donstuAdvanced Engineering Research (Rostov-on-Don)Advanced Engineering Research (Rostov-on-Don)2687-1653Don State Technical University10.23947/1992-5980-2017-17-1-55-66donstu-246Research ArticleMACHINE BUILDING AND MACHINE SCIENCEМАШИНОСТРОЕНИЕ И МАШИНОВЕДЕНИЕAdvanced device for measuring linear and angular components of small displacements of monitor object surfacesПерспективное устройство для измерения линейной и угловых составляющих малых перемещений поверхностей объектов контроляМирошниченкоИгорь ПавловичMiroshnichenkoIgor P.ipmir@rambler.ruДонской государственный технический университетРоссияDon State Technical UniversityRussian Federation2017270220181715566Copyright © Miroshnichenko I.P., 20172017Мирошниченко И.П.Miroshnichenko I.P.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.vestnik-donstu.ru/jour/article/view/246

Introduction. Measuring the linear and angular components of small displacements of the monitor object surfaces is considered. A high-precision non-contact device based on the advanced laser technologies and methods of optical interferometry, namely a double-pass laser interferometer with integrated branches, is developed to perform these measurements. The calculated and experimental validation of the device is offered. Thus, the quality and condition of the materials and products can be controlled by means of the acoustic non-destructive methods. Materials and Methods. New software and mathematical models describing optical fields of the interference patterns generated by the interferometer under consideration are offered. Various types of beam splitters and cases of polarization are used under the numerical simulation of the intensity distributions in the interference patterns. Research Results. New mathematical models and software for the numerical simulation of the optical radiation intensity fields in the interference patterns considering both linear and angular components of small displacement of the surface of the test object are developed. A new interference technique of measuring small linear and angular displacements is developed and theoretically grounded. It allows combining the meter measuring capabilities for both small linear and angular displacements of the monitor object surfaces in a single tool. New optical interference methods and means for the noncontact measurements of small linear and angular movements of the monitor object surfaces that implement the method capabilities and extend the functionality of the known indicators of small displacements are offered. Discussion and Conclusions. The obtained results can be used for the high-precision measurements of small linear and angular displacements of surfaces of the objects under control. Areas of application are the following: experimental research; assessment and diagnostics of the structural materials samples; investigations of fast wave processes in the layered structures of complex shape made of the anisotropic composite materials. The methods developed in this study are applicable in such industries as mechanical engineering, shipbuilding, aircraft engineering, instrument making, power engineering, and etc.

Введение. Статья посвящена измерениям линейных и угловых составляющих малых перемещений поверхностей объектов контроля. Для выполнения таких измерений разработано высокоточное бесконтактное устройство, основанное на современных лазерных технологиях и методах оптической интерферометрии, а именно двухходового лазерного интерферометра с совмещенными ветвями. Представлено расчетно-экспериментальное обоснование данного устройства. Таким образом, качество и состояние материалов и изделий могут контролироваться с помощью акустических неразрушающих методов. Материалы и методы. Предложены новые программное обеспечение и математические модели, которые описывают оптические поля интерференционных картин, создаваемые рассматриваемым интерферометром. При численном моделировании распределений интенсивности в интерференционных картинах использованы различные виды светоделителей и различные случаи поляризации. Результаты исследования . Разработаны новые математические модели и программное обеспечение для численного моделирования полей интенсивности оптического излучения в интерференционных картинах, учитывающие как линейную, так и угловые составляющие малого перемещения поверхности объекта контроля. Разработан и научно обоснован новый интерференционный метод измерений малых линейных и угловых перемещений, позволяющий объединить в одном измерительном средстве возможности измерителя как малых линейных, так и угловых перемещений поверхностей объектов контроля. Предложены новые оптические интерференционные способы и средства для бесконтактных измерений малых линейных и угловых перемещений поверхностей объектов контроля, реализующие возможности метода и расширяющие функциональность известных измерителей малых перемещений. Обсуждение и заключения . Полученные результаты могут быть использованы для высокоточных измерений малых линейных и угловых перемещений поверхностей объектов контроля. Сферы применения: экспериментальные исследования, оценка и диагностика состояния образцов конструкционных материалов; исследования быстропротекающих волновых процессов в слоистых конструкциях сложной формы, выполненных из анизотропных композиционных материалов. Методы, разработанные в рамках данного исследования, применимы в таких отраслях, как машиностроение, судостроение, авиастроение, приборостроение, энергетика и т. д.

азерный интерферометризмерения малых перемещенийлинейные перемещенияугловые перемещенияобъект контролядиагностика состоянияlaser interferometermeasuring small displacementslinear displacementsangular displacementsobject under controlcondition diagnosisReferencesМирошниченко, И. П. Результаты экспериментальных исследований интерференционного измерителя малых перемещений / И. П. Мирошниченко, А. Г. Серкин // Измерительная техника. - 2006. - № 5. - С. 22-25.Miroshnichenko, I.P., Serkin, A.G. Rezul'taty eksperimental'nykh issledovaniy interferentsionnogo izmeritelya malykh peremeshcheniy. [Results of experimental studies on interferometers for small displacements.] Measurement Technique, 2006, no. 5, pp. 22–25 (in Russian).Экспериментальная установка для исследования процессов дефектообразования в ленточных высокотемпературных сверхпроводниках / И. П. Мирошниченко [и др.] // Металлург. - 2006. - № 7. - С. 77-78.Miroshnichenko, I.P., et al. Eksperimental'naya ustanovka dlya issledovaniya protsessov defektoobrazovaniya v lentochnykh vysokotemperaturnykh sverkh- provodnikakh. [Experimental plant for research of defect formation in band high temperature superconductors.] Metallurgist, 2006, no. 7, 77–78 (in Russian).Мирошниченко, И. П. Методы измерения смещений поверхности объектов контроля лазерными интерферометрами / И. П. Мирошниченко, В. Е. Алехин, В. П. Сизов // Дефектоскопия. - 2007. - № 2. - С. 53-61.Miroshnichenko, I.P., Alekhin, V.E., Sizov, V.P. Metody izmereniya smeshcheniy poverkhnosti ob''ektov kontrolya lazernymi interferometrami. [Use of Laser Interferometers for Measuring Displacements of the Surfaces of Tested Objects.] Russian Journal of Nondestructive Testing, 2007, no. 2, pp. 53–61 (in Russian).Мирошниченко, И. П. Особенности использования интерференционных измерителей малых перемещений при решении задач диагностики технического состояния конструкций / И. П. Мирошниченко, А. Г. Серкин // Дефектоскопия. - 2007. - № 4. - С. 31-38.Miroshnichenko, I.P., Serkin, A.G. Osobennosti ispol'zovaniya interferentsionnykh izmeriteley malykh peremeshcheniy pri reshenii zadach diagnostiki tekhnicheskogo sostoyaniya konstruktsiy. [Using Interferometers for the Measurement of Small Displacements during Solution of the Problems of the State of Structures.] Russian Journal of Nondestructive Testing, 2007, no. 4, pp. 31–38 (in Russian).Экспериментальное исследование особенностей метода подсвечивания поверхности объекта контроля для измерения смещений лазерными интерферометрами / В. Е. Алехин [и др.] // Дефектоскопия. - 2007. - № 9. - С. 37-43.Alekhin, V.E., et al. Eksperimental'noe issledovanie osobennostey metoda podsvechivaniya poverkhnosti ob''ekta kontrolya dlya izmereniya smeshcheniy lazernymi interferometrami. [Experimental Study of the Features of the Method for Illuminating the Surface of a Tested Object for Measuring Displacements with Laser Interferometers.] Russian Journal of Nondestructive Testing, 2007, no. 9, pp. 37–43 (in Russian).Мирошниченко, И. П. Экспериментальное обоснование интерференционного метода измерения перемещений на основе подсвечивания поверхности объекта контроля / И. П. Мирошниченко, В. Е. Алехин, А. Г. Серкин // Измерительная техника. - 2008. - № 10. - С. 26-30.Miroshnichenko, I.P., Alekhin, V.E., Serkin, A.G. Eksperimental'noe obosnovanie interferentsionnogo metoda izmereniya peremeshcheniy na osnove podsvechivaniya poverkhnosti ob''ekta kontrolya. [Experimental study on interference method of measuring displacements on the basis of monitor object surface lightening.] Measurement Technique, 2008, no. 10, pp. 26–30 (in Russian).Мирошниченко, И. П. Усовершенствованная экспериментальная установка для исследования процессов дефектообразования в образцах конструкционных материалов / И. П. Мирошниченко, А. Г. Серкин // Металлург. - 2010. - № 3. - С. 68-69.Miroshnichenko, I.P., Serkin, A.G. Usovershenstvovannaya eksperimental'naya ustanovka dlya issledovaniya protsessov defektoobrazovaniya v obraztsakh konstruktsionnykh materialov. [Improved experimental plant for investigation of defect formation processes in samples of constructional materials.] Metallurgist, 2010, no. 3, pp. 68–69 (in Russian).Novel Test Means and Techniques Based on Optical Interferometry and Acoustic Emission to Study Displacements of Object Surfaces and Damage of High-Temperature Superconductive Tapes and Related Composites / I. P. Miroshnichenko [et al.] // Piezoelectrics and Related Materials: Investigations and Applications. - New York : Nova Science Publishers, 2012. - P. 238-282.Miroshnichenko, I.P., et al. Novel Test Means and Techniques Based on Optical Interferometry and Acoustic Emission to Study Displacements of Object Surfaces and Damage of High-Temperature Superconductive Tapes and Related Composites. Piezoelectrics and Related Materials: Investigations and Applications. New York: Nova Science Publishers, 2012, pp. 238–282.Novel Optical Means for Measurement of Displacements of Surfaces of the Control Objects at Diagnostics of Materials and Goods / I.P. Miroshnichenko [et al.] // Physics and Mechanics of New Materials and their Applications. - New York : Nova Science Publishers, 2013. - P. 145-154.Miroshnichenko, I.P., et al. Novel Optical Means for Measurement of Displacements of Surfaces of the Control Objects at Diagnostics of Materials and Goods. Physics and Mechanics of New Materials and their Applications. New York: Nova Science Publishers, 2013, pp. 145–154.Miroshnichenko, I. P. Novel Optic Devices for Measurement of Displacements Based on Method of Control Object Highlighting by Using Laser Interferometer / I. P. Miroshnichenko, I. A. Parinov, S.-H. Chang // Advanced Materials - Studies and Applications. - New York : Nova Science Publisher, 2015. - P. 437-452.Miroshnichenko, I. P., Parinov, I. A., Chang , S.-H. Novel Optic Devices for Measurement of Displacements Based on Method of Control Object Highlighting by Using Laser Interferometer. Advanced Materials — Studies and Applications. New York: Nova Science Publisher, 2015, pp. 437–452.Mathematical Models, Program Software, Technical and Technological Solutions for Measurement of Displacements of the Control Object Surfaces by Laser Interferometer / I.P. Miroshnichenko [et al.] // Advanced Materials Manufacturing, Physics, Mechanics and Applications. Springer Proceedings in Physics. - Cham ; Heidelberg ; New York ; Dordrecht ; London : Springer International Publishing, 2016. - Vol. 175. - P. 341-356.Miroshnichenko, I.P., et al. Mathematical Models, Program Software, Technical and Technological Solutions for Measurement of Displacements of the Control Object Surfaces by Laser Interferometer. Advanced Materials Manufacturing, Physics, Mechanics and Applications. Springer Proceedings in Physics. Cham; Heidelberg; New York; Dordrecht; London: Springer International Publishing, 2016, vol. 175, pp. 341– 356.Мирошниченко, И. П. Численное исследование метода измерений малых линейных и угловых перемещений лазерными интерферометрами / И. П. Мирошниченко, А. Г. Серкин, В. П. Сизов // Измерительная техника. - 2007. - № 1. - С. 9-13.Miroshnichenko, I.P., Serkin, A.G., Sizov, V.P. Chislennoe issledovanie metoda izmereniy malykh lineynykh i uglovykh peremeshcheniy lazernymi interferometrami. [Numerical study on method of measuring small linear and angular displacements by laser interferometers.] Measurement Technique, 2007, no. 1, pp. 9–13 (in Russian).Мирошниченко, И. П. Унифицированный метод измерения малых линейных и угловых перемещений поверхностей объектов контроля / И. П. Мирошниченко, А. Г. Серкин // Дефектоскопия. - 2008. - № 5. - С. 23-27.Miroshnichenko, I.P. Unifitsirovannyy metod izmereniya malykh lineynykh i uglovykh peremeshcheniy poverkhnostey ob''ektov kontrolya. [A Unified Method for Measuring Small Linear and Angular Displacements of the Surfaces of Tested Objects.] Russian Journal of Nondestructive Testing, 2008, no. 5, pp. 23–27 (in Russian).Мирошниченко, И. П. Использование точечного источника излучения для расширения функциональных возможностей измерителя перемещений / И. П. Мирошниченко, А. Г. Серкин, В. П. Сизов // Оптический журнал. - 2008. - Т. 75, № 7. - С. 41-47.Miroshnichenko, I.P., Serkin, A.G., Sizov, V.P. Ispol'zovanie tochechnogo istochnika izlucheniya dlya rasshireniya funktsional'nykh vozmozhnostey izmeritelya peremeshcheniy. [Using the point-light source to extend the functionality of the displacement controller.] Journal of Optical Technology, 2008, vol. 75, no. 7, pp. 41–47.Способ измерения линейных и угловых перемещений : патент 2388994 Рос. Федерация : G01B 11/00, G01B 9/02 / И. П. Мирошниченко, А. Г. Серкин, В. П. Сизов. - № 2008141364/28 ; заявл. 20.10.08 ; опубл. 10.05.10, Бюл. № 13. - 8 с.Miroshnichenko, I.P., Serkin, A.G., Sizov, V.P. Sposob izmereniya lineynykh i uglovykh peremeshcheniy: patent 2388994 Ros. Federatsiya: G01B 11/00, G01B 9/02. [A method for measuring linear and angular displacements.] Patent RF, no. 2388994, 2010 (in Russian).Способ измерения линейной и угловых составляющих малых перемещений поверхностей объектов контроля : патент 2606245 Рос. Федерация : G01B 11/24 / И. П. Мирошниченко, И. А. Паринов, В. П. Сизов. - № 2015140197/28 ; заявл. 21.09.15 ; опубл. 10.01.17, Бюл. № 1. - 11 с.Miroshnichenko, I.P., Parinov, I.A., Sizov, V.P. Sposob izmereniya lineynoy i uglovykh sostavlyayushchikh malykh peremeshcheniy poverkhnostey ob''ektov kontrolya: patent 2606245 Ros. Federatsiya : G01B 11/24. [A method for measuring linear and angular components of small displacements of monitor object of surfaces.] Patent RF, no. 2606245, 2017 (in Russian).Miroshnichenko, I.P., Serkin, A.G. Rezul'taty eksperimental'nykh issledovaniy interferentsionnogo izmeritelya malykh peremeshcheniy. [Results of experimental studies on interferometers for small displacements.] Measurement Technique, 2006, no. 5, pp. 22-25 (in Russian).Miroshnichenko, I.P., Serkin, A.G. Rezul'taty eksperimental'nykh issledovaniy interferentsionnogo izmeritelya malykh peremeshcheniy. [Results of experimental studies on interferometers for small displacements.] Measurement Technique, 2006, no. 5, pp. 22-25 (in Russian).Miroshnichenko, I.P., et al. Eksperimental'naya ustanovka dlya issledovaniya protsessov defektoobrazovaniya v lentochnykh vysokotemperaturnykh sverkh-provodnikakh. [Experimental plant for research of defect formation in band high temperature superconductors.] Metallurgist, 2006, no. 7, 77-78 (in Russian).Miroshnichenko, I.P., et al. Eksperimental'naya ustanovka dlya issledovaniya protsessov defektoobrazovaniya v lentochnykh vysokotemperaturnykh sverkh-provodnikakh. [Experimental plant for research of defect formation in band high temperature superconductors.] Metallurgist, 2006, no. 7, 77-78 (in Russian).Miroshnichenko, I.P., Alekhin, V.E., Sizov, V.P. Metody izmereniya smeshcheniy poverkhnosti ob''ektov kontrolya lazernymi interferometrami. [Use of Laser Interferometers for Measuring Displacements of the Surfaces of Tested Objects.] Russian Journal of Nondestructive Testing, 2007, no. 2, pp. 53-61 (in Russian).Miroshnichenko, I.P., Alekhin, V.E., Sizov, V.P. Metody izmereniya smeshcheniy poverkhnosti ob''ektov kontrolya lazernymi interferometrami. [Use of Laser Interferometers for Measuring Displacements of the Surfaces of Tested Objects.] Russian Journal of Nondestructive Testing, 2007, no. 2, pp. 53-61 (in Russian).Miroshnichenko, I.P., Serkin, A.G. Osobennosti ispol'zovaniya interferentsionnykh izmeriteley malykh peremeshcheniy pri reshenii zadach diagnostiki tekhnicheskogo sostoyaniya konstruktsiy. [Using Interferometers for the Measurement of Small Displacements during Solution of the Problems of the State of Structures.] Russian Journal of Nondestructive Testing, 2007, no. 4, pp. 31-38 (in Russian).Miroshnichenko, I.P., Serkin, A.G. Osobennosti ispol'zovaniya interferentsionnykh izmeriteley malykh peremeshcheniy pri reshenii zadach diagnostiki tekhnicheskogo sostoyaniya konstruktsiy. [Using Interferometers for the Measurement of Small Displacements during Solution of the Problems of the State of Structures.] Russian Journal of Nondestructive Testing, 2007, no. 4, pp. 31-38 (in Russian).Alekhin, V.E., et al. Eksperimental'noe issledovanie osobennostey metoda podsvechivaniya poverkhnosti ob''ekta kontrolya dlya izmereniya smeshcheniy lazernymi interferometrami. [Experimental Study of the Features of the Method for Illuminating the Surface of a Tested Object for Measuring Displacements with Laser Interferometers.] Russian Journal of Nondestructive Testing, 2007, no. 9, pp. 37-43 (in Russian).Alekhin, V.E., et al. Eksperimental'noe issledovanie osobennostey metoda podsvechivaniya poverkhnosti ob''ekta kontrolya dlya izmereniya smeshcheniy lazernymi interferometrami. [Experimental Study of the Features of the Method for Illuminating the Surface of a Tested Object for Measuring Displacements with Laser Interferometers.] Russian Journal of Nondestructive Testing, 2007, no. 9, pp. 37-43 (in Russian).Miroshnichenko, I.P., Alekhin, V.E., Serkin, A.G. Eksperimental'noe obosnovanie interferentsionnogo metoda izmereniya peremeshcheniy na osnove podsvechivaniya poverkhnosti ob''ekta kontrolya. [Experimental study on interference method of measuring displacements on the basis of monitor object surface lightening.] Measurement Technique, 2008, no. 10, pp. 26-30 (in Russian).Miroshnichenko, I.P., Alekhin, V.E., Serkin, A.G. Eksperimental'noe obosnovanie interferentsionnogo metoda izmereniya peremeshcheniy na osnove podsvechivaniya poverkhnosti ob''ekta kontrolya. [Experimental study on interference method of measuring displacements on the basis of monitor object surface lightening.] Measurement Technique, 2008, no. 10, pp. 26-30 (in Russian).Miroshnichenko, I.P., Serkin, A.G. Usovershenstvovannaya eksperimental'naya ustanovka dlya issledovaniya protsessov defektoobrazovaniya v obraztsakh konstruktsionnykh materialov. [Improved experimental plant for investigation of defect formation processes in samples of constructional materials.] Metallurgist, 2010, no. 3, pp. 68-69 (in Russian).Miroshnichenko, I.P., Serkin, A.G. Usovershenstvovannaya eksperimental'naya ustanovka dlya issledovaniya protsessov defektoobrazovaniya v obraztsakh konstruktsionnykh materialov. [Improved experimental plant for investigation of defect formation processes in samples of constructional materials.] Metallurgist, 2010, no. 3, pp. 68-69 (in Russian).Miroshnichenko, I.P., et al. Novel Test Means and Techniques Based on Optical Interferometry and Acoustic Emission to Study Displacements of Object Surfaces and Damage of High-Temperature Superconductive Tapes and Related Composites. Piezoelectrics and Related Materials: Investigations and Applications. New York: Nova Science Publishers, 2012, pp. 238-282.Miroshnichenko, I.P., et al. Novel Test Means and Techniques Based on Optical Interferometry and Acoustic Emission to Study Displacements of Object Surfaces and Damage of High-Temperature Superconductive Tapes and Related Composites. Piezoelectrics and Related Materials: Investigations and Applications. New York: Nova Science Publishers, 2012, pp. 238-282.Miroshnichenko, I.P., et al. Novel Optical Means for Measurement of Displacements of Surfaces of the Control Objects at Diagnostics of Materials and Goods. Physics and Mechanics of New Materials and their Applications. New York: Nova Science Publishers, 2013, pp. 145-154.Miroshnichenko, I.P., et al. Novel Optical Means for Measurement of Displacements of Surfaces of the Control Objects at Diagnostics of Materials and Goods. Physics and Mechanics of New Materials and their Applications. New York: Nova Science Publishers, 2013, pp. 145-154.Miroshnichenko, I. P., Parinov, I. A., Chang , S.-H. Novel Optic Devices for Measurement of Displacements Based on Method of Control Object Highlighting by Using Laser Interferometer. Advanced Materials - Studies and Applications. New York: Nova Science Publisher, 2015, pp. 437-452.Miroshnichenko, I. P., Parinov, I. A., Chang , S.-H. Novel Optic Devices for Measurement of Displacements Based on Method of Control Object Highlighting by Using Laser Interferometer. Advanced Materials - Studies and Applications. New York: Nova Science Publisher, 2015, pp. 437-452.Miroshnichenko, I.P., et al. Mathematical Models, Program Software, Technical and Technological Solutions for Measurement of Displacements of the Control Object Surfaces by Laser Interferometer. Advanced Materials Manufacturing, Physics, Mechanics and Applications. Springer Proceedings in Physics. Cham; Heidelberg; New York; Dordrecht; London: Springer International Publishing, 2016, vol. 175, pp. 341-356.Miroshnichenko, I.P., et al. Mathematical Models, Program Software, Technical and Technological Solutions for Measurement of Displacements of the Control Object Surfaces by Laser Interferometer. Advanced Materials Manufacturing, Physics, Mechanics and Applications. Springer Proceedings in Physics. Cham; Heidelberg; New York; Dordrecht; London: Springer International Publishing, 2016, vol. 175, pp. 341-356.Miroshnichenko, I.P., Serkin, A.G., Sizov, V.P. Chislennoe issledovanie metoda izmereniy malykh lineynykh i uglovykh peremeshcheniy lazernymi interferometrami. [Numerical study on method of measuring small linear and angular displacements by laser interferometers.] Measurement Technique, 2007, no. 1, pp. 9-13 (in Russian).Miroshnichenko, I.P., Serkin, A.G., Sizov, V.P. Chislennoe issledovanie metoda izmereniy malykh lineynykh i uglovykh peremeshcheniy lazernymi interferometrami. [Numerical study on method of measuring small linear and angular displacements by laser interferometers.] Measurement Technique, 2007, no. 1, pp. 9-13 (in Russian).Miroshnichenko, I.P. Unifitsirovannyy metod izmereniya malykh lineynykh i uglovykh peremeshcheniy poverkhnostey ob''ektov kontrolya. [A Unified Method for Measuring Small Linear and Angular Displacements of the Surfaces of Tested Objects.] Russian Journal of Nondestructive Testing, 2008, no. 5, pp. 23-27 (in Russian).Miroshnichenko, I.P. Unifitsirovannyy metod izmereniya malykh lineynykh i uglovykh peremeshcheniy poverkhnostey ob''ektov kontrolya. 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Federatsiya: G01B 11/00, G01B 9/02. [A method for measuring linear and angular displacements.] Patent RF, no. 2388994, 2010 (in Russian).Miroshnichenko, I.P., Serkin, A.G., Sizov, V.P. Sposob izmereniya lineynykh i uglovykh peremeshcheniy: patent 2388994 Ros. Federatsiya: G01B 11/00, G01B 9/02. [A method for measuring linear and angular displacements.] Patent RF, no. 2388994, 2010 (in Russian).Miroshnichenko, I.P., Parinov, I.A., Sizov, V.P. Sposob izmereniya lineynoy i uglovykh sostavlyayushchikh malykh peremeshcheniy poverkhnostey ob''ektov kontrolya: patent 2606245 Ros. Federatsiya : G01B 11/24. [A method for measuring linear and angular components of small displacements of monitor object of surfaces.] Patent RF, no. 2606245, 2017 (in Russian).Miroshnichenko, I.P., Parinov, I.A., Sizov, V.P. Sposob izmereniya lineynoy i uglovykh sostavlyayushchikh malykh peremeshcheniy poverkhnostey ob''ektov kontrolya: patent 2606245 Ros. Federatsiya : G01B 11/24. [A method for measuring linear and angular components of small displacements of monitor object of surfaces.] Patent RF, no. 2606245, 2017 (in Russian).

The authors declare that there are no conflicts of interest present.