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.     

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     

Coherence characteristics of light-emitting diodes

We report the measurement of coherence characteristics of light-emitting diodes (LEDs). Experiments were performed using red and green color LEDs directly illuminating the Young's double slit kept in the far-zone. Fourier transform fringe analysis technique was used for the measurement of the visibility of interference fringes from which the modulus of degree of spectral coherence was determined. Low degree of spectral coherence, typically 0.4 for red and 0.2 for green LED with double-slit separation of 400 μm was observed. A variable slit was then kept in front of the LEDs and the double slit was illuminated with the light coming out of the slit. Experiments were performed with various slit sizes and the visibility of the interference fringes was observed. It was found that visibility of the interference fringes changes drastically in presence of variable slit kept in front of LEDs and a high degree of spectral coherence, typically 0.85 for red and 0.8 for green LED with double-slit separation of 400 μm and rectangular slit opening of 500 μm was observed. The experimental results are compared with the theoretical counterparts. Coherence lengths of both the LEDs were also determined and it was obtained 5.8±2 and 24±4 μm for green and red LEDs, respectively.     

Spectral-mismatch-induced resolution limit of interferometric fiber Fabry-Perot sensor system

The mismatch of fiber Bragg gratings (FBGs) in spectral profiles can lead to a severe degraded resolution of the constructed fiber Fabry-Perot (FFP) sensor system through its effect on the fringe visibility. The variation of visibility induced by spectral mismatch and the corresponding phase resolution limit are analyzed theoretically and experimentally. Theoretical analyses are based on the approximation of Gaussian profiles to the reflection spectra of weak FBGs, especially with consideration of side lobes. The investigation provides an insight into the evolution of the fringe visibility caused by spectral mismatch, and shows good agreement with experimental results. An optimum phase resolution of about 55 μrad/Hz^1/2 above 100 Hz is achieved for a nearly 4 m-long FFP sensor by matching spectral profiles of the gratings and balancing path length differences of the tandem interferometers.     

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。     

The mean probability of photon capture of resonance radiation in atomic absorption spectroscopy

The mean probability of photon capture Ψ, obtained via an approximation to the complementary escape factor Λ, for calcium and zinc resonance lines at 4226.73 and 2138.56 Å have been determined from their atomic absorption measurements. Calculations are performed for Gaussian, Lorentzian, and Voigt spectral line shapes. Tabulations and graphical plots of the mean probability of photon capture, Ψ, with the optical depth in the center of Doppler profile, τ_D, and the number density of free atoms in the ground state N, are provided.     

A new formula for fringe localization in holographic interferometry

Holographic interferometry generally involves the interference of two or more speckle fields reflected from or transmitted through a diffused object. The visibility of the resulting fringes depends on the degree of coherence of the interfering speckle fields. Through a statistical analysis it is found that the degree of coherence of speckle fields is essentially a function of the relative speckle displacement and average speckle size. The analysis leads to a new physical model for holographic interferometry. With this model the problem of fringe formation and localization may be analyzed and formulated in terms of speckle movement. A new formula for ideal fringe localization is then derived from the analysis. Furthermore, a localization factor V_c, i.e. the visibility of the holographic fringes, is introduced to analyze the partial fringe localization in holographic interferometry, which is of practical interest to most researchers.     

Analysis of Two Spectral Lines with Gaussian Profile by Using Photon Statistics. Comparison with Other Profile Shapes

In this paper we study the behavior of the errors involved in the determination of the parameters characterizing two spectral lines with Gaussian profile by means of the measurement of the intensity correlation function g⁽²⁾(τ) and by a multichannel system. The results obtained with both methods are compared. We also compare this results with those obtained when two lines with Lorentzian profile are analyzed.     

纳米流体激光自混频功率谱及其计算

激光自混频技术可用于纳米颗粒和纳米流体的探测。在纳米流体自混频信号自相关函数的基础上,理论推导了功率谱函数的表达式。结果表明,纳米流体的激光自混频信号功率谱是洛伦兹线型和高斯线型的卷积,即佛赫特(Voigt)线型。通过数值计算研究了各种典型情况下激光自混频信号功率谱的频谱特征,颗粒定向运动速度决定了多普勒频移和高斯线宽,颗粒粒度决定了洛伦兹线型的宽度,颗粒粒度和速度与功率谱之间的对应关系为纳米流体的测量提供了理论基础。     

温度和压强的变化对谱线线型峰值的影响

谱线线型是用于气体浓度测量中的一个重要参数。本文基于温度(压强)变化会引起相应压强(温度)的变化这一点,考虑温度和压强同时变化对气体线型峰值的影响。通过分析氟化氢的吸收谱线,发现可用Lorentzian线型来计算峰值吸收系数的温度和压强范围都扩大,而Gaussian线型在绝大数情况下不能用来计算峰值吸收系数;在一定的温度范围和压强范围内,如果只考虑压强或温度的变化,由此计算的三种线型峰值(Gaussian,Lorentzian和Voigt)的相对误差大于0.1。因此,在计算线型峰值时,需考虑压强和温度同时变化对线型峰值的影响。最后分别讨论了甲烷、二氧化碳、一氧化碳及一氧化氮,得到与氟化氢结论相似的结论,结论的不完全相同是由于每种气体在波数、压力展宽系数、相对分子质量及温度系数上的不同而导致。     

An analytical derivation of a popular approximation of the Voigt function for quantification of NMR spectra

The approximation of the Voigt line shape by the linear summation of Lorentzian and Gaussian line shapes of equal width is well documented and has proved to be a useful function for modeling in vivo (1)H NMR spectra. We show that the error in determining peak areas is less than 0.72% over a range of simulated Voigt line shapes. Previous work has concentrated on empirical analysis of the Voigt function, yielding accurate expressions for recovering the intrinsic Lorentzian component of simulated line shapes. In this work, an analytical approach to the approximation is presented which is valid for the range of Voigt line shapes in which either the Lorentzian or Gaussian component is dominant. With an empirical analysis of the approximation, the direct recovery of T(2) values from simulated line shapes is also discussed.     

A geometric analysis of the probe volume in a dual beam laser Doppler velocimeter

The probe volume of the dual beam laser Doppler velocimeter is analyzed from a geometrical standpoint. The volume is graphically reconstructed and the existence of the characteristic dual beam laser Doppler velocimeter fringes is demonstrated. The fringes are analyzed and are shown to be composed of moving tubes or pockets of coherent radiation. The composition of the light is analyzed and the extent of the coherence of the laser radiation within the light pockets is considered. The scattered light from the tubes is analyzed and the coherence enhancement of the fringe structure is shown. This information is used in an attempt to resolve the controversy as to whether the dual beam laser Doppler velocimeter is governed by a fringe counting phenomena or by a beating phenomena of light from two sources of coherent radiation of different frequencies.     

Spectral analysis of a laser beam

The formulas of the dependence of the spectral laser power distribution and its spectral half-width on the physical parameters of its laser active medium are derived. In addition it is found that, if the gain line profile has a Lorentzian or Gaussian distribution, the spectral laser power distribution is of a Lorentzian profile. The spectral halfwidth of the laser beam in both cases are slightly different form each other. For a general gain line profile, the spectral laser power distribution behaves as a differential form like that of the gain line profile.The spectral halfwidth of He/Ne laser beam having powers (0·5 mW, 1·0 mW, 3·0 mW and 50 mW) and that of their longitudinal modes, the laser gain factor and the difference between the population atomic densities of the upper and lower energy levels for the laser line transition are experimentally determined.     

The profile of the Fe 372·00 nm line excited in a hollow cathode discharge

The profile of the Fe 372·00 nm line emitted in the negative glow of a hollow-cathode discharge is analyzed. The value of the discharge current was varied within the range 7–15 mA, the neon pressure being 1·22–4·40 Torr. The Lorenzian and Gaussian components of the recorded line profile were corrected for instrumental broadening. A correlation was found to exist between the Gaussian component and the cathode voltage drop. The half-width of the Lorentzian component shows the expected dependence on gas pressure. Under the operating conditions used, this component is approx. 10² times greater than the natural one. No dependence on the discharge current was observed. The emitted line profiles may be considered to be Voigt functions with the Voigt parameter varying in the range 3·2 × 10^-2 to 5.5 × 10^-2     

Optical fiber curvature sensor based on few mode fiber

An optical fiber curvature sensor based on interference between LP₀₁–LP₀₂ modes of a circularly symmetric few mode fiber (FMF) is presented. The device consists of two single-mode fiber and a 10-cm FMF. The two single-mode fiber is offset-spliced to each end of the FMF. When the optical fiber is kept straight and fixed, the interference pattern appears in the transmitted spectrum. As the fiber device is bent, the visibility of the interference fringes (at 1530 nm) decreases, reaching values close to 0.3. The dynamic range of the device can be tailored by the proper selection of the length of FMF. The relationship between the fringe visibility and the curvature is linear while the curvature is between 11 m⁻¹ and 16 m⁻¹. The result indicates that the compact sensor can be used in the measurement of large curvature, which is also important in structural health monitoring.     

Coherent and incoherent spectral broadening in a photonic crystal fiber

The coherence of the spectral broadening process is the key requisite for the application of supercontinua in frequency combs. We investigate the coherence of two subsequent supercontinuum pulses created in a photonic crystal fiber pumped by a femtosecond laser. We measure Young interference fringes from a Michelson-type interferometer at different wavelengths of the output spectrum and analyze their dependence on pump intensity and polarization. The visibility of these fringes is a direct measure of the coherence of the spectral broadening processes.     

基于吸收光谱的光程长度测量方法研究

基于吸收光谱的基本原理,通过计算比尔-朗伯定律数学表达式中的参数实现了光程长度的测量。分析了高斯线型、洛伦兹线型和Voigt线型,采用了Voigt线型对光谱信号进行拟合。研究了Voigt线型峰值计算方法、洛伦兹线宽计算和误差函数求解三个内容。利用可调谐半导体激光吸收谱技术(TDLAS)中的直接吸收谱技术测量了氧气的吸收光谱,得到拟合的光谱峰值数据。将峰值数据带入比尔-朗伯定律数学表达式中,计算出实验光程长度为66.55 cm。对比测量值66.04 cm,测量精度为0.78%,该方法用于光程长度测量是可行的。     

Effect of the laser axial modes on the coherence length of the laser beam

The effect of the presence of the axial modes within the spectral halfwidth of a laser spectral line on the visibility of its interference fringes is represented. It is found in case of axial modes with equal spectral halfwidths that the dominant factor in determining the coherence length of the laser beam is the spectral halfwidth of its axial mode and not the spectral halfwidth of the laser line. For the case of a laser beam with axial modes of different spectral halfwidths, the calculation shows a coherence length, closer to the mode with the smaller halfwidth.     

Fast transforms for speckle photography fringe analysis

Two image processing techniques for automatic analysis of the Young's fringes diffraction patterns from a double-exposure speckle photograph are described. The techniques involve two-dimensional spectral analysis of the image using the Fast Fourier Transform (FFT) or the Fast Walsh Transform (FWT). The accuracy and reliability of the two techniques are compared as a function of the fringe visibility, and the number of pixels used to represent the image. Walsh analysis is found to offer the same accuracy as Fourier analysis, but in about one third the computation time. The Fourier method is more reliable with fringes of the lowest visibility, however. The ideas presented have relevance to the general problem of detecting and accurately determining the frequency components of a sinusoid in the presence of noise.     

Diode Laser Spectroscopy of Water Vapor in 1.8 μM: Line Profile Measurements

A diode laser spectrometer has been used for high accuracy H₂O line profile measurements near 5475 cm⁻¹. Measured lineshapes have been least-squares fitted by Voigt profile with a floating Gaussian component. Gaussian component pressure dependence resulting from the Dicke narrowing effect is observed. Line intensities, self- and air-induced broadenings, and shifts of five water vapor lines are presented.