Voigt线型函数及其最大值的研究

研究了多普勒和洛伦兹线型函数卷积形式的Voigt线型函数, 给出了它的最大值.结果表明, Voigt线型函数是关于中心频率的对称函数, Voigt线型函数的最大值由多普勒和洛伦兹线型函数的半宽度决定, 与中心频率无关, 且比洛伦兹和多普勒线型函数的最大值都小.提出了利用Voigt线型函数最大值和半宽度获得多普勒线型函数和洛伦兹线型函数的方法, 并利用Monte Carlo方法进行了验证. 关键词： Voigt线型函数 半宽度 最大值 傅里叶变换     

Harmonic detection with tunable diode lasers —two-tone modulation

The minimum absorption detectable by a tunable diode laser spectrometer utilising harmonic techniques is often limited by interference fringes generated by scattered light. The sensitivity of the spectrometer to absorption can be increased by applying a jitter modulation. In this paper, the theory of harmonic response for single- and two-tone modulation over optical fringes and Lorentzian absorption lines is developed and compared to experimental measurements. A simple analytic expression for the two-tone harmonic line shape is derived. This expression provides a physical understanding of the effects of the second modulation, and a means to unravel the effects of the second modulation on the linewidth and line shape. For a specific choice of the jitter frequency and phase, it is possible to simultaneously minimise the fringe signal and increase the harmonic absorption signal. The results of this investigation are applicable to trace gas detection using tunable diode lasers, and to other areas of spectroscopy and magnetic resonance where harmonic techniques are used.This work was supported by the Natural Sciences and Engineering Research Council of Canada, and the Ontario Ministry of the Environment     

非共轴三阶自相关中的倍频过程影响分析

针对非共轴三阶自相关法测试中对二倍频光束的要求,采用分步傅里叶变换方法对入射高斯光束,使用KDP晶体I类匹配的二倍频过程时间波形演变规律进行数值模拟,给出二倍频光束波形仍为高斯分布的入射基频光能量范围.不同二倍频效率下基频光与倍频光脉宽比值不同,所得的三阶自相关函数脉宽则不同,导致与脉冲形状有关的半高宽度换算因子不是固定值.分析结果对三阶自相关仪的参数设计和三阶自相关法测试中的误差分析有一定理论指导意义.     

Principle of temperature,velocity and pressure of upper atmospheric wind measurement for the Voigt profile

Using the accurate expression of the Fourier transform of the pure Voigt spectral line profile, we present the principle of the passive optical method to measure temperature, velocity, and pressure of atmospheric wind for the Voigt profile. Through discussion, from the Gaussian, Lorentzian and Voigt profiles, we find that velocity will not be affected, pressure can be derived for Lorentzian and Voigt profiles, and temperature will be affected greatly. By simulation and comparison, we find that temperature derived from the Voigt profile is greater than that from the Gaussian profile, and it is less than that from the Lorentzian profile. This discussion will be significant in accurate upper atmospheric wind measurement.     

基于波长调制技术的激光器调制特性研究

在流场诊断技术中,可调谐半导体吸收光谱技术（TDLAS）成为主要的诊断技术之一,其可实现非接触、原位检测。波长调制（WMS）和直接吸收(DA)是两种最常用的TDLAS气体传感方法,在目标含量很低或者极端流场环境下,波长调制技术呈现出更多的优势,检测灵敏度与直接吸收相比可以提高1～2个数量级。在近红外波长调制技术应用领域,分布反馈式（DFB）半导体激光器成为流场诊断技术的光源选择之一,无论利用谐波信号（或者归一化谐波信号）的线型拟合,还是选择谐波信号的峰值来反演流场参数,吸收模型的准确建立均十分重要。在模型建立时,激光器频率-时间响应以及光强-时间响应的准确表示尤为重要。为解决吸收模型准确建立问题,提出了一种准确测量激光器调制参数的完整方法,通过实验测量了用于探测水汽吸收的1 392和1 469 nm激光器的调制特性,研究了分布反馈式激光器的调制参数随调制幅度,调制频率以及工作温度的变化。根据该方法得到的调制参数,建立吸收模型,测得常温下空气中水汽浓度为1.97%,直接吸收方法测得浓度为1.99%,验证了该测量方法的准确性。研究表明,调制深度随调制幅度的增加线性增加,随调制频率的增加非线性单调减小,随工作温度的升高线性增加;激光器的出光强度和频率同时被调制,强度变化超前频率变化的相位,随调制幅度的变化不明显,随调制频率的增加单调增加,随工作温度的升高单调减小;归一化一次谐波振幅和二次振幅均随调制幅度的增加而增加,随调制频率的增加而减小,随工作温度的变化不明显。在吸收光谱应用领域,波长调制技术发挥的作用愈加重要,调制系数与谐波信号的峰值息息相关,在波长调制技术应用时,选取适当的调制参数,有利于得到合适的谐波信号,可通过改变调制幅度、调制频率、工作温度得到最优调制系数。研究了近红外分布反馈式半导体激光器的调制特性,该方法同样适用于不同封装和不同波段激光器调制特性的研究,利于推广吸收光谱技术在各领域的应用。     

Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first-derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.     

Accurate extraction method for the FM response of tunable diode lasers based on wavelength modulation spectroscopy

An accurate wavelength modulation spectroscopy based method to measure the dynamics of the wavelength modulation behavior of tunable diode lasers is introduced in this paper. This method requires only standard equipment and a simple mechanical setup. Under the condition of a constant laser modulation current, the wavelength modulation amplitude can be determined by analysis of the distance between the two zero crossings of the measured second harmonic spectrum of gas absorption. When measuring at different modulation frequencies, the frequency response of the current-to-wavelength tuning coefficient can be obtained. The use of a frequency analyzer instead of a lock-in amplifier to obtain the second harmonic spectrum has two advantages: it provides a higher bandwidth and allows for very precise detection of the zero crossings because of the logarithmic output. The results exhibit very good agreement with a reference measurement performed with a fast FTIR Spectrometer. PACS 42.60.Fc; 42.62.Fi; 42.55.Fx     

渐变折射率传感气室中干涉噪声的数值模拟与分析

在直接红外吸收式光纤气体传感器中，由渐变折射率（Graduated Refractive Index，GRIN）棒透镜构成的微型传感气室有着广泛的应用。分析了GRIN气室中的干涉噪声信号和甲烷信号，并利用MATLAB对干涉噪声信号的幅值与分布反馈式半导体激光器（DFBLD）的频率调制幅度之间的关系以及干涉噪声对气体检测灵敏度的影响进行了数值模拟与分析。当前谐波检测技术是气体检测的一种非常重要的技术，这种技术需要检测气体吸收信号的一次、二次或更高次谐波。而GRIN气室的二次干涉噪声对浓度信号有很大的影响，研究发现当频率调制幅度达到某些特定频率值时，二次干涉噪声信号的幅值变为零，通过调整气室参数和DFBLD的调制频率可以削减干涉噪声的影响从而提高谐波检测技术的检测灵敏度。     

佛克脱光谱线型干涉图的理论及其应用研究

在一般压强的条件下,佛克脱光谱线型(高斯光谱线型和洛伦兹光谱线型的卷积)是最接近实际的光谱线型,但由于其没有具体的表达式,所以在实际应用中常采用各种近似来表示佛克脱光谱线型。文章未采用任何近似,计算了佛克脱光谱线型干涉图的具体表达式,表明虽然佛克脱光谱线型没有具体表达式,但其干涉图是可以严格求解的。而且其变换结果为一实函数,与高斯光谱线型和洛伦兹光谱线型的变换结果的表达式非常相似,因而可以进行谱线综合展宽的各种计算,而不是像有的文献所预言的有实部和虚部两部分,给计算带来困难。计算结果与实验结果一致。作为应用的一个实例,作者指出了其在大气风场测量中的重要应用。此计算对气体展宽在傅里叶变换光谱仪中的应用方面具有非常重要的意义。     

On possibility of using the lowest odd harmonics of the phase modulation frequency in the output signal of the fiber-optic ring interferometer for detection of the sagnac effect

The possibility of using the lowest harmonics of the phase modulation frequency in the output signal of the fiber-optic ring interferometer (FRI) for detection of the FRI rotation angular velocity is considered. It is shown that the use of the third harmonic of the phase modulation frequency is optimal, since, in this case, the effect of insignificant admixture of the second harmonic of the phase modulation frequency on the FRI baseline shift can be completely eliminated. When processing the signal using the first or the fifth harmonic of the phase modulation frequency, it is possible to compensate for the FRI baseline shift because of its weak dependence on the phase modulation amplitude. Upon processing of the FRI output signal using higher odd harmonics of the phase modulation frequency, the signal-to-noise ratio noticeably decreases.     

Efficient second-harmonic generation for a high-intensity femtosecond pulse in the absence of group synchronism of interacting waves

A method is proposed to compensate for the influence of the group velocity mismatch on the frequency conversion efficiency for any ratio between the coefficients of square and cubic nonlinearities. The method allows the limiting efficiency of the frequency doubling to be achieved. This efficiency corresponds to the cases of phase and group synchronisms. For this purpose, it is necessary to apply a low-frequency phase modulation of the input radiation at the frequency of the first harmonic in combination with the optimal selection of the wavenumber mismatch. In practice, under certain conditions, this modulation can be obtained only with the aid of the wavenumber mismatch, whose optimal value is determined by the group velocity mismatch. The generation efficiency can be increased several times by introducing a phase shift in certain cross sections of the medium.     

Voigt线型两翼拟合非均匀流场吸光度的方法研究

在吸收光谱领域特别是可调谐半导体激光直接吸收光谱(dTDLAS)技术中, 需要精确测量吸收光谱的积分吸光度值以精确反演出流场温度、组分浓度等参数。对于非均匀流场,单光路吸收光谱测量时,由于沿测量路径的谱线展宽随流场状态的变化而变化,见诸文献的研究主要采用Voigt或Lorentz线型对吸光度曲线拟合处理或直接对吸光度曲线数值积分获取积分吸光度值,针对方法可能引入的误差进行了模拟分析,并提出Voigt线型两翼拟合吸光度的方法来获取吸收光谱的积分吸光度值,以减小拟合误差。采用流场测量中常用的H₂O作为目标气体,选取了8条具有不同低态能级的吸收线,以实验室平焰炉为原型建立两种非均匀流场模型,并通过分段法对流场非均匀性进行等效处理。分别采用Voigt线型拟合法、数值积分法和Voigt线型两翼拟合法模拟计算两模型的积分吸光度值,通过与理论积分吸光度值对比得出各方法的误差大小,从而确定出在不同的非均匀流场情况下相适应的积分吸光度值获取方法。     

基于谱线频率特征的调谐二极管激光吸收光谱参数分析

调谐激光二极管吸收光谱(TDLAS)技术因其高分辨率、高灵敏度和快速测量等优点在工业生产、环境污染监测等方面受到广泛应用。波长调制光谱（wavelength modulation spectrum, WMS）的二次谐波信号经常用作气体浓度反演的检测信号。TDLAS检测性能与系统参数,如锁相放大器的时间常数、扫描幅度、扫描频率、调制幅度、调制频率等的选取紧密相关,实际测量中各参数的选择多以谱线形态特征为依据,参数之间的关联性未能得到较好体现。由于信号的采样与处理均在频域对谱线产生作用,各参数之间的作用相互关联。然而很少有研究参数对谱线频域的影响,针对此问题,在一定的理论基础上通过实验分别观察各调制参数对二次谐波信号的影响。通过保持其他参数不变,只改变一个参数的方法,得出各个参数对信号线型、频率特征及噪声引入的影响规律,继而分析并验证了多参数联合变化对谱线频带的决定作用。与基于时域特征的传统方法相比,基于谱线频率特征分析一方面具有与谱线信号采集检测处理机理相近的优点,另一方面可以直观得到各参数对主频带的影响和不同频率信号的衰减趋势。总结出基于频率特征的各参数的基本选取方法,以谱线频带和截止频率相互关系为判定标准,截止频率的大小由锁相放大器时间常数决定。通过设置合适的时间常数和扫描参数使信号频带与截止频率相近但不相交,使谱线频带内频率分量不产生衰减,频带外噪声得到最大抑制;再根据锁相放大器的性能和信号信噪比来确定调制参数,使谱线主频幅度最大;最后根据系统需求确定采样率。单周期采样点不变时,低扫描频率时检测精度相对提高但耗时较长;反之,扫描频率提高,速度变快但检测精度下降。通过联合影响规律调整关联参数,减小硬件限制对参数最优值选取造成的影响。可在考虑系统检测需求与硬件条件限制的前提下,通过参数选择得到最优二次谐波信号,为此技术的实际应用提供了参数优化的实验依据与参考方法。     

TDLAS波长调制压力测量法参数优化

使用TDLAS技术进行动态压力测量已经成为压力测量领域的研究热点。波长调制法实验装置较为复杂,需要对多个参数进行设置,选择出最优的预设参数能够取得更好的实验效果,获得更高的测量精度。目前波长调制法的实验参数设置基本凭借个人经验,使用Matlab程序仿真结合波长调制法的TDLAS测量技术,能够对实验中需要进行预设的重要参数进行了分析。通过计算4990cm-1波段和6330cm-1波段附近的多条吸收峰,发现4990.09cm-1波段处的吸收峰更适合作为波长调制法的测量波段。以4990.09cm-1处的吸收峰为研究对象,进行了波长调制法压力测量仿真建模,计算了调制度、调谐频率和调制频率对二次谐波幅值和对称性的影响并深入地分析了影响因素,总结了其变化规律。在综合考虑抗噪性能和测量精度的情况下,选择了调制度为2.5,调谐频率30Hz,调制频率5kHz为最佳实验参数。基于Matlab的仿真模型能够快速计算大量参数点,更加直观地分析出对参数的影响趋势,为实验仪器和预设参数的选择提供依据。     

Second-harmonic detection with tunable diode lasers — Comparison of experiment and theory

A series of experiments are carried out by current modulating a tunable diode laser, and slowly ramping the wavelength to scan weak absorption lines in gases at pressures ranging from 2 to 60 Torr. A lock-in amplifier detects the second harmonic (2f) of the modulation frequency, and the experimental 2f signals are compared with theory. Detailed measurements are made on Lorentzian, Voigt, and Gaussian line profiles, over a wide range of modulation amplitudes. Excellent agreement between experiment and calculation is obtained in all cases. This quantitative understanding enables one to derive true lineshapes and linewidths of very weak absorption lines from measurements of 2f lineshapes only. Results are applicable to trace gas detection using tunable diode lasers, and to other areas of spectroscopy and magnetic resonance where harmonic detection techniques are routinely employed to monitor weak signals.This work was supported in part by the National Science and Engineering Research Council, Canada     

Absorption line profile recovery based on residual amplitude modulation and first harmonic integration methods in photoacoustic gas sensing

Two methods for recovery of gas absorption line profiles are presented in this paper using photoacoustic spectroscopy and tunable diode laser spectroscopy (TDLS) with wavelength modulation (WM). A theoretical analysis based on Fourier coefficients is given in order to describe the various components that arise under simultaneous intensity and frequency modulation. The first method makes use of the residual amplitude modulation (RAM) signal which is always present in current modulation of distributed feedback (DFB) tunable diode lasers. The second method involves integration of a near-pure first harmonic derivative signal, separated from other distorting components by appropriate choice of the lock-in detection phase in the case of low modulation index. Good agreement is obtained with both methods between the experimental results and the theoretical simulation for the P17 absorption line of acetylene at 1535.39 nm but the second method gives a much improved accuracy and signal-to-noise ratio in lineshape recovery with photoacoustic spectroscopy.     

可调谐二极管激光吸收光谱技术参数选择及优化

可调谐二极管激光吸收光谱技术(TDLAS)系统性能受调制参数,如调制度、调制频率、扫描幅度及扫描频率影响,实际测量中各参数不存在明确的选择依据。针对此问题,文章在一定的理论基础上通过实验分别观察各调制参数对二次谐波信号的影响,通过分析检测信号的特征,如幅值、信噪比、对称性及峰宽得出其变化规律,总结出在不同系统功能和需求下系统各调制参数的优化依据及方法。系统在计算浓度和温度时应优先考虑幅值和信噪比,从而使调制度达到最佳值,调制频率和扫描频率取较小值;在线形推导压强时优先考虑信号的对称性和峰宽,根据计算的具体要求确定调制参数;扫描幅度的确定以得到完整谐波信号为准;再根据系统的速度和精度需求调整扫描频率。该研究为此类系统工作状态的确定提供了实验依据。     

Overview of the New OMAH Technique for Scaling OMA Mode Shapes

Methods for scaling mode shapes determined by operational modal analysis (OMA) have been extensively investigated in the last years. A recent addition to the range of methods for scaling OMA mode shapes is the so-called OMAH technique, which is based on exciting the structure by harmonic forces applied by an actuator. By applying harmonic forces in at least one degree-of-freedom (DOF), and measuring the response in at least one response DOF, while using at least as many frequencies as the number of mode shapes to be scaled, the mode shape scaling (modal mass) of all modes of interest may be determined. In previous publications on the method the authors have proven that the technique is easy and robust to apply to both small scale and large scale structures. Also, it has been shown that the technique is capable of scaling highly coupled modes by using an extended multiple reference formulation. The present paper summarizes the theory of the OMAH method and gives recommendations of how to implement the method for best results. It is pointed out, as has been shown in previous papers, that the accuracy of the mode scaling is increased by using more than one response DOF, and by selecting DOFs with high mode shape coefficients. To determine the harmonic force and responses, it is recommended to use the three-parameter sine fit method. It is shown that by using this method, the measurement time can be kept short by using high sampling frequency and bandpass filtering whereas spectrum based methods require long measurement times. This means that even for structures with low natural frequencies, the extra measurement time for scaling the mode shapes can be kept relatively short.     

Doppler振镜正弦调制多光束激光外差二次谐波测量角度的方法

提出了一种多光束激光外差测微小角度的新方法. 基于激光外差技术和Doppler效应, 通过做简谐振动的Doppler振镜对不同时刻入射光的正弦调制, 把待测角度信息加载到外差信号的频率差中, 经信号解调后可以得到待测角度参数值, 经加权平均处理可以提高待测角度的测量精度. 利用这种新方法, 通过Matlab仿真了平面标准镜不同入射角的模拟结果, 表明该仿真结果的最大相对误差小于0.789677%. 关键词： 角度测量 多光束激光外差 激光Doppler技术 Fourier分析