{"id":15406,"date":"2023-01-13T09:43:42","date_gmt":"2023-01-13T07:43:42","guid":{"rendered":"http:\/\/journals.khnu.km.ua\/vestnik\/?p=15406"},"modified":"2023-02-15T00:48:22","modified_gmt":"2023-02-14T22:48:22","slug":"avtomatyzovanyj-parametrychnyj-syntez-shyrokokutnyh-okulyariv-z-polem-zoru-90","status":"publish","type":"post","link":"https:\/\/journals.khnu.km.ua\/vestnik\/?p=15406","title":{"rendered":"\u0410\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0437\u043e\u0432\u0430\u043d\u0438\u0439 \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0439 \u0441\u0438\u043d\u0442\u0435\u0437 \u0448\u0438\u0440\u043e\u043a\u043e\u043a\u0443\u0442\u043d\u0438\u0445 \u043e\u043a\u0443\u043b\u044f\u0440\u0456\u0432 \u0437 \u043f\u043e\u043b\u0435\u043c \u0437\u043e\u0440\u0443 90\u00b0"},"content":{"rendered":"

<\/p>\n

\u0410\u0412\u0422\u041e\u041c\u0410\u0422\u0418\u0417\u041e\u0412\u0410\u041d\u0418\u0419 \u041f\u0410\u0420\u0410\u041c\u0415\u0422\u0420\u0418\u0427\u041d\u0418\u0419 \u0421\u0418\u041d\u0422\u0415\u0417 \u0428\u0418\u0420\u041e\u041a\u041e\u041a\u0423\u0422\u041d\u0418\u0425 \u041e\u041a\u0423\u041b\u042f\u0420\u0406\u0412 \u0417 \u041f\u041e\u041b\u0415\u041c \u0417\u041e\u0420\u0423 90\u00b0<\/p>\n

AUTOMATED PARAMETRIC SYNTHESIS OF WIDE-ANGLE EYEPIECES WITH 90-DEG FIELD OF VIEW<\/p>\n

\u0421\u0442\u043e\u0440\u0456\u043d\u043a\u0438: 213-218. \u041d\u043e\u043c\u0435\u0440: \u21166, 2022 (315)\u00a0\u00a0<\/strong> \"\"<\/a>
\n\u0410\u0432\u0442\u043e\u0440\u0438:<\/strong>
\n\u0421\u041e\u041a\u0423\u0420\u0415\u041d\u041a\u041e \u0412\u044f\u0447\u0435\u0441\u043b\u0430\u0432
\n\u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0423\u043a\u0440\u0430\u0457\u043d\u0438
\n\u00ab\u041a\u0438\u0457\u0432\u0441\u044c\u043a\u0438\u0439 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0456\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0433\u043e\u0440\u044f \u0421\u0456\u043a\u043e\u0440\u0441\u044c\u043a\u043e\u0433\u043e\u00bb
\nORCID ID: 0000-0001-5057-182X<\/a>
\ne-mail: sokurenko2@meta.ua
\n\u041a\u0420\u0418\u0416\u041d\u0406\u0419 \u0410\u043d\u0434\u0440\u0456\u0439
\n\u041d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u0438\u0439 \u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442 \u0423\u043a\u0440\u0430\u0457\u043d\u0438
\n\u00ab\u041a\u0438\u0457\u0432\u0441\u044c\u043a\u0438\u0439 \u043f\u043e\u043b\u0456\u0442\u0435\u0445\u043d\u0456\u0447\u043d\u0438\u0439 \u0456\u043d\u0441\u0442\u0438\u0442\u0443\u0442 \u0456\u043c\u0435\u043d\u0456 \u0406\u0433\u043e\u0440\u044f \u0421\u0456\u043a\u043e\u0440\u0441\u044c\u043a\u043e\u0433\u043e\u00bb
\ne-mail: akryzhnii@ukr.net
\nSOKURENKO Vyacheslav, KRYZH\u0406Y Andriy
\nNational Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
\nDOI:<\/strong> https:\/\/www.doi.org\/10.31891\/2307-5732-2022-315-6-213-218<\/a><\/p>\n

\u0410\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u043c\u043e\u0432\u043e\u044e \u043e\u0440\u0438\u0433\u0456\u043d\u0430\u043b\u0443<\/strong><\/p>\n

\u0412 \u0434\u0430\u043d\u0456\u0439 \u0440\u043e\u0431\u043e\u0442\u0456 \u0437\u0434\u0456\u0439\u0441\u043d\u0435\u043d\u043e \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0439 \u0430\u0431\u0435\u0440\u0430\u0446\u0456\u0439\u043d\u0438\u0439 \u0441\u0438\u043d\u0442\u0435\u0437 \u0441\u0435\u0440\u0456\u0457 \u043e\u043f\u0442\u0438\u0447\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0448\u0438\u0440\u043e\u043a\u043e\u043a\u0443\u0442\u043d\u0438\u0445 \u043e\u043a\u0443\u043b\u044f\u0440\u0456\u0432 \u0437 \u0440\u0456\u0437\u043d\u043e\u044e \u043a\u0456\u043b\u044c\u043a\u0456\u0441\u0442\u044e \u043b\u0456\u043d\u0437 \u0434\u043b\u044f \u0432\u0438\u043a\u043e\u0440\u0438\u0441\u0442\u0430\u043d\u043d\u044f \u0443 \u0442\u0435\u043b\u0435\u0441\u043a\u043e\u043f\u0430\u0445 \u0430\u0431\u043e \u043c\u0456\u043a\u0440\u043e\u0441\u043a\u043e\u043f\u0430\u0445. \u041e\u043a\u0443\u043b\u044f\u0440\u0438 \u0437\u0430\u0431\u0435\u0437\u043f\u0435\u0447\u0443\u044e\u0442\u044c \u043a\u0443\u0442\u043e\u0432\u0435 \u043f\u043e\u043b\u0435 \u0437\u043e\u0440\u0443 90\u00b0, \u0432\u0438\u0434\u0438\u043c\u0435 \u0437\u0431\u0456\u043b\u044c\u0448\u0435\u043d\u043d\u044f 17,9\u00d7, \u0434\u0456\u0430\u043c\u0435\u0442\u0440 \u0432\u0438\u0445\u0456\u0434\u043d\u043e\u0457 \u0437\u0456\u043d\u0438\u0446\u0456 4 \u043c\u043c \u0442\u0430 \u0457\u0457 \u0432\u0456\u0434\u0434\u0430\u043b\u0435\u043d\u043d\u044f 16\u00a0\u043c\u043c. \u041f\u0456\u0434 \u0447\u0430\u0441 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0443 \u043e\u043f\u0442\u0438\u0447\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u0432\u0438\u0441\u0443\u0432\u0430\u043b\u0438\u0441\u044f \u0432\u0438\u043c\u043e\u0433\u0438 \u0434\u043e \u043a\u043e\u0440\u0435\u043a\u0446\u0456\u0457 \u0442\u0435\u0442\u0430-\u0434\u0438\u0441\u0442\u043e\u0440\u0441\u0456\u0457 \u0442\u0430 \u0434\u043e\u0441\u044f\u0433\u043d\u0435\u043d\u043d\u044f \u043d\u0430\u0439\u0432\u0438\u0449\u043e\u0457 \u044f\u043a\u043e\u0441\u0442\u0456 \u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u044f. \u041f\u0440\u043e\u0446\u0435\u0441 \u0441\u0438\u043d\u0442\u0435\u0437\u0443 \u0437\u0434\u0456\u0439\u0441\u043d\u044e\u0432\u0430\u0432\u0441\u044f \u0437\u0430 \u0434\u043e\u043f\u043e\u043c\u043e\u0433\u043e\u044e \u0430\u043b\u0433\u043e\u0440\u0438\u0442\u043c\u0443 \u0435\u0432\u043e\u043b\u044e\u0446\u0456\u0439\u043d\u043e\u0457 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0457 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457, \u0440\u0435\u0430\u043b\u0456\u0437\u043e\u0432\u0430\u043d\u043e\u0433\u043e \u0432 \u043f\u0440\u043e\u0433\u0440\u0430\u043c\u043d\u043e\u043c\u0443 \u0437\u0430\u0431\u0435\u0437\u043f\u0435\u0447\u0435\u043d\u043d\u0456 \u0434\u043b\u044f \u043f\u0440\u043e\u0454\u043a\u0442\u0443\u0432\u0430\u043d\u043d\u044f \u043e\u043f\u0442\u0438\u0447\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c PODIL. \u041e\u0442\u0440\u0438\u043c\u0430\u043d\u0456 \u0440\u0435\u0437\u0443\u043b\u044c\u0442\u0430\u0442\u0438 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0443 \u043e\u0441\u043d\u043e\u0432\u043d\u0438\u0445 \u0430\u0431\u0435\u0440\u0430\u0446\u0456\u0439 \u0442\u0430 \u0444\u0443\u043d\u043a\u0446\u0456\u0439 \u044f\u043a\u043e\u0441\u0442\u0456 \u043f\u0456\u0434\u0442\u0432\u0435\u0440\u0434\u0436\u0443\u044e\u0442\u044c \u0432\u0438\u0441\u043e\u043a\u0443 \u044f\u043a\u0456\u0441\u0442\u044c \u0437\u043e\u0431\u0440\u0430\u0436\u0435\u043d\u043d\u044f \u0441\u0438\u043d\u0442\u0435\u0437\u043e\u0432\u0430\u043d\u0438\u0445 \u043e\u043a\u0443\u043b\u044f\u0440\u0456\u0432.
\n\u041a\u043b\u044e\u0447\u043e\u0432\u0456 \u0441\u043b\u043e\u0432\u0430:<\/strong> \u0448\u0438\u0440\u043e\u043a\u043e\u043a\u0443\u0442\u043d\u0438\u0439 \u043e\u043a\u0443\u043b\u044f\u0440, F-\u0442\u0435\u0442\u0430 \u0434\u0438\u0441\u0442\u043e\u0440\u0441\u0456\u044f, \u043f\u043e\u043b\u0435 \u0437\u043e\u0440\u0443, \u041c\u041f\u0424, \u043f\u0430\u0440\u0430\u043c\u0435\u0442\u0440\u0438\u0447\u043d\u0438\u0439 \u0441\u0438\u043d\u0442\u0435\u0437, \u0430\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0437\u0430\u0446\u0456\u044f.<\/p>\n

\u0420\u043e\u0437\u0448\u0438\u0440\u0435\u043d\u0430 \u0430\u043d\u043e\u0442\u0430\u0446\u0456\u044f \u0430\u043d\u0433\u043b\u0456\u0439\u0441\u044c\u043a\u043e\u044e \u00a0\u043c\u043e\u0432\u043e\u044e<\/strong><\/p>\n

Designing a wide-angle eyepiece\u2019s optical system is a multidimensional problem that cannot currently be solved analytically. The final solution should meet specific requirements on the distortion properties, as well as different user-defined restrictions: overall dimensions, lateral color, etc. To solve this problem, we propose to apply one of the global optimization algorithms, which excludes the necessity of having initial solutions with good image quality. In this work, we carry out parametric aberration synthesis of a series of wide-angle eyepieces with a different number of lenses for use in telescopes or microscopes. All optical systems provide the 90-degree angular field of view, the 17.9\u00d7 magnification, the 4-mm exit pupil diameter, and the 16-mm eye relief. The parametric synthesis process itself was carried out in an automated mode with the global optimization algorithm based on modified differential evolution. This algorithm was implemented and examined earlier in software PODIL intended for optical systems design. The computer simulations showed that the time interval necessary for automated designing such eyepieces (with a total number of unknown variables up to 60) is about 20 hours.\u00a0The evaluated aberrations and image quality functions confirmed the high image quality of the designed optical systems of the developed wide-angle eyepieces. The user-defined technical requirements and restrictions set in the merit function are completely met in found solutions. All developed optical systems are well corrected on theta distortion: its value does not exceed 0.6% over the whole field.\u00a0Future research can be directed onto testing automated design capabilities for other types of optical systems with extreme performances.
\nKeywords:<\/strong> wide-angle eyepiece, F-theta distortion, field of view, MTF, parametric synthesis, automation.<\/p>\n

\u041b\u0456\u0442\u0435\u0440\u0430\u0442\u0443\u0440\u0430<\/strong><\/p>\n

    \n
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  3. Choosing an Eyepiece \u2013 Step by Step. Al Nagler. Tele Vue Optics. 2014. URL: https:\/\/www.televue.com\/pdf\/Eyepiece_AASNY_2014_May_June_ChoosingEPs.pdf<\/li>\n
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  5. Tele Vue Nagler Type-4 17mm Eyepiece (2″) Overview. Tele Vue Optics, Inc. 2022. URL: https:\/\/www.bhphotovideo.com\/c\/product\/329433-REG\/Tele_Vue_EN4_17_0_Nagler_Type_4_17mm.html#:~:text=Inspired%20by%20the%20venerable%20Nagler,optimized%20for%20deep-sky%20viewing<\/li>\n
  6. Scientific 82\u00b0 Series 14 mm Eyepiece (1.25″). Explore Scientific, LLC. 2022. URL: https:\/\/explorescientificusa.com\/products\/82-14mm<\/li>\n
  7. Haupt R, Haupt S. Practical Genetic Algorithms. 2004. 253 p.<\/li>\n
  8. Ali \u041c., Zabinsky B. A numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global Optimization Test Problems. J. of Global Optimization. 2005. Vol. 31. \u0420. 635\u2013672.<\/li>\n
  9. \u0421\u043e\u043a\u0443\u0440\u0435\u043d\u043a\u043e \u0412. \u041c., \u041d\u0435\u0434\u0456\u043b\u044e\u043a \u0412. \u0421. \u0427\u0438\u0441\u043b\u043e\u0432\u0435 \u0434\u043e\u0441\u043b\u0456\u0434\u0436\u0435\u043d\u043d\u044f \u0441\u0442\u043e\u0445\u0430\u0441\u0442\u0438\u0447\u043d\u0438\u0445 \u043c\u0435\u0442\u043e\u0434\u0456\u0432 \u0431\u0435\u0437\u043f\u0435\u0440\u0435\u0440\u0432\u043d\u043e\u0457 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0457 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457. \u041d\u0430\u0443\u043a\u043e\u0432\u0456 \u0432\u0456\u0441\u0442\u0456 \u041d\u0422\u0423\u0423 “\u041a\u041f\u0406”. 2012. \u2116 1. C. 81-88.<\/li>\n
  10. \u0421\u043e\u043a\u0443\u0440\u0435\u043d\u043a\u043e \u0412. \u041c., \u041c\u0430\u043a\u0430\u0440\u0435\u043d\u043a\u043e \u042f. \u0406. \u0420\u043e\u0437\u0440\u043e\u0431\u043a\u0430 \u043e\u043f\u0442\u0438\u0447\u043d\u0438\u0445 \u0441\u0438\u0441\u0442\u0435\u043c \u043c\u0435\u0442\u043e\u0434\u0430\u043c\u0438 \u0433\u043b\u043e\u0431\u0430\u043b\u044c\u043d\u043e\u0457 \u043e\u043f\u0442\u0438\u043c\u0456\u0437\u0430\u0446\u0456\u0457. \u0412\u0456\u0441\u043d\u0438\u043a \u041d\u0422\u0423\u0423 “\u041a\u041f\u0406”. \u0421\u0435\u0440\u0456\u044f \u043f\u0440\u0438\u043b\u0430\u0434\u043e\u0431\u0443\u0434\u0443\u0432\u0430\u043d\u043d\u044f. 2015. \u2116 50(2). C. 51-60.<\/li>\n
  11. \u0421\u043e\u043a\u0443\u0440\u0435\u043d\u043a\u043e \u0412. \u041c., \u0411\u0443\u0439\u043b\u043e\u0432 \u0406. \u0421. \u0417\u0430\u0441\u0442\u043e\u0441\u0443\u0432\u0430\u043d\u043d\u044f \u0430\u0434\u0430\u043f\u0442\u0438\u0432\u043d\u043e\u0433\u043e \u043c\u0435\u0442\u043e\u0434\u0443 \u0434\u0438\u0444\u0435\u0440\u0435\u043d\u0446\u0456\u0439\u043d\u043e\u0457 \u0435\u0432\u043e\u043b\u044e\u0446\u0456\u0457 \u041a\u043e\u0448\u0456 \u0434\u043b\u044f \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043a\u0443 \u043e\u0431\u2019\u0454\u043a\u0442\u0438\u0432\u0456\u0432. \u0412\u0456\u0441\u043d\u0438\u043a \u041d\u0422\u0423\u0423 “\u041a\u041f\u0406”. \u0421\u0435\u0440\u0456\u044f \u043f\u0440\u0438\u043b\u0430\u0434\u043e\u0431\u0443\u0434\u0443\u0432\u0430\u043d\u043d\u044f. 2016. \u2116 51(1). C. 41-47.<\/li>\n
  12. \u0421\u043e\u043a\u0443\u0440\u0435\u043d\u043a\u043e \u0412. \u041c., \u0412\u0430\u043a\u0443\u043b\u0435\u043d\u043a\u043e \u041c. \u041c. \u0410\u0432\u0442\u043e\u043c\u0430\u0442\u0438\u0437\u043e\u0432\u0430\u043d\u0438\u0439 \u0440\u043e\u0437\u0440\u0430\u0445\u0443\u043d\u043e\u043a \u043e\u043a\u0443\u043b\u044f\u0440\u0456\u0432 \u0437 \u0434\u0438\u0444\u0440\u0430\u043a\u0446\u0456\u0439\u043d\u0438\u043c\u0438 \u043e\u043f\u0442\u0438\u0447\u043d\u0438\u043c\u0438 \u0435\u043b\u0435\u043c\u0435\u043d\u0442\u0430\u043c\u0438. \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443: \u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439, 2018. \u21161 (257). C. 107-112.<\/li>\n
  13. \u0421\u043e\u043a\u0443\u0440\u0435\u043d\u043a\u043e \u0412. \u041c., \u0422\u0440\u043e\u0441\u0442\u044f\u043d\u0441\u044c\u043a\u0430 \u041e. \u0412. \u0421\u0438\u043d\u0442\u0435\u0437 \u043e\u043f\u0442\u0438\u0447\u043d\u043e\u0457 \u0441\u0438\u0441\u0442\u0435\u043c\u0438 \u043e\u043a\u0443\u043b\u044f\u0440\u0430 \u0434\u043b\u044f \u043c\u0456\u043a\u0440\u043e\u0434\u0438\u0441\u043f\u043b\u0435\u044f \u0437 \u0432\u0438\u0441\u043e\u043a\u043e\u044e \u0440\u043e\u0437\u0434\u0456\u043b\u044c\u043d\u043e\u044e \u0437\u0434\u0430\u0442\u043d\u0456\u0441\u0442\u044e. \u0412\u0456\u0441\u043d\u0438\u043a \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u043e\u0433\u043e \u043d\u0430\u0446\u0456\u043e\u043d\u0430\u043b\u044c\u043d\u043e\u0433\u043e \u0443\u043d\u0456\u0432\u0435\u0440\u0441\u0438\u0442\u0435\u0442\u0443: \u0422\u0435\u0445\u043d\u0456\u0447\u043d\u0456 \u043d\u0430\u0443\u043a\u0438. \u0425\u043c\u0435\u043b\u044c\u043d\u0438\u0446\u044c\u043a\u0438\u0439, 2019. \u2116 6 (279). C. 206-210.<\/li>\n<\/ol>\n

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