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.
1. Anischenko V. S., Vadivasova T. E. Lektsii po nelineynoy dinamike: Uchebnoye posobiye dlya studentov vuzov. obuchayushchikhsya po spetsialnosti "Radiofizika i elektronika" i "Fizika" [Lectures on nonlinear dynamics: A manual for university students studying in the specialty: "Radiophysics and Electronics" and "Physics"], Saratov: Saratov University Press, 2010, 322 p.
2. Bobro Yu. G., Melnik V.N., Voloshin V.U., Shostak A. V. Printsipy fraktalnosti v mekhanike razrusheniya metallov [Principles of fractality in the mechanics of the destruction of metals], Proceedings of the Russian Academy of Sciences. Metals, 1997, No. 2, pp. 119–122.
3. Bovik Al. Handbook of Image and Video Processing. Academic Press., A Harcourt Science and Technology Company, 2000, 891 p.
4. Boyde A., Ross H. F. Photogrammetry and Scanning electron microscopy. Photogrammetric Record. 1975, vol. 8, no. 46, pp. 408–457.
https://doi.org/10.1111/j.1477-9730.1975.tb00805.x
5. Burkhardt R. Untersuchungen zur kalibrirung eines Elektronen mikroskopes. Mitt. geod. Inst. Techn. Univ. Graz. 1980, no. 35.
6. Feder E. Fraktaly: Per. s angl. [Fractals: Translation from English], Moscow, MIR, 1991, 254 p.
7. Ghosh S. K. Photogrammetric calibration of a scanning electron microscope. Photogrammetria. 1975, vol. 31, no. 31, pp. 91–114.
https://doi.org/10.1016/0031-8663(75)90008-3
8. Ghosh S. K., Nagaraja H. Scanning Electron Micrography and Photogrammetry. Photogrammetric Engineering and Remote Sensing. 1976, vol. 42, no. 5. pp. 649–657.
9. Gonzalez R. Ñ., Woods R. E., Eddins S. L. Cyfrovaja obrabotka izobrazhenij v srede MATLAB [Digital Image Processing using MATLAB]. Moscow, Technosfera, 2006. 616 p.
10. Cromley R. G. Digital Cartography. 1992 by Prentice-Hall. 317 p.
11. Howell P. A practical method for the correction of distortions in SEM photogrammetry. Proc. Of the Annual Scanning Electron Microscope Symposium. Chicago, Illinois. 1975, pp. 199–206.
12. Ivanchuk O. M., Khrupin I. V. Struktura ta funkcii prohramnoho kompleksu "Dimicros" dlja opracjuvannja REM-zobrazhen na cufrovij fotohrammetrychnij stanciji [Structure and function of the program complex «Dimicros» processing of SEM images on a digital photogrammetric station], Recent advances in geodetic science and industry, Lviv, 2012, issue 1(23), pp. 193–197.
13. Ivanchuk O. M. Doslidzhennja tochnosti vyznachennja dijsnych velychyn zbilshennja (masshtabu) cyfrovych REM-zobrazhen, otrymanych na REM JCM-5000 (NeoScope) firmy JEOL [Investigation of the accuracy of the actual values increase (scale) digital SEM images obtained by SEM JCM-5000 (NeoScope) company JEOL], Geodesy, cartography and aerial photography, Lviv, 2012, issue 76, pp. 80–84.
14. Ivanchuk O. M., Barfels T., Heeg J., Heger W. Doslidzhennja velychyn heometrychnykh spotvoren cyfrovykh REM-zobrazhen, otrymanykh na REM DSM-960A (Carl Zeiss, Nimechchyna) ta tochnosti jich vrachuvannja [Research quantities of geometric distortion of digital SEM images obtained by SEM DSM-960A (Carl Zeiss, Germany) and the accuracy of their incorporation], Geodesy, cartography and aerial photography, Lviv, 2013, issue 78, pp. 120– 126.
15. Ivanchuk O. Doslidzhennja heometrychnykh spotvoren cyfrovykh REM-zobrazen, otrymanykh na REM JCM-5000 (NeoScope) ta jikh aproksymacija [Researching geometric distortion digital SEM images obtained on SEM JCM-5000 (NeoScope) and their approximation], Scientific Papers of Donetsk National Technical University. Series: geological. Donetsk, 2013. Vol. 1 (18), pp. 91–97.
16. Ivanchuk O., Chekajlo M. Doslidzhennja pokhybok zbilshennja (masshtabu) cyfrovykh REM-zobrazhen, otrymanykh na REM-106I (Sumy, Ukraina) za dopomohoju specialnykh test-objektiv [Research errors increase (scale) digital SEM images obtained on SEM-106I (Sumy, Ukraine) with special test facilities], Geodesy, cartography and aerial photography, Lviv, 2014, issue 79, pp. 82–88.
17. Ivanchuk O. Doslidzhennja heometrychnykh spotvoren cyfrovykh REM-zobrazen, otrymanykh na REM-106I (Sumy, Ukraina) [Researching geometric distortion digital SEM images obtained at the SEM-106 and (Sumy, Ukraine)], Recent advances in geodetic science and industry, Lviv, 2014, issue II (28), pp. 74-77.
18. Ivanchuk O. Osoblyvosti kalibruvannja heometrychnykh spotvoren cyfrovykh REM-zobrazhen, otrymanykh na riznykh REM [Features Calibration geometric distortion of digital SEM images obtained at different SEM], Recent advances in geodetic science and industry, Lviv, 2015, issue I (29), pp. 68-173.
19. Ivanchuk O. Doslidzhennja heometrychnykh spotvoren cyfrovykh REM-zobrazen, otrymanykh na REM JSM-7100F (JEOL, Japonija) ta tochnist jikh aproksymaciji [Research geometric distortion of SEM digital images obtained with SEM JSM-7100F (JEOL, Japan) and the accuracy of approximation], Geodesy, cartography and aerial photography, Lviv, 2015, issue 81, pp. 101–109.
20. Ivanchuk O., Tumska O. Development and research of technology for automation of the calibration and account of digital SEM images having geometric distortion obtained with JCM –5000 (Neoscope) (JEOL, Japan), Geodesy, cartography and aerial photography, Lviv, 2016, issue 84, pp. 56–64.
21. Ivanchuk O., Tumska O. Metodyka avtomatyzovanogo vyznachennya koordynat tsentriv vuzliv test-objekta za yogo REM-zobrazhennyamy z vykorystannyam zasobiv MatLab [Technique of automated determination of the coordinates of the test-object nodes by its SEM images using MatLab tools], Recent advances in geodetic science and industry, Lviv, 2017, issue I (33), pp. 158–165.
22. Kostyshyn M.T., Mustafin K.S. Kvantovaja elektronika [Quantum Electronics], Kyiv, 1982, issue 23, pp. 29–33.
23. Kalantarov E. I., Sagyndykova M. Zh. Photogrammetricheskaja kalibrovka electronnych microskopov [Photogrammetric calibration of electron microscopes], Proceedings of the universities. Surveying and aerial photography, Moscow, 1983, issue 4, pp. 76–80.
24. Mandelbrot B. The fractal geometry of nature. N. Y.: Freeman, 1983, 469 p.
25. Melnik V. N., Sokolov V. N., Ivanchuk O. M., Tumskaja O. V., Shebatinov M. P. Kalibrovka geometricheskikh iskazhenij REM-snimkov [Calibration of geometric distortion SEM images], Manuscript deposited at VINITI, Moscow, 1984, issue 528, 18 p.
26. Melnik V. N., Sokolov V. N. Fraktalnaya i stereometricheskaya otsenki REM-izobrazheniy sherokhovatykh poverkhnostey [Fractal and stereometric estimations of SEM images of rough surfaces], Proceedings of the Russian Academy of Sciences. The series is physical, 1993, no. 8, pp. 99-105.
27. Melnik V. N., Bobro Yu. G., Shostak A. V., Voloshin V. U. Opredeleniye fraktalnosti poverkhnostey razrusheniya po dannym REM-stereoizmereniy [Determination of the fractality of fracture surfaces according to SEM-stereo measurements], Friction and wear, 1996, T. 16, no. 6, pp. 38–41.
28. Melnik V. M., Voloshin V. U., Tarasyuk F. P., J. Blinder Yu.S. Metody kilkisno¿ kharakterystyky mikrostruktury gruntu [Methods of quantitative characterization of soil microstructure], Bulletin of Lviv State University. Geographic series, Ivan Franko National University of Lviv; Editor-in-Chief S. Poznyak, Lviv, 1999, no. 25, pp. 24–27.
29. Melnik V. M, Voloshin V. U. Otsinka destruktyvnykh zmin kistkovoji tkanyny metodamy strukturnoji funktsiji ta fraktalnogo analizu [Evaluation of destructive changes in bone tissue by the methods of structural function and fractal analysis], Scientific Bulletin of the Volyn State University named after Lesya Ukrainka, Lutsk, 2002, no. 3, pp. 166–171.
30. Melnik V. M., Shostak A. V. Rastrovo-elektronna stereomikrofraktohrafija [Raster electron stereomikrofraktografition], Luck, Vezha, 2009, 469 p.
31. Potapov A. A, Gulyaev Yu. V., Nikitov S. A., Pakhomov A. A., Herman V. A. Noveyshiye metody obrabotki izobrazheniy [The newest methods of image processing], Moscow, FIZMATLIT, 2008, 496 p.
32. Richardson L. The Problem of Contiguity: An Appendix of Statistic of Deadly Quarrels. General Systems Year Book. 1961, no. 6, pp. 139–187.
33. Shostak A. V. Metody i modeli mikrophotogrammetrii u prukladnych naukovych doslidzhennjach. Dokt. Diss. [Methods and models mikrophotogrammetry in applied research. Doct. Diss.]. Kyiv, 2012. 28 p.