocus has been so far carried out by visual inspection, a tedious process even for skilled operators. In particular, accurate determination of astigmatism depends on time-consuming photographic processes or 2-dimensional Fourier transform (2D-FT), making use of a fact that ellipses drawn by the spectrum power band of amorphous materials images represent the property of astigmatism.
This paper describes a fast method for detecting astigmatism, based on the steady randomness of amorphous materials. Because parameters of ellipses can be detected from spectra on at least three lines passing the origin of the frequency domain, there is no need to calculate the whole 2D-FT. The linear spectra are rapidly derived by the use of Radon transform, yielding the computation time of O(Nlog2N) for N×N-pixel images contrasted against the 2D-FT method with O(N2log2N).
The prototype employs eight lines on which data reduction from 128×128 pixel images into linear arrays are accomplished.
Test runs with 8086/8087 microcomputer demonstrate the computation time of 2s, compared with 40s by the 2D-FT method. The accuracy of detection is approximately ±10% for strength and ±10° for direction. The speed can be improved up to the order of 100ms by employing some circuitry and a signal processor.
