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Article(id=1322567036966916845, tenantId=1146029695717560320, journalId=1281212831689347082, issueId=1322567020940481144, articleNumber=null, orderNo=null, doi=10.14075/j.jgg.2025.05.155, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=research-article, receivedDate=1746633600000, receivedDateStr=2025-05-08, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793254153719, onlineDateStr=2026-10-29, pubDate=1776182400000, pubDateStr=2026-04-15, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793254153719, onlineIssueDateStr=2026-10-29, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793254153719, creator=13701087609, updateTime=1793254153719, updator=13701087609, issue=Issue{id=1322567020940481144, tenantId=1146029695717560320, journalId=1281212831689347082, year='2026', volume='46', issue='4', pageStart='392', pageEnd='521', issueExtLink='null', onlineDate='null', pubDate='1776182400000', pubDateStr='2026-04-15', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793254149899, creator='13701087609', updateTime=1793254149899, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=467, endPage=472, ext={EN=ArticleExt(id=1322567037151466222, articleId=1322567036966916845, tenantId=1146029695717560320, journalId=1281212831689347082, language=EN, title=Traceability Analysis of Length Reference Error of Laser Interferometry Absolute Gravimeter Based on Thermally Stable Frequency Laser, columnId=null, journalTitle=Journal of Geodesy and Geodynamics, columnName=null, runingTitle=null, highlight=null, articleAbstract=

The laser interferometry absolute gravimeter uses the stable frequency laser wavelength as the precise length reference, and the selection of reference source directly affects the accuracy and precision of the measurement results. We focus on the differences in engineering applications between iodine saturated absorption stable frequency lasers and thermally stable frequency lasers. The wavelength accuracy and repeatability of thermally stable frequency lasers are analyzed in detail. We construct a beat frequency measurement system based on iodine stable frequency laser reference, which achieves the measurement of wavelength accuracy and repeatability of thermal stable frequency laser. A statistical processing model with the same final result of absolute gravity measurement is spmpled to quantify the repeatability and accuracy of output wavelength of the tested laser. The results show that the output wavelength accuracy of the tested thermally stable frequency laser is better than 4×10-9 nm, and the repeatability is better than 1.86×10-6 nm. That is, during the locking process of the thermal stable frequency laser, the gravity measurement error caused by wavelength accuracy is much smaller than 1 μGal, and the absolute gravity measurement error caused by wavelength repeatability is 2.79 μGal, which is acceptable for the absolute gravity measurement requirement of 10 μGal observation accuracy. This provides a complete metrological basis for the engineering application of absolute gravity instruments based on thermal stable frequency lasers in field environment.

, authors=Zilu LI1, Qiong WU1, *, Yang ZHANG1, Yongzhuo NIU1, Yixiang TANG1, authorsList=Zilu LI, Qiong WU, Yang ZHANG, Yongzhuo NIU, Yixiang TANG, authorCompany=null, correspAuthors=Qiong WU, authorNote=null, correspAuthorsNote=null, copyrightStatement=All rights reserved. Unauthorized reproduction is prohibited., copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322567040032953080, articleId=1322567036966916845, tenantId=1146029695717560320, journalId=1281212831689347082, language=CN, title=基于热稳频激光器的激光干涉绝对重力仪长度基准误差溯源分析, columnId=1281933709121138897, journalTitle=大地测量与地球动力学, columnName=地球动力学, runingTitle=null, highlight=null, articleAbstract=

激光干涉绝对重力仪以稳频激光波长作为精密长度基准, 其基准源选择会直接影响测量结果的准确度和精度。针对碘饱和吸收稳频激光器与热稳频激光器的工程应用差异, 重点分析热稳频激光器的波长精度和重复性问题。通过构建基于碘稳频激光基准的拍频测量系统, 实现了热稳频激光器波长精度和重复性的测量, 对绝对重力测量最终结果相同的统计处理模型进行采样, 量化被测激光器输出波长的重复性和精度。结果表明, 被测热稳频激光器输出波长精度优于4×10-9 nm, 重复性优于1.86×10-6 nm。即热稳频激光器在锁定过程中, 波长精度引起的重力测量误差远小于1 μGal, 波长的重复性引起的绝对重力测量示值误差为2.79 μGal, 这对于观测精度为10 μGal的绝对重力测量需求而言可以接受, 为基于热稳频激光器的绝对重力仪器在野外环境下的工程化应用提供了完整的计量学依据。

, authors=李子路1, 吴琼1, *, 张旸1, 牛永卓1, 汤一翔1, authorsList=李子路, 吴琼, 张旸, 牛永卓, 汤一翔, authorCompany=null, correspAuthors=吴琼, authorNote=

李子路, 硕士生, 主要研究方向为激光干涉绝对重力仪研发, E-mail:

, correspAuthorsNote=
吴琼, 研究员, 主要研究方向为激光干涉绝对重力测量、重力梯度测量和相对重力测量仪器的研发与应用, E-mail:
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李子路, 硕士生, 主要研究方向为激光干涉绝对重力仪研发, E-mail:

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李子路, 硕士生, 主要研究方向为激光干涉绝对重力仪研发, E-mail:

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Repeatability test results of the tested laser wavelength

, figureFileSmall=null, figureFileBig=null, tableContent=
频差/MHz 频差精度/kHz 波长测量值/nm 波长精度/nm
399.454 2.99 632.990 678 7 3.99×10-9
401.079 1.12 632.990 676 5 1.49×10-9
402.888 0.69 632.990 674 1 0.92×10-9
402.989 1.04 632.990 673 9 1.39×10-9
401.891 0.91 632.990 675 4 1.22×10-9
400.586 0.93 632.990 677 2 1.24×10-9
输出波长平均值/nm 632.990 676
波长重复性/nm 1.86×10-6
重力加速度测量值误差/μGal 2.79
), ArticleFig(id=1322567044638298919, tenantId=1146029695717560320, journalId=1281212831689347082, articleId=1322567036966916845, language=CN, label=表1, caption=

被测激光器波长重复性测试结果

, figureFileSmall=null, figureFileBig=null, tableContent=
频差/MHz 频差精度/kHz 波长测量值/nm 波长精度/nm
399.454 2.99 632.990 678 7 3.99×10-9
401.079 1.12 632.990 676 5 1.49×10-9
402.888 0.69 632.990 674 1 0.92×10-9
402.989 1.04 632.990 673 9 1.39×10-9
401.891 0.91 632.990 675 4 1.22×10-9
400.586 0.93 632.990 677 2 1.24×10-9
输出波长平均值/nm 632.990 676
波长重复性/nm 1.86×10-6
重力加速度测量值误差/μGal 2.79
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基于热稳频激光器的激光干涉绝对重力仪长度基准误差溯源分析
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李子路 1 , 吴琼 1, * , 张旸 1 , 牛永卓 1 , 汤一翔 1
大地测量与地球动力学 | 地球动力学 2026,46(4): 467-472
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大地测量与地球动力学 |地球动力学 2026 , 46 (4) : 467 -472
基于热稳频激光器的激光干涉绝对重力仪长度基准误差溯源分析
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李子路, 硕士生, 主要研究方向为激光干涉绝对重力仪研发, E-mail:

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李子路1 , 吴琼1, * , 张旸1, 牛永卓1, 汤一翔1
作者信息
  • 1 中国地震局地球物理研究所, 北京, 100081
通讯作者:
吴琼, 研究员, 主要研究方向为激光干涉绝对重力测量、重力梯度测量和相对重力测量仪器的研发与应用, E-mail:
作者简介:

李子路, 硕士生, 主要研究方向为激光干涉绝对重力仪研发, E-mail:

Traceability Analysis of Length Reference Error of Laser Interferometry Absolute Gravimeter Based on Thermally Stable Frequency Laser
Zilu LI1 , Qiong WU1, * , Yang ZHANG1, Yongzhuo NIU1, Yixiang TANG1
Affiliations
  • 1 Institute of Geophysics, CEA, Beijing 100081, China
出版时间: 2026-04-15 doi: 10.14075/j.jgg.2025.05.155
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激光干涉绝对重力仪以稳频激光波长作为精密长度基准, 其基准源选择会直接影响测量结果的准确度和精度。针对碘饱和吸收稳频激光器与热稳频激光器的工程应用差异, 重点分析热稳频激光器的波长精度和重复性问题。通过构建基于碘稳频激光基准的拍频测量系统, 实现了热稳频激光器波长精度和重复性的测量, 对绝对重力测量最终结果相同的统计处理模型进行采样, 量化被测激光器输出波长的重复性和精度。结果表明, 被测热稳频激光器输出波长精度优于4×10-9 nm, 重复性优于1.86×10-6 nm。即热稳频激光器在锁定过程中, 波长精度引起的重力测量误差远小于1 μGal, 波长的重复性引起的绝对重力测量示值误差为2.79 μGal, 这对于观测精度为10 μGal的绝对重力测量需求而言可以接受, 为基于热稳频激光器的绝对重力仪器在野外环境下的工程化应用提供了完整的计量学依据。

热稳频激光器  /  绝对重力仪  /  长度基准误差  /  绝对重力测量

The laser interferometry absolute gravimeter uses the stable frequency laser wavelength as the precise length reference, and the selection of reference source directly affects the accuracy and precision of the measurement results. We focus on the differences in engineering applications between iodine saturated absorption stable frequency lasers and thermally stable frequency lasers. The wavelength accuracy and repeatability of thermally stable frequency lasers are analyzed in detail. We construct a beat frequency measurement system based on iodine stable frequency laser reference, which achieves the measurement of wavelength accuracy and repeatability of thermal stable frequency laser. A statistical processing model with the same final result of absolute gravity measurement is spmpled to quantify the repeatability and accuracy of output wavelength of the tested laser. The results show that the output wavelength accuracy of the tested thermally stable frequency laser is better than 4×10-9 nm, and the repeatability is better than 1.86×10-6 nm. That is, during the locking process of the thermal stable frequency laser, the gravity measurement error caused by wavelength accuracy is much smaller than 1 μGal, and the absolute gravity measurement error caused by wavelength repeatability is 2.79 μGal, which is acceptable for the absolute gravity measurement requirement of 10 μGal observation accuracy. This provides a complete metrological basis for the engineering application of absolute gravity instruments based on thermal stable frequency lasers in field environment.

thermally stable frequency laser  /  absolute gravimeter  /  length reference error  /  absolute gravity measurement
李子路, 吴琼, 张旸, 牛永卓, 汤一翔. 基于热稳频激光器的激光干涉绝对重力仪长度基准误差溯源分析. 大地测量与地球动力学, 2026 , 46 (4) : 467 -472 . DOI: 10.14075/j.jgg.2025.05.155
Zilu LI, Qiong WU, Yang ZHANG, Yongzhuo NIU, Yixiang TANG. Traceability Analysis of Length Reference Error of Laser Interferometry Absolute Gravimeter Based on Thermally Stable Frequency Laser[J]. Journal of Geodesy and Geodynamics, 2026 , 46 (4) : 467 -472 . DOI: 10.14075/j.jgg.2025.05.155
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重力场是反映地球内部物质结构及其变迁的地球物理基本场，高精度绝对重力观测资料是地震监测预报[1]、地球科学研究[2]、资源勘探[3]、惯性导航[4]、深空探索[5]等领域的基础战略数据。
随着精密机械、电子技术和激光技术的不断进步，国内外高精度绝对重力仪的研发和工程化、产品化开发得到快速发展，多家科研团体基于激光干涉或冷原子干涉原理，开展绝对重力测量仪器研究，构造样机并积极参与到国际绝对重力比对活动中[6]。目前国际上仅有美国Micro-g公司提供商用高精度绝对重力仪FG5-X和A-10型绝对重力仪，前者稳定测量环境的准确度为1~2 μGal[7]，而更适用于野外观测的A10型绝对重力仪的测量准确度为±10 μGal[8]；国内浙江大学[9]、华中科技大学[10-11]、中国科学技术大学[12]、北京大学[13]等单位开展了冷原子干涉型绝对重力仪的研制，中国地震局地球物理研究所[14]、中国计量科学研究院[15]、中国科学院精密测量科学与技术创新研究院[16-17]、清华大学[18]等单位开展了激光干涉型绝对重力仪的研制。
基于迈克尔逊干涉测量原理设计的激光干涉绝对重力仪，通过测量真空系统中做自由下落运动的落体相对于参考棱镜的时间-位移坐标，获取高精度重力加速度绝对值[19-20]，其测量结果通过长度基准和时间基准完成量值溯源。其中时间基准由铷原子频率标准提供，长度基准由稳频激光器提供[21]。稳频激光器可分为两种，一种是碘饱和吸收稳频激光器，其波长的重复性和精度一般优于1×10-10 nm，但在使用过程中对环境的要求较高，如电源纹波、环境振动、温湿度均会影响波长的锁定状态。另一种是热稳频激光器，虽然波长的重复性和精度一般在10-9 nm量级，但环境适应能力更强，一般可维持数月不失锁，是流动测量中激光干涉型绝对重力仪的首选光源[5]，热稳频激光器的波长精度和重复性也是测量结果的重要误差源。
本文基于碘稳频激光器构建激光波长拍频测量系统，对项目组激光干涉型绝对重力仪采用的热稳频激光器波长的重复性和精度进行测量，采用绝对重力测量结果总体均值和精度的标准计算方法，构建误差传递模型，对测量数据进行处理。通过波长重复性和精度分析，量化其对绝对重力测量结果的误差影响，为热稳频激光器在流动绝对重力测量中的应用提供理论支撑，同时给出μGal级激光干涉型绝对重力仪热稳频激光器波长重复性和精度的需求技术指标。
1 热稳频激光波长及精度测试方法
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1.1 热稳频激光波长及精度对绝对重力测量结果的误差分析
激光干涉型绝对重力仪在每次测量中均可以获取落体自由下落的时间-位移坐标，通过式(1)的最小二乘拟合计算，获取测量的重力加速度值：
$\begin{gathered}s_i=s_0+v_0 t_i+\frac{1}{2} g t_i^2+\frac{1}{2} s_0 \gamma t_i^2+ \\\frac{1}{6} v_0 \gamma t_i^2+\frac{1}{24} g \gamma t_i^2\end{gathered}$
式中，s0、v0分别为落体自由下落的初始位移和速度；g为测点位置仪器测量高度处的重力加速度值；γ为测点位置垂向重力梯度；ti和si为落体自由下落过程中第i个时间-位移坐标。
实际测量过程一般连续测量25 h，通过分组和计算总体平均的方式获取重力加速度测量值。在每次测量中，使用激光波长计算位移坐标，因此波长的精度误差会直接耦合进入最终测量结果中。
在绝对重力测量中，一般每30 min完成1组测量，而单组测量结果一般为组内多次测量结果的算术平均值。因此首先假设组内n个测量结果，其算术平均值 ${\bar x}$可表示为：
$\bar{x}=\frac{\left(x_1+\sigma_{x_1}\right)+\left(x_2+\sigma_{x_2}\right)+\cdots+\left(x_n+\sigma_{x_n}\right)}{n}$
式中，x1，x2，…, xn为组内单次测量结果；σx1，σx2，…, σxn为每次测量中由波长不确定度所引入的测量误差。本文主要讨论激光波长对绝对重力测量结果的影响，因此暂不考虑其他误差源。
根据误差传递理论，式(2)计算的单组平均值 ${\bar x}$中源自激光波长不确定度的误差可表示为：
$\sigma_{\bar{x}}=\sqrt{\sigma_{x_1}^2\left(\frac{\partial \bar{x}}{\partial x_1}\right)^2+\sigma_{x_2}^2\left(\frac{\partial \bar{x}}{\partial x_2}\right)^2+\cdots+\sigma_{x_n}^2\left(\frac{\partial \bar{x}}{\partial x_n}\right)^2}=\sqrt{\frac{\sum\limits_{i=1}^n\left(x_i-\bar{x}\right)^2}{n(n-1)}}$
假设共测量获取m组观测数据，每组平均值为$\bar{x}_1, \bar{x}_2, \cdots, \bar{x}_m$，各组平均值对应的激光波长误差为$\sigma_{\bar{x}_1}, \sigma_{\bar{x}_2}, \cdots, \sigma_{\bar{x}_m}$。根据各组的波长误差值，设计每组平均值对总体平均值的影响权重：各组平均值的权重与其误差的平方成反比，权数为1时各个平均值的误差为k，则各个平均值的权重分别为$\frac{k^2}{\sigma_{\bar{x}_1}{ }^2} , \frac{k^2}{\sigma_{\bar{x}_2}{ }^2}, \cdots, \frac{k^2}{\sigma_{\bar{x}_m}{ }^2 } $，m组观测数据对应的总体平均值为：
$\overline{\bar{x}}=\frac{w_1 \bar{x}_1+w_2 \bar{x}_2+\cdots+w_m \bar{x}_m}{w_1+w_2+\cdots+w_m}=\frac{\sum\limits_{k=1}^m w_k \bar{x}_k}{\sum\limits_{k=1}^m w_k} \frac{\sum\limits_{k=1}^m \frac{1}{\sigma_{\bar{x}_k}{ }^2} \bar{x}_k}{\sum\limits_{k=1}^m \frac{1}{\sigma_{\bar{x}_k}{ }^2}}$
式中，$w_1=\frac{k^2}{\sigma_{\bar{x}_1}{ }^2}, w_2=\frac{k^2}{\sigma_{\bar{x}_2}{ }^2}, \cdots, w_m=\frac{k^2}{\sigma_{\bar{x}_m}{ }^2}$。
波长精度对$\overline{\bar{x}}$的误差可表达为：
$\sigma_{\overline{\bar{x}}}=\frac{k}{\sum\limits_{k=1}^m w_k}=\frac{1}{\sqrt{\sum\limits_{k=1}^m \frac{1}{\sigma_{\bar{x}_k}{ }^2}}}$
由此可以说明，式(3)和式(5)在数学表达形式上与常规绝对重力测量中单组观测值的均值统计、多组观测值的整体均值统计及其不确定度表征方法具有一致性。基于这种等效性原理，针对被测热稳频激光器拍频测量数据，本文采用同样的统计处理模型，计算激光波长标定值及其精度。该方法继承了绝对重力测量结果处理的标准范式，为将热稳频激光器作为绝对重力测量长度基准时的误差评估提供了客观有效的依据。
1.2 波长重复性和精度对绝对重力测量结果影响的模拟计算
在不考虑直流分量和线性漂移的条件下，激光干涉型绝对重力仪单次下落获取的干涉信号可表示为[22]：
$U\left(t_i\right)=U \cos \left(\frac{4 \mathsf{π}}{\lambda} S\left(t_i\right)\right)$
式中，S(ti)=S0+V0ti+0.5gti2为落体自由下落过程的位移，其中g为仪器测量高度处的重力加速度值，即不考虑垂直梯度条件下简化处理的式(1)；U为模拟的干涉信号振幅；λ为激光波长。
对于式(6)模拟的干涉信号，基于Hilbert变换提取干涉信号瞬时相位，通过相位解缠提取落体自由下落过程中的时间-位移坐标[23-24]，再利用最小二乘拟合计算重力加速度g的估计值$\hat{g} $，计算过程中通过不断改变激光波长来获取波长精度对$\hat{g}$的误差影响曲线。
在模拟计算中，假设激光波长λ变化范围为±1×10-6 nm，ti从30~200 ms等间距变化，干涉信号采样频率为100 MHz，仪器测量高度处的重力加速度值g为980 110 343.0 μGal，模拟计算结果如图 1所示。可以看出，±1×10-6 nm的激光波长变化可引起约3.0 μGal的重力测量值变化，且两者成明显的线性关系。
1.3 激光波长拍频测量原理
激光波长拍频测量系统通过测量被测激光器与参考激光器的频率差，获取被测激光器波长及其统计特征，具体如图 2所示。该系统主要由激光光源模块、光学耦合与干涉模块、光电探测与信号处理模块、控制与显示模块组成。
激光光源模块由被测激光源和参考激光源组成，参考激光源为整个测量系统的基准，被测激光源即为需要完成输出激光波长测定的激光器。假设参考光源输出的激光频率为f0，拍频测量系统可以输出被测激光源输出激光频率与f0的频率差Δf±δf，则被测激光源输出的激光频率f1可表示为：
$f_1=f_0+\Delta f \pm \mathsf{δ} f$
式中，δf为频率差Δf的误差值。假设光速为c，则被测激光输出的激光波长λ1可表示为：
$\lambda_1=\frac{c}{f_0+\Delta f}$
激光波长λ1的误差可表示为：
$\frac{c}{f_0+\Delta f+\mathsf{δ} f} \leqslant \lambda_1 \leqslant \frac{c}{f_0+\Delta f-\mathsf{δ} f}$
2 热稳频激光器拍频测试结果分析
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2.1 实验室条件下波长精度测试
将AI-05碘稳频激光器作为参考激光源，输出激光频率锁定在F峰，输出激光波长标准值为632.991 212 590 nm。被测激光器为中国计量科学研究院研制的SM633型热稳频激光器。测试过程中实验室环境温度为24.0 ℃，相对湿度为35.8%，测试时间为2025-02-25—26，图 3中蓝色曲线为被测激光器输出激光频率的拍频测量原始数据。
考虑到课题组研制的激光干涉型绝对重力仪单次测量时间为30 s，包含落体的提升、等待、释放和软承接4个阶段，其中释放阶段落体为自由下落状态，在该状态下完成落体相对于参考棱镜时间-位移坐标的测量，有效测量时间为100 ms。将被测激光器波长数据每30个采样点进行1次平均，结果如图 3中黄色曲线所示，每个平均值作为单次绝对重力测量中激光波长采用值。
在拍频测量过程中，主要通过拍频测量原理获取基准激光器(碘稳频激光器)和被测激光器(热稳频激光器)输出激光频率的差值，得到被测激光器的真空波长。拍频测量系统中输出信号的采集是使用单独的数据采集系统，前端通过GHz光电接收器接收拍频信号，通过对应的数据采集系统完成信号的采集和处理，并输出被测激光器输出激光的波长。
但在绝对重力测量时，落体自由下落过程中输出的信息包含落体相对于参考点的自由下落信息的干涉信号，最大瞬时频率约为5 MHz，该信号是通过100 MHz采样率的采集系统进行数字化。根据迈克尔逊干涉测量原理，每半个激光波长形成一条完整的干涉信号, 这里的激光波长对应拍频测量系统给出的被测激光器的波长。
总的来说，拍频测量系统对包含基准激光器和被测激光器频差的信号进行单独采样，获得被测激光器的波长值, 绝对重力仪输出的干涉信号同样被单独采样，然后通过测量得到的被测激光器的波长值提供长度基准，计算落体自由下落过程中相对于参考点的位移信息。
在计算波长值及其精度时，将每50个激光波长采用值作为1组，统计单组激光波长平均值和精度，结果如图 4所示。可以看出，本次拍频得到的被测激光器输出激光频率比参考频率高399.454 4 MHz，对应的精度为2.99 kHz，对应的激光波长值为632.990 678 7 nm，精度为3.99×10-9 nm。
2.2 波长重复性
被测激光器波长的重复性测试需要多次重启被测激光器，为了保证被测激光器入锁状态完全一致，在每次重启之前，激光器关机时间不少于1 h，使激光器充分冷却。重复性测试共进行6次，每次测量时间不少于10 h，采用均方根误差表征6次测量结果的重复性，具体结果见表 1。
2.3 观测环境温度变化对被测激光器波长的影响
虽然被测激光器采用热膨胀系数低的材料制作谐振腔，但环境温度的起伏变化仍会间接影响谐振腔腔长，进而引起输出激光波长的变化[25]。对此，本文于2021-05-08—09在测量环境无温控条件下利用同样的拍频测量系统和参考激光源，对被测激光器的波长进行测定并计算由此引入的绝对重力测量误差。
实验过程中环境温度存在降温和升温2个过程，降温过程为2021-05-08 23:00—05-09 04:00，升温过程为2021-05-09 04:00—17:00。测试结果表明，降温过程导致被测激光器波长降低约0.1×10-6 nm，升温过程导致被测激光器波长升高约4×10-6 nm。由图 1可知，降温过程使重力加速度值偏小约0.15 μGal，升温过程使重力加速度值增大约6 μGal，温度变化与波长变化呈现明显的线性相关性。
3 结语
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本文借助绝对重力测量中对最终测量结果的统计处理模型，利用激光波长拍频测量系统，对被测热稳频激光器波长及其精度进行量化评估，得到以下结论：
1) 被测热稳频激光器在锁定状态下，其输出波长变化一般在10-9 nm量级，该量级下引起的绝对重力测量误差远小于1 μGal(波长变化1×10-6 nm引起约1.5 μGal的重力测量误差)，可不考虑热稳频激光器锁定状态下输出激光波长变化对测量结果的影响。
2) 被测热稳频激光器重复性为1.86×10-6 nm，可引起2.79 μGal的重力测量误差，该长度基准误差会存在于多个测点的流动重力测量结果中。
3) 温度变化会引起热稳频激光器输出激光波长的漂移，测试结果表明，10 ℃温差引入的重力测量误差约为6 μGal，影响关系呈明显的线性，这就要求在流动绝对重力测量过程中测量环境温度应尽量保持一致，推荐温度最大变化量不超过5 ℃或对环境温度进行精确记录并完成后期修正。
基金
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  • 中国地震局地球物理研究所基本科研业务费(DQJB24X26)
  • 中国地震科学实验场工程建设项目
文献
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doi: 10.14075/j.jgg.2025.05.155
  • 接收时间：2025-05-08
  • 首发时间：2026-10-29
  • 出版时间：2026-04-15
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  • 收稿日期：2025-05-08
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中国地震局地球物理研究所基本科研业务费(DQJB24X26)
中国地震科学实验场工程建设项目
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    1 中国地震局地球物理研究所, 北京, 100081

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吴琼, 研究员, 主要研究方向为激光干涉绝对重力测量、重力梯度测量和相对重力测量仪器的研发与应用, E-mail:
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