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

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dc.citation.epage64
dc.citation.journalTitleГеодезія, картографія і аерофотознімання : міжвідомчий науково-технічний збірник
dc.citation.spage53
dc.citation.volume85
dc.contributor.affiliationНаціональний університет “Львівська політехніка”
dc.contributor.affiliationLviv Polytechnic National University
dc.contributor.authorІванчук, О.
dc.contributor.authorТумська, О.
dc.contributor.authorIvanchuk, O.
dc.contributor.authorTumska, O.
dc.coverage.placenameЛьвів
dc.date.accessioned2018-09-24T12:03:46Z
dc.date.available2018-09-24T12:03:46Z
dc.date.created2017-03-28
dc.date.issued2017-03-28
dc.description.abstractМетою цієї роботи є встановлення та дослідження фрактальних та метричних характеристик зображень, отриманих за допомогою растрових електронних мікроскопів (РЕМ). Методика. Дослідження ґрунтуються на опрацюванні даних вимірювань цифрових РЕМ-зображень тест-об’єкта, отриманих на чотирьох типах сучасних РЕМ у діапазоні збільшень від 1000х до 30000х (крат). Результати. Встановлено аналітичне співвідношення між фіксованим на шкалі приладу і “фрактальним” збільшенням (масштабом). Виконано розрахунок коефіцієнтів подібності Af та експоненціальних показників Df для фрактальних збільшень (масштабів) уздовж осей х та у для 4-х типів РЕМ. Отримано і наведено формули для розрахунку можливого діапазону збільшень зображень тест-об’єкта залежно від кроку тест-об’єкта, розміру піксела та масштабу. Отримані співвідношення для обчислення фрактальних масштабів дають змогу автоматично визначити дійсне збільшення (масштаб) РЕМ-зображень і разом з визначеними коефіцієнтами поліномів ефективно усувають їхні дисторсійні спотворення. Наукова новизна. Розроблена авторами методика отримання фрактальних та метричних характеристик РЕМ-зображень виконана вперше в Україні. Запропонована методика супроводжується на всіх її етапах авторським програмним забезпеченням і показала свою ефективність та доцільність. Практична значущість. Застосування цієї методики встановлення та врахування фрактальних і метричних характеристик цифрових РЕМ-зображень дає змогу з більшою точністю визначати дійсні значення збільшень (масштабів) цифрових РЕМ-зображень та величини їхніх геометричних спотворень. Врахування цих характеристик РЕМ-зображень дає змогу суттєво підвищити точність отримання просторових кількісних параметрів мікроповерхонь дослідних об’єктів, а, отже, покращити їхні експлуатаційні та економічні характеристики. Отримані характеристики можуть бути додатковими важ- ливими кількісними параметрами для виявлення особливостей цифрових РЕМ зображень.
dc.description.abstractThe 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.
dc.format.extent53-64
dc.format.pages12
dc.identifier.citationIvanchuk O. A study of fractal and metric properties of images based on measurements data of multiscale digital SEM images of a test object obtained / O. Ivanchuk, O. Tumska // Геодезія, картографія і аерофотознімання : міжвідомчий науково-технічний збірник. — Львів : Видавництво Львівської політехніки, 2017. — Том 85. — С. 53–64.
dc.identifier.citationenIvanchuk O. A study of fractal and metric properties of images based on measurements data of multiscale digital SEM images of a test object obtained / O. Ivanchuk, O. Tumska // Heodeziia, kartohrafiia i aerofotoznimannia : mizhvidomchyi naukovo-tekhnichnyi zbirnyk. — Lviv : Vydavnytstvo Lvivskoi politekhniky, 2017. — Vol 85. — P. 53–64.
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/42811
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.relation.ispartofГеодезія, картографія і аерофотознімання : міжвідомчий науково-технічний збірник (85), 2017
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dc.relation.referencesenIvanchuk O. M. Doslidzhennja tochnosti vyznachennja
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dc.relation.referencesenREM-zobrazhen, otrymanych na REM JCM-5000
dc.relation.referencesen(NeoScope) firmy JEOL [Investigation of the
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dc.relation.referencesen(NeoScope) company JEOL], Geodesy, cartography
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dc.relation.referencesenDoslidzhennja velychyn heometrychnykh spotvoren
dc.relation.referencesencyfrovykh REM-zobrazhen, otrymanykh na REM DSM-960A (Carl Zeiss, Nimechchyna) ta tochnosti
dc.relation.referencesenjich vrachuvannja [Research quantities of geometric
dc.relation.referencesendistortion of digital SEM images obtained by SEM
dc.relation.referencesenDSM-960A (Carl Zeiss, Germany) and the
dc.relation.referencesenaccuracy of their incorporation], Geodesy, cartography
dc.relation.referencesenand aerial photography, Lviv, 2013, issue 78, pp. 120– 126.
dc.relation.referencesenIvanchuk O. Doslidzhennja heometrychnykh spotvoren
dc.relation.referencesencyfrovykh REM-zobrazen, otrymanykh na REM
dc.relation.referencesenJCM-5000 (NeoScope) ta jikh aproksymacija
dc.relation.referencesen[Researching geometric distortion digital SEM
dc.relation.referencesenimages obtained on SEM JCM-5000 (NeoScope) and their approximation], Scientific Papers of
dc.relation.referencesenDonetsk National Technical University. Series:
dc.relation.referencesengeological. Donetsk, 2013. Vol. 1 (18), pp. 91–97.
dc.relation.referencesenIvanchuk O., Chekajlo M. Doslidzhennja pokhybok
dc.relation.referencesenzbilshennja (masshtabu) cyfrovykh REM-zobrazhen,
dc.relation.referencesenotrymanykh na REM-106I (Sumy, Ukraina) za
dc.relation.referencesendopomohoju specialnykh test-objektiv [Research
dc.relation.referencesenerrors increase (scale) digital SEM images obtained
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dc.subjectрастровий електронний мікроскоп (РЕМ)
dc.subjectтест-об’єкт
dc.subjectцифрове РЕМ-зображення
dc.subjectфрактальні та метричні властивості цифрових РЕМ-зображень
dc.subjectдійсні збільшення (масштаби)
dc.subjectгеометричні спотворення цифрових РЕМ-зображень
dc.subjectscanning electron microscope (SEM)
dc.subjectthe test object
dc.subjectdigital SEM image
dc.subjectfractal and metric properties of digital SEM images
dc.subjectreal increase (scale)
dc.subjectgeometric distortion of digital SEM images
dc.subject.udc528.721.287
dc.subject.udc537.533.35
dc.titleA study of fractal and metric properties of images based on measurements data of multiscale digital SEM images of a test object obtained
dc.title.alternativeДослідження фрактальних та метричних властивостей зображень за даними вимірювань різномасштабних цифрових РЕМ-зображень тест-об’єкта
dc.typeArticle

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Геодезія, картографія і аерофотознімання. – 2017. – Випуск 85