Doppler Spectra of Centimeter and Millimeter Microwaves Backscattered from a Rough Water Surface at low Grazing Angles

We present the results of processing of X- and Ka-band radar signals backscattered from a rough water surface at low grazing angles. Processing is made by the method of decomposing a Doppler spectrum into three basic line profiles. Each of these profiles corresponds to a certain scattering mechanism. Comparative evaluations of the contribution of the Bragg mechanism described by the Gaussian line profile and two non-Bragg mechanisms described by the Lorentz and Voigt profiles are obtained.     

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.     

Photon trajectories in incoherent atomic radiation trapping as Lévy flights

Photon trajectories in incoherent radiation trapping for Doppler, Lorentz, and Voigt line shapes under complete frequency redistribution are shown to be Lévy flights. The jump length (r) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power law r(-3/2), while for Doppler the asymptotic is r(-2)(ln(r)(-1/2). For the Voigt profile, the asymptotic form always has a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents.     

Spectrum profiles in the presence of stark,Lorentz and Doppler broadenings

The nearest neighbor approximation of the Stark broadening is used, together with the standard Lorentzian and Doppler profiles, to compute convoluted line profiles. Two universal profile functions are obtained which are analogous to the Voigt function.     

Asymmetry and speed-dependent effects on the 748.8 nm self-broadened neon line

Using an interferometric method, detailed analysis of the self-broadened 748.8 nm Ne line shapes emitted from the glow discharge of neon was performed, where departures from the ordinary Voigt profile were observed. These departures are shown to be consistent with fits of the speed-dependent asymmetric Voigt profile to experimental profiles. It was shown that neglecting the correlation between Doppler and collisional broadening may cause errors in determined line shape parameter values. Coefficients of the pressure broadening, shift and collision-time asymmetry are determined and compared with those calculated in the adiabatic approximation for the van der Waals and Lennard-Jones potentials.     

Spectral Intensity and Lineshape Measurements in the First Overtone Band of HF Using Tunable Diode Lasers

High-resolution absorption lineshapes for the P(3) and P(6) transitions of the first overtone (v = 2-0) band of HF at 296 K have been measured using a pair of distributed feedback diode lasers operating near 1.31 and 1.34 μm, respectively. Spectral line intensities and self-broadening parameters were determined by fitting the measured spectra with Voigt, Galatry, and Rautian lineshape models. Voigt profiles fit the low-pressure (<10 Torr) spectra of the P(3) transition reasonably well due to the relatively strong collisional broadening effect. Lineshape measurements of the P(6) transition (for pressures ranging from 5 to 60 Torr) show significant variation from the Voigt lineshape model due to velocity-changing collisions that effectively reduce the Doppler component of the spectral line. Lineshape models that include motional (Dicke) narrowing effects, Galatry (soft collision) and Rautian (hard collision) profiles yield significant improvements in the spectral lineshape fits compared with Voigt profiles. The collisional broadening coefficient (gamma) of the P(6) transition obtained from a Voigt fit is approximately 4% lower than those found with either Galatry or Rautian profile fits. The measured intensities and self-broadening coefficients are compared with values in the HITRAN database and previous measurements. Copyright 1999 Academic Press.     

激光诱导Al等离子体中的Doppler效应

用Nd:YAG脉冲激光烧蚀Al靶产生等离子体,利用时间分辨技术采集Al等离子体辐射的时间分辨信息,使用光学多道分析系统(OMA Ⅲ)记录Al等离子体辐射光谱,从而获得激光诱导Al等离子体时间分辨光谱。分别利用Lorentz函数、Gauss函数以及这两种函数的线性叠加函数(后简称叠加函数),对Al原子共振双线Al Ⅰ 396.15 nm,Al Ⅰ 394.40 nm进行拟合分析,解析出实验谱线所含的Lorentz和Gauss线形成分。通过对比这两种线形成分发现,实验谱线主要由Lorentz线形成分所组成,Gauss线形成分相对少得多。通过对比Lorentz函数与叠加函数对实验谱线的拟合曲线,给出了Doppler效应展宽谱线的直观图像,估算了Doppler效应导致谱线的增宽量。结果发现,Doppler效应引起的Al共振谱线增宽约2×10-3～8×10-3 nm,这与理论计算结果6.7×10-3 nm符合得很好。因此,通过拟合分析与理论计算,对激光诱导Al等离子体中的Doppler效应给以圆满解释。     

Integrated absorption of a spectral line with the Voigt profile

A simple approximation has been found for the integrated absorpton of a spectral line with Voigt profile. It is expressed in terms of the integrated absorption of the Doppler and Lorentz profiles. The maximum error is 8%.     

Some remarks about relativistic line profiles

We give, by analogy with relativistic kinetic theory, a fully relativistic definition of line profiles. Some examples are given. Relativistic broadening of lines produces asymmetries and blue-shifting. We have also calculated the relativistic Voigt profile.     

Radiation trapping in an alkali-vapor-noble-gas mixture excited by a strong laser pulse

We analyze the nonlinear, non-stationary radiation trapping process in a cell filled with a noble gas and an alkali vapor excited by a short intense laser pulse. We derive analytical approximations for the total density of the excited atoms, and for the radiation emerging from the cell. The considered lineshapes are pure Doppler, Voigt, and pure Lorentzian profiles. We confirm that the emergent radiation can decay faster than with the natural lifetime of the atomic transition. We also show that as we increase the noble gas pressure, the decay of the emergent radiation becomes slower at early times and faster at late times.     

Optical Escape Factors for Bound-bound and Free-bound Radiation from Plasmas. I. Constant Source Function

Optical escape factors for bound-bound and free-bound radiation have been calculated by solving the equation of radiative transfer with the assumption that the corresponding source functions are space-independent. The general expression for bound-bound transitions yields for large optical depths—within a correction factor of order unity—Holstein's asymptotic expressions for the two limiting cases of a Doppler and a dispersion profile. Application to the more general case of a Voigt profile leads to an analytical formula which permits a rapid estimate of the escape factor for any optical depth. Numerical application to the resonance lines of neutral helium-which are broadened by Stark and Doppler effects—shows that under certain plasma conditions most of the higher members of the resonance series remain optically thin.—The general expression obtained for the escape factor of free-bound radiation has been applied to the resonance continuum of neutral helium. The numerical results show that the resonance continuum remains optically thin as long as the optical depth in the center of the He resonance line (λ = 584 Å) remains smaller than 10⁴ to 10⁵. A similar result is obtained for atomic hydrogen.     

Lineshape analysis of the J = 3 ← 2 and J = 5 ← 4 rotational transitions of room temperature CO broadened by N2, O2, CO2 and noble gases

Collisional relaxation has been considered for millimeter lines of carbon monoxide at room temperature. Accurate measurements of carbon dioxide- and rare gases-broadened widths have been performed on the J = 3 ← 2 rotational line of ¹²CO by using a video-type spectrometer. Measurements of nitrogen-, oxygen-, and xenon-broadened widths of the J = 5 ← 4 rotational line of ¹³CO were also carried by using a frequency-modulated spectrometer. A lineshape study performed on all the investigated binary systems provide confirmation that Voigt profile is not a suitable model to analyse experimental lines in the millimeter-waves region. On one hand, using this profile in the low pressure range, i.e. in the Doppler regime, the retrieved collisional linewidths do not follow a linear variation with the perturbing gas pressure. On the other hand, regardless of the pressure, lineshapes exhibit a narrowed profile. An accurate analysis of the pressure dependence of relaxation rates show that the Galatry profile is not appropriate and that experimental lineshapes are actually Speed Dependent Voigt profiles. Accurate broadening parameters were retrieved from this profile and compared to previous reported values and predictions calculated from the Robert-Bonamy formalism. Finally a variation of the ratio of relaxation speed dependence to broadening parameters versus relative masses of the collision partners is presented.     

An empirical study on the importance of a speed-dependent Voigt line shape model for tropospheric water vapor profile remote sensing

We use high quality ground-based solar absorption spectra measured in close coincidence with Vaisala RS92 radiosonde in situ water vapor profiles to demonstrate that a Voigt line shape model yields systematic errors in the remotely sensed tropospheric water vapor profiles. We analyse absorption signatures of 4 H₂¹⁶O and 2 HD¹⁶O bands situated between 790 and 4710 cm⁻¹. We find that applying a speed-dependent Voigt line shape model instead of a Voigt line shape model significantly improves the agreement between the water vapor profiles obtained by the radiosondes and by infrared remote-sensing in the different bands. An optimal agreement is obtained for a Γ₂ (relaxation rate for speed-dependence) of 6-21% of Γ₀ (Voigt relaxation rate), which is consistent to the values derived from laboratory experiments. Our study suggests that further extensive laboratory investigations of line shape models are a key for improving the quality of modern water vapor remote sensing products.     

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。     

低压下飞秒激光诱导Cu等离子体的诊断及空间分布实验研究

本文分别利用Gauss、Lorentz和Voigt函数对10Pa背景气压下飞秒激光诱导Cu等离子体光谱进行了拟合分析,结果表明,光谱在150ns内与Lorentz线型符合较好,200ns后与Gauss线型符合较好,Voigt线型与实验谱线一直符合较好。本文还对等离子体的电子密度和温度进行了诊断,并给出了它们随时间的演化;由发射光谱强度的时空演化,推知了等离子体的空间分布;利用时间飞行谱(TOF)得出了等离子体初期沿垂直靶面的膨胀速度。     

Correlation effects in the theory of combined doppler and pressure broadening—I. Classical theory

A classical Fourier amplitude theory of combined Doppler and pressure broadening in the impact approximation is developed which treats phase changes changes due ti translation and collision on an equal basis. Radiator motion is accounted for properly by including speed dependence in the collision frequency and velocity dependence in the distribution function for phase shifts and final velocities as the result of a collision. The resulting theory is shown to be equivalent to a previous kinetic equation formulation of the problem. The one-perturber and classical analogue of the quantum one-interacting-level approximations are derived. In the latter case, a simple expression for the line shape in terms of speed dependent width and shift functions is obtained without approximation. Correlation effects are investigated by means of model speed dependent width and shift functions calculated for an inverse power interaction using straight line trajectories. The model shows no departure from a Voigt profile for the r^-3 interaction and for the r^-6 and r^-12 interactions the resulting profile is narrower in the core than the Voigt and in general asymmetric. Analysis of correlated profiles as Voigt profiles is shown under some conditions to lead to non-linear density dependence in the width and shifts resulting in extra- polation anomalies and to significant errors in temperatures inferred from Doppler widths. Results are compared with previous work.     

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。     

Separation of the overlapping spectral lines using derivative spectra

A code package is written to determine the maximum positions and half-widths of overlapping spectral lines forming the total profile. This package allows us to reconstruct spectral line profiles forming the total shape based on the experimental spectrum. An analysis is carried out based on the n-th derivatives of the line shape under study. The package calculates the Doppler, Lorentz and Voigt profiles and their n-th order derivatives and constructs spectral line profiles forming the spectral line under consideration and the corresponding total profile. These codes can be used both in molecular and in atomic spectroscopy, if need be. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 80–85, April, 2006.     

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     

Doppler effect in resonant photoemission from SF6: correlation between Doppler profile and Auger emission anisotropy

Fragmentation of the SF6 molecule upon F 1s excitation has been studied by resonant photoemission. The F atomiclike Auger line exhibits the characteristic Doppler profile that depends on the direction of the photoelectron momentum relative to the polarization vector of the radiation as well as on the photon energy. The measured Doppler profiles are analyzed by the model simulation that takes account of the anisotropy of the Auger emission in the molecular frame. The Auger anisotropy extracted from the data decreases with an increase in the F-SF5 internuclear distance.