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With the rapid development of industrial manufacturing, people are stricter and stricter for measuring accuracy and demanding for measurable objects. The demand for a new generation of industrial measurement has evolved from the cooperative target toward the diffuse surface object with faster measurement speed and higher precision. Frequency modulated continuous wave (FMCW) laser ranging technology has proved to be an efficient method in the high-precision ranging fields for absolute distance measurement of a diffuse reflecting target.However, its accuracy is subjected to the stability of continuous-wave light source which cannot scan frequency linearly, which further leads to the instability of beat frequency and poor spectrum resolution. Generally, this problem could be solved by the active linearization technique and the post-processing technique. The most popular method is the non-uniform interval resampling technique, which belongs to the post-processing scheme and uses the zero-crossings or peaks of a long delay Mach-Zehnder interferometer signal as triggers for acquiring the measurement signal data. This technique is low cost, easy to be integrated into FMCW ladar system, and especially suitable for short-range small-band scanning measurements. However, in the large-bandwidth long-distance measurement cases, due to the jitter and dispersion of a long fiber, the spectrum obtained by this method is deteriorated such as the spectral broadening and distance shifting, so the range position cannot be determined precisely. To improve the precision, the fast Fourier transform, chirp Z transform and the multiple signal classification methods are used to obtain the distance spectral information. There are also other methods to solve this problem, but there is no common precision evaluation method to test the validities of these methods.In this paper, a precision evaluation method of measuring the FMCW absolute distance based on two-fiber interferometer is presented. A lower Cramer-Rao lower bound on the variance of distance parameter of the resampled signal in the presence of noise is derived. It shows that the precision of absolute distance is affected by the signal-to-noise ratio of the system and chirp bandwidth. This result is verified experimentally.Besides, the proposed method is not restricted to any distance estimation algorithm. According to this boundary, an optimal distance estimation method could be chosen. Moreover, a simulation of range precision versus signal-to-noise ratio and bandwidth is also demonstrated. When the chirped bandwidth is equal to 20 nm and the signal-to-noise ratio of absolute distance measurement interferometer is raised to more than 70 dB, the obtained precision is below 1 μm. This method can provide a theoretical reference for improving the precision of FMCW distance measurement and it could be widely used in the future.
[1] Scharstein D, Szeliski R 2003 Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Madison, USA, June 18-20, 2003 p195
[2] Miller M E, Lefsky M, Pang Y 2011 Remote Sens. Environ. 115 298
[3] Cabral A, Rebordao J 2007 Opt. Engin. 46 073602
[4] Baumann E, Giorgetta F R, Deschênes J D, Swann W C, Coddington I, Newbury N R 2014 Opt. Express 22 24914
[5] Mateo A B, Barber Z W 2015 Appl. Opt. 54 6019
[6] Weid J P, Passy R, Mussi G, Gisin N 1997 J. Lightw. Technol. 15 1131
[7] Li G, Wang R, Song Z, Zhang K, Wu Y, Pan J 2017 Appl. Opt. 56 3257
[8] Chen Y, Aguirre A D, Hsiung P L, Huang S W, Mashimo H, Schmitt J M, Fujimoto J G 2008 Opt. Express 16 2469
[9] Roos P A, Reibel R R, Berg T, Kaylor B, Barber Z W, Babbitt W R 2009 Opt. Lett. 34 3692
[10] Barber Z W, Giorgetta F R, Roos P A, Coddington I, Dahl J R, Reibel R R, Greenfield N, Newbury N R 2011 Opt. Lett. 36 1152
[11] Qin J, Zhou Q, Xie W, Xu Y, Yu S, Liu Z, Tong Y, Dong Y, Hu W 2015 Opt. Lett. 40 4500
[12] Moore E D, Mcleod R R 2008 Opt. Express 16 13139
[13] Yksel K, Wuilpart M, Mégret P 2009 Opt. Express 17 5845
[14] Liu G, Xu X, Liu B, Chen F, Hu T, Lu C, Gan Y 2017 Opt. Commun. 386 57
[15] Shi G, Zhang F, Qu X, Meng X 2014 Opt. Eng. 53 122402
[16] Meng X S, Zhang F M, Qu X H 2015 Acta Phys. Sin. 23 230601 (in Chinese) [孟祥松, 张福民, 曲兴华 2015 物理学报 23 230601]
[17] Pan H, Zhang F, Shi C, Qu X 2017 Appl. Opt. 56 6956
[18] Zheng J 2004 Appl. Opt. 43 4189
[19] Ye Z F 2009 Statistical Signal Processing (Hefei: University of Science and Technology of China Press) p255 (in Chinese) [叶中付 2009 统计信号处理(合肥: 中国科学技术大学出版社) 第255页]
[20] Swann W C, Gilbert S L 2005 J. Opt. Soc. Am. B 22 1749
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[1] Scharstein D, Szeliski R 2003 Proceedings of the 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Madison, USA, June 18-20, 2003 p195
[2] Miller M E, Lefsky M, Pang Y 2011 Remote Sens. Environ. 115 298
[3] Cabral A, Rebordao J 2007 Opt. Engin. 46 073602
[4] Baumann E, Giorgetta F R, Deschênes J D, Swann W C, Coddington I, Newbury N R 2014 Opt. Express 22 24914
[5] Mateo A B, Barber Z W 2015 Appl. Opt. 54 6019
[6] Weid J P, Passy R, Mussi G, Gisin N 1997 J. Lightw. Technol. 15 1131
[7] Li G, Wang R, Song Z, Zhang K, Wu Y, Pan J 2017 Appl. Opt. 56 3257
[8] Chen Y, Aguirre A D, Hsiung P L, Huang S W, Mashimo H, Schmitt J M, Fujimoto J G 2008 Opt. Express 16 2469
[9] Roos P A, Reibel R R, Berg T, Kaylor B, Barber Z W, Babbitt W R 2009 Opt. Lett. 34 3692
[10] Barber Z W, Giorgetta F R, Roos P A, Coddington I, Dahl J R, Reibel R R, Greenfield N, Newbury N R 2011 Opt. Lett. 36 1152
[11] Qin J, Zhou Q, Xie W, Xu Y, Yu S, Liu Z, Tong Y, Dong Y, Hu W 2015 Opt. Lett. 40 4500
[12] Moore E D, Mcleod R R 2008 Opt. Express 16 13139
[13] Yksel K, Wuilpart M, Mégret P 2009 Opt. Express 17 5845
[14] Liu G, Xu X, Liu B, Chen F, Hu T, Lu C, Gan Y 2017 Opt. Commun. 386 57
[15] Shi G, Zhang F, Qu X, Meng X 2014 Opt. Eng. 53 122402
[16] Meng X S, Zhang F M, Qu X H 2015 Acta Phys. Sin. 23 230601 (in Chinese) [孟祥松, 张福民, 曲兴华 2015 物理学报 23 230601]
[17] Pan H, Zhang F, Shi C, Qu X 2017 Appl. Opt. 56 6956
[18] Zheng J 2004 Appl. Opt. 43 4189
[19] Ye Z F 2009 Statistical Signal Processing (Hefei: University of Science and Technology of China Press) p255 (in Chinese) [叶中付 2009 统计信号处理(合肥: 中国科学技术大学出版社) 第255页]
[20] Swann W C, Gilbert S L 2005 J. Opt. Soc. Am. B 22 1749
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