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Frequency-modulated continuous-wave laser interferometry displacement sensor based on centroid peak-finding
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摘要:
调频连续波激光干涉技术在精密测量领域中应用广泛，针对其高精度位移解调问题，本文将质心法应用于其拍频信号的解调中，提出了一种基于质心寻峰法的相位解调算法并进行实验与分析。提出的算法在对截取的拍频信号进行平滑滤波与分峰截幅等处理基础上，通过质心坐标公式得到拍频信号的质心，质心横坐标即为峰值位置，最后通过相位鉴别算法解调出位移。在仿真中设置信噪比(SNR)为15 dB，算法的相位误差为0.016 rad，位移误差为2.04 nm。搭建调频连续波激光干涉位移测量系统进行实验验证，实验结果表明：当固定距离为44 mm时，位移随机误差标准差为2.18 nm。与常规的过零点检测法进行对比分析，结果表明该算法的测量误差降低了49%，分辨率获得了提高，具有广泛的应用前景。
Abstract:The frequency-modulated continuous wave laser interferometry is widely used in the field of precision measurement. Aiming at its high-precision displacement demodulation problem, this paper applies the centroid method to the demodulation of its beat signal, proposes a phase demodulation algorithm based on the centroid peak-seeking method, and carries out experiments and analysis. Based on the smooth filtering and peak clipping of the intercepted beat signal, the proposed algorithm obtains the centroid of the beat signal through the centroid coordinate formula. The abscissa of the centroid is the peak position. Finally, the phase discrimination algorithm demodulates the displacement. In the simulation, the SNR is set to 15 dB, the phase error of the algorithm is 0.016 rad, and the displacement error is 2.04 nm. A frequency-modulated continuous wave laser interference displacement measurement system was built for experimental verification. The experimental results show that when the fixed distance is 44 mm, the standard deviation of random displacement error is 2.18 nm. Compared with the conventional zero crossing detection method, the measurement error of the algorithm is reduced by 49%, the resolution is improved, and the algorithm has broad application prospects.
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Overview: Frequency-modulated continuous wave laser interferometry technology has broad application prospects in modern industrial production due to its advantages of large dynamic range, high precision, and high reliability. The frequency-modulated continuous wave laser is coupled with the Fabry-Perot interferometer in the optical field through optical fiber devices. The signal light and reference light of the interferometer propagate along the same optical fiber arm, which is extremely sensitive to displacement information. The measurement information can be obtained by demodulating the beat signal generated when the reference signal interferes with the measurement signal. In phase demodulation, the extreme point position of the beat frequency signal in one cycle is converted into a change in the initial phase to achieve displacement demodulation. But a beat frequency signal is a kind of sine signal with low signal noise, unequal amplitude, and frequency. It needs signal preprocessing to facilitate the subsequent extreme point location. Determining the precise position of the peak is the key problem in displacement demodulation.
Aiming at the demodulation problem of frequency modulation continuous wave interference beat frequency signal, this paper applies the centroid method to the field of the beat frequency signal demodulation and proposes a phase demodulation algorithm based on the centroid peak finding method. Compared with the existing phase demodulation algorithm, the algorithm does not need amplitude correction. After smooth filtering and minimum point positioning of the signal, the peak point position of the beat frequency signal can be accurately obtained by the centroid method, and the displacement amount can be obtained after phase demodulation according to this peak point position. A frequency-modulated continuous wave interferometric ranging system was constructed, and test experiments were carried out. The random error distribution of the displacement is verified when the length of the F-P cavity is fixed, and the standard deviation of the error is 2.18 nm. In order to compare the centroid peak-finding method proposed in this paper with the conventional zero-crossing detection method, the displacement random error of the two methods is obtained by using the built frequency modulated continuous wave ranging system with fixed different distances, and its standard deviation is calculated. Experimental results show that the measurement error of the method proposed in this paper is reduced by 49% compared to the traditional zero-crossing detection method. It has important research significance in the field of laser interferometry and has broad application prospects in the field of precision measurement.
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图 1 锯齿波调制时参考波与信号波的频率关系
Figure 1. Frequency relationship between reference wave and signal wave in sawtooth wave modulation
图 2 基于过零点检测法的相位解调算法流程图
Figure 2. Flow chart of phase demodulation algorithm based on zero-crossing detection method
图 4 基于质心寻峰法相位解调算法流程图
Figure 4. Flow chart of the phase demodulation algorithm based on centroid peak-finding method
图 5 10~60 dB信噪比对应的相位误差与位移误差。(a)过零点检测法；(b)质心寻峰法
Figure 5. Phase error and displacement error corresponding to 10~60 dB signal to noise ratio. (a) Zero-crossing detection method; (b) Centroid peak-finding method
图 6 调频连续波激光干涉位移传感器原理图
Figure 6. Schematic diagram of a frequency-modulated continuous-wave laser interference displacement sensor
图 7 调频连续波干涉位移测量系统实物图
Figure 7. Physical drawing of FMCW interferometric displacement measurement system
图 8 采集得到的拍频信号与锯齿波信号。(a)锯齿波调制信号；(b)拍频信号
Figure 8. Beat signal and sawtooth signal acquired. (a) Sawtooth signal; (b) Beat signal
图 9 过零点检测法固定F-P腔腔长44 mm时位移随机误差及分布。(a)固定距离位移随机误差；(b)随机误差分布
Figure 9. Random error and distribution of displacement when the length of the F-P cavity is 44 mm fixed by zero-crossing detection method. (a) Random error of displacement fixed distance; (b) Random error distribution
图 10 质心寻峰法固定F-P腔腔长44 mm时位移随机误差及分布。(a)固定距离位移随机误差；(b)随机误差分布
Figure 10. The random error and distribution of displacement when the length of the F-P cavity is 44 mm fixed by the centroid peak-finding method. (a) Random error of displacement fixed distance; (b) Random error distribution
图 11 不同F-P腔腔长过零点检测法与质心寻峰法的位移随机误差标准差对比图
Figure 11. Comparison of the standard deviation of displacement random error between zero-crossing detection method and centroid peak-finding method when F-P cavity length is different
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