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The proposed method consists of the collimated lasers, beam splitters, focusing lens, quadrant photodiode detectors, a high-precision steel ball, and a special mirror fixed to the rotary axis. The mathematical model is established byoptical ray tracing, and the corresponding optical path is also simulated by OpticStudio. Meanwhile, an adjusting mechanism for X\u2013Y micro-displacement, based on the elastic deformation of the material, is designed to adjust the installation eccentricity error of the high-precision steel ball. The calibration results of the proposed system demonstrate that the displacement errors are \u00b10.25 \u00b5m within the measuring range of \u00b110 \u00b5m, and the tilt angle errors are \u00b10.6 arcsec within the measuring range of \u00b125 arcsec. Taking a direct drive (DD) motor as the test object, the radial error motions of the rotary axis range from \u22123.2 to 4.1 \u00b5m, the axial error motions range from \u22124.9 to 4.7 \u00b5m, and the tilt error motions around the X and Y axes range from \u22122.8 to 1.8 arcsec and \u22122.6 to 2.0 arcsec, respectively.<\/jats:p>","DOI":"10.1063\/5.0127199","type":"journal-article","created":{"date-parts":[[2022,12,19]],"date-time":"2022-12-19T13:41:56Z","timestamp":1671457316000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":10,"title":["An optical method based auto-collimation for measuring five degrees of freedom error motions of rotary axis"],"prefix":"10.1063","volume":"93","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1305-4003","authenticated-orcid":false,"given":"Huining","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology 1 , Hefei 230009, China"},{"name":"Anhui Province Key Laboratory of Measuring Theory and Precision Instrument, Hefei University of Technology 2 , Hefei 230009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenjing","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology 1 , Hefei 230009, China"},{"name":"Anhui Province Key Laboratory of Measuring Theory and Precision Instrument, Hefei University of Technology 2 , Hefei 230009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0638-7088","authenticated-orcid":false,"given":"Mengyao","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology 1 , Hefei 230009, China"},{"name":"Anhui Province Key Laboratory of Measuring Theory and Precision Instrument, Hefei University of Technology 2 , Hefei 230009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haojie","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Instrument Science and Opto-electronics Engineering, Hefei University of Technology 1 , Hefei 230009, China"},{"name":"Anhui Province Key Laboratory of Measuring Theory and Precision Instrument, Hefei University of Technology 2 , Hefei 230009, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liandong","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Control Science and Engineering, China University of Petroleum (UPC) 3 , Qingdao 266580, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2022,12,19]]},"reference":[{"key":"2023081010165288300_c1","year":"2015"},{"issue":"12","key":"2023081010165288300_c2","first-page":"37","article-title":"The third round method of roundness determination (in Japanese)","volume":"32","year":"1966","journal-title":"Precis. 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