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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2025-16-1-5-13</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-23</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Phase-contrast method for determining the size of the effective focal spot of a nanofocus X-ray tube</article-title><trans-title-group xml:lang="ru"><trans-title>Фазоконтрастный метод определения размера эффективного фокусного пятна нанофокусной рентгеновской трубки</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0009-0009-8428-9588</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Манушкин</surname><given-names>А. А.</given-names></name><name name-style="western" xml:lang="en"><surname>Manushkin</surname><given-names>A. A.</given-names></name></name-alternatives><bio xml:lang="en"><p>Alexey A. Manushkin</p><p>Volgogradskiy, 42, Moscow, 109316</p></bio><email xlink:type="simple">manushkinaa@mail.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0001-8806-0603</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Потрахов</surname><given-names>Н. Н.</given-names></name><name name-style="western" xml:lang="en"><surname>Potrakhov</surname><given-names>N. N.</given-names></name></name-alternatives><bio xml:lang="en"><p>Nikolay N. Potrakhov</p><p>Professora Popova, 5, St. Petersburg, 197022</p></bio><email xlink:type="simple">nnpotrahov@etu.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-6284-0246</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Кострин</surname><given-names>Д. К.</given-names></name><name name-style="western" xml:lang="en"><surname>Kostrin</surname><given-names>D. K.</given-names></name></name-alternatives><bio xml:lang="en"><p>Dmitrii K. Kostrin</p><p>Professora Popova, 5, St. Petersburg, 197022</p></bio><email xlink:type="simple">dkkostrin@mail.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-4968-7857</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Гук</surname><given-names>К. К.</given-names></name><name name-style="western" xml:lang="en"><surname>Guk</surname><given-names>K. K.</given-names></name></name-alternatives><bio xml:lang="en"><p>Karina K. Guk</p><p>Professora Popova, 5, St. Petersburg, 197022</p></bio><email xlink:type="simple">kkguk@etu.ru</email><xref ref-type="aff" rid="aff-2"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="en">“Diagnostika-M” LLC<country>Russian Federation</country></aff></aff-alternatives><aff-alternatives id="aff-2"><aff xml:lang="en">Saint Petersburg Electrotechnical University “LETI”<country>Russian Federation</country></aff></aff-alternatives><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>01</day><month>06</month><year>2025</year></pub-date><volume>16</volume><issue>1</issue><fpage>5</fpage><lpage>13</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Manushkin A.A., Potrakhov N.N., Kostrin D.K., Guk K.K., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Манушкин А.А., Потрахов Н.Н., Кострин Д.К., Гук К.К.</copyright-holder><copyright-holder xml:lang="en">Manushkin A.A., Potrakhov N.N., Kostrin D.K., Guk K.K.</copyright-holder><license license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/23">https://nanojournal.ifmo.ru/jour/article/view/23</self-uri><abstract><p>The work is devoted to the development of a method for testing the focal spot size of nanofocus and microfocus X-ray tubes based on phase contrast radiography of test objects. The method is based on the comparison of the interference X-ray image with the calculated values obtained by the exact numerical solution of the wave equation. The high sensitivity of the method to the size of the source is ensured by the fusion of interference fringes with contrast of different signs. The formation of X-ray phase contrast images of test objects is analyzed on the basis of the wave equation using numerical modeling of the intensity profile. An analytical expression has been obtained to estimate the size of the X-ray tube focus. The results of calculations of phase contrast profiles for a nylon fishing line and a reference nanofocus test are presented.</p></abstract><trans-abstract xml:lang="ru"><p>Работа посвящена развитию метода тестирования размера фокусного пятна нанофокусных и микрофокусных рентгеновских трубок на основе фазоконтрастной рентгенографии тестовых объектов. В основе метода лежит сопоставление интерференционного рентгеновского изображения с расчетными значениями, полученными при точном численном решении волнового уравнения. Высокая чувствительность метода к размерам источника обеспечивается слиянием интерференционных полос с контрастом разного знака. На основе волнового уравнения с использованием численного моделирования профиля интенсивности проанализировано формирование рентгеновских фазоконтрастного изображения тестовых объектов. Получено аналитическое выражение для оценки размера фокуса рентгеновской трубки Приведены результаты расчетов профилей фазового контраста для капроновой лески и эталонного нанофокусного теста.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>рентгеновские лучи</kwd><kwd>фазовый контраст</kwd><kwd>интерференция</kwd><kwd>неразрушающий контроль</kwd><kwd>тестовый объект</kwd></kwd-group><kwd-group xml:lang="en"><kwd>X-rays</kwd><kwd>phase contrast</kwd><kwd>interference</kwd><kwd>non-destructive testing</kwd><kwd>test object</kwd></kwd-group><funding-group xml:lang="en"><funding-statement>The work was carried out with the financial support of the Ministry of Education and Science of the Russian Federation (by Agreement dated February 09, 2023, No. 075-11-2023-006, state contract identifier 000000S407523Q6V0002).</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Staroverov N.E. 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