外差激光干涉仪中的高精度相位测量研究
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摘要
空间引力波探测计划(如LISA, Laser Interferometer Space Antenna)和下一代地球重力场反演计划(如GRACE Follow-on mission)都将采用星间激光测距系统来测量卫星间的微小位移变化。星间距的变化引起激光拍频信号的相位变化,高精度的相位测量技术是星间激光测距系统中的关键技术之一,也是本课题研究的重点。
在空间激光测距的地面演示实验中,我们逐步搭建了十米基线的激光外差测距平台和基于零差锁相环的应答式激光干涉仪,另外在基于silicate bonding粘接工艺的干涉仪上利用自研的锁相环相位计实现了皮米量级的位移测量和定位控制。
针对地面的激光干涉测距系统,我们发展了基于相关分析的相位测量技术,其基本原理是正弦信号的互相关函数零时刻值与其相位差的余弦值或正弦值成正比。我们比较了反正弦算法和反正切算法的优缺点；在选取了反正切算法之后,分析量化误差与随机误差的影响,着重讨论了非整周采样相位误差的影响,首次推导了非整周采样相位测量误差的表达式,这也是本文的创新点之一；最后,通过双路信号的差分测量实现了在1mHz～10Hz频段相位测量噪声本底达到1.2×10-6rad/HZ1/2,并验证了非整周采样误差的影响。实验结果表明,尽管该技术的测量噪声本底小,但不能满足未来星间激光测距中由于卫星间的相对运动造成的多普勒频移高达1MHz以上的条件。
因此,我们研制了基于锁相环原理的相位计,实现了相位测量噪声本底接近lx10-6rad/Hz1/2,主要受限于采样时间抖动和相位读取噪声。由于在星间激光测距中,接收到的激光功率十分微弱,测量信号的信噪比以及温度等环境变化将对相位测量电路产生影响。基于此,我们通过调制实验测量了相位与时钟抖动、温度、测量信号信噪比之间的关系。我们首次讨论了利用锁相环相位计测量星间速度的问题,并比较了直接读取法和相位差分法测速的噪声和精度,两种方法的测量精度分别受限于时钟的频率稳定度和相位输出的时间抖动,综合结果表明直接读取法更适合于星间测速。
我们将锁相环相位计应用于皮米量级的定位控制和激光外差锁相实验,定位控制的分辨率优于50pm,激光外差锁相完成了初步实验测试。
Inter-satellite laser ranging system is used to measure the change in inter-satellite distance for the next generation of the Earth's gravity recovery (e.g. GRACE Follow-on mission) and the spaceborne gravitational waves detection mission (e.g. LISA, Laser Interferometer Space Antenna). This tiny distance change will induce the phase shift of the beat note between the received and local laser beams. Hence, high precision phase measurement is one of the key techniques in the inter-satellite laser ranging system and is the major research work presented in this thesis.
In order to develop a high precision laser ranging system, we constructed a prototype of10-m-baseline heterodyne laser interferometer, and following a transponder-type interferometer with homodyne optical phase-locked loop (OPLL). Besides, a home-made digital PLL-based phasemeter was implemented with an ultra-stable heterodyne interferometer that was built by using silicate bonding technique for demonstrating picometer-level displacement measurement and positioning control.
In addition to PLL-based phasemeter, we develop another digital phase detection method based on the cross-correlation analysis. The basic principle is that the sine or cosine value of phase s is proportion to the cross-correlation value at zero time lag of two sinewave signals. The pros and cons between the arcsine and arctangent arithmetics are compared. When the latter method is chosen, the effects of sampling quantization error, intrinsic white noise, and non-integral-cycle sampling error on phase measurement are analyzed. We find that the non-integer-cycle sampling could result in a cyclic error that has not been reported ever. We use a high-performance data acquisition system to carry out the cross-correlation-based phase measurement. A noise level of1.2x10-6rad/Hz1/2@(1mHz～10Hz) is obtained, and the non-integral-cycle sampling error is observed.
The application of the phase measurement based on the cross-correlation is limited by the frequency change of the measured (interference) signal. The Doppler-induced frequency shift caused by the relative motion between two satellites is typically more than1MHz, so that the PLL-based phase measurement is a better method for most inter-satellite ranging applications. Therefore, we have develop a PLL-based phasemeter and achieve a background noise (dominated by sampling time jitter and phase readout noise) of about1x10-6rad/Hz1/2. The possible error sources, such as temperature fluctuation and intrinsic white noise, had been investigated. For inter-satellite range-rate monitoring, the direct read frequency (DRF) and differential phase time series (DPS) methods are compared, and the result show that the precisions are limited by the stability of the internal oscillator and the sampling-time jitter, respectively.
To demonstrate the useful applications of PLL-based phasemeter, we use it for picometer positioning control and heterodyne optical PLL. A resolution of50pm for positioning control with laser interferometer has been achieved, and the preliminary result of heterodyne optical phase locking will be discussed in the last chapter.
在空间激光测距的地面演示实验中,我们逐步搭建了十米基线的激光外差测距平台和基于零差锁相环的应答式激光干涉仪,另外在基于silicate bonding粘接工艺的干涉仪上利用自研的锁相环相位计实现了皮米量级的位移测量和定位控制。
针对地面的激光干涉测距系统,我们发展了基于相关分析的相位测量技术,其基本原理是正弦信号的互相关函数零时刻值与其相位差的余弦值或正弦值成正比。我们比较了反正弦算法和反正切算法的优缺点；在选取了反正切算法之后,分析量化误差与随机误差的影响,着重讨论了非整周采样相位误差的影响,首次推导了非整周采样相位测量误差的表达式,这也是本文的创新点之一；最后,通过双路信号的差分测量实现了在1mHz～10Hz频段相位测量噪声本底达到1.2×10-6rad/HZ1/2,并验证了非整周采样误差的影响。实验结果表明,尽管该技术的测量噪声本底小,但不能满足未来星间激光测距中由于卫星间的相对运动造成的多普勒频移高达1MHz以上的条件。
因此,我们研制了基于锁相环原理的相位计,实现了相位测量噪声本底接近lx10-6rad/Hz1/2,主要受限于采样时间抖动和相位读取噪声。由于在星间激光测距中,接收到的激光功率十分微弱,测量信号的信噪比以及温度等环境变化将对相位测量电路产生影响。基于此,我们通过调制实验测量了相位与时钟抖动、温度、测量信号信噪比之间的关系。我们首次讨论了利用锁相环相位计测量星间速度的问题,并比较了直接读取法和相位差分法测速的噪声和精度,两种方法的测量精度分别受限于时钟的频率稳定度和相位输出的时间抖动,综合结果表明直接读取法更适合于星间测速。
我们将锁相环相位计应用于皮米量级的定位控制和激光外差锁相实验,定位控制的分辨率优于50pm,激光外差锁相完成了初步实验测试。
Inter-satellite laser ranging system is used to measure the change in inter-satellite distance for the next generation of the Earth's gravity recovery (e.g. GRACE Follow-on mission) and the spaceborne gravitational waves detection mission (e.g. LISA, Laser Interferometer Space Antenna). This tiny distance change will induce the phase shift of the beat note between the received and local laser beams. Hence, high precision phase measurement is one of the key techniques in the inter-satellite laser ranging system and is the major research work presented in this thesis.
In order to develop a high precision laser ranging system, we constructed a prototype of10-m-baseline heterodyne laser interferometer, and following a transponder-type interferometer with homodyne optical phase-locked loop (OPLL). Besides, a home-made digital PLL-based phasemeter was implemented with an ultra-stable heterodyne interferometer that was built by using silicate bonding technique for demonstrating picometer-level displacement measurement and positioning control.
In addition to PLL-based phasemeter, we develop another digital phase detection method based on the cross-correlation analysis. The basic principle is that the sine or cosine value of phase s is proportion to the cross-correlation value at zero time lag of two sinewave signals. The pros and cons between the arcsine and arctangent arithmetics are compared. When the latter method is chosen, the effects of sampling quantization error, intrinsic white noise, and non-integral-cycle sampling error on phase measurement are analyzed. We find that the non-integer-cycle sampling could result in a cyclic error that has not been reported ever. We use a high-performance data acquisition system to carry out the cross-correlation-based phase measurement. A noise level of1.2x10-6rad/Hz1/2@(1mHz～10Hz) is obtained, and the non-integral-cycle sampling error is observed.
The application of the phase measurement based on the cross-correlation is limited by the frequency change of the measured (interference) signal. The Doppler-induced frequency shift caused by the relative motion between two satellites is typically more than1MHz, so that the PLL-based phase measurement is a better method for most inter-satellite ranging applications. Therefore, we have develop a PLL-based phasemeter and achieve a background noise (dominated by sampling time jitter and phase readout noise) of about1x10-6rad/Hz1/2. The possible error sources, such as temperature fluctuation and intrinsic white noise, had been investigated. For inter-satellite range-rate monitoring, the direct read frequency (DRF) and differential phase time series (DPS) methods are compared, and the result show that the precisions are limited by the stability of the internal oscillator and the sampling-time jitter, respectively.
To demonstrate the useful applications of PLL-based phasemeter, we use it for picometer positioning control and heterodyne optical PLL. A resolution of50pm for positioning control with laser interferometer has been achieved, and the preliminary result of heterodyne optical phase locking will be discussed in the last chapter.
引文
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[19]http://www.thinksrs.com/products/SR620.htm
[20]吴智睿.数字相位计的研究与设计：[硕士学位论文].哈尔滨：哈尔滨工程大学,2009.
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[2]Taylor J H, Fowler L A, McCulloch P M. Measurements of general relativistic effects in the binary pulsar PSR1913+16. Nature,1999,277(437)
[3]Weber J. Gravitational-Wave-Detector Events. Physical Review Letters,1968,20 (23):1307-1308
[4]Bender P, Brillet A, Cruise A M, et al. Laser Interferometer Space Antenna-A Cornerstone Mission for the observation of gravitational waves:System and Technology Study Report. ESA-SCI,2000.1～342
[5]Ballmer S W. LIGO interferometer operating at design sensitivity with application to gravitational radiometry:[PhD thesis]. USA: Massachusetts Institute of Technology,2006
[6]Bender P, Brillet A, Ciufolini I, et al. Laser Interferometer Space Antenna for the detection and observation of gravitational waves:Pre-Phase A Report (Second edition). Germany:the Max Planck Institute for Gravitational Physics,1998.1～206
[7]Danzmann K, Rudiger A. LISA technology-concept, status, prospects. Classical and Quantum Gravity,2003,20:S1～S9
[8]Bender P L, Hall J L, Ye J, et al. Satellite-Satellite Laser Links for Future Gravity Missions. Space Science Reviews,2003,108:377～384
[9]Hough J, Robertson D, Ward H, et al. LISA～The Interferomter. Advances in Space Research,2003,32 (7):1247～1250
[10]Jennrich O, Binetruy P, Colpi M, et al. Revealing a hidden Universe:opening a new chapter of discovery. European Space Agency, Yellow Book,2011.
[11]许厚泽.卫星重力研究：21世纪大地测量研究的新热点.测绘科学,2001,26(3)：1-4
[12]Nagano S, Hosokawa M, Kunimori H, et al. Development of a simulator of a satellite-to-satellite interferometer for determination of the Earth's gravity field. Review of Scientific Instruments,2005,76(124501):1～10
[13]Dehne M, Cervantes F G, Sheard B, et al. Laser interferometer for spaceborne mapping of the Earth's gravity field. Journal of Physics:Conference Series 154 (7th International LISA Symposium),2009, (012023):1-6
[14]Pierce R, Leitch J, Stephens M, et al. Intersatellite range monitoring using optical interferometry. Applied Optics,2008,47(27):5007-5018
[15]Sheard B S, Heinzel G, Danzmann K, et al. Intersatellite laser ranging instrument for the GRACE follow-on mission. Journal of Geodesy,2012,86(12):1083-1095
[16]冉将军,许厚泽,沈云中等.新一代GRACE重力卫星反演地球重力场的预期精度.地球物理学报,2012,55(9)：2898-2908
[17]Scully M O, Zubairy M S. Quantum optics. United Kingdom:Cambridge University Press,1997.101
[18]葛宪生.用于相位测量的多通道信号采集和处理系统的设计：[硕士学位论文].哈尔滨：哈尔滨工程大学,2009.
[19]http://www.thinksrs.com/products/SR620.htm
[20]吴智睿.数字相位计的研究与设计：[硕士学位论文].哈尔滨：哈尔滨工程大学,2009.
[21]Liang Y R, Duan H Z, Yeh H C, et al. Fundamental limits on the digital phase measurement method based on cross-correlation analysis. Review of Scientific Instruments,2012,83(095110):1-6
[22]Wand V, Guzman F, Heinzel G, Danzmann K. LISA Phasemeter Development. in: Proceedings of the 6th International LISA symposium,2006, (873):689-696
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