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The algorithm can effectively reduce the measurement error caused by the noise introduced in the optical path and circuit. Because of the low signal\u2212to\u2212noise ratio of the measurement signal, a dynamic filter with variable coefficients is designed. The role of the bi\u2212quadrature lock\u2212in amplifier algorithm in the problem of different amplitudes among the measurement signal, reference signal, and uncertainty of the frequency difference of the dual\u2212frequency laser is analyzed. With the aid of the heterodyne interferometry platform, the error in the solution results of the proposed algorithm and the conventional algorithm is compared. The results indicate that the maximum deviation of the phase increment of the algorithm does not exceed 6 mrad, the single\u2212cycle phase difference can be subdivided by 1024, and the system resolution reaches 0.15 nm.<\/jats:p>","DOI":"10.3390\/s22145422","type":"journal-article","created":{"date-parts":[[2022,7,21]],"date-time":"2022-07-21T03:34:40Z","timestamp":1658374480000},"page":"5422","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Design and Implementation of a Subnanometer Heterodyne Interference Signal Processing Algorithm with a Dynamic Filter"],"prefix":"10.3390","volume":"22","author":[{"given":"Qilin","family":"Zeng","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Key Laboratory of Optoelectronic Information Processing, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengyi","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Key Laboratory of Optoelectronic Information Processing, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xianming","family":"Xiong","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Key Laboratory of Optoelectronic Information Processing, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Du","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Key Laboratory of Optoelectronic Information Processing, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wentao","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Key Laboratory of Optoelectronic Information Processing, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhicheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Key Laboratory of Optoelectronic Information Processing, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peng","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering and Automation, Guilin University of Electronic Technology, Guilin 541004, China"},{"name":"Key Laboratory of Optoelectronic Information Processing, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lihua","family":"Lei","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Online Test and Control Technology, Shanghai 201203, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"045102","DOI":"10.1117\/1.OE.60.4.045102","article-title":"Influence of installation error of grating interferometer on high-precision displacement measurement","volume":"60","author":"Du","year":"2021","journal-title":"Opt. 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[Master\u2019s Thesis, Harbin Institute of Technology]."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Yang, Y., Yamamoto, K., Dovale \u00c1lvarez, M., Wei, D., Esteban Delgado, J.J., M\u00fcller, V., Jia, J., and Heinzel, G. (2022). On-Axis Optical Bench for Laser Ranging Instruments in Future Gravity Missions. Sensors, 22.","DOI":"10.3390\/s22052070"},{"key":"ref_9","unstructured":"Cai, H.J. (2015). Research on Phase Subdivision Technology of Picometer Resolution Dual-Frequency Laser Interferometer. [Master\u2019s Thesis, Harbin Institute of Technology]."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Hines, A.S., Valdes, G., and Guzman, F. (2021). Investigation and Mitigation of Noise Contributions in a Compact Heterodyne Interferometer. Sensors, 21.","DOI":"10.3390\/s21175788"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"74939","DOI":"10.1109\/ACCESS.2021.3081152","article-title":"Real-Time Direction Judgment System of Sub-Nanometer Scale Grating Ruler","volume":"9","author":"Li","year":"2021","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.camwa.2021.05.031","article-title":"A residual based a posteriori error estimators for AFC schemes for convection-diffusion equations","volume":"97","author":"Jha","year":"2021","journal-title":"Comput. Math. Appl."},{"key":"ref_13","unstructured":"Xiong, X.M., Zhang, W., Zhang, Z., Zeng, Q.L., Du, H., Xu, S.H., Zhang, Y.T., and Zhao, Z. (2021). A Closed-Loop Controlled Synchronous Dynamic Gain Compensation Method for Laser Interferometry. (ZL202110578721.0), CN Patent."},{"key":"ref_14","unstructured":"Xiong, X.M., Zhang, Z., Zhang, W., Du, H., Zeng, Q.L., Xu, S.H., Zhang, Y.T., and Zhao, Z. (2021). APD High Signal-to-Noise Ratio Gain Automatic Selection Control Device and Method. (Application CN202110577057.8), CN Patent."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.isatra.2020.11.021","article-title":"Design of Atangana\u2013Baleanu\u2013Caputo fractional-order digital filter","volume":"112","author":"Gupta","year":"2021","journal-title":"ISA Trans."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"153651","DOI":"10.1016\/j.aeue.2021.153651","article-title":"The matrix-based design and realization of digital parametric equalizer","volume":"134","author":"Jongsataporn","year":"2021","journal-title":"AEU - Int. J. Electron. Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"82402","DOI":"10.1109\/ACCESS.2021.3085704","article-title":"Technique to Adjust Adaptive Digital Filter Coefficients in Residue Number System Based Filters","volume":"9","author":"Kaplun","year":"2021","journal-title":"IEEE Access"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"108040","DOI":"10.1016\/j.sigpro.2021.108040","article-title":"Low-area and accurate inner product and digital filters based on stochastic computing","volume":"183","author":"Abdellatef","year":"2021","journal-title":"Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2078","DOI":"10.1109\/LSP.2021.3116517","article-title":"Fast Convergence Method for Scaling Window Sidelobe Magnitude","volume":"28","author":"Lim","year":"2021","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1155\/2005\/917832","article-title":"An experimental assessment of transverse adaptive fir filters as applied to vibrating structures identification","volume":"12","author":"Castello","year":"2005","journal-title":"Shock Vib."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1109\/TCSI.2020.2978765","article-title":"Improving Architectures of Binary Signed-Digit CORDIC with Generic\/Specific Initial Angles","volume":"67","author":"Mahdavi","year":"2020","journal-title":"IEEE Trans. Circuits Syst. I Regul. 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