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Abstract
We demonstrate a novel scheme to increase the accuracy of time-delay measurement of an insufficient stimulated Brillouin scattering (ISBS) based pulse compression system. It is realized by relating the time delay with the pulse compression gain, which is accumulated by a lock-in amplifier (LIA). We theoretically demonstrate that the time delay is proportional to the accumulated gain via the LIA. In the experiment, the pulse compression gain is accumulated through lock-in detection. It narrows down the detection bandwidth and reduces the influence from the broadband noise. The time-delay measurement is completed in a real-time manner and thus provides a possible solution to realizing a high-speed process in the future. The accuracy of measurement of a linear frequency modulated (LFM) signal with a bandwidth of 1 GHz is 1 ns.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Time-delay measurement is an efficient technology widely used in various aspects such as laser ranging, integrated optical sensor, and target detection [1–3]. In the last decade, several photonics-assisted schemes of time-delay measurement, such as oscillating optoelectronic oscillators [4], time-difference-of-arrival (TDOA) of a microwave [5], and pulse compression [6], have been proposed to improve the accuracy of measurement. Pulse compression is an important signal processing technique of high range resolution and strong detection power [6,7]. However, due to the limited bandwidth of electronic devices, problems occur when processing a broadband and high frequency microwave signal [8,9].
Recently, an all-optical pulse compression method based on stimulated Brillouin scattering (SBS) has been presented to realize time-delay measurement [10]. Stimulated Brillouin scattering is an acousto-optic interaction where the acoustic wave inherits the amplitude and phase information from the pump lightwave [11,12]. The SBS gain naturally satisfies the matched filtering response in the analog domain [13]. However, this method still demands a high-sampling-rate measurement since the range resolution of each pulse compression result must be extracted from the high-repetition-rate probe pulse train to calculate the time delay. It is against the original intention of applying the time-delay method in a low-sampling-rate measurement through the SBS process in the analog domain. Besides, the time-delay measurement is either a real-time or a high-speed process since the computational process is performed in the back end.
In this letter, we propose a novel scheme to improve the accuracy of measurement by changing the time-delay measurement into the pulse compression gain detection. The experiment is carried out via insufficient SBS (ISBS) interaction. Insufficient interaction occurs either when the counter-propagating pump and probe lightwaves interact with each other partially or when the interaction time is too short to accumulate the SBS gain. The pulse compression gain is found to be proportional to the interaction part, which is dependent on the time delay through theoretical analysis. Lock-in detection is applied in the pump lightwave to accumulate the insufficient pulse compression gain. Eventually, a one-to-one corresponding relationship between the time delay and the accumulated ISBS based pulse compression gain is established. Compared with the method in [10], this method contributes to transferring the high-sampling-rate measurement to a low-sampling-rate one, providing a possible solution to realizing a real-time and high-speed process. Thanks to lock-in detection which reduces the noise influence, the proposed method increases the accuracy of measurement of the time delay from 7 ns to 1 ns when the linear frequency modulated (LFM) signal with a bandwidth of 1 GHz is experimentally tested.
2. Principle
Most SBS-based applications, such as optical filters, optical delay lines, and optoelectronic oscillators, utilize sufficient SBS interaction [14–16]. Therefore, in conventional setups, researchers mainly focus on the schemes to ensure that the pump and probe lightwaves can interact with each other more sufficiently to produce a higher gain. For example, the fiber under test in the SBS sensing scenario typically has an enough length of over 100 km. Insufficient interaction leads to reduced SBS and gain fluctuations such as output noise, thereby affecting the performance of the system [17]. A number of studies have been carried out to suppress the insufficient SBS interactions. However, in our proposed method, not only the insufficient SBS interaction is utilized but also the insufficiency is amplified instead of suppressed.
The working principle of the time-delay measurement which exploits the ISBS based pulse compression gain is illustrated in Fig. 1. The microwave signal with an unknown time delay $\Delta t$ is modulated on the pump lightwave. The microwave signal has a period of ${T_{pump}}$ and its duration is $\tau $. The counter-propagating probe lightwave is a high-repetition-rate pulse train (the repetition rate, typically tens of MHz, is higher than the reciprocal of the period of the microwave signal). The probe lightwave has a period of ${T_{probe}}$. When the first pulsed pump lightwave is launched into the fiber, the nearest probe pulse, i.e. the K-th probe pulse, is the first to interact with the pump lightwave in Fig. 1(a). The time delay $\Delta t$ of the microwave signal is defined as the time difference between the first modulated pump is received and the first probe pulse enters the fiber. A preliminary coarse estimate of $\Delta t$ can be decided between the (K-1)-th and K-th probe pulse, i.e. $({K - 1} ){T_{probe}} + T < \Delta t < K{T_{probe}}$, where T denotes the time for travelling through the fiber. In order to obtain the exact time-delay information, a more accurate estimate within the probe lightwave period is essential.
Fig. 1. Working principle of the time-delay measurement via accumulating the ISBS based pulse compression gain. (a) Insufficient SBS interaction between the pump and probe lightwaves. (b) Several probe pulses meet different portions of the pump lightwave and the entire compressed probe pulse train.
The following analysis is focused on the probe lightwave period. If the condition of ${T_{probe}} < \tau $ is satisfied, the K-th probe pulse only encounters a small portion of the pump pulse signal. The SBS interaction between the probe and pump lightwaves is insufficient. The pulse compression gain carried by ISBS interaction is less than its counterpart by sufficient SBS interaction where the probe pulse meets the entire pump lightwave signal. If the optical fiber is long enough ($T > \tau $), there are several probe pulses with sufficient SBS interaction. Otherwise, all interactions are insufficient. Consequently, the pulse compression gain of each probe pulse alters with a different interaction portion of the pump lightwave, which depends on the time delay.
The time-delay measurement in [10] is realized by relating the time delay with the pulse compression resolution. One has to measure the resolution of the pulse compression result in each probe pulse at first. The measurement is completed after transferring the resolution into time-delay information. The pulse compression resolution is measured on a high-repetition-rate probe pulse train ($1/{T_{probe}}$). Besides, the pulse compression result is drifting so the resolution is easily influenced by the unstable system. In order to achieve an accurate result, it is essential to measure several resolutions of each probe pulse and take an average. Consequently, the measuring process is either real-time or high-speed.
Compared with the method in [10], the proposed method of accumulating all the pulse compression gains and analyzing the variation of the accumulated gain drastically reduces the sampling rate ($1/{T_{pump}}$). The accumulating process is realized through lock-in detection. Lock-in detection is commonly used in Brillouin optical correlation domain analysis (BOCDA) to acquire the Brillouin gain spectrum [18,19]. It is known for its ability to detect signals deeply buried in the noise. However, it is seldom used in microwave signal processing. With lock-in detection, we accumulate the insufficient SBS gain in each probe pulse to obtain the time delay. This is similar to the process of locating and accumulating the correlation peak in BOCDA. The pulse compression gains of the probe pulses are measured through a lock-in amplifier (LIA) synchronized to the reference signal which is used for chopping the pulsed pump signal. The accumulated pulse compression gain is obtained through narrowing down the bandwidth of detection to the reference frequency. In this way, the broadband intense noise is reduced.
The principle of lock-in detection is illustrated in Fig. 2. The chopping signal, of which the frequency differs from the probe and pump lightwaves, is used to modulate the pump lightwave and serves as a reference signal for LIA. After counter-propagating with the chopped pump lightwave, the compressed probe pulses in Fig. 1(b) are also chopped with the same frequency. When these probe pulses enter the LIA, their modulation frequency is the same as the reference frequency. In this sense, the pulse compression gain is amplified and the noise with random frequency is reduced. The time constant of LIA is the same as ${T_{pump}}$. Hence, the output of LIA is constant and corresponds to a specific time delay. Another benefit of lock-in detection is that the LIA has a quick response. Once the probe pulses enter the LIA, the output is immediately processed and given in a real-time manner. Therefore, lock-in detection is a real-time and high-speed process which relieves the pressure from back-end digital signal processing.
The portion of the pump lightwave in the ISBS interaction alters as the time delay varies. The ISBS gain in each probe pulse alters with the time delay. The accumulated ISBS based pulse compression gain within the pulsed pump lightwave period also varies with the time delay, leading to a one-to-one corresponding relationship between the time delay and the accumulated gain. The SBS based pulse compression gain of the detected probe pulse is proportional to the autocorrelation function of the pump lightwave [13]:
As illustrated in Eq. (1), the pulse compression gain is proportional to the autocorrelation function of the pump lightwave. The difficulty and accuracy of the time-delay measurement depend on the waveform of the microwave signal. As long as the time-frequency relation of the microwave signal is monotonous, the signal is suitable for the proposed method. However, it is better to have a more linear time-frequency relation so that it can resist the influence of the noise and recover high accuracy time-delay information. The linear frequency modulation (LFM) signal is used in the following theoretical analysis and experiment.
The accumulated ISBS based pulse compression gain can be described by a Sinc function:
The time delay is only related to probe pulses with ISBS interactions. By combining these compressed probe pulses, the accumulated gain as a function of the time delay is given by:
The portion ${P_n}$ is denoted as:
Figure 3 depicts the simulation results of the accumulated pulse compression gain with and without lock-in detection as a function of time delays. The non-lock-in detection method is achieved by accumulating the pulse compression gains through digital signal processing in the back end. The lock-in detection method is achieved by accumulating the probe pulse train through the LIA. The time for travelling through the fiber T is 5 $\mathrm{\mu }\textrm{s}$ and the duration of the pump pulse signal $\tau $ is 4.096 $\mathrm{\mu }\textrm{s}$. The pump lightwave period ${T_{pump}}$ is 16.384 $\mathrm{\mu }\textrm{s}$ and the probe lightwave period ${T_{probe}}$ is 256 ns. The duration of the probe pulse signal is 0.5 ns. The white Gaussian noise is used to testify the system capacity of resisting noise influence. The signal to noise ratio (SNR) is set to 18 dB. The period of the chopping signal is (1/2)$\mathrm{\pi }$ $\mathrm{\mu }\textrm{s}$. Besides the phonon lifetime in the silica fiber is 10 ns [11]. Both of the methods prove the one-to-one corresponding relationship between the time delay and the accumulated pulse compression gain in Fig. 3(a) and Fig. 3(b). The relation curve in Fig. 3 is defined as the amplitude comparison function (ACF). Comparing Fig. 3(b) with Fig. 3(a), the lock-in detection method has a higher linearity and is robust to noise influence.
Fig. 3. Simulation results of the amplitude comparison function (ACF) curve (a) with and without noise using digital signal processing in the back end and (b) with and without noise using lock-in detection. The gain is normalized to the maximum value.
3. Experimental results
The experimental setup is depicted in Fig. 4. The lightwave is generated from a distributed-feedback laser diode (DFB-LD, NEL NLK1C6DAAA) and is divided into the upper and lower light paths by a 50:50 fiber coupler. The lightwave in the upper path is modulated by an LFM pulse signal through a single sideband modulator (SSBM1, Photline MXIQ-LN-40) and serves as the pump lightwave. The lightwave in the lower path, which is shaped by a high-repetition-rate pulse train via an electro-optic modulator (EOM, Eospace AX-6K5-10-PFU-PFUP-R4), is used as the probe lightwave. Both modulation signals are generated by an Arbitrary Waveform Generator (AWG1, Keysight M8195A). The modulated pump lightwave is chopped by an AWG2 (Keysight 81150A) through SSBM2. Erbium-doped fiber amplifiers (EDFA1, EDFA2 and EDFA3) are utilized to compensate for the power loss after modulation and optimize the optical power of the pump and probe lightwaves. The pump and probe lightwaves are launched into the dispersion compensation fiber (DCF) from two ends. The average powers of the pump and probe lightwaves to enter the fiber are 18 dBm and 10 dBm, respectively. The ISBS based pulse compression gain is converted into electrical voltage through a photo-detector (PD) and is separated by a power divider. One of the outputs is input into an oscilloscope (OSC, Tektronix DSA70804) for a coarse estimate of the time delay. The other one is put into the LIA (Signal Recovery, 7280 DPS Lock-in Amplifier) to obtain the ACF curve and an accurate estimate of the time delay. The reference signal used in the LIA is the same as the chopping signal produced by the AWG2. The processing unit (PU) is used to store and process the output of the LIA. An optical spectrum analyzer (OSA, YOKOGAWA AQ6370C) is used to monitor the sideband modulation of the pump lightwave. The DCF is chosen for a better SNR since it has a better Brillouin gain coefficient ${g_B}$ than the single mode fiber (SMF) [20]. The fiber length used for ISBS interaction is 1 km. The bandwidth of the PD is 300 MHz.
Fig. 4. Experimental setup of the time-delay measurement of a microwave signal by lock-in detection to accumulate the ISBS based pulse compression gain. DFB-LD: distributed-feedback laser diode. PC: polarization controller. AWG: arbitrary waveform generator. EOM: electro-optic modulator. SSBM: single sideband modulator. EDFA: erbium-doped fiber amplifier. DCF: dispersion compensation fiber. PD: photo-detector. OSC: oscilloscope. OSA: optical spectrum analyzer. LIA: lock-in amplifier. PU: processing unit.
The pump and probe lightwave parameters are the same as their counterparts in the simulation. The frequency range of the LFM pulsed pump signal starts from 9.6895 GHz, which is equal to the Brillouin frequency shift (BFS). The bandwidth of the LFM pulsed pump signal is 1 GHz. A cosine signal is used as the chopping signal and its period is (1/2$)\mathrm{\pi }{\; \mathrm{\mu} s}$. Since the light path lengths of pump and probe lightwaves are uncertain, the time difference between the pump and probe pulse signals generated by AWG1 is used as the time delay. The coarse estimate of the time delay focuses on which probe pulse is the first one to interact with the pump lightwave. However, the accurate estimate of the time delay cares for the exact time within the probe lightwave period. In this case, we change the time delay from 0 ns to 256 ns which is equal to the probe lightwave period to testify the relationship and obtain the ACF curve. Figure 5(a) shows the coarse estimate of time delay before accumulating. Although the SBS gain of each probe is modulated with a cosine function, the trend of the envelope of the gains in first several probe pulses is rising which means the SBS gain increases along with the increase of the time delay in each probe pulse. It proves that the SBS interactions in these probe pulses are insufficient. The coarse estimate can be decided by locating the first interaction pulse. However, it is hard to determine it since the SBS gain varies as a cosine function. Therefore, we use the reflection of the pump lightwave to determine the first interaction probe pulse, namely the 0-th probe pulse. The frequency of the reflection lightwave is about 10 GHz away from probe lightwave. Note that it does not affect the pulse compression results and can be eliminated by an optical filter. After applying lock-in detection and going through the time delay within ${T_{probe}}$, the ACF curve is obtained in Fig. 5(b). In order to measure the time delay of an unknown signal, we have to obtain the system ACF curve at first. Then the first interaction probe pulse determines the coarse estimate of the time delay. After comparing the accumulated gain with the ACF curve, the accurate estimate of the time-delay measurement is completed. Combining both the coarse and accurate time delay results, the estimate of the time delay is fulfilled.
Fig. 5. Experimental results of (a) the coarse estimate and (b) the accurate estimate with the measured ACF curve.
Another issue worth discussing is the accuracy of measurement. Figure 6 compares the experimental ACF curve with the ideal one according to Eq. (3). The accuracy is defined as the average error of the experimental results. It is calculated by taking the average of each time delay error with the ideal time delay as a function of the normalized LIA output. Comparing with the method in [10], the accuracy of the time-delay measurement is improved from 7 ns to 1 ns. When the interaction portion of the pump lightwave is less than the lifetime of the phonon, the actual Brillouin gain spectrum spreads. Therefore, when the time delay changes from 0 ns to 256 ns, the accumulated gain grows slower in the first 10 ns.
Fig. 6. Comparison between the measured ACF curve and the ideal ACF curve. The gain is normalized to the maximum value.
4. Conclusion
We demonstrate a novel scheme of time-delay measurement in an ISBS based all-optical pulse compression system. The scheme establishes the relationship between the time delay and the accumulated pulse compression gain through theoretical derivation. With lock-in detection to realize the accumulating process, the detection bandwidth is narrowed down and the high-sampling-rate measurement is transferred into a low-sampling-rate one. Additionally, the pulse compression gains are amplified and the noise influence is reduced, keeping high linearity of the ACF curve. The average accuracy of measurement when testing an LFM signal with a bandwidth of 1 GHz is about 1 ns. As a matter of fact, the scheme provides a possible solution to realizing a high-speed time-delay measurement system in a real-time manner in the future.
Funding
National Key Research and Development Program of China (Program No. 2019YFB2203700); National Natural Science Foundation of China (Grant No. 61822508).
Disclosures
The authors declare no conflicts of interest.
See Supplement 1 for supporting content.
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