{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,28]],"date-time":"2025-05-28T17:08:40Z","timestamp":1748452120847,"version":"3.40.5"},"reference-count":24,"publisher":"Optica Publishing Group","issue":"9","license":[{"start":{"date-parts":[[2022,3,15]],"date-time":"2022-03-15T00:00:00Z","timestamp":1647302400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2022,3,15]],"date-time":"2022-03-15T00:00:00Z","timestamp":1647302400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2022,3,20]]},"abstract":"<jats:p>The hysteresis behavior of piezoelectric actuators degrades the positioning accuracy\n\t\t\t\t\tand bandwidth of nano-positioning systems. Therefore, considering the\n\t\t\t\t\thysteresis of piezoelectric deformable mirrors is completely essential\n\t\t\t\t\tand also improves the modeling accuracy of adaptive optics layouts.\n\t\t\t\t\tBecause of the unique adaptability and mathematical flexibility of the\n\t\t\t\t\tBouc\u2013Wen model it has gained popularity, and as a result, in many\n\t\t\t\t\tscientific applications, it is one of the most conventional models\n\t\t\t\t\ttypically employed to describe nonlinear hysteretic systems. Among\n\t\t\t\t\tdifferent deformable mirrors, a unimorph piezoelectric deformable\n\t\t\t\t\tmirror is a suitable choice to be used in adaptive optics systems\n\t\t\t\t\tbecause of its relative convenience and cost-effective production.\n\t\t\t\t\tThis paper proposes a new, to the best of our knowledge, approach to\n\t\t\t\t\tdetermine the influence function and the voltage control matrix of a\n\t\t\t\t\tspecific unimorph mirror by considering a simplified inverse Bouc\u2013Wen\n\t\t\t\t\thysteresis model as a frequency function. Then the results for two\n\t\t\t\t\tselected standard Zernike modes, defocus and astigmatism-x, have been\n\t\t\t\t\tsimulated using Comsol Multiphysics and MATLAB at a range of 5 to\n\t\t\t\t\t100\u00a0Hz. For a more comprehensive comparison, the root-mean-square\n\t\t\t\t\terror and the coefficients of the Zernike terms have been applied as\n\t\t\t\t\ttwo criteria. According to the simulation results, the hysteresis\n\t\t\t\t\teffect of piezoelectric actuators has been significantly compensated\n\t\t\t\t\tby applying the inverse Bouc\u2013Wen model at different frequencies,\n\t\t\t\t\tespecially for higher frequencies. The effectiveness of the inverse\n\t\t\t\t\tBouc\u2013Wen model to compensate the hysteresis has been observed in\n\t\t\t\t\tastigmatism-x mode slightly more than in the defocus\n\t\t\t\t\tmode.<\/jats:p>","DOI":"10.1364\/ao.448707","type":"journal-article","created":{"date-parts":[[2022,2,14]],"date-time":"2022-02-14T19:00:13Z","timestamp":1644865213000},"page":"2293","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Calculation of the modified control matrix for a selected unimorph\n\t\t\t\tdeformable mirror to compensate the piezoelectric hysteresis effect using\n\t\t\t\tthe inverse Bouc\u2013Wen model"],"prefix":"10.1364","volume":"61","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6664-9131","authenticated-orcid":true,"given":"M. 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