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Weak light phase locking is an important part of intersatellite laser interference ranging. Phase-locked loop (PLL) is used to track the phase of heterodyne interference optical signal. Owing to shot noise, laser frequency and other kinds of noise, there is a phase difference between the internal PLL local oscillator and the heterodyne signal, while the phase detection range of the PLL is only one period. If the phase difference exceeds the phase detection range at a certain time, the local oscillator may enter the wrong operating point under feedback regulation, resulting in cycle clip, which leads to subsequent phase reconstruction errors. In this paper, a cycle clip diagnosis method based on the detection background of gravitational waves is proposed. Based on the original PLL, an auxiliary frequency phase divider with larger phase detection range is introduced, which can provide a basis for judging whether the cycle clip occurs in the PLL. In this paper, a digital weak-light PLL model is established to evaluate the influence of various noise. The theoretical spectral density of the error phase is given according to the two main kinds of noise (laser phase noise and particle noise). Considering the limited detection range of PLL, large error phase may lead to cycle clip, making the PLL work at the wrong locking point. A phase meter with smaller frequency division phase range can be used to solve this problem. First, the input heterodyne sine signal is converted into in-phase square wave N frequency division. Then the phase difference is determined by comparing the output signal with output signal reduced by 1/N through the time-to-degital converter (TDC) Based on the theory of PLL and noise, the theoretical model of frequency division phase meter is established. The simulation results show that the frequency division phase meter can realize a wide range of phase detection under the current theoretical framework and has the ability to judge the cycle clip of weak light phase locking. It can be used in the weak- light phase locking task represented by LISA.
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Keywords:
- space gravitational wave detection /
- weak light phase locking /
- cycle slip /
- frequency division phase meter
[1] Danzmannk K, Prince T, Binetruy P 2011 LISA Assessment Study Report http://sci.esa.int/web/lisa/-/48364-lisa-assessment-study-report-yellow-book 2011 [2022-10-1]
[2] Gong X, Xu S, Bai S, et al. 2011 Class. Quantum Grav. 28 094012
Google Scholar
[3] eLISA Consortium 2013 arXiv: 1305.5720 v1 [astro-ph]
[4] Luo Z R, Liu H S, Jin G 2018 Opt. Laser Technol. 105 146
Google Scholar
[5] Bender P. L, Begelman M. C, Gair J. R 2013 Class. Quantum Grav. 30 165017
Google Scholar
[6] Danzmann K, Rudiger A 2003 Class. Quantum Grav. 20 1
Google Scholar
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Google Scholar
[8] Sheard B S, Heinzel G, Danzmann K, Shaddock D A, Klipstein W M, Folkner W M 2012 J. Geodesy 86 12
[9] Paul W M 2005 Class. Quantum Grav. 22 243
Google Scholar
[10] Dong Y, Liu H, Luo Z R, Li Y, Jin G 2016 Sci. China Tech. Sci. 59 730
Google Scholar
[11] Gerberding O, Sheard B, Bykov L, et al. 2013 Class. Quantum Grav. 30 235029
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[23] 梁浴榕 2013 博士学位论文 (武汉: 华中理工大学)
Liang Y R 2013 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese)
[24] Francis S P 2017 Ph. D. Dissertation (Canberra Australian: National University)
[25] Miller R L 1937 Proc. I. R. E 27 446
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图 1 星间激光干涉系统及锁相环
Figure 1. Intersatellite laser interference system and phase-locked loop (PLL).
图 2 锁相环构成
Figure 2. Phase locked loop structure.
图 3 线性锁相环模型框图
Figure 3. Block diagram of the linearized PLL model.
图 4 误差相位标准差与带宽关系 (a)自由运转激光; (b)稳频激光
Figure 4. Standard deviation of phase error as a function of bandwidth: (a) Free-running laser; (b) frequency-stabilized laser.
图 5 锁相环中的周跳
Figure 5. Cycle slipping in a phase locked loop.
图 6 (a)方波信号相位差测量; (b)分频后的方波信号
Figure 6. (a) Square wave signal phase difference measurement; (b) square wave signal after frequency division.
图 7 分频相位计模型
Figure 7. Frequency division phase meter model.
图 8 (a)构造的激光相位噪声谱密度与谱密度理论值; (b) 构造的散粒噪声谱密度与谱密度理论值
Figure 8. (a) The constructed spectral density and theoretical value of spectral density of laser phase noise; (b) the constructed spectral density and theoretical value of spectral density of granular noise.
图 9 (a)滤波后得到的正弦信号序列; (b)将正弦信号转方波并经过10分频后的结果
Figure 9. (a) The sinusoidal signal sequence obtained after filtering; (b) converting sinusoidal signal into square wave and passing through 10 frequency division.
图 10 分频相位计输出正确地表示相位差
Figure 10. The output of frequency divider phase meter correctly represents the phase difference.
图 11 (a), (b) NCO相位减小或增大
$2{\text{π }}$ 分频相位计的输出; (c), (d) NCO相位减小或增大$4{\text{π }}$ 分频相位计的输出; (e), (f) NCO相位减小或增大$6{\text{π }}$ 分频相位计的输出Figure 11. (a), (b) NCO phase decreases or increases by one period, the output of the frequency divider phase meter; (c), (d) NCO phase decreases or increases for two periods, the output of the divider phase meter; (e), (f) NCO phase decreases or increases for three periods, the output of the divider phase meter.
图 12 一段时间内的误差相位和分频相位计输出
Figure 12. Error phase and frequency division phase meter output over a period of time.
表 1 弱光锁相噪声总结
Table 1. Noise of weak light phase locking.
噪声名称 谱密度/(${\text{cycles} } \cdot { { {\text{Hz} } } ^{ - 1/2} }$) 噪声性质 激光相位噪声 $4.77 \times (1\;\text{Hz}/f)$ 相位噪声 NCO读出噪声 $9 \times {10^{ - 14}}$ 相位噪声 寄存器量化噪声 $0.6 \times ({ { { {10}^{ - 6} }~{\text{Hz} } } }/{f})$ 相位噪声 时钟噪声 $2.1 \times (10^{-6}\;{\rm Hz}/f)$ 相位噪声 散粒噪声 $6.9 \times {10^{ - 6}}$ 加性噪声 ADC量化噪声 $0.56 \times {10^{ - 6}}$ 加性噪声 
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[1] Danzmannk K, Prince T, Binetruy P 2011 LISA Assessment Study Report http://sci.esa.int/web/lisa/-/48364-lisa-assessment-study-report-yellow-book 2011 [2022-10-1]
[2] Gong X, Xu S, Bai S, et al. 2011 Class. Quantum Grav. 28 094012
Google Scholar
[3] eLISA Consortium 2013 arXiv: 1305.5720 v1 [astro-ph]
[4] Luo Z R, Liu H S, Jin G 2018 Opt. Laser Technol. 105 146
Google Scholar
[5] Bender P. L, Begelman M. C, Gair J. R 2013 Class. Quantum Grav. 30 165017
Google Scholar
[6] Danzmann K, Rudiger A 2003 Class. Quantum Grav. 20 1
Google Scholar
[7] Shaddock D, Ware B, Halverson P G, Spero R E, Klipstein B 2006 AIP Conf. Proc. 873 654
Google Scholar
[8] Sheard B S, Heinzel G, Danzmann K, Shaddock D A, Klipstein W M, Folkner W M 2012 J. Geodesy 86 12
[9] Paul W M 2005 Class. Quantum Grav. 22 243
Google Scholar
[10] Dong Y, Liu H, Luo Z R, Li Y, Jin G 2016 Sci. China Tech. Sci. 59 730
Google Scholar
[11] Gerberding O, Sheard B, Bykov L, et al. 2013 Class. Quantum Grav. 30 235029
Google Scholar
[12] Liao A C, Ni W T, Shy J T 2002 Int. J. Mod. Phys. D 11 1075
Google Scholar
[13] Samuel P F, Timothy T L, Kirk M, Andrew J S, Robert L W, David E M, Daniel A S 2014 Opt. Lett. 39 5251
Google Scholar
[14] Jiang Y Z, Jin X L, YEH H C, Liang Y R 2021 Opt. Express 29 18336
Google Scholar
[15] Liang Y R, Feng Y J, Xiao G Y 2021 Rev. Sci. Instrum. 92 124501
Google Scholar
[16] Wang G, Ni W T 2019 Res. Astron. Astrophys. 19 058
Google Scholar
[17] Xu M Y, Wu H Z, Liang Y R, Luo D, Wang P P, Tan Y J, Shao C G 2022 Sensors 22 7349
Google Scholar
[18] Gardner F M 2005 Phaselock Techniques (New Jersey: John Wiley&Sons) pp66–71
[19] Wand V, Guzman F, Heinzel G, Danzmann K 2006 AIP Conf. Proc. 873 689
Google Scholar
[20] Bykov I, Delgadol J, Marín Antonio F. G, Heinzel G, Danzmann K 2009 J. Phys. Conf. Ser. 154 012017
Google Scholar
[21] Valliyakalayil J T, Sutton A J H, Spero R E, Shaddock D A, Kirk M 2022 Phys. Rev. D 105 062005
Google Scholar
[22] Zhang Y, Hines A S, Valdes G, Guzman F 2021 Sensors 21 5788
Google Scholar
[23] 梁浴榕 2013 博士学位论文 (武汉: 华中理工大学)
Liang Y R 2013 Ph. D. Dissertation (Wuhan: Huazhong University of Science and Technology) (in Chinese)
[24] Francis S P 2017 Ph. D. Dissertation (Canberra Australian: National University)
[25] Miller R L 1937 Proc. I. R. E 27 446
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