Fraunhofer Lines Research Articles

A convolution algorithm of differential coefficients of liquid water based on vibrational Raman scattering

Inelastic vibrational Raman scattering by liquid water is one significant limitation to the accuracy of the retrieval of trace gas constituents in atmosphere over waters, particularly over clear ocean waters, while using satellite data with differential optical absorption spectroscopy technique (DOAS). The effect which is similar to the Ring effect in atmosphere results in the filling-in of Fraunhofer lines, which is known as solar absorption lines. The inelastic component of the liquid water scattering causes a net increase of radiance in the line because more radiations shift to the wavelength of an absorption line than from this wavelength to other wavelengths. The solar spectrum transmitting atmosphere is convolved with vibrational Raman scattering coefficient of liquid water, divided by the original computed spectrum, with a cubic polynomial subtracted off, to create differential water Ring spectrum. This method is suggested in order to obtain an effective differential water Ring coeffient for the DOAS fitting process, which could be used to improve the accuracy of the retrieval of the trace gases concentration. The method does not rely on radiative transfer model of water, which would be time-consuming and depending on lot of parameters. Therefore, it is very fast and convenient.

A double plateau and unprecendented circumstellar variable sodium in the transient SN 2011A

AbstractWe present optical photometry and spectrosopy of the transient SN 2011A. Our data spans 140 days after discovery including BVRIu'g'r'i'z' photometry and a sequence of 11 spectra. First classified as a type IIn supernova due to the presence of narrow Hα emission, this object shows exceptional characteristics. Firstly, the light curve shows a double plateau; a property only before observed in the impostor object SN 1997bs. Secondly SN 2011A has a very low luminosity for a type IIn supernova placing it between the type IIn supernovae and impostor classes in terms of luminosity. Thirdly, SN 2011A shows low velocity and high equivalent width sodium doublet absorption which increases with time and is most likely of circumstellar origin. This evolution is also accompanied by a change of line profile. When the absorption becomes stronger, a P-Cygni profile appears.

The anomalous sodium doublet D2/D1spectral line intensity ratio – a manifestation of CCD's presaturation effect

Download options Please wait... Article information DOI https://doi.org/10.1039/C2JA30239J Article type Paper Submitted 20 Jun 2012 Accepted 24 Oct 2012 First published 24 Oct 2012 Download Citation J. Anal. At. Spectrom., 2013,28, 92-97 BibTex EndNote MEDLINE ProCite ReferenceManager RefWorks RIS Permissions Request permissions The anomalous sodium doublet D2/D1 spectral line intensity ratio – a manifestation of CCD's presaturation effect B. Kasalica, S. Stojadinović, I. Belča, M. Sarvan, L. Zeković and J. Radić-Perić, J. Anal. At. Spectrom., 2013, 28, 92 DOI: 10.1039/C2JA30239J To request permission to reproduce material from this article, please go to the Copyright Clearance Center request page. If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given. If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page. Read more about how to correctly acknowledge RSC content. Social activity Tweet Share Search articles by author Bećko Kasalica Stevan Stojadinović Ivan Belča Mirjana Sarvan Ljubiša Zeković Jelena Radić-Perić

The Physics and Plasma Chemistry of an RF Needle in a Saltwater Aerosol

Experiments involving the insertion of a tungsten needle powered by an ~1-kW radio-frequency (RF) generator into a flowing saltwater mist produced by a nebulizer are described. The tip of the tungsten electrode is estimated to have a temperature near the 5555-°C vaporization temperature of tungsten. Values of E/N close to the electrode tip are estimated to be greater than the breakdown threshold of humid air. This arrangement of RF-powered electrode and flowing saltwater aerosol produces a flame of some 30 cm high having strong light emission near the 589-nm sodium-D lines. We present a model demonstrating that the emission trapped in the core along the length of the flame arises primarily from Na(3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> P → 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> S) with some Na <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> * emission. The rising flame cools slowly due to a combination of the opacity of the hot gas, the large heat capacity of the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O molecules in the flame, and the exothermicity of the plasma chemistry in the afterglow.

Remote sensing of near-infrared chlorophyll fluorescence from space in scattering atmospheres: implications for its retrieval and interferences with atmospheric CO&amp;lt;sub&amp;gt;2&amp;lt;/sub&amp;gt; retrievals

Abstract. With the advent of dedicated greenhouse gas space-borne spectrometers sporting high resolution spectra in the O2 A-band spectral region (755–774 nm), the retrieval of chlorophyll fluorescence has become feasible on a global scale. If unaccounted for, however, fluorescence can indirectly perturb the greenhouse gas retrievals as it perturbs the oxygen absorption features. As atmospheric CO2 measurements are used to invert net fluxes at the land–atmosphere interface, a bias caused by fluorescence can be crucial as it will spatially correlate with the fluxes to be inverted. Avoiding a bias and retrieving fluorescence accurately will provide additional constraints on both the net and gross fluxes in the global carbon cycle. We show that chlorophyll fluorescence, if neglected, systematically interferes with full-physics multi-band XCO2 retrievals using the O2 A-band. Systematic biases in XCO2 can amount to +1 ppm if fluorescence constitutes 1% to the continuum level radiance. We show that this bias can be largely eliminated by simultaneously fitting fluorescence in a full-physics based retrieval. If fluorescence is the primary target, a dedicated but very simple retrieval based purely on Fraunhofer lines is shown to be more accurate and very robust even in the presence of large scattering optical depths. We find that about 80% of the surface fluorescence is retained at the top-of-atmosphere, even for cloud optical thicknesses around 2–5. We further show that small instrument modifications to future O2 A-band spectrometer spectral ranges can result in largely reduced random errors in chlorophyll fluorescence, paving the way towards a more dedicated instrument exploiting solar absorption features only.

Enthalpies of Dilution, Volumetric Properties, and Refractive Indices of N,N′-Hexamethylenebisacetamide in Aqueous Xylitol or d-Mannitol Solutions at T = 298.15 K

The enthalpies of dilution (ΔdilHm), apparent molar volumes (Vϕ), and refractive indices (nD) of N,N′-hexamethylenebisacetamide (HMBA) in aqueous solutions of xylitol and d-mannitol were respectively determined at 298.15 K with the methods of isothermal microcalorimetry, density, and refractive-index measurements. The enthalpic interaction coefficients (h2, h3, and h4), limiting partial molar volumes (Vϕ0), and transfer partial molar volumes (ΔtrsVϕ0) from water to solutions and molar refractions at the sodium-D line (RD) were deduced from the experimental data in the polyols molality range (0 to 0.9) mol·kg–1. The important parameters were interpreted to understand the interactions among solvated solute molecules in HMBA–xylitol (or mannitol)–water ternary systems. The results indicated that the number of hydroxyls in the both polyols could evidently affect the parameters.

Passive remote sensing of solar-induced fluorescence spectra of crude oil

The solar-induced fluorescence (SIF) of a simulated oil slick is remotely retrieved from the infilling of the solar Fraunhofer lines of its radiance spectrum acquired by means of a sub-nanometric spectral resolution fluorescence lidar operated in passive mode (i.e. as a spectroradiometer). SIF data, retrieved from the infilling of several Fraunhofer lines selected in the 390–660 nm range, were exploited to reconstruct the oil fluorescence spectrum. This spectrum was finally compared with laser-induced fluorescence spectra acquired on the same oil slick by using the fluorescence lidar. The results open new prospects for the remote sensing of oils and their classification.

Synthesis and characterization of a novel carboxyl group containing (co)polyimide with sulfur in the polymer backbone

Soluble functional (co)polyimides are of great interest in the area of separation processes or optical applications, due to their excellent mechanical-, thermal- and optical properties, their superior processability and the ability to adapt their properties to a wide range of special applications. Therefore, two series of novel (co)polyimides containing fluorinated sulfur- and carboxylic acid groups consisting of 4,4′-(hexafluoroisopropylidene)di(phthalic anhydride) (6FDA), 3,5-diaminobenzoic acid (DABA), 4,4′-diaminodiphenylsulfide (4,4′-SDA) and 3,3′-diaminodiphenylsulfone (3,3′-DDS) were synthesized in a two-step polycondensation reaction. The synthesized copolymers were characterized by using NMR, FTIR, GPC, and DSC. Furthermore, with regard to processing and potential applications, the thermal stability, solubility in common organic solvents, moisture uptake, and transparency were investigated. Compared to commercially available transparent polymers, i.e., polymethylmethacrylate and cycloolefin polymers, the sulfur (co)polyimides containing carboxyl groups showed much higher glass-transition temperatures, comparably low moisture uptake and high transmission at the sodium D-line. Furthermore, good solubility in commonly used organic solvents makes them very attractive as high-performance coating materials.

Filling-in of near-infrared solar lines by terrestrial fluorescence and other geophysical effects: simulations and space-based observations from SCIAMACHY and GOSAT

Abstract. Global mapping of terrestrial vegetation fluorescence from space has recently been accomplished with high spectral resolution (ν/Δν &gt; 35 000) measurements from the Japanese Greenhouse gases Observing SATellite (GOSAT). These data are of interest because they can potentially provide global information on the functional status of vegetation including light-use efficiency and global primary productivity that can be used for global carbon cycle modeling. Quantifying the impact of fluorescence on the O2-A band is important as this band is used for photon pathlength characterization in cloud- and aerosol-contaminated pixels for trace-gas retrievals including CO2. Here, we examine whether fluorescence information can be derived from space using potentially lower-cost hyperspectral instrumentation, i.e., more than an order of magnitude less spectral resolution (ν/Δν ~ 1600) than GOSAT, with a relatively simple algorithm. We discuss laboratory measurements of fluorescence near one of the few wide and deep solar Fraunhofer lines in the long-wave tail of the fluorescence emission region, the calcium (Ca) II line at 866 nm that is observable with a spectral resolution of ~0.5 nm. The filling-in of the Ca II line due to additive signals from various atmospheric and terrestrial effects, including fluorescence, is simulated. We then examine filling-in of this line using the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) satellite instrument. In order to interpret the satellite measurements, we developed a general approach to correct for various instrumental artifacts that produce false filling-in of solar lines in satellite measurements. The approach is applied to SCIAMACHY at the 866 nm Ca II line and to GOSAT at 758 and 770 nm on the shoulders of the O2-A feature where there are several strong solar Fraunhofer lines that are filled in primarily by vegetation fluorescence. Finally, we compare temporal and spatial variations of SCIAMACHY additive signals with those of GOSAT and the Enhanced Vegetation Index (EVI) from the MODerate-resolution Imaging Spectroradiometer (MODIS). Although the derived additive signals from SCIAMACHY are extremely weak at 866 nm, their spatial and temporal variations are consistent with chlorophyll a fluorescence or another vegetation-related source. We also show that filling-in occurs at 866 nm over some barren areas, possibly originating from luminescent minerals in rock and soil.

THE Na 8200 Å DOUBLET AS AN AGE INDICATOR IN LOW-MASS STARS

We investigate the use of the gravity sensitive neutral sodium (NaI) doublet at 8183 Angstroms 8195 Angstroms (Na 8200 Angstrom doublet) as an age indicator for M dwarfs. We measured the Na doublet equivalent width (EW) in giants, old dwarfs, young dwarfs, and candidate members of the Beta Pic moving group using medium resolution spectra. Our Na 8200 Angstrom doublet EW analysis shows that the feature is useful as an approximate age indicator in M-type dwarfs with (V-K_s) >= 5.0, reliably distinguishing stars older and younger than 100 Myr. A simple derivation of the dependence of the Na EW on temperature and gravity supports the observational results. An analysis of the effects of metallicity show that this youth indicator is best used on samples with similar metallicity. The age estimation technique presented here becomes useful in a mass regime where traditional youth indicators are increasingly less reliable, is applicable to other alkali lines, and will help identify new-low mass members in other young clusters and associations.

Retrieval and global assessment of terrestrial chlorophyll fluorescence from GOSAT space measurements

The recent advent of very high spectral resolution measurements by the Fourier Transform Spectrometer (FTS) on board the Greenhouse gases Observing SATellite (GOSAT) platform has made possible the retrieval of sun-induced terrestrial chlorophyll fluorescence (Fs) on a global scale. The basis for this retrieval is the modeling of the in-filling of solar Fraunhofer lines by fluorescence. This contribution to the field of space-based carbon cycle science presents an alternative method for the retrieval of Fs from the Fraunhofer lines resolved by GOSAT-FTS measurements. The method is based on a linear forward model derived by a singular vector decomposition technique, which enables a fast and robust inversion of top-of-atmosphere radiance spectra. Retrievals are performed in two spectral micro-windows (∼2–3nm width) containing several strong Fraunhofer lines. The statistical nature of this approach allows to avoid potential retrieval errors associated with the modeling of the instrument line shape or with a given extraterrestrial solar irradiance data set. The method has been tested on 22 consecutive months of global GOSAT-FTS measurements. The fundamental basis of this Fs retrieval approach and the results from the analysis of the global Fs data set produced with it are described in this work. Among other findings, the data analysis has shown (i) a very good comparison of Fs intensity levels and spatial patterns with the state-of-the-art physically-based Fs retrieval approach described in Frankenberg et al. (2011a), (ii) the overall good agreement between Fs annual and seasonal patterns and other space-based vegetation parameters, (iii) the need for a biome-dependent scaling from Fs to gross primary production, and (iv) the apparent existence of strong directional effects in the Fs emission from forest canopies. These results reinforce the confidence in the feasibility of Fs retrievals with GOSAT-FTS and open several points for future research in this emerging field.

Fraunhofer-type absorption lines in double-pulse laser-induced plasma

We studied the confocal double-pulse laser-induced plasma in the very beginning of its life. It was found that the second laser pulse fired 0.7 to 5 µs after the first pulse produces plasma which, during the first 0 to 20 ns, resembles solar configuration. There is a very hot and compact plasma core that radiates a broad continuum spectrum and a much larger and cooler outer shell. The light from the hot core passes through the cold outer shell and is partly absorbed by atoms and ions that are in ground (or close to ground) states. This produces absorption lines that are similar to Fraunhofer lines observed in the sun spectrum. The possibility to use these absorption lines for new direct and calibration free laser-induced breakdown spectroscopy analytical applications, both in laboratory and industrial conditions, is proved.

The Spectrometer

In the fall of 1999 I was shown an Ocean Optics spectrometer-in-the-computer at St. Patricks College at Maynooth, Ireland, and thought that I had seen heaven. Of course, it could not resolve the sodium D-lines (I had done that many years before with a homemade wire diffraction grating1), and I began to realize that inside was some familiar old technology. In this paper I would like to discuss its ancestors.

Demonstrations of optical spectra with a video camera

The use of a video camera may markedly improve demonstrations of optical spectra. First,the output electrical signal from the camera, which provides full information about apicture to be transmitted, can be used for observing the radiant power spectrum on thescreen of a common oscilloscope. Second, increasing the magnification by thecamera enhances the resolution of the spectra displayed by a colour monitor.In particular, it becomes possible to resolve the sodium doublet at 579 nm (Δλ = 0.6 nm).

A SURVEY OF ALKALI LINE ABSORPTION IN EXOPLANETARY ATMOSPHERES

We obtained over 90 hours of spectroscopic observations of four exoplanetary systems with the Hobby-Eberly Telescope (HET). Observations were taken in transit and out of transit, and we analyzed the differenced spectra---i.e., the transmission spectra---to inspect it for absorption at the wavelengths of the neutral sodium (\ion{Na}{1}) doublet at $\lambda\lambda5889, 5895$ and neutral potassium (\ion{K}{1}) at $\lambda7698$. We used the transmission spectrum at \ion{Ca}{1} $\lambda6122$---which shows strong stellar absorption but is not an alkali metal resonance line that we expect to show significant absorption in these atmospheres---as a control line to examine our measurements for systematic errors. We use an empirical Monte Carlo method to quantity these systematic errors. In a reanalysis of the same dataset using a reduction and analysis pipeline that was derived independently, we confirm the previously seen \ion{Na}{1} absorption in HD 189733b at a level of $(-5.26\pm1.69)\times10^{-4}$ (the average value over a 12 \AA{} integration band to be consistent with previous authors). Additionally, we tentatively confirm the \ion{Na}{1} absorption seen in HD 209458b (independently by multiple authors) at a level of $(-2.63\pm0.81)\times10^{-4}$, though the interpretation is less clear. Furthermore, we find \ion{Na}{1} absorption of $(-3.16\pm2.06)\times10^{-4}$ at $<3\sigma$ in HD 149026b; features apparent in the transmission spectrum are consistent with real absorption and indicate this may be a good target for future observations to confirm. No other results (\ion{Na}{1} in HD 147506b and \ion{Ca}{1} and \ion{K}{1} in all four targets) are significant to $\geq 3\sigma$, although we observe some features that we argue are primarily artifacts.

Fluorescence, temperature and narrow-band indices acquired from a UAV platform for water stress detection using a micro-hyperspectral imager and a thermal camera

The remote detection of water stress in a citrus orchard was investigated using leaf-level measurements of chlorophyll fluorescence and Photochemical Reflectance Index (PRI) data, seasonal time-series of crown temperature and PRI, and high-resolution airborne imagery. The work was conducted in an orchard where a regulated deficit irrigation (RDI) experiment generated a gradient in water stress levels. Stomatal conductance (Gs) and water potential (Ψ) were measured over the season on each treatment block. The airborne data consisted on thermal and hyperspectral imagery acquired at the time of maximum stress differences among treatments, prior to the re-watering phase, using a miniaturized thermal camera and a micro-hyperspectral imager on board an unmanned aerial vehicle (UAV). The hyperspectral imagery was acquired at 40 cm resolution and 260 spectral bands in the 400-885 nm spectral range at 6.4 nm full width at half maximum (FWHM) spectral resolution and 1.85 nm sampling interval, enabling the identification of pure crowns for extracting radiance and reflectance hyperspectral spectra from each tree. The FluorMOD model was used to investigate the retrieval of chlorophyll fluorescence by applying the Fraunhofer Line Depth (FLD) principle using three spectral bands (FLD3), which demonstrated that fluorescence retrieval was feasible with the configuration of the UAV micro-hyperspectral instrument flown over the orchard. Results demonstrated the link between seasonal PRI and crown temperature acquired from instrumented trees and field measurements of stomatal conductance and water potential. The sensitivity of PRI and Tc–Ta time-series to water stress levels demonstrated a time delay of PRI vs Tc–Ta during the recovery phase after re-watering started. At the time of the maximum stress difference among treatment blocks, the airborne imagery acquired from the UAV platform demonstrated that the crown temperature yielded the best coefficient of determination for Gs (r 2 = 0.78; p < 0.05) and Ψ (r 2 = 0.34; p < 0.001). Among the narrow-band indices calculated, the PRI 515 index (reference band = 515 nm) obtained better results than PRI 570, with r 2 = 0.59 (p < 0.01) for Gs, and r 2 = 0.38 (p < 0.001) for Ψ. The BGI1 index calculated from the blue (R 400) and green (R 550) bands resulted on the highest significance levels (p < 0.001) for both Gs (r 2 = 0.62) and Ψ (r 2 = 0.49). Out of the structural indices assessed, RDVI, MTVI1 and TVI showed greater sensitivity for Gs (r 2 = 0.6; p < 0.01) and Ψ (p < 0.001) than NDVI. Chlorophyll fluorescence calculated from the micro-hyperspectral imagery with the FLD3 method tracked stress levels, obtaining r 2 = 0.67 (p < 0.05) with stomatal conductance, and r 2 = 0.66 (p < 0.001) with water potential. The work presented in this manuscript demonstrates the feasibility of thermal, narrow-band indices and fluorescence retrievals obtained from a micro-hyperspectral imager and a light-weight thermal camera on board small UAV platforms for stress detection in a heterogeneous tree canopy where very high resolution is required.

Technical Note: A new discrete ordinate first-order rotational Raman scattering radiative transfer model – implementation and first results

Abstract. Rotational Raman scattering in the Earth's atmosphere explains the filling-in of Fraunhofer lines in the solar spectrum. A new model including first-order rotational Raman scattering has been developed, based on a reimplementation of the versatile discrete ordinate radiative transfer (DISORT) solver in the C computer language. The solver is fully integrated in the freely available libRadtran radiative transfer package. A detailed description is given of the model including the spectral resolution and a spectral interpolation scheme that considerably speeds up the calculations. The model is used to demonstrate the effect of clouds on top and bottom of the atmosphere filling-in factors and differential optical depths. Cloud effects on vertical profiles of the filling-in factor are also presented. The spectral behaviour of the model is compared against measurements under thunderstorm and aerosol loaded conditions.

Volumetric Properties and Refractive Indices of N,N′-Hexamethylenebisacetamide in Aqueous Glucose and Sucrose Solutions

Densities (ρ) of N,N′-hexamethylenebisacetamide (HMBA) in pure water and aqueous glucose and sucrose solutions have been measured at T = (288.15, 293.15, 298.15, 303.15, and 308.15) K with a quartz vibrating-tube densimeter. These experimental data have been used to calculate some important physical parameters, including apparent molar volumes (Vϕ), limiting partial molar volumes (Vϕ0), and transfer partial molar volumes (ΔtrsVϕ0). Another physical parameter, molar refraction at the sodium-D line (RD), has been computed from the refractive index (nD) measured by a refractometer at 298.15 K. The variations of all above parameters are discussed in terms of interactions occurring in the solutions.

Spectrophotometric measurement of the Extragalacic Background Light

AbstractThe Extragalactic Background Light (EBL) at UV, optical and NIR wavelengths consists of the integrated light of all unresolved galaxies along the line of sight plus any contributions by intergalactic matter including hypothetical decaying relic particles. The measurement of the EBL has turned out to be a tedious problem. This is because of the foreground components of the night sky brightness, much larger than the EBL itself: the Zodiacal Light (ZL), Integrated Starlight (ISL), Diffuse Galactic Light (DGL) and, for ground-based observations, the Airglow (AGL) and the tropospheric scattered light. We have been developing a method for the EBL measurement which utilises the screening effect of a dark nebula on the EBL. A differential measurement in the direction of a high-latitude dark nebula and its surrounding area provides a signal that is due to two components only, i.e. the EBL and the diffusely scattered ISL from the cloud. We present a progress report of this method where we are now utilising intermediate resolution spectroscopy with ESO's VLT telescope. We detect and remove the scattered ISL component by using its characteristic Fraunhofer line spectral signature. In contrast to the ISL, in the EBL spectrum all spectral lines are washed out. We present a high quality spectrum representing the difference between an opaque position within our target cloud and several clear OFF positions around the cloud. We derive a preliminary EBL value at 400 nm and an upper limit to the EBL at 520 nm. These values are in the same range as the EBL lower limits derived from galaxy counts.Unit: We will use in this paper the abbreviation 1 cgs = 10−9erg s−1cm−2sr−1Å−1

A convolution algorithm to calculate differential cross sections of the Ring effect in the Earth’s atmosphere based on rotational Raman scattering

The Ring effect refers to the filling in of Fraunhofer lines, which is mainly attributed to the rotational Raman scattering of solar spectra by N2 and O2 molecules in the atmosphere. The Ring effect is one of the most significant factors affecting the accuracy of retrieving concentrations of atmospheric trace gases, such as NO2 and SO2, from satellite observations through differential optical absorption spectroscopy. First in this study, the solar spectrum measured by the Ozone Monitoring Instrument onboard NASA Aura is convolved with the rotational Raman cross section of the atmosphere, which is calculated from the rotational Raman cross sections of N2 and O2 molecules, and divided by the original solar spectrum. The slowly varying term is removed by fitting it with a cubic polynomial to obtain the differential Ring spectrum. The results agree well with the calculations using a radiative transfer model (R 2=0.9663). Second, the differential Ring spectrum is computed using two fixed wavelengths of 410 nm and 488 nm, and the resulting differential Ring spectra are similar to that calculated with varying wavelengths and agree well with the calculation using the radiative transfer model (R 2=0.9624 and 0.9639 respectively). The computation time using the fixed wavelength is about 0.128% of that using a varying wavelength. Finally, we found that the frequency spectrum of the Raman cross sections for the atmosphere, N2 molecules and O2 molecules are similar; thus, the Raman cross section of N2 or O2 molecules can be used to compute the approximate Ring effect for simplicity.