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Abstract
We propose a laser ranging calibration optical path system using multiple optoelectronic oscillators (OEOs) that provides long range, high precision, low cost and high stability. A phase locked loop is used to control the length of the calibration optical path, which is measured with high precision by alternating the oscillations between the measurement loop and the reference loop. The calibration optical path length exceeds 9000 m with the stability of 6.8 µm during 3 minutes, and the relative measurement accuracy of the calibration optical path reaches 6.9 × 10−10.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Long-range, high-precision absolute distance measurement (ADM) is of fundamental importance in applications such as satellite ranging and large machinery manufacturing [1–3]. With the development of satellite formation technology, intense research interest has been given to measuring the distance between satellites via lasers with high precision to form a high-precision space measurement baseline [4,5], which can greatly improve the accuracy of ground and deep space observations [6]. With the launch of the GRACE, the K-band microwave radar on board can even measure inter-satellite relative distances with a precision of micrometer [5]. Additionally, in the free-space laser time-frequency transfer between satellites over a distance of tens of kilometers, it needs to measure the time delay of the optical frequency comb between satellites with an accuracy of femtosecond, which also means the intersatellite relative distances is measured with an accuracy of micrometer [7]. However, it is difficult to calibrate inter-satellite distances in orbit with high precision. Consequently, calibration technology for inter-satellite ranging equipment on earth shows important scientific significance. To meet the growing demand in these areas such as long-range, high-precision, and lower cost, many laser ranging calibration approaches have been designed and implemented, including Global Navigation Satellite System (GNSS) positioning, baseline calibration, vacuum pipeline calibration, and optical fiber calibration [8–11].
For the calibration technology of laser ranging, baseline calibration is a common method, and the distances between pillars can be determined at ground level from 3100 to 6000 m with uncertainties ranging from 0.1 mm to 0.3 mm [12]. Although extended-length standard devices have been established in several countries, they have not been universally adopted to calibrate laser ranging because of expense, even though they can achieve high precision. With the development of GNSS, using GNSS positioning to calibrate laser ranging has been proposed [4]. The GNSS is not only affordable but also convenient to form a kilometers of calibration optical path. Nevertheless, it’s difficult for GNSS to obtain higher accuracy than centimeter of calibration measurement [13]. In fact, atmospheric disturbance is the limitation for the distance measurement and calibration of baseline calibration and GNSS systems [14–16]. To overcome atmospheric disturbance, ranging and calibration in a vacuum pipeline has been proposed. Although a vacuum pipeline’s measurement accuracy can reach 10 µm, it is too costly to build kilometers of optical tunnel [9].
Due to the low loss and convenience, optical fiber can achieve kilometers optical length simply without atmospheric disturbance [17]. However, optical fiber is sensitive to temperature, polarization disturbance, light source wavelength disturbance and so on [18]. Only optical fiber with high stability and accurate length measurements can be utilized to simulate the spatial distances between satellites. Thus, inter-satellite ranging equipment can be calibrated indoors, which can bring great convenience to laser ranging field.
In this paper, we propose a novel method for solving the ground calibration problems and test long range and high-precision inter-satellite ranging load. We use a separate stability loop to get a stable calibration path and obtain its accurate length with measurement and reference loops at the same time. Using optoelectronic oscillators (OEOs), the compensation of optical fiber disturbances and high-precision measurements of long fiber length are achieved synchronously. To verify the feasibility of the method, a system experiment based on 9 km high-precision optical path is carried out. The experimental results show that the standard deviations of the optical length of the calibration path are about 6.4 µm and 6.8 µm during 2.2 seconds and 3 minutes test respectively when the calibration path average measurement optical length is about 9214.401952 m.
2. Experimental principle
2.1 Overview of general principles
To emulate an inter-satellite optical path on the ground, an optical fiber with high-stability and high-precision optical length is required. The basic structure of the optical calibration system based on OEOs is shown in Fig. 1. It consists of three self-starting OEOs which come together as a cross-reference architecture by wavelength division multiplexing (WDM), including a stability loop, measurement loop and reference loop.
As shown in Fig. 1, the orange line refers to the stability loop which contains a phase-locked loop (PLL) and piezoactuator (PZT). The black and red lines refer to the measurement loop and reference loop, which have commonalities in addition to the long single-mode fiber (SMF1, optical length of approximately 9 km) and PZT. SMF1 and PZT are used to form the calibration path shown as the green line in Fig. 1, which is used to emulate the long-range optical path between satellites. Additionally, the space optical path built by two collimators (CL) in the reference loop, which length is determined with high precision, is used as the measurement benchmark during the measurement process. By alternately oscillating the measurement loop and reference loop, the length of the calibration path can be measured with high precision. Besides, the calibration path is used to calibrate the the test ranging equipment (TE) by using a lens and mirror (MR) to connect the ranging equipment to the calibration system.
In this way, the length of the long-range calibration optical path is stable and can be measured with high precision by using multiple OEOs. We discuss how to control the optical length of the calibration path $L_d$ in Section 2.2. In addition, the determination of the calibration path’s optical length $L_d$ are given in Section 2.3. Finally, the usage method of the calibration system is described in Section 2.4.
2.2 Stability of the calibration path
Providing a long optical path with stable optical length is the core goal for a calibration instrument. Consequently, the calibration path is placed in the common part of the stability loop and measurement loop, and changes in the optical length due to environmental disturbance lead to the variations in the oscillation frequency of the stability loop.
According to the basic principle of optoelectronic oscillator (OEO) [19], the fundamental frequency of OEO $f_b$ is determined by the total group delay time $\tau$ of the loop. Then, the relationship between the fundamental frequency $f_b$ and the cavity length of the OEO loop $L$ can be expressed as
where $c$ is the speed of light in a vacuum, and $n$ is the equivalent refractive index of the OEO loop. In the experiment, the optical length of SMF1, the refractive index of which is approximately 1.5, is approximately 9 km. Since the length of the SMF1 is much longer than that of the rest part in the OEO, the estimated $L$ was about 9km. Owing to the advantage of the accumulative magnification effect in high-order oscillation mode $N_{h}$, the measurement accuracy of the optical path change $\Delta L$ can be vastly improved [20,21]. The high-order oscillation frequency $f_h$ will change greatly if the OEO oscillates in high-order oscillation mode $N_h$.Therefore, the cavity length $L$ of OEO when it oscillates at high-order oscillation mode can be given by
Thus, we can actively control the cavity length of the stability loop using a PLL with an ultra-stable reference signal [22]. When the length of the cavity loop changes, the PLL will control the PZT to compensate for it. Since the length of the calibration path is much longer than that of the remaining part of the OEO, the stability of the cavity loop length can be considered the stability of the calibration path. Therefore, the stability of the calibration path can be ensured.
2.3 Determination of the calibration path’s optical length $L_d$
According to Eq. (2), the entire loop length of OEO can be calculated by the oscillation frequency. However, the length of the calibration path cannot be accurately measured because the loop length of OEO includes not only the calibration path, but also other parts (such as the modulator, amplifier and photodetector). Additionally, it is difficult to distinguish the length change between the calibration path and the other components when the oscillation frequency changes. Consequently, we propose that the other components in addition to the calibration path share the common loop of the measurement loop and the reference loop. Although changes in environmental conditions will affect the length of the other components and lead to OEO frequency drifts, it can be eliminated by alternately oscillating the measurement loop and the reference loop at a sufficiently fast switching speed.
The OEO system oscillate between the measurement loop and reference loop alternately via the microwave switch (MR), thus the optical path is switched between the calibration path and the space optical path (1m), which length is accurately measured. The cavity length of the reference loop $L_r$ can be expressed as
where $L_s$ is the length of the space optical path, and $L_o$ is the optical length of the common part of the measurement loop and reference loop.As for the cavity length of the measurement loop $L_m$, it can be given by
where $L_d$ is the optical length of the calibration path. Since the measurement loop and reference loop share the OEO loop except for the calibration path and the space optical path, subtracting Eq. (4) from Eq. (3), yields the following equation:As $L_s$ is known, the cavity length $L_m$ and $L_r$ can be accurately measured by the high-order oscillation frequency of the measurement loop and reference loop, respectively. Therefore, the optical length of the calibration path $L_d$ becomes
In our experiments, both $L_m$ and $L_r$ contain $L_o$ as a common part of the measurement loop and reference loop. The measurement loop and reference loop oscillated alternately to eliminate the length change in the common part $L_o$ during the changes in environmental conditions. Consequently, the calibration path $L_d$ can be measured with high precision.
2.4 Calibration system usage
As mentioned above, a long-range optical path with high precision and high stability can be used for ground calibration and testing. The intense pulsed light (IPL) emitted by TEs can be coupled into the calibration path through CL3 and WDM1. Then, the IPL passes through the calibration path, which is composed mainly of SMF1 and PZT. Finally, the IPL output through WDM2, reflected by the reflector (MR) and then returned to the TE according to the original optical path. The optical path taken by the ranging pulse is twice the length of the calibration path to be measured. We can calibrate the ranging equipment by comparing the optical length of the ca1ibration path with the ranging results.
3. Experimental setup
3.1 Experimental schematic diagram
A schematic diagram of the optical calibration system based on OEOs is shown in Fig. 2. The modulators for both the stability loop and measurement loop are AM20 model of AFR, whose operating mode are linear points.
Fig. 2. Schematic diagram of the optical calibration system based on OEOs. LD: laser diode, MOD: modulator, OS: 2x2 magneto-optic switch, OC: optical couple, the coupling Ratio is 20:80, CL: collimator, SMF1: single-mode fiber, EDFA: erbium-doped fiber amplifier, PD: photodetector, AMP: amplifier, MS: microwave switch, BPF: bandpass filter, PS: phase shifter, MC: microwave coupler, MIX: mixer, LF: loop filter, PZT: piezoactuator, WDM: wavelength division multiplexing, PLL: phase-locked loop.
In the stability loop, light from laser diode 1 (LD1, optical output power of 10 mW, wavelength is 1550.92 nm and linewidth is 10 MHz) is introduced into modulator 1 (MOD1, modulation bandwidth of 20 GHz, transmission loss is 7.5 dB), the output of which is passed through the calibration path, which is shared by the stability loop and the measurement loop with WDM1 and WDM2. Then, the light signal is detected with PD1 (3 dB response bandwidth of 14 GHz), amplified by AMP1 and filtered by BFP1 (the center frequency is 10 GHz, 3-dB bandwidth is 10 MHz). Before being fed back to MOD1, the signal is introduced to microwave coupler 1 (MC1) and divided into two paths. One is introduced to feed back to MOD1 to form the stability loop and the other is introduced to the RF input of the PLL, filtered by the loop filter (LF), amplified by AMP2 and fed back to the PZT to realize phase-locked control. Additionally, we use an ultra-stable signal of 100 MHz generated from a rubidium atomic clock (for which the long-term stability of the frequency reaches $5\times 10^{-12}$ ) to serve as the reference frequency of the PLL. In this experiment, the experimental setup of 9 km length calibration path is mainly limited by the adjustment capability of the PZT. Nevertheless, the 9 km calibration path is also used to exploring the upper length limit of this system. A long optical fiber can be placed in the common part of the measurement loop and reference loop to form a high-Q cavity when the calibration path is too short to form a high-Q cavity.
Both the measurement loop and reference loop consist of LD2(optical output power of 10 mW, wavelength is 1550.14 nm and linewidth is 10 MHz), MOD2(modulation bandwidth of 20 GHz, transmission loss is 7.5 dB), OS, optical couple(OC, coupling ratio of 20:80), EDFA, PD2, MS and MC2. SMF1 and PZT are used to emulate the long-range optical path between satellites which is shared by the measurement loop and stability loop. The EDFA is used to amplify optical signals after the OC. The OC is used to coupling the measurement loop and reference loop together, and the coupling ratio of port C is $80{\% }$ while that of port D is $20{\% }$. Two collimators are placed at a fixed interval of 1m to form a stable space optical path in reference loop to serve as the measurement benchmark during the measurement process. The OS changes its status (parallel or cross), whereas the measurement loop and reference loop oscillate alternately. When the OS is in cross status, the calibration path to be measured is included in the measurement loop. In this status, the measurement loop was oscillated between the low-order mode and high-order mode alternately by using the MS. The light output of LD2 passes in turn through MOD2, OS, WDM1, SMF1, PZT, WDM2, EDFA, PD2 and MS. Besides that, when the MS switches to port E in the measurement loop, the low-order oscillation mode of measurement loop is selected. After port E of MS, the signal is introduced to the PS after amplification by AMP3 and filtration by BPF2(the center frequency is 300 MHz, and the 3-dB bandwidth is 10 MHz). When the MS switches to port F in the measurement loop, a high-order oscillation mode of the measurement loop is selected. The signal after port F of MS is introduced to MC3 after amplification by AMP4 and filtration by BPF3 (the center frequency is 9.9 GHz, and the 3-dB bandwidth is 10MHz). Before being fed back to MOD2, both high- and low- order oscillation frequencies are divided into two parts by MC3 and MC4. One is introduced to feed back to the MOD2 to form OEO loop and the other is introduced to frequency counter. When the OS is in the parallel state, the space optical path is included in the reference loop. Additionally, the reference loop works in the same way as the measurement loop.
According to Sections 2.2 and 2.3, when the OEO oscillates in high-order mode, the value of high-order $N_{h}$ in Eq. (2) can be $10^5-10^6$. Consequently, the measurement accuracy of the optical path of the OEO can be improved substantially with the help of the accumulative magnification effect. $N_{h}$ is given by
where $[]$ refers to the operation of rounding a number and $f_b^{*}$ denotes the roughly measured fundamental frequency. The correctness of $N_h$ is ensured as long as the accuracy of $f_b^{*}$ is guaranteed, allowing us to further obtain an accurate fundamental frequency $f_b$. Therefore, $f_b$ can be given by:After an accurate fundamental frequency $f_b$ can be measured, the loop length $L$ can be calculated with high precision. By substituting Eq. (7) and Eq. (8) into Eq. (2), $L$ can be rewritten as
To obtain an accurate cavity length of OEO, we need to complete the acquisition of the high-order oscillation frequency $f_h$ and correct oscillation mode number of high-order $N_h$. Taking the cavity length of the measurement loop $L_m$ as an example, the detailed calculation methodologies of the required parameters are given in Sections 3.2, 3.3 and 3.4.
3.2 Frequency acquisition
We can obtain an accurate cavity length if we can measure the fundamental frequency of the measurement loop $f_{bm}$ precisely. As the value of high order $N_h$ is an integer, to ensure the correctness of the value of $N_h$, the rough fundamental frequency of the measurement loop $f_{bm}^{*}$ should be in the range ${f_{hm}}/({N_{h}}+0.5)<{f_{bm}^{*}}<{f_{hm}}/({N_{h}}-0.5)$, where $f_{hm}$ is the high-order oscillation frequency of the measurement loop. Thus, the measurement accuracy of $f_{bm}^{*}$ should be within ${f_{hm}}/({N_{h}}-0.5)-{f_{hm}}/({N_{h}}+0.5)\approx \pm {f_{hm}}/(2{N_{h}}^2)$.
By recombining Eq. (2), to ensure the correctness of $N_h$, the measurement accuracy of the fundamental frequency should be higher than
where $L_m$ is the cavity length of the measurement loop.Since the length of the calibration path is much longer than that of the remaining part of the measurement loop, the estimated $L_m$ is approximately 9 km and the fundamental frequency of the measurement loop is approximately 33 kHz. To ensure the correctness of $N_h$, the error of the roughly measured fundamental frequency of the measurement loop $f_{bm}^{*}$ should be less than 0.05 Hz when the high-order oscillation frequency $f_{hm}$ is approximately 9.9 GHz.
Because the fundamental frequency of the measurement loop is much less than the 3-dB bandwidth of BFP2 and BFP3, the measurement loop may oscillate in an arbitrary mode within the bandpass when the measurement loop oscillates alternately in high- and low- order. Additionally, the differences in oscillation frequencies observed in different oscillation modes are multiples of the fundamental frequency. Therefore, the fundamental frequency can be measured in this way. Directly measuring $f_{bm}^{*}$ in high-order oscillation mode is unsuitable due to the limited accuracy of the frequency counter(1 Hz @ 10 GHz). However, please note that the frequency counter can reach higher resolution at low frequency (0.01 Hz @ 300 MHz), and the fundamental frequency can be measured directly in low-order oscillation mode when the oscillation frequency is 300 MHz. Consequently, the low-order mode oscillation is selected first to obtain the fundamental frequency.
Notably, circuits can lead to different group delay times when the MS directly selects the high- and low-order oscillation modes. The microwave phase shifter (PS) is subsequently adjusted by using a vector network analyzer (R&S ZHB40) to ensure that the two delays approximately equal.
Additionally, to improve the measurement speed and the accuracy of the high-order oscillation frequency $f_{hm}$, the high-order oscillation frequency after MC2 is mixed with a 9.55 GHz microwave source (Agilent E8257D) by MIX. The oscillation frequency is approximately 350 MHz after MIX and is acquired by the frequency counter with an accuracy of 0.01 Hz.
In next Section 3.3, we describe in detail how to calculate the precise fundamental frequency of the measurement loop $f_{bm}$ from low-order mode oscillation frequency.
3.3 Determination of the precise fundamental frequency $f_{bm}$
During the switch between the OS and MS, the low-order mode oscillation frequency of the measurement loop $f_{lm}$ are measured at different times, the differences of which are defined as $\Delta f_{mi}$. $\Delta f_{mi}$ are integer multiples of the fundamental frequency. The greatest common divisor of $\Delta f_{mi}$ are defined as $f_{bm\ gcd}$, and
where $\Delta N_{lm}^i$ is the mode number of $\Delta f_{mi}$. The $\Delta f_{mi}$ values lower than 150 kHz are chosen to calculate the fundamental frequency of the measurement loop to reduce the computational complexity.As $\Delta N_{lm}^i$ is an integer and $\Delta f_{mi}$ are lower than 150 kHz, the accuracy of $\Delta f_{mi}$ should be higher than $\pm \frac {c^2}{2n^2{L_m}^2\Delta f_{mi}}=3.7\ \mathrm {kHz}$ according to Eq. (10), which is easy to satisfy. In this case, $\Delta f_{mi}$ and $f_{bm\ gcd}$, for the purposes of calculation, can be rounded on the order of kHz.
Above all, $\Delta N_{lm}^i$ can be given by:
$f_{bm1}^*=\Delta f_{mi}/\Delta N_{lm}^i$ is defined as the roughly calculated measurement loop fundamental frequency. Additionally, we can obtain the correct low-order mode $N_{lm}$ by using $f_{bm1}^*$. However, to ensure the correctness of $N_{lm}$, the measurement accuracy of $f_{bm1}^*$ should be within $\pm \frac {c^{2}}{2n^{2}{L_{m}}^{2}f_{lm}}=\pm 2\,\mathrm {Hz}$ when the measurement loop oscillates in the low-order mode. This also means that the difference in the measurement loop length between two adjacent measurements should be within $cN_{lm}/(nf_{lm})-c(N_{lm}\pm 0.5)/(nf_{lm})=\pm c/(2nf_{lm})$, which is $\pm 0.33$ m. Meeting this requirement becomes easier when the measurement interval is short in our experiment. Hence, the values of the low-order oscillation mode $N_{lm}$ are given by Eq. (11) and Eq. (12):The fundamental frequency of the measurement loop $f_{bm2}^*$ is determined by the low-order oscillation frequency $f_{lm}$ and the value of the low-order oscillation mode $N_{lm}$, consequently, $f_{bm2}^*$ can rewritten as:
Since the measurement accuracy of is 0.01 Hz, the accuracy of the calculated fundamental frequency of the measurement loop $f_{bm2}^*$ can satisfy the requirement of $\pm$0.05 Hz, and the correctness of $N_{hm}$ can be guaranteed.
3.4 Data processing strategy
By substituting Eq. (14) into Eq. (2), the loop length of the measurement loop $L_m$ can be rewritten as
The length of the reference loop $L_r$ can be calculated in the same way. For the reference loops, the fundamental frequency $f_{br}$ is approximately 3.5 MHz when the loop length is approximately 86 m (mainly composed of erbium-doped fiber in EDFA, fiber pigtails of optical devices and circuit delays). In this experiment, a high-Q cavity can be formed by an 86 m cavity length so that the line-width of the reference loop oscillation frequency is on the order of mHz [23]. The alternate oscillation of the measurement loop and reference loop is realized by switching the status of the optical switch.
The complete measurement process is shown in Fig. 3(a). The OS changes in turn, while the measurement loop and reference loop oscillate alternately. The OS is switched at a frequency of 10 Hz. The OS and MS change their statuses at the same time, while the MS is switched at a frequency of 20 Hz. Therefore, the low- and high-order modes oscillate alternately when the measurement loop and reference loop oscillate, respectively. When measuring the measurement loop length $L_m$, the OS is set to port A, and the MS is switched in turn to measure $f_{lm}$ and $f_{hm}$ alternately. Afterward, the OS is set to port B, and $f_{lr}$ and $f_{hr}$ are measured alternately. Finally, $L_m$ and $L_r$ are calculated, as shown in Fig. 3(b). From Eq. (6), $L_d$ can be rewritten as:
Fig. 3. (a) Measurement process, P: parallel status, C: cross status, F: port F, E: port E; (b) loop length of the measurement loop and the reference loop.
4. Experimental results
4.1 Stability loop measurement
In the experiment, a PLL was added to control the loop length of the stability loop. The stability loop can be considered the loop length controller of SMF1 because SMF1 is the main part of the stability loop, the length of which is much longer than that of the other parts. To reduce the error caused by the other parts, the loop length of the other parts should be as short as possible. The oscillation frequency of the stability loop is stabilized when the loop length is successfully controlled. Additionally, a rubidium atomic clock (with a long-term frequency stability of $5\times 10^{-12}$ was used to serve as reference frequency. The stability of the OEO oscillation frequency, oscillating in 10 GHz, was measured when the PLL was locked. We measured the maximum oscillation frequency change $\Delta f_{h}$ in 3 minutes by using electrospectrometer (Agilent N9010A). The measurement results are shown in Fig. 4. When the PLL was locked, the change of the oscillation frequency of the stability loop was within 8 Hz. The relationship between the high-order oscillation frequency change $\Delta f_{h}$ and the fundamental frequency change $\Delta f_{b}$ is
According to Eq. (1) and Eq. (17), the change in the loop length of the stability loop $\Delta L_{stab}$ can be given by:
where $f_{stab}$ is the oscillation frequency of the stability loop and the loop length of the stability loop $L_{stab}$ was approximately 9000 m. In this case, $\Delta L_{stab}$ was within 7.4 µm.4.2 Length and precision of the calibration path
In the experiment, a rubidium atomic clock was also used as time reference for the frequency counter (Keysight 53230A) to ensure accurate frequency measurements. Additionally, the oscillation mode changed every 50 ms as the MS status changed. Therefore, five frequency points were acquired during every oscillation while the frequency counter’s gate time was 10 ms, whose average was taken as the oscillation frequency. Between 0 and 50 ms, the OS was set to parallel status, the MS was set to port E, the reference loop was oscillated in low-order mode and $f_{lr}$ was measured. Between 50 and 100 ms, the MS was set to port F, the reference loop was oscillated in high-order mode and $f_{hr}$ was measured. Then, between 100 and 150 ms, the OS was set to cross status while the MS was set to port E, the measurement loop was oscillated in low-order mode and $f_{lm}$ was measured. Between 150 and 200 ms, the MS was set to port F, the measurement loop was oscillated in high-order mode and $f_{hm}$ was measured, and so on. The results of the low-order and high-order mode oscillation frequencies are shown in Fig. 5. Here, the sampled frequencies are indicated by grey crosses.
The abandoned points, whose frequencies are between high- and low- order oscillation frequencies when the MS and OS are switching, are caused by the unstable oscillating stages of the OEOs. Each time the high- or low-order mode oscillates, five frequency points are obtained by a frequency counter, and the middle four frequency points are averaged. Additionally, the average values of $f_{lr}$ and $f_{lm}$ are indicated by red and black circles while $f_{hr}$ and $f_{hm}$ are indicated by green and orange squares, respectively, as shown in Fig. 5.
During the measurement process, mode hopping occurs, and $f_{lr}$ and $f_{lm}$ oscillate in different modes at different times. According to Section 3, from Eq. (11) to Eq. (14), the precise fundamental frequency of measurement loop $f_{bm}^{'}$ is approximately 32266.074 Hz and the precise fundamental frequency of reference loop $f_{br}^{'}$ is approximately 3475770.489 Hz. From Eq. (15), the loop length of the measurement loop and the reference loop are measured. To verify the measurement accuracy of $L_d$, we continuously measure the optical length of the calibration path 11 times and process it. As shown in Fig. 6(a), 11 measurement results are obtained, where the red circles indicate the loop length of the measurement loop and the black squares indicate the loop length of the reference loop. As we can see, $L_m$ and $L_r$ follow the same trend in length change. In our experiment, $L_m$ is about 9299.705369 m and $L_r$ is about 86.320375 m. From Eq. (13), the optical length of the calibration path $L_d$ is shown in Fig. 6(b) with blue diamonds. With the calibration path, the optical length is 9214.384994 m, and the standard deviation of $L_d$ are around 6.4 µm. The relative measurement accuracy of the calibration path reaches $6.9\times 10^{-10}$. Despite the similar trend changes in the length of the measurement loop and reference loop, the optical length of the calibration path tends to stabilize after mutual cancellation of the loop. Therefore, the impact of the environment on the measurement accuracy can be indeed reduced by the use of the reference loop to compensate for the change in the common part.
Fig. 6. (a) Measured loop length of the measurement loop and reference loop; (b) Calculated length of $L_d$.
4.3 Stability of the calibration path test
To verify the working stability of the system at room temperature, we conduct 3-minutes measurement contrast experiment of $L_d$ by enabling the stability loop or not. In the experiment, SMF1, WDM1, WDM2, OC and PZT are placed in an airtight box, and the length of $L_d$ was measure every 15 seconds and the measurement results are shown in Fig. 7.
Fig. 7. (a) Measured loop length under loop length control; (b) Measured loop length without loop length control.
As shown in Fig. 7(a), the loop length is measured under loop length control by the stability loop. In addition, the loop length is measured without loop length control, as shown in Fig. 7(b). The loop length of both the measurement loop and reference loop increase with time, which indicates that the length of the common part $L_o$ increasing with the increase of EDFA temperature. The standard deviation of $L_d$ are 6.8 µm during 3-minutes test when we control the loop length by using the stability loop. However, the standard deviation of the calibration optical path $L_d$ is 38.3 µm without using the stability loop. Due to the usage of the phase-locked loop, the stability of OEO’s cavity length is determined by the stability of the reference clock, which long-term frequency stability of $5\times 10^{-12}$. And thus, the repeatability and stability of our scheme can be ensured. In this case, the impact of the environment on the calibration loop length can be reduced by using the stability loop to compensate for the change in the calibration path.
4.4 Prospects for practical application
According to Section 4.3, our method can provide a stable calibration optical path. In the field of laser radar [24], communication [25], large machinery manufacturing [26] and measurement equipment [27], high-precision and large range are required for laser ranging. The performance of the optical calibration path stability realized by the current scheme shows that the system can flexibly build arbitrary length calibration optical paths within the 9 km optical range. Therefore, our scheme can be better suited to the calibration of ranging equipment in various field. Additionally, if the adjustment capability of the PZT is improved, the scheme can achieve longer lengths of stable optical calibration path in the future.
5. Conclusion
We propose a useful method for providing a length-stable calibration optical path with a length that can be measured precisely based on alternately oscillating OEOs. In our system, the calibration optical path is formed as the main part of the stability loop to keep the length of the calibration optical path stable. Additionally, the measurement loop and the reference loop are oscillated alternately to measure the length of the calibration optical path while eliminating the effects of environmental disturbances. We combine high-precision measurements and optical length stabilization together based on a long optical fiber (optical length is about 9 km), and the optical length of this highly stable calibration optical path can be measured with high precision (µm-level accuracy). The experimental results show that the standard deviation of the calibration optical path length are within 7 µm during 3 minutes as the relative measurement accuracy reaches $6.9\times 10^{-10}$. With future improvements in fiber tensioner performance, this scheme is expected to achieve longer lengths of stable optical calibration path. Moreover, this highly stable calibration path can be used in large-scale metrology and aerospace application in the future.
Funding
National Natural Science Foundation of China (61835003, 62005194).
Acknowledgments
We sincerely thank the editors and anonymous reviewers for their contributions to this paper.
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.
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