A Comparison of Different Methods of Separation of Continuous Overlapping Spectral Lines

Several methods of separation of continuous overlapping spectral lines are compared. In the majority of methods, the profile of each line is modeled by a Gaussian or Lorentzian, and total measured spectrum z is processed. Number of lines N and their parameters are usually estimated by the method of derivatives; however, the differentiation of noisy spectrum z causes large errors. To improve the differentiation accuracy, it is proposed to use smoothing splines. In the Fourier-self-deconvolution method, apodization (artificial truncation of the interferogram) is used to resolve overlapping lines, which makes it possible to resolve lines, but at the expense of a significant decrease in their widths. In this work, reducing the widths of lines is not used for their resolution, but rather, true line profiles are reconstructed by minimizing the residual functional with the modified coordinate-descent method using the decremental-constraint technique, and also, for comparison, with the Nelder–Mead simplex method. In the Manoilov method, the parameters of lines (peaks) are determined from convolutions of spectrum derivatives with individual peaks. In that method, the notion of the degree of overlap has been also introduced. In this work, we introduce a generalized degree of overlap for the case in which the amplitudes, widths, and spacings between neighboring lines are different. Numerical illustrations are presented.     

Application of pressure broadening theory to the calculation of atmospheric oxygen and water vapor microwave absorption

The problem of the pressure broadening of spectral lines is investigated with respect to the microwave absorption of two terrestrial atmospheric gases, oxygen and water vapor. A formalism and accompanying computational procedures under the impact approximation and using the Liouville (line) Space concept introduced by Baranger and elaborated by Fano are employed. It is desired that the theory would obviate the necessity for specific line shapes, provide a means of computing line widths and account for line overlapping effects from first principles. The present approach is found to be generally adequate for the treatment of O₂ absorption on comparison with experimental data for line widths, absorption coefficients and zenity opacities. While H₂O line widths are satisfactorily predicted, estimated resonance overlapping effects are found to be far from sufficient (accounting for at most ~ 5%) to explain the theoretically controversial anomalous absorption.     

Resonance absorption band model

A model is derived for the resonance absorption of molecular bands composed of Lorentzian lines that is suitable for calculating fluorescence from irradiated air. The model is based on an explicit functional form derived for the resonance absorption of a single Lorentzian line which properly accounts for the possibility of unequal emission and absorption line widths. A procedure for rapid numerical computation of this function is given. This function yields a model for the resonance absorption of molecular bands composed of either overlapping or separated lines. A significant savings in computation time is obtained by using the model in place of exact expressions for resonance absorption. Examples are given for the resonance absorption of the N₂⁺ First Negative band system.     

Density Measurements from the Asymmetry of the Lyman ζ Line in a Vacuum Spark Lithium Discharge

A lithium spectrum is obtained form vacuum spark discharges using a grazing-incidence flat-field spectrometer. Hydrogen-like lines up to Lyman η are identified in the spectrum. The spectrum is analyzed, and it is found that the experimental line widths increase along the Lyman series. An asymmetry between the blue and red wings appears in the profile of the Lyman ζ line, and becomes significant in the profile of the Lyman ? line. A relatively new method is used to estimate an electron density of 1 ± 0.4 × 10¹⁸cm^?3 from the experimental degree of asymmetry between the blue and the red wings of the Lyman ζ line. This result is compared with an analysis of the experimental widths of two optically thin lines, namely, Lyman δ and Lyman ζ. In this analysis an electron density of 1.2±0.5 × 10¹⁸cm^?3 is deduced. The principal quantum number of Lyman η (n=8) is used in the Inglis-Teller formula for the last line seen before the merging of the lines with the continuum, and the estimated electron density is found to be 2.0 × 10¹⁸cm^?3 for the lithium plasma. Thus, it is demonstrated that the new method employing the asymmetry of the lineshapes in dense plasmas yields results consistent with the analysis of the widths of the lines. However, it requires obtaining the profile of just one spectral line, which is a great advantage. The reference data on the Stark broadening of the Lyman ζ line is also tabulated, which was previously unavailable in the literature.     

High resolution emission spectra of laser-excited molecular iodine as the excitation frequency is tuned through and away from resonance

We have studied the ΔJ = 2 rotationally shifted emission lines in the region of the strong absorption of molecular iodine which occurs within the 5145 Å argon ion laser line. We used an etalon tuned, single frequency argon ion laser with a linewidth of 20 MHz to excite the iodine emission and recorded the spectra of the rotational lines with Fabry-Perot spectrometers having resolutions up to 70 MHz (0.0023 cm^-1). To overcome Doppler linewidth limitations we took spectra of the emission at small angles to the exciting beam and found the lines to have widths less than our instrumental resolution and frequencies which accurately tuned with the incident laser frequency. We recorded the emission lines for laser frequencies in the absorption line center and out into the absorption wing. Our spectra show that the intensity of the emission lines follows the absorption line profile while the frequency of the emission lines is determined by the laser frequency; the intensity is maximum at the absorption line center, falling by 10⁴ as the laser frequency is moved off the line center, while the line position maintains a constant frequency shift from the laser frequency.     

Information content of a planetary spectrum

The information content of equivalent widths and line profiles is investigated when all of the pressure-broadened lines belong to a unique spectrum. The parameters which can be derived without a priori knowledge of the planetary atmosphere are emphasized. In general, the analysis of equivalent widths alone does not allow one to distinguish between different atmospheric models. A scattering indicator, which is a dimensionless number derived from the shape of line wings, is found to determine the influence of scattering in the absorption process.     

Widths and shifts of HF vibration-rotation absorption lines induced by pressure of rare gases

Widths and shifts of the HF vibration-rotation absorption spectrum, induced by the pressure of rare gases, have been calculated using the Kolb-Griem-Baranger theory, for the pure rotation, 0–1, and 0–2 bands. Agreement between the calculated and experimental widths is good in general, but the calculated shifts, though having a qualitatively correct m-dependence for the most part, exceed the experimental values by a factor of 1·3-2·0. Isotropic effects are included to all orders, leading to three major consequences: (1) a criticism is made regarding one of the assumption underlying Anderson's approximation number two, (2) a reason is provided for the differences in widths of R and P branch lines of the same ∣m∣ within a given band, and (3) the previously unexplained increase in widths with increasing ∣m∣ in the 0–2 band with xenon is explained.     

EPR and IR spectral studies on Mn ions in nickel maleate tetrahydrate single crystals

Electron paramagnetic resonance (EPR) studies have been carried out on Mn²⁺ ions doped in nickel maleate tetrahydrate single crystals in the temperature range 103-413 K on X-band frequency. The EPR spectrum at room temperature exhibits a group of five fine structure transitions each splits into six hyperfine components. Angular variation studies reveal the presence of a single site and it is found that Mn²⁺ ions enter the lattice substitutionally. From the observed EPR spectrum, the spin-Hamiltonian parameters have been evaluated. The variation of zero-field splitting parameter (D) with temperature is measured. The observed EPR spectra exhibit a large anisotropy in the widths of Mn²⁺ resonance lines. The widths of Mn²⁺ resonance lines increase with the Zeeman field intensity and these observations have been discussed in detail. The infrared spectrum exhibits bands characteristic of the carboxylic acid salts.     

Absolute and relative line intensity measurements when the spectral lines are not optically thin

The curves of growth were used in order to determine the Doppler absorption coefficient at the line center, k_D0, from absolutely measured line intensities (equivalent widths) and theoretical widths. It is shown that the relative line intensities from a single path and a double path may be used for the determination of absorption coefficients and absolute oscillator strengths, for estimating absorption at the inhomogeneous ends of a plasma column, and for assessing the approach to thermal equilibrium.Measurements were carried out on the red argon lines arising from the 4s–4p transition arrays. The influence of plasma diagnostics on the f-value is considered, and our f-values are compared with other measurements.     

Collisional line shifting and broadening in the fundamental P-branch of CO in Ar between 214 and 324 K

The collisional shifts and widths of several P-branch spectral lines in the fundamental band of CO-Ar have been measured at temperatures between 214 and 324 K and pressures between 0.025 and 1 atm. The widths have been determined using a line shape model based on the solution of the transport/relaxation equation for the appropriate off-diagonal element of the density matrix. The model uses a realistic molecular potential energy surface to calculate the speed dependence of the collisional broadening, and a rigid sphere potential to calculate the translational motion. It is found that both the shifting and broadening coefficients follow a power law dependence on the temperature. Additionally, it is demonstrated that studies have tended to overestimate the accuracy of collisional widths when the line shape model used to obtain the widths involves multiple fitted line shape parameters or fails to fit the measured spectra within the experimental noise.     

梯-型三能级系统中自发辐射的量子相干控制

采用从基态到第一激发态为双激光场驱动的物理模型,对梯形三能级系统中自发辐射的相干控制进行了分析,通过变换驱动激光场之间的相对相位得到了一些主要结果.共振激发时,谱线呈现出三个谱峰的对称形式.当初始相位相同时,两边辐射峰值较高而中间峰值较低.随着初相位差的增加,两边谱峰之间的距离逐渐增大,谱线的高度逐渐下降,中心谱线的高度随着初始相位差的增加逐渐增大,宽度逐渐变小,直至成为一条较为尖锐的线,实现了对两边谱峰的完全抑制效应.采用下能级为双激光场激发的梯-型三能级系统,通过变换激光场之间的相对相位,实现了对激发态自发辐射的量子相干控制,观察到自发辐射光谱的抑制及谱线的猝灭等效应.     

Experimental study of stark broadening of nitrogen ion lines in a theta pinch plasma

We have studied the Stark broadening of the 3s-3p, 3p-3d and 3d-4f emission lines of the nitrogen II, III, and IV ions emitted from a hot plasma. The plasma was created by a 60 kJ, 60 kV single turn coil theta pinch, where the fill gas was 3 torr of (49%He+51%N₂). The plasma was diagnosed by measuring the Stark-broadened profile of the He(II) 4686 Å line and by taking shadowgrams of the plasma development. It was found that the ionization stage distribution and thus the electron density departed from that predicted by Saha-Boltzmann equilibrium relations. The analysis of the plasma parameters gave an electron density of 1.4 x 10¹⁸ cm^-3. The electron temperature was measured from the relative intensities of emission lines as well as from the line-to-continuum ratio and was found to be 5.0 eV. The line profiles have been fitted to Lorentzian profiles and the thus measure line widths are compared with earlier experimental data as well as with simple theoretical calculations. We find that our line widths are broader than earlier data taken at lower densities if we assume a linear scaling of the half width with the density. A simple Lorentzian profile fits in most cases quite well to the observed line profile. The simple calculations can predict the linewidths within 20% for the low lying levels of both the singly and doubly ionized nitrogen while the predictions are far too narrow for the higher lying levels from the multiply ionized atoms.     

Analysis of tunable diode-laser spectra of Q(J,0) lines in CH3F near 1475 cm using a multispectrum fitting technique

We have analyzed the methyl fluoride ^RQ(J,0)Q branch lines located near 1475 cm⁻¹ using a simultaneous multi-spectrum fitting technique. In this analysis we have used previously recorded diode-laser data in which we collected many data points covering only one or two Q branch lines in a particular run. The analysis consists of simultaneously fitting 57 spectra collected with numerous pressure and path length conditions for all absorption lines. The data are concatenated to create one continuous spectrum of the Q branch. We have determined the intensity and self-broadened widths at 296 K for 23 ^RQ(J,0) lines.     

Stark-Effekt-Verbreiterung der Neon I-Übergänge mit schwacher Feldstärkeabhängigkeit (2p 5 3s-2p 5 3p)

The half widths of Stark-broadened Ne I spectral lines (2p ⁵ 3s-2p ⁵ 3p) were measured in wall stabilized arc plasmas (pressurep=1 atm, andp=3 atm) consisting of several gas components (Ar 68%, Ne 27%, He 3%, H₂ 2%). The theoretical half widths of two spectral lines (λ=6,266.50 Å,λ=6,163.59 Å) with known calculated broadening parameters according to Griem differ by a factor 1.8 to 1.9 from the measured widths. Within the errors of Griem's line broadening calculations of about 20% there was agreement between experimental and theoretical half widths regarding two other spectral lines (λ=5,881.90 Å,λ=5,852.49 Å). Calculated adiabatic widths are smaller than the widths according to Griem. Therefore in some cases the deviation of the adiabatic widths from the measured widths is smaller than the difference between Griem widths and experimental ones. Static quadratic coefficients of NeI transitions 2p ⁵ 3s-2p ⁵ 3p calculated from measured Stark-broadened lines showed wavelength displacements in the order of 0.005 Å referring to an electrical field of 100 kV/cm. The determined coefficients are 10² times smaller than those values measurable by known methods of emission spectroscopy.     

Collisional parameters of H2O lines: effects of vibration

A complex semiclassical model for the calculation of line widths and shifts of H₂O broadened by N₂, derived from the Robert and Bonamy approach, is tested by comparisons with measurements for selected transitions in various vibrational bands. The lines retained, which involve rotational states with Kc=J or J−1 have been chosen for two reasons. The first is that they show large variations of the widths with J and thus enable a severe test of the model. The second is that, as explained in this paper, they are well-suited for the study of the effects of vibration on the collisional parameters. The measured values have been extracted from an updated version of a database built years ago (JQSRT 52 (1994) 481) that contains all available measurements. Comparisons between experimental and calculated widths and shifts at room temperature illustrate the quality of the model and clearly demonstrate, for the first time, that there is a vibrational dependence of the broadening. Values of collisional parameters are first studied in fundamental bands. This shows that the theoretical approach accounts for most of the dependence of broadening and shifting on rotational quantum numbers: the variations of γ, which reach a factor of nearly 20 from low to high J values, are correctly accounted for by the model as are some specific features of the shifts δ. Analysis confirms that the bending and stretching vibrations have significantly different effects on δ, due to the vibrational dependence of the intermolecular potential. On the other hand, differences on the widths are rather small with slightly smaller broadening for lines of the bending band. Calculations show that there is a spectroscopic effect, due to the larger rotational constant A in the v₂=1 state. Calculations made for overtone bands involving numerous quanta of the stretching vibration are then presented. They predict that a significant dependence of the width should be observed for high J lines due to the effect of vibration on the interaction potential. This is confirmed by comparisons with measurements for lines involving a change of three and four quanta of stretching vibration.     

Application of pattern recognition in molecular spectroscopy: Automatic line search in high-resolution spectra

An expert system has been developed for the initial analysis of a recorded spectrum, namely, for the line search and the determination of line positions and intensities. The expert system is based on pattern recognition algorithms. Object recognition learning allows the system to achieve the needed flexibility and automatically detect groups of overlapping lines, whose profiles should be fit together. Gauss, Lorentz, and Voigt profiles are used as model profiles to which spectral lines are fit. The expert system was applied to processing of the Fourier transform spectrum of the D₂O molecule in the region 3200–4200 cm^?1, and it detected 4670 lines in the spectrum, which consisted of 439000 dots. No one experimentally observed line exceeding the noise level was missed.     

H2-broadening,shifting and mixing coefficients of the doublets in the ν2 and ν4 bands of PH3 at room temperature

The broadening, shifting and mixing coefficients of the doublet spectral lines in the ν₂ and ν₄ bands of PH₃ perturbed by H₂ have been determined at room temperature. Indeed, the collisional spectroscopic parameters: intensities, line widths, line shifts and line mixing parameters, are all grouped together in the collisional relaxation matrix. To analyse the collisional process and physical effects on spectra of phosphine (PH₃), we have used the measurements carried out using a tunable diode-laser spectrometer in the ν₂ and ν₄ bands of PH₃ perturbed by hydrogen (H₂) at room temperature. The recorded spectra are fitted by the Voigt profile and the speed-dependent uncorrelated hard collision model of Rautian and Sobelman. These profiles are developed in the studies of isolated lines and are modified to account for the line mixing effects in the overlapping lines. The line widths, line shifts and line mixing parameters are given for six A₁ and A₂ doublet lines with quantum numbers K = 3n,?(n = 1,?2, …) and overlapped by collisional broadening at pressures of less than 50 mbar.     

Temperature dependence of EPR spectrum of Mn2+ doped in ammonium iodide single crystals

EPR of Mn²⁺ doped in ammonium iodide single crystal has been studied at X-band in the temperature range 573–577 K. The observed temperature dependence of line widths and spin Hamiltonian parameter b₂⁰ below room temperature is related to the structural transformations in the crystal. The coexistence of high temperature phase (NaCl) and low temperature phase (CsCl) is attributed to the large thermal hysteresis in line widths and b₂⁰. The dissociation of ion vacancy pairs occurs near 500 K and is reflected in the reversible change of an anisotropic EPR spectrum in an isotropic sextet near this temperature. The ion vacancy pair models for NaCl and CsCl phases are discussed along with the effects of thermal processing of the samples. Heating the crystals above 500 K leads to expulsion of Mn²⁺ impurity from the crystal.     

Calculated line broadening coefficients in the ν2 band of CH3D perturbed by helium

Line broadening coefficients have been calculated, at room temperature, for lines in the P and R branches of the ν₂ band of monodeuterated methane. A properly symmetrized semiclassical model with parabolic relative trajectories has been used. Two interaction potential models have been considered. The first is a Lennard-Jones type atom-atom potential, while the second one was derived from ab initio calculations. The calculated line widths were compared to the available experimental data and a satisfactory agreement was found, although the model contains no other adjustable parameters than the four atomic Lennard-Jones ones. Nonetheless, failures of calculations have also been evidenced for the highest rotational quantum numbers.     

The effect of GaAs(001) substrate roughness on the magnetic properties of epitaxial Fe films

The effect of GaAs(001) surface roughness on the magnetic properties of MBE-grown Fe films having a thickness t in the interval from 12 to 140 Å is investigated by the ferromagnetic resonance method. The films were deposited at room temperature with rates of 9 and 3 Å/min. For films grown on substrates with the rms deviation of the roughness σ≈10 and 30 Å, the spectrum is essentially dependent on the relationship between t and σ. At t≤σ and t≥3σ, a single absorption line is observed, whereas at σ≤t≤3σ, two absorption lines are present. These features of the spectra are related to the island growth of the films and the influence of roughness on island coalescence.