基于飞秒光频梳的绝对距离测量技术研究
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摘要
长度作为七个基本物理量之一，其精确测量在前沿基础科学和先进技术应用中具有极为重要的意义。随着飞秒光频梳的出现，飞秒脉冲激光器开始应用于绝对距离测量。相对于传统测距方法中的连续激光、脉冲激光和白光等光源，锁定的飞秒脉冲激光器具有十分独特的优势，在时域上可以看作是一系列等间隔的脉冲序列，而频域上则可以提供从微波频率直到光频的一系列等间隔频率分布。本论文在国家自然科学基金和北京市自然科学基金的支持下，围绕飞秒光学频率梳绝对距离测量技术进行了深入的研究和探索。主要研究内容包括以下几个方面：
(1)分析了现有各种绝对距离测量方法，介绍了飞秒光学频率梳绝对距离测量技术国内外研究现状及发展趋势。
(2)综述了基于飞秒光学频率梳的绝对距离测量原理，归纳了飞秒激光器光学频率梳的应用和激光频率锁定与溯源的基本原理。
(3)在色散脉冲传播理论的基础上，提出了飞秒光学频率梳引入非平衡迈克尔逊干涉仪的互相关离散模型。在考虑相速度、群速度和群延时色散前提下，建立了超短脉冲在不同中心波长、频谱形状和大气条件下绝对测距互相关模型。仿真结果表明，随着传播距离的增大互相关模型具有稳定啁啾和线性加宽；而大气压强、温度、湿度和二氧化碳含量的微小变化只引起互相关图形的移动，不产生任何线性加宽或啁啾。
(4)在飞秒绝对测距互相关离散模型的基础上，提出了飞秒光学频率梳引入非平衡迈克尔逊干涉仪中的互相关连续模型。基于连续模型和二次近似算法研究了互相关中最亮条纹的位置，得到互相关图案中最亮条纹的位置随延迟距离做非线性变化，当达到一定距离后，最亮条纹移动呈线性变化。提出了非线性色散深度的概念，当距离大于非线性色散深度时，互相关的形成由光谱轮廓确定，而相干模式的每个强度点只由一个固定频率确定。
(5)在白光色散干涉的基础上，提出了光谱分辨干涉飞秒绝对测距方法。分析了理想采样下以及光学频率梳滤出模式（3648和1824两个模式数量）情况下，光谱分辨干涉方法的性能指标。仿真结果表明光谱分辨干涉法的最小测量距离为6.3μm，非模糊范围为5.75mm，测量精度为±4μm。采用适当的组合测量方法，最大测量距离可以扩展到任意长度。研制了飞秒光谱分辨干涉法中用于滤出光梳模式的法布里-珀罗标准具，设计并实现了光谱分辨干涉法飞秒绝对测距实验装置，实验数据表明，测距范围达到±1mm，测量偏差达到±5μm。
Length is one of the seven basic physical quantities. The accurate measurement oflength has extremely important significance in the forefront of basic science and advancedtechnology applications. With the advent of femtosecond optical frequency comb, thefemtosecond pulse laser is used in the absolute distance measurement. Compared to lightsources used in traditional ranging method such as continuous wave laser, pulsed laser andwhite light, femtosecond pulse laser has very unique advantages. It can be considered as aseries of equally spaced pulse sequence in the time domain which can provide a series ofequally spaced frequency distribution from microwave frequencies to optical frequencies inthe frequency domain. The research in this dissertation was supported by National NaturalScience Foundation and Beijing Natural Science Foundation. The research and explorationof the absolute distance measurement based on femtosecond optical frequency comb waspresented in the paper. The main research contents are as the followings:
(1) The existing methods of absolute distance measurement are analyzed. The domesticand international research present situation and the development trend of the absolutedistance measurement techniques based on femtosecond optical frequency comb areintroduced.
(2) The absolute distance measurement principles based on femtosecond opticalfrequency comb are summarized. The two basic principles of femtosecond laser and itsfrequency locking and traceability are concluded.
(3) Based on the dispersion pulse propagation theory, the discrete model of thecross-correlation signal the femtosecond optical frequency comb propagating in anunbalanced Michelson interferometer is proposed. Considering phase velocity, groupvelocity and the group delay dispersion the model of the cross-correlation functions of theultrashort pulse sequence propagating in air is built with different pulse center wavelength,different spectral distribution and with the change of environmental parameters. Thesimulation results show that the cross-correlation pattern has stable chirp and linearbroadening with the increase of propagation distance, but the minor changes of theenvironmental parameters, such as air pressure, temperature, humidity, and CO2content, give rise to the shift of the correlations patterns without any chirp or linear broadening.
(4) Based on the discrete model of the cross-correlation patterns of the femtosecondabsolute distance measurement, the continuous model of the cross-correlation functions offemtosecond optical frequency comb propagating in an unbalanced Michelson interferometeris developed. By introducing the continuous model and quadratic approximation, theposition of the brightest fringe in the correlation pattern is found out. The simulation resultsshow that the position of the brightest fringe in the correlation pattern varies non-linearly forshort delay distances, and when a specific distance is reached, the brightest fringe varieslinearly. The concept of the non-linear dispersion depth is proposed. It is showed that theshape of the cross-correlation patterns at the distances greater than the non-linear dispersiondepth is determined by the source spectral profile. It is also observed that each intensity pointof the correlation pattern is formed by the contribution of one dominant stationary frequency.
(5) Femtosecond absolute distance measurement of spectrally resolved interferometryon the basis of white light dispersion interference is advanced. The performance of spectrallyresolved interferometry method in the case of3648and1824filtered optical modes ofoptical frequency comb, with reference to the case of ideal sampling is summarized.Simulation results show that the minimum measurable distance of this method is6.3μm, thenon-ambiguity range is5.75mm and the measurement accuracy is±4μm. The maximumdistance can be extended to arbitrary length. The Fabry-Perot etalon, which is used to filterout the optical frequency comb mode, is developed. The setup of spectrally-resolvedinterferometry for absolute distance measurement is designed and realized. The experimentresult shows that the distance measurement range is±1mm, and the measurement differencereaches±5μm.
(1)分析了现有各种绝对距离测量方法，介绍了飞秒光学频率梳绝对距离测量技术国内外研究现状及发展趋势。
(2)综述了基于飞秒光学频率梳的绝对距离测量原理，归纳了飞秒激光器光学频率梳的应用和激光频率锁定与溯源的基本原理。
(3)在色散脉冲传播理论的基础上，提出了飞秒光学频率梳引入非平衡迈克尔逊干涉仪的互相关离散模型。在考虑相速度、群速度和群延时色散前提下，建立了超短脉冲在不同中心波长、频谱形状和大气条件下绝对测距互相关模型。仿真结果表明，随着传播距离的增大互相关模型具有稳定啁啾和线性加宽；而大气压强、温度、湿度和二氧化碳含量的微小变化只引起互相关图形的移动，不产生任何线性加宽或啁啾。
(4)在飞秒绝对测距互相关离散模型的基础上，提出了飞秒光学频率梳引入非平衡迈克尔逊干涉仪中的互相关连续模型。基于连续模型和二次近似算法研究了互相关中最亮条纹的位置，得到互相关图案中最亮条纹的位置随延迟距离做非线性变化，当达到一定距离后，最亮条纹移动呈线性变化。提出了非线性色散深度的概念，当距离大于非线性色散深度时，互相关的形成由光谱轮廓确定，而相干模式的每个强度点只由一个固定频率确定。
(5)在白光色散干涉的基础上，提出了光谱分辨干涉飞秒绝对测距方法。分析了理想采样下以及光学频率梳滤出模式（3648和1824两个模式数量）情况下，光谱分辨干涉方法的性能指标。仿真结果表明光谱分辨干涉法的最小测量距离为6.3μm，非模糊范围为5.75mm，测量精度为±4μm。采用适当的组合测量方法，最大测量距离可以扩展到任意长度。研制了飞秒光谱分辨干涉法中用于滤出光梳模式的法布里-珀罗标准具，设计并实现了光谱分辨干涉法飞秒绝对测距实验装置，实验数据表明，测距范围达到±1mm，测量偏差达到±5μm。
Length is one of the seven basic physical quantities. The accurate measurement oflength has extremely important significance in the forefront of basic science and advancedtechnology applications. With the advent of femtosecond optical frequency comb, thefemtosecond pulse laser is used in the absolute distance measurement. Compared to lightsources used in traditional ranging method such as continuous wave laser, pulsed laser andwhite light, femtosecond pulse laser has very unique advantages. It can be considered as aseries of equally spaced pulse sequence in the time domain which can provide a series ofequally spaced frequency distribution from microwave frequencies to optical frequencies inthe frequency domain. The research in this dissertation was supported by National NaturalScience Foundation and Beijing Natural Science Foundation. The research and explorationof the absolute distance measurement based on femtosecond optical frequency comb waspresented in the paper. The main research contents are as the followings:
(1) The existing methods of absolute distance measurement are analyzed. The domesticand international research present situation and the development trend of the absolutedistance measurement techniques based on femtosecond optical frequency comb areintroduced.
(2) The absolute distance measurement principles based on femtosecond opticalfrequency comb are summarized. The two basic principles of femtosecond laser and itsfrequency locking and traceability are concluded.
(3) Based on the dispersion pulse propagation theory, the discrete model of thecross-correlation signal the femtosecond optical frequency comb propagating in anunbalanced Michelson interferometer is proposed. Considering phase velocity, groupvelocity and the group delay dispersion the model of the cross-correlation functions of theultrashort pulse sequence propagating in air is built with different pulse center wavelength,different spectral distribution and with the change of environmental parameters. Thesimulation results show that the cross-correlation pattern has stable chirp and linearbroadening with the increase of propagation distance, but the minor changes of theenvironmental parameters, such as air pressure, temperature, humidity, and CO2content, give rise to the shift of the correlations patterns without any chirp or linear broadening.
(4) Based on the discrete model of the cross-correlation patterns of the femtosecondabsolute distance measurement, the continuous model of the cross-correlation functions offemtosecond optical frequency comb propagating in an unbalanced Michelson interferometeris developed. By introducing the continuous model and quadratic approximation, theposition of the brightest fringe in the correlation pattern is found out. The simulation resultsshow that the position of the brightest fringe in the correlation pattern varies non-linearly forshort delay distances, and when a specific distance is reached, the brightest fringe varieslinearly. The concept of the non-linear dispersion depth is proposed. It is showed that theshape of the cross-correlation patterns at the distances greater than the non-linear dispersiondepth is determined by the source spectral profile. It is also observed that each intensity pointof the correlation pattern is formed by the contribution of one dominant stationary frequency.
(5) Femtosecond absolute distance measurement of spectrally resolved interferometryon the basis of white light dispersion interference is advanced. The performance of spectrallyresolved interferometry method in the case of3648and1824filtered optical modes ofoptical frequency comb, with reference to the case of ideal sampling is summarized.Simulation results show that the minimum measurable distance of this method is6.3μm, thenon-ambiguity range is5.75mm and the measurement accuracy is±4μm. The maximumdistance can be extended to arbitrary length. The Fabry-Perot etalon, which is used to filterout the optical frequency comb mode, is developed. The setup of spectrally-resolvedinterferometry for absolute distance measurement is designed and realized. The experimentresult shows that the distance measurement range is±1mm, and the measurement differencereaches±5μm.
引文
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