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Abstract

With the rapid development of modern technology, high-precision absolute distance measurement is playing an important role in many applications, such as scientific research, aviation and industry measurement. Among the above various measurement methods, how to realize higher-accuracy, larger-scale, and faster-speed measurement is particularly important. In the traditional technique for long-distance measurement, the emergence of optical frequency comb (OFC) provides a breakthrough technology for accurately measuring the absolute value of distance. The OFC can be considered as a multi-wavelength source,whose phase and repetition rate are locked. The OFC is a very useful light source that can provide phase-coherent link between microwave and optical domain, which has been used as a source in various distance measurement schemes that can reach an extraordinary measurement precision and accuracy. A variety of laser ranging methods such as dual-comb interferometry and dispersive interferometer based on femtosecond laser have been applied to the measuring of absolute distance. In this paper, the factors affecting the resolution and the non-ambiguous range of spectral interferometry ranging using OFC are particularly discussed. We also analyze the systematic errors and the limitations of traditional transform methods based on Fourier transform, which can conduce to the subsequent research. To address the problem caused by low resolution and unequal frequency interval, we propose a data processing method referred to as equal frequency interval resampling. The proposed method is based on cubic spline interpolation and can solve the error caused by the frequency spectrum broadening with the increase of distance. Moreover, we propose a new method based on least square fitting to calibrate the error introduced by the low resolution of interferometry spectrum obtained with fast Fourier transform (FFT). With the proposed method, the simulation results show that the systematic error is less than 0.2 μm in the non-ambiguity range and the system resolution is greatly improved. Finally, anabsolute distance measurement system based on Michelson interferometer is built to verify theproposed method. The measurement results compared with those obtained by using a high-precision commercial He-Ne laser interferometer show that the distance measurement accuracy is lower than 3 μm at any distancewithin the non-ambiguity range. The experimental results demonstrate that our data processing algorithm is able to increase the accuracy of dispersive interferometry ranging with OFC.

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Authors and contacts

Corresponding author:Zhang Fu-Min,zhangfumin@tju.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant Nos. 51675380, 51775379), the National Key R&D Program of China (Grant No. 2018YFB2003501) and the Key Technologies R&D Program of Tianjin, China (Grant No. 18YFZCGX00920)

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Cited By

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实验序号	L/mm	传统FFT法误差/μm	等频率间隔重采样误差/μm	峰值拟合误差/μm
1	0.5250	9.1031	2.8944	0.161990
2	0.8250	21.1607	2.8344	0.165549
3	0.9000	24.1751	–0.1799	0.010804
4	1.0005	28.6943	–4.6991	–0.166222
5	1.2000	36.2327	–0.239	0.000102
6	1.5000	36.2927	–0.2999	–0.008146
7	1.9950	51.3887	–3.3983	–0.183495
8	3.0000	84.5830	–0.5998	–0.038114
9	4.9950	135.9718	–3.998	–0.177303
10	7.0050	190.3629	1.5986	0.114618

DownLoad: CSV

实验序号	L/mm	传统FFT法误差/μm	等频率间隔重采样误差/μm	峰值拟合误差/μm
1	0.0023	–2.3015	1.6570	0.0218
2	0.0037	–3.6001	3.0337	–0.7335
3	0.1000	3.2167	0.1031	0.8437
4	0.4997	–1.8309	0.4975	0.2267
5	0.9998	2.0097	1.0011	–0.9828
6	3.1307	–4.2793	3.1336	1.1003
7	4.9980	–13.2375	4.9995	–0.1739
8	6.2364	157.3300	6.2308	–1.9198
9	6.2511	无法定位	6.2551	–2.9791
10	9.3629	无法定位	1.5705	–2.1087

DownLoad: CSV

${f_{{\rm{CEO}}}}$	光频梳偏移频率
${f_{{\rm{rep}}}}$	光频梳重复频率
${T_{\rm{R}}}$	光频梳脉冲时域间隔
$\Delta {\varphi _{{\rm{ce}}}}$	群、相速度差异造成的相位偏移
$E\left( \upsilon \right)$	光频梳脉冲电场信号
${E_{{\rm{ref}}}}(\upsilon )$	参考光电场信号
${E_{\rm{t}}}(\upsilon )$	测量光电场信号
a	参考光功率因数
b	测量光功率因数
$I(\upsilon )$	光谱仪接收的频域干涉信号
${{2ab}/ {{a^2} + {b^2}}}$	调制深度
$I(t)$	经FFT变换后的$I(\upsilon )$
L	测量臂和参考臂光程差/2
$\Delta t$	2L造成时间差
τ	干涉信号振荡频率τ=L/c
c	真空光速
n	折射率
${L_{\rm{c}}}$	相干长度
$\partial f$	相干长度公式中的频率带宽
$\Delta \upsilon $	FFT变换的频率分辨力
$\Delta L$	FFT变换的距离分辨力=$\Delta \upsilon $*c
${L_{{\rm{NAR}}}}$	频域干涉法的非模糊范围
f	频率
${\rm{d}}f$	光谱仪频率分辨力
${\rm{d}}\lambda $	光谱仪波长微分量
W	频谱范围
$\Delta w$	波长范围上下限之差
B	频谱宽度
${\lambda _{{\rm{cen}}}}$	W的中心处波长
${f_{\rm{s}}}$	光谱仪采样频率
$\Delta \lambda $	光谱仪采样波长间隔
N	光谱仪采样点数
${L_{{\rm{NAR0}}}}$	${f_{{\rm{rep}}}} = 250{\rm{ MHz}}$理想情况下非模糊范围
${L_{{\rm{NAR1}}}}$	光谱仪的非模糊范围
${L_{{\rm{NAR2}}}}$	${f_{{\rm{rep}}}} = 40{\rm{ GHz}}$非模糊范围
$\Delta f$	波长需转化为频率时的频率变化量
${\lambda _1}$	波长需转化为频率时的对应波长
$p\left( x \right)$	二项式拟合公式
${p_1}$	二项式拟合二次项
${p_2}$	二项式拟合一次项
${p_3}$	二项式拟合常数项

DownLoad: CSV

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Vol. 68, Issue 19 - 2019-10-05

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