A study of fractal and metric properties of images based on measurements data of multiscale digital sem images of a test object obtained

1
Lviv Polytechnic National University
2
Lviv polytechnic National University

Purpose. The goal of this work is to establish and study the fractal and metric characteristics of images obtained with scanning electron microscopes (SEM). Methods. This approach is based on the processing of measurements data of digital SEM images of a test object obtained on four types of modern SEM in the magnification range from 1000x to 30000x. Results. The analytical relationship between the increase that was set on the device scale and the “fractal” increase (scale) is established. The similar coefficients Axf (Ayf)  and the exponential factors Dxf (Dyf)   for fractal magnifications (scales) along the x and y axes are calculated for 4 types of SEM. Formulas are obtained for calculating the possible range magnifications of the images of test object depending the test object spacing, pixel size and scale. The obtained relationships for the calculation of fractal scales allow to automatically determine the real increase (scale) of SEM images and using the calculated coefficients of the polynomials, effectively eliminate their distortions. Scientific novelty. The technique developed by the authors for obtaining fractal and metric characteristics of SEM images was performed for the first time in Ukraine. The proposed methodology is accompanied at all stages by the author's software and demonstrated its effectiveness and expediency. The practical significance. The application of this method of establishing and accounting for the fractal and metric characteristics of digital SEM images makes it possible to more precisely determine the real values of the increases (scales) of digital SEM images and the values of their geometric distortions. Taking into account these characteristics of SEM images makes it possible to significantly improve the accuracy of obtaining spatial quantitative parameters of the micro surfaces of research facilities, and consequently improve their operational and economic characteristics. The obtained characteristics can be additional important quantitative parameters for revealing the features of digital SEM images.

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