Open Access
Add to BibSonomy
Abstract
The laser scanning interferometry system has been successfully applied to many measurement fields because of its efficient measurement ability. However, the practical application ability of this measurement method is restricted due to the laser tuning nonlinearity. In this paper, the fiber ring resonator is equidistant in the frequency domain, which is used as the external clock signal to resample the main interference signal so as to realize the equifrequency sampling of the laser scanning interference system and correct the tuning nonlinearity. The final experimental result shows that this method can effectively reduce the phase noise caused by tuning nonlinearity and improve the performance of the system.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. INTRODUCTION
Laser tuning interferometry systems have attracted extensive attention because of their superior performance in the fields of length measurement, distributed optical fiber sensors, communication network monitoring, etc. The beat signal has a corresponding functional relationship with the frequency of the tuning laser, which is used to identify any position of the sensing fiber. However, tuning nonlinearity will break this relationship and reduce the addressing ability, which will greatly affect the performance of the system in practical engineering applications, Therefore, how to solve this problem has become a research frontier [1,2].
At present, tuning nonlinearity can be corrected mainly by adding an auxiliary optical path to the system to obtain the instantaneous phase or optical frequency information of the laser and processing the main interference signal through the corresponding algorithm [3]. Bowen used a Mach–Zehnder interferometer to obtain a sinusoidal signal, extracted the zero crossing point as the external clock signal, and resampled the measurement signal of the main interferometer to realize equal frequency sampling of the system [4]. Ahn also used a Mach–Zehnder interferometer and Hilbert transform to obtain the phase information of the tuning laser, subdivided it into equal phases, then sampled the main interferometer signal in equal frequencies [5]. The advantage of this method is that the structure of the system is simple, but it is not effective in practical engineering application, because the zero crossing is easy to be disturbed and fluctuates, and the subsequent processing is complex. Deng used a Fabry–Perot etalon to solve the above problems [6]. Since the Fabry–Perot etalon is essentially a resonator, its transmission spectrum is a series of equidistant single peaks in frequency, which can directly carry out equal frequency sampling on the main interference signal so there is no need for subsequent processing. According to the Nyquist criterion, the external clock signal should be twice the frequency of the measurement signal; however, the Fabry–Perot etalon free spectral range (FSR) is large due to its own length limitation, which ultimately affects the measurement length of the system. It can be seen that the complexity and applicability of subsequent algorithms limit the further development and application of tuning nonlinear correction.
In this paper, a nonlinear correction method of tuning laser based on fiber ring resonator is introduced. By resampling the main interference signal through the transmission spectrum from the optical fiber ring resonator, this method can reduce the complexity of the system. Furthermore, different free spectrum ranges can be set due to the adjustable length of the optical fiber in the resonator. The first part mainly introduces the current methods for correcting tuning nonlinearity; The second part presents the influence of tuning nonlinearity; te third part gives the principle of nonlinear correction of scanning interference system based on ring resonator; the fourth part builds experiments to verify our method.
2. INFLUENCE OF TUNING NONLINEARITY
This part introduces the working principle of the scanning interference system. If the laser has tuning nonlinearity, the output optical frequency is
where ${v_{{\rm non}}}(t)$ is the instantaneous frequency in the case of nonlinear tuning, and ${v_n}(t)$ is the tuning nonlinear term. Hence, the light fields of the measurement arm and the reference arm can be expressed as [7]
Fig. 1. Spectrum diagram obtained by Fourier transform when the laser is (a) linear tuning and (b) nonlinear tuning.
3. NONLINEAR CORRECTION METHOD BASED ON RING RESONATOR
This part mainly presents the principle of the optical fiber ring resonator. The structure diagram is shown in Fig. 2. The laser enters the coupler from port 1 and splits into two beams, one of which is coupled to port 3; the other enters the loop from port 4 and propagates to port 2, where it enters the coupler and forms a cycle [8,9].
According to [9], and considering the boundary conditions ${k_r} = {1 -}({1 -}{\eta _0})({1 -}{\delta _0}){e^{- 2\alpha L}}$, the relationship between port 3, port 4, and port 1 is expressed as
As can be seen from the above description, the transmission spectrum of the ring resonator is equidistant in the frequency domain, so the nonlinearity can be reflected by the peak interval in the time domain (also known as the transmission light field), which is used as the external clock signal to resample the main interference signal, so as to correct the phase noise caused by the nonlinearity of the tuning laser, as shown in Fig. 4.
In order to simplify the calculation process, the initial phase of the interference signal is not considered, so formula (2) can be written as
According to formula (4), the FSR of the output transmission spectrum of the ring resonator is only related to the cavity length and refractive index, so the position of each peak in the transmission spectrum in the frequency domain can be expressed as
where $m = {1},{2},{3} \ldots$, and ${v_c}$ is the initial frequency. The interference signal is resampled with each peak value as the sampling point, so formula (5) can be expressed as where summation represents resampling of the original signal, and ${\phi _c}$ is the initial phase introduced by ${v _c}$. It can be seen from the above process that by using the transmitted light field of the ring resonator as the trigger signal, the equal frequency sampling of the interference signal is realized, so that the phase term of nonlinear tuning in the signal disappears and becomes the term only related to FSR, thus correcting nonlinearity. It should be noted that in order to ensure all the information reflects the original signal, according to the Nyquist criterion, the resampling rate should be more than twice the frequency of the original signal.The resampling rate can be expressed numerically as
where $\gamma$ is the tuning speed. Assuming that the refractive index of the single-mode fiber is 1.5 and the tuning range of the scanning interference system is 250 GHz/s, the relationship between the FSR and the resampling rate and the length of the ring resonator is shown in Fig. 5. In order to ensure the Nyquist criterion, the resonator length needs to be increased for long-range measurement to improve the resampling rate.Fig. 5. (a) Relationship between FSR and length; (b) relationship between resampling rate and length.
According to the above process, we can control the FSR by changing the resonator length so as to control the resampling rate of the system, which is the same as the principle of the Fabry–Perot etalon and the Mach–Zehnder interferometer. However, the principle of the Fabry–Perot etalon is to achieve resonance through two mirrors; the integration of the system will be limited if the length is increased for a higher resampling rate. In addition, the use of the Mach–Zehnder interferometer requires very complex signal processing, including Hilbert change and unwrapping, thus making the system even more complex. According to the above process, the advantage of nonlinear tuning correction using optical fiber ring resonator is that the FSR can be controlled only by changing the length of the delay fiber in the ring resonator, which can further greatly improve the integration of the system, and because the ring resonator’s output is already a pulse signal, we can directly extract the pulse position to resample the original signal while ignoring the subsequent signal processing such as Hilbert transform and unwrapping.
4. INFLUENCE OF TUNING NONLINEARITY
In this part, experiments were performed to verify the feasibility of the above methods. The schematic diagram of measuring the optical path is shown in Fig. 6. The coupler 1 divides the tuning light into the main interferometer and the ring resonator, samples two groups of signals at the same time, and then resamples the interference signal of the main interferometer. The experimental diagram of measuring the optical path is shown in Fig. 7. After actual measurement, the length of the ring resonator and the sensing fiber are 2 and 0.28 m, respectively. The spectral ratio of the coupler is 1:99. The detectors are PDA05CF2 InGaAs photodetector from Thorlabs, and the detection bandwidth is ${\rm DC}\sim{150}\;{\rm MHz}$. The sampling frequency of the acquisition card is 10 MHz.
The time-domain signals of the calibration optical path and the instrument are collected synchronously through the above system, and the acquisition results are obtained as displayed in Fig. 8(a) and Fig. 8(b), respectively. Figure 8(c) is a partial enlargement of Fig. 8(a), which shows that the experimental signal of the ring resonator is consistent with the simulation result. A Fourier transform is performed on the main signal of the instrument without resampling by the ring resonator; the results are shown in Fig. 9(a). It can be seen from the figure that the spatial resolution at the end of the sensing fiber is seriously reduced, and the signal at the joint is buried in the noise, indicating that the signal in the distance domain was seriously degraded and broadened due to the tuning nonlinearity.
Fig. 8. Experimental signal. (a) Transmission spectrum of ring resonator; (b) main interferometer signal; (c) local transmission spectrum of ring resonator.
Fig. 9. Distance domain signal of main interferometer (a) without nonlinear correction; (b) with nonlinear correction; (c) partial enlarged view of FC/APC position; (d) partial enlarged view of pigtail.
The position of the peak was recorded as the external clock signal to resample the interference signal and perform the Fourier transform. The results are shown in Fig. 9(b). The scattering intensity of the reflection points at each location is generally increased by 10 dB compared with that of Fig. 9(a). Two peaks of the signal can be clearly seen in the range domain, which are the FC/APC connector of the sensing fiber and the fiber tail, respectively. The local enlarged views of the two position signals are shown in illustrations 9(c) and 9(d), and the numbers in the figure represent the number of measuring points on the sensing optical fiber. Moreover, according to the calculation law $\Delta z = c/2n\Delta v$, the distance between sampling points of our experiment should be 400 µm, (the tuning range is 250 GHz, and the refractive index is 1.5), and the spatial resolution of FC/APC is 2.5 mm. Similarly, the spatial resolution of the fiber tail is 1.6 mm. In addition, the distance between FC/APC and the end of the optical fiber is calculated as 0.2852 m, which is different from the actual optical fiber because the linewidth of the laser leads to local noise in the system and the nonlinear correction is not complete. In addition, the signal intensity between sampling points at FC/APC is 5 dB, 7 dB lower than that at the end of the optical fiber because the intensity of the reflected light at the end of the optical fiber is higher due to Fresnel reflection. The above experimental result proves that our proposed method effectively reduces the phase noise caused by the tuning nonlinearity and greatly improves the signal-to-noise ratio and the spatial resolution.
5. CONCLUSION
In this paper, the nonlinear correction of a scanning interference system is realized by using a ring resonator. First, the working principle of the ring resonator is described. Second, the scanning interference system is presented, and the large phase noise is introduced due to tuning nonlinearity, which leads to the degradation of signal energy in the distance domain and the reduction of spatial resolution. Finally, the nonlinear correction method based on fiber ring resonator is introduced. The equal frequency sampling is realized by recording the position of the transmission light field of the ring resonator in the time domain as the external clock source so as to correct the tuning nonlinearity. The effectiveness of this method is verified by experiments. Compared with the Fabry–Perot etalon and auxiliary interferometer, this method has higher integration and lower complexity because the size of the system can be reduced by merely changing the delay fiber without complex subsequent processing.
Funding
National Natural Science Foundation of China (52075131).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
REFERENCES
1. M. Froggatt and J. Moore, “High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter,” Appl. Opt. 37, 1735–1740 (1998). [CrossRef]
2. S. Y. Zhao, J. W. Cui, and J. B. Tan, “Nonlinearity correction in OFDR system using a zero crossing detection-based clock and also the self-reference,” Sensors 19, 3660 (2019). [CrossRef]
3. E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express 16, 13139–13149 (2008). [CrossRef]
4. B. Feng, K. Liu, T. Liu, and J. Jiang, “Improving OFDR spatial resolution by reducing external clock sampling error,” Opt. Commun. 363, 74–79 (2016). [CrossRef]
5. T. J. Ahn and D. Y. Kim, “Analysis of nonlinear frequency sweep in high-speed tunable laser sources using a self-homodyne measurement and Hilbert transformation,” Appl. Opt. 46, 2394–2400 (2007). [CrossRef]
6. Z. W. Deng, Z. G. Liu, S. W. Gu, X. Jia, W. Deng, and H. Yan, “Frequency-scanning interferometry for depth mapping using the Fabry–Perot cavity as a reference with compensation for nonlinear optical frequency scanning,” Opt. Commun. 455, 124556 (2020). [CrossRef]
7. S. Venkatesh and W. V. Sorin, “Phase noise considerations in coherent optical FMCW reflectometry,” J. Lightwave Technol. 11, 1694–1700 (1993). [CrossRef]
8. Z. Xu, Q. Sun, B. Li, Y. Luo, W. Lu, D. Liu, P. P. Shum, and L. Zhang, “Highly sensitive refractive index sensor based on two cascaded microfiber knots with Vernier effect,” Opt. Express 23, 6662–6672 (2015). [CrossRef]
9. X. S. Yao and L. Maleki, “Optoelectronic oscillator for photonic systems,” IEEE J. Quantum Electron. 32, 1141–1149 (1996). [CrossRef]
