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NASA NTRS2012

Analysis of Pulsed Lidar Measurements of Atmospheric CO2 Column Absorption During the ASCENDS 2009-2011 Airborne Campaigns

We have developed a pulsed lidar technique for measuring the tropospheric CO2 concentrations as a candidate for NASA's ASCENDS mission and have demonstrated the CO2 and O2 measurements from aircraft. Our technique uses two pulsed lasers allowing simultaneous measurement of a single CO2 absorption line near 1572 nm, O2 extinction in the Oxygen A-band, surface height and backscatter profile. The lasers are stepped in wavelength across the CO2 line and an O2 line doublet during the measurement. The column densities for the CO2 and O2 are estimated from the differential optical depths (DOD) of the scanned absorption lines via the IPDA technique. For the 2009 ASCENDS campaign we flew the CO2 lidar on a Lear-25 aircraft, and measured the absorption line shapes of the CO2 line using 20 wavelength samples per scan. Measurements were made at stepped altitudes from 3 to 12.6 km over the Lamont OK, central Illinois, North Carolina, and over the Virginia Eastern Shore. Although the received signal energies were weaker than expected for ASCENDS, clear CO2 line shapes were observed at all altitudes. Most flights had 5-6 altitude steps with 200-300 seconds of recorded measurements per step. We averaged every 10 seconds of measurements and used a cross-correlation approach to estimate the range to the scattering surface and the echo pulse energy at each wavelength. We then solved for the best-fit CO2 absorption line shape, and calculated the DOD of the fitted CO2 line, and computed its statistics at the various altitude steps. We compared them to CO2 optical depths calculated from spectroscopy based on HITRAN 2008 and the column number densities calculated from the airborne in-situ readings. The 2009 measurements have been analyzed and they were similar on all flights. The results show clear CO2 line shape and absorption signals, which follow the expected changes with aircraft altitude from 3 to 13 km. They showed the expected nearly the linear dependence of DOD vs altitude. The measurements showed ~ 1 ppm random errors for 8-10 km altitudes and ~30 sec averaging times. For the 2010 ASCENDS campaigns we flew the CO2lidar on the NASA DC-8 and added an 02lidar channel. During July 2010 we made measurements of CO2 and O2 column absorption during longer flights over Railroad Valley NV, the Pacific Ocean and over Lamont OK. CO2 measurements were made with 30 steps/scan, 300 scans/sec and improved line resolution and receiver sensitivity. Analysis of the 2010 CO2 measurements shows the expected ~linear change of DOD with altitude. For measurements at altitudes> 6 km the random errors were 0.3 ppm for 80 sec averaging times. For the summer 2011 ASCENDS campaigns we made further improvements to the lidar's CO2 line scan and receiver sensitivity. We demonstrated measurements over the California Central Valley, to stratus cloud tops over the Pacific Ocean, over mountain regions with snow, and over several areas with broken clouds. Details of the lidar measurements and their analysis will be described in the presentation.

Abshire, J. B.↗
NASA NTRS2012

Pulsed Lidar Measurements of Atmospheric CO2 Column Absorption and Range During the ASCENDS 2009-2011 Airborne Campaigns

We have developed a pulsed lidar technique for measuring the tropospheric CO2 concentrations as a candidate for NASA's ASCENDS mission and have demonstrated the CO2 and O2 measurements from aircraft. Our technique uses two pulsed lasers allowing simultaneous measurement of a single CO2 absorption line near 1572 nm, O2 extinction in the Oxygen A-band, surface height and backscatter profile. The lasers are stepped in wavelength across the CO2 line and an O2 line doublet during the measurement. The column densities for the CO2 and O2 are estimated from the differential optical depths (DOD) of the scanned absorption lines via the IPDA technique. For the 2009 ASCENDS campaign we flew the CO2 lidar only on a Lear-25 aircraft, and measured the absorption line shapes of the CO2 line using 20 wavelength samples per scan. Measurements were made at stepped altitudes from 3 to 12.6 km over the Lamont OK, central Illinois, North Carolina, and over the Virginia Eastern Shore. Although the received signal energies were weaker than expected for ASCENDS, clear C02 line shapes were observed at all altitudes. Most flights had 5-6 altitude steps with 200-300 seconds of recorded measurements per step. We averaged every 10 seconds of measurements and used a cross-correlation approach to estimate the range to the scattering surface and the echo pulse energy at each wavelength. We then solved for the best-fit CO2 absorption line shape, and calculated the DOD of the fitted CO2 line, and computed its statistics at the various altitude steps. We compared them to CO2 optical depths calculated from spectroscopy based on HITRAN 2008 and the column number densities calculated from the airborne in-situ readings. The 2009 measurements have been analyzed in detail and they were similar on all flights. The results show clear CO2 line shape and absorption signals, which follow the expected changes with aircraft altitude from 3 to 13 km. They showed the expected nearly the linear dependence of DOD vs altitude. The measurements showed -1 ppm random errors for 8-10 km altitudes and -30 sec averaging times. For the 2010 ASCENDS campaigns we flew the CO2 lidar on the NASA DC-8 and added an O2 lidar channel. During July 2010 we made measurements of CO2 and O2 column absorption during longer flights over Railroad Valley NV, the Pacific Ocean and over Lamont OK. CO2 measurements were made with 30 steps/scan, 300 scans/sec and improved line resolution and receiver sensitivity. Analysis of the 2010 CO2 measurements shows the expected -linear change of DOD with altitude. For measurements at altitudes> 6 km the random errors were 0.3 ppm for 80 sec averaging times. For the summer 2011 ASCENDS campaigns we made further improvements to the lidar's CO2 line scan and receiver sensitivity. The seven flights in the 2011 Ascends campaign were flown over a wide variety of surface and cloud conditions in the US, which produced a wide variety of lidar signal conditions. Details of the lidar measurements and their analysis will be described in the presentation.

Abshire, J. B.↗
NASA NTRS1987

IOS and ECS line coupling calculation for the CO-He system - Influence on the vibration-rotation band shapes

Line coupling coefficients resulting from rotational excitation of CO perturbed by He are computed within the infinite order sudden approximation (IOSA) and within the energy corrected sudden approximation (ECSA). The influence of this line coupling on the 1-0 CO-He vibration-rotation band shape is then computed for the case of weakly overlapping lines in the 292-78 K temperature range. The IOS and ECS results differ only at 78 K by a weak amount at high frequencies. Comparison with an additive superposition of Lorentzian lines shows strong modifications in the troughs between the lines. These calculated modifications are in excellent quantitative agreement with recent experimental data for all the temperatures considered. The applicability of previous approaches to CO-He system, based on either the strong collision model or exponential energy gap law, is also discussed.

Boissoles, J.↗
NASA NTRS1978

Measurements of earth-space attenuation at 230 GHz

Measurements of attenuation at 230 GHz through the total atmosphere due to the presence of oxygen and water vapor molecules, clouds, and rain are presented. The measurements were carried out using a specially designed superheterodyne receiver mounted on a sun tracker. Simultaneous measurements were also carried out at 13 GHz. For a measuring site close to sea level at Holmdel, NJ, the 'clear-sky' zenith attenuation was found as a function of the measured ground water vapor density. When the ground temperature was below about 7 C, most cloud and overcast gave less than 0.5-dB attenuation, whereas with a ground temperature greater than 13 C, cloud attenuation was 8-10 times greater. Calculations of zenith attenuation in the 230-GHz atmospheric window were also made using the Gross analytic line shape, Schulze-Tolbert empirical line shape, and an empirically modified Gross line shape. These calculations were based on determinations of water vapor density and temperature made at the measurement site, and on radiosonde measurements made at a distance of 80 km away.

Wrixon, G. T.↗
NASA NTRS2011

Analysis of Pulsed Airborne Lidar Measurements of Atmospheric CO2 Column Absorption from 3-13 km Altitudes

We have developed a pulsed lidar technique for measuring the tropospheric CO2 concentrations as a candidate for NASA's ASCENDS space mission [1]. It uses two pulsed laser transmitters allowing simultaneous measurement of a CO2 absorption line in the 1575 nm band, O2 extinction in the Oxygen A-band, surface height and backscatter profile. The lasers are precisely stepped in wavelength across the CO2 line and an O2 line region during the measurement. The direct detection receiver measures the energies of the laser echoes from the surface along with the range profile of scattering in the path. The column densities for the CO2 and O2 gases are estimated from the ratio of the on- and off-line signals via the integrated path differential absorption (IPDA) technique. The time of flight of the laser pulses is used to estimate the height of the scattering surface and to reject laser photons scattered in the atmosphere. We developed an airborne lidar to demonstrate an early version of the CO2 measurement from the NASA Glenn Lear-25 aircraft. The airborne lidar stepped the pulsed laser's wavelength across the selected CO2 line with 20 wavelength steps per scan. The line scan rate is 450 Hz, the laser pulse widths are 1 usec, and laser pulse energy is 24 uJ. The time resolved laser backscatter is collected by a 20 cm telescope, detected by a NIR photomultiplier and is recorded on every other reading by a photon counting system [2]. During August 2009 we made a series of 2.5 hour long flights and measured the atmospheric CO2 absorption and line shapes using the 1572.33 nm CO2 line. Measurements were made at stepped altitudes from 3-13 km over locations in the US, including the SGP ARM site in Oklahoma, central Illinois, north-eastern North Carolina, and over the Chesapeake Bay and the eastern shore of Virginia. Although the received signal energies were weaker than expected for ASCENDS, clear CO2 line shapes were observed at all altitudes, and some measurements were made through thin clouds. The Oklahoma and east coast flights were coordinated with a LaRC/ITT CO2 lidar on the LaRC UC-12 aircraft, and in-situ measurements were made using its CO2 sensor and radiosondes. We have conducted an analysis of the ranging and IPDA lidar measurements from these four flights. Most flights had 5-6 altitude steps with 200-300 seconds of recorded measurements per step. We used a cross-correlation approach to process the laser echo records. This was used to estimate the range to the scattering surface, to define the edges of the laser pulses and to determine echo pulse energy at each wavelength. We used a minimum mean square approach to fit an instrument response function and to solve for the best-fit CO2 absorption line shape. We then calculated the differential optical depth (DOD) of the fitted CO2 line. We computed its statistics at the various altitude steps, and compare them to the DODs calculated from spectroscopy based on HITRAN 2008 and the column conditions calculated from the airborne in-situ readings. The results show the lidar and in-situ measurements have very similar DOD change with altitude and greater than 10 segments per flight where the scatter in the lidar measurements are less than or equal to 1ppm. We also present the results from subsequent CO2 column absorption measurements, which were made with stronger detected signals during three flights on the NASA DC-8 over the southwestern US in during July 2010.

Abshire, James B.↗
NASA NTRS1995

Investigation of the collision line broadening problem as applicable to the NASA Optical Plume Anomaly Detection (OPAD) system, phase 1

As a final report for phase 1 of the project, the researchers are submitting to the Tennessee Tech Office of Research the following two papers (reprinted in this report): 'Collision Line Broadening Effects on Spectrometric Data from the Optical Plume Anomaly System (OPAD),' presented at the 30th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, 27-29 June 1994, and 'Calculation of Collision Cross Sections for Atomic Line Broadening in the Plume of the Space Shuttle Main Engine (SSME),' presented at the IEEE Southeastcon '95, 26-29 March 1995. These papers fully state the problem and the progress made up to the end of NASA Fiscal Year 1994. The NASA OPAD system was devised to predict concentrations of anomalous species in the plume of the Space Shuttle Main Engine (SSME) through analysis of spectrometric data. The self absorption of the radiation of these plume anomalies is highly dependent on the line shape of the atomic transition of interest. The Collision Line Broadening paper discusses the methods used to predict line shapes of atomic transitions in the environment of a rocket plume. The Voigt profile is used as the line shape factor since both Doppler and collisional line broadening are significant. Methods used to determine the collisional cross sections are discussed and the results are given and compared with experimental data. These collisional cross sections are then incorporated into the current self absorbing radiative model and the predicted spectrum is compared to actual spectral data collected from the Stennis Space Center Diagnostic Test Facility rocket engine. The second paper included in this report investigates an analytical method for determining the cross sections for collision line broadening by molecular perturbers, using effective central force interaction potentials. These cross sections are determined for several atomic species with H2, one of the principal constituents of the SSME plume environment, and compared with experimental data.

Dean, Timothy C.↗
NASA NTRS1972

Infrared spectra of CO2 in the atmospheres of Earth and Venus

A theoretical calculation was made of the CO2 infrared spectra of Earth and Venus atmospheres. The calculations cover line intensity, line shape, and line position. Theoretical results were compared with those observed by Nimbus 3 satellite and were found to be in reasonable agreement.

Maguire, W. C.↗
NASA NTRS1999

Sensitivity of Temperature Profiles Retrieved from Mars Global Surveyor Thermal Emission Spectrometer (MGS/TES) Observations to the GSFC Synthetic Mars Model Atmosphere

Part of the task of interpreting IR spectral features observed by MGS/TES due to surface minerals requires distinguishing those IR signatures from atmospheric signatures of gas and dust. Surface-atmosphere separation for MGS/TES depends on knowledge of the retrieved temperature profile. In turn, the temperature retrieval Erom the observed data depends on molecular parameters including 15 micron CO2 line shape or line intensities which contribute to defining the Mars synthetic radiative transfer model. Using a simple isothermal, homogeneous single layer model of Pinnock and Shine, we find the ratio of (the error in degrees Kelvin of the retrieved temperature profile) to (the percentage error in the absorption coefficient) (deg K/percent) to be 0.4 at 200K. This ratio at 150K and 250K is 0.2 and 0.6, respectively. A more refined model, incorporating observed MGS/TES retrieved temperature profiles, the TES instrumental resolution and the most recent molecular modelling, will yield an improved knowledge of this error sensitivity. We present results of such a sensitivity study to determine the dependence of temperature profiles inverted from MGS/TES on these and other molecular parameters. This work was supported in part by NASA's Mars Data Analysis Program.

Maguire, William C.↗
NASA NTRS1998

Modeling Molecular Opacities Using Galileo Probe Observations

Data from the Net Flux Radiometer (NFR) experiment on the Galileo mission has been successfully collected and analyzed through 1996. As data was received, the best available laboratory spectroscopic data and was used in the reduction procedure. Since then newer and more accurate spectroscopic data has become available. During this agreement, research efforts focused on re-analysis of certain aspects of the data which benefited from recent improvements in spectroscopic databases, and from a more exact treatment of certain aspects of the physical theory of line shape and line broadening. In addition, a brief survey was completed of the available information, both theoretical and observational, of the absorption, reflection and transmission spectra of the atmospheres of the various types of planets that could reasonably be expected to occur in other solar systems.

Freedman, Richard S.↗
NASA NTRS1998

Modeling Molecular Opacities using Galileo Probe Observations

Data from the Net Flux Radiometer (NFR) experiment on the Galileo mission has been successfully collected and analyzed through 1996. As data was received, the best available laboratory spectroscopic data and was used in the reduction procedure. Since then newer and more accurate spectroscopic data has become available. During this agreement, research efforts focused on re-analysis of certain aspects of the data which benefited from recent improvements in spectroscopic databases, and from a more exact treatment of certain aspects of the physical theory of line shape and line broadening. In addition, a brief survey was completed of the available information, both theoretical and observational, of the absorption, reflection and transmission spectra of the atmospheres of the various types of planets that could reasonably be expected to occur in other solar systems.

Freedman, Richard S.↗
NASA NTRS2012

Spectral Line Parameters Including Temperature Dependences of Self- and Air-Broadening in the 2 (left arrow) 0 Band of CO at 2.3 micrometers

Temperature dependences of pressure-broadened half-width and pressure-induced shift coefficients along with accurate positions and intensities have been determined for transitions in the 2<--0 band of C-12 O-16 from analyzing high-resolution and high signal-to-noise spectra recorded with two different Fourier transform spectrometers. A total of 28 spectra, 16 self-broadened and 12 air-broadened, recorded using high- purity (greater than or equal to 99.5% C-12-enriched) CO samples and CO diluted with dry air(research grade) at different temperatures and pressures, were analyzed simultaneously to maximize the accuracy of the retrieved parameters. The sample temperatures ranged from 150 to 298K and the total pressures varied between 5 and 700 Torr. A multispectrum nonlinear least squares spectrum fitting technique was used to adjust the rovibrational constants (G, B, D, etc.) and intensity parameters (including Herman-Wallis coefficients), rather than determining individual line positions and intensities. Self-and air-broadened Lorentz half-width coefficients, their temperature dependence exponents, self- and air-pressure-induced shift coefficients, their temperature dependences, self- and air-line mixing coefficients, their temperature dependences and speed dependence have been retrieved from the analysis. Speed-dependent line shapes with line mixing employing off-diagonal relaxation matrix element formalism were needed to minimize the fit residuals. This study presents a precise and complete set of spectral line parameters that consistently reproduce the spectrum of carbon monoxide over terrestrial atmospheric conditions.

Devi, V. Malathy↗
NASA NTRS2010

Ultra-High Resolution Spectroscopic Remote Sensing: A Microscope on Planetary Atmospheres

Remote sensing of planetary atmospheres is not complete without studies of all levels of the atmosphere, including the dense cloudy- and haze filled troposphere, relatively clear and important stratosphere and the upper atmosphere, which are the first levels to experience the effects of solar radiation. High-resolution spectroscopy can provide valuable information on these regions of the atmosphere. Ultra-high spectral resolution studies can directly measure atmospheric winds, composition, temperature and non-thermal phenomena, which describe the physics and chemistry of the atmosphere. Spectroscopy in the middle to long infrared wavelengths can also probe levels where dust of haze limit measurements at shorter wavelength or can provide ambiguous results on atmospheric species abundances or winds. A spectroscopic technique in the middle infrared wavelengths analogous to a radio receiver. infrared heterodyne spectroscopy [1], will be describe and used to illustrate the detailed study of atmospheric phenomena not readily possible with other methods. The heterodyne spectral resolution with resolving power greater than 1,000.000 measures the true line shapes of emission and absorption lines in planetary atmospheres. The information on the region of line formation is contained in the line shapes. The absolute frequency of the lines can be measured to I part in 100 ,000,000 and can be used to accurately measure the Doppler frequency shift of the lines, directly measuring the line-of-sight velocity of the gas to --Im/s precision (winds). The technical and analytical methods developed and used to measure and analyze infrared heterodyne measurements will be described. Examples of studies on Titan, Venus, Mars, Earth, and Jupiter will be presented. 'These include atmospheric dynamics on slowly rotating bodies (Titan [2] and Venus [3] and temperature, composition and chemistry on Mars 141, Venus and Earth. The discovery and studies of unique atmospheric phenomena will also be described, such as non-thermal and lasing phenomena on Mars and Venus, mid-infrared aurora on Jupiter [5], and results of small body impacts on Jupiter [6]. The heterodyne technique can also be applied for detailed study of the Earth's stratosphere and mesosphere by measuring trace constituent abundances and temporal and spatial variability as well as winds, which provide information of transport. All ground-based measurements will be described as complementary and supporting studies for on-going and future space missions [7] (Mars Express, Venus Express, Cassini Huygens, JUNO, ExoMars Trace Gas Orbiter, and the Europa Jupiter System Mission, an Earth Science Venture Class missions), Proposed instrument and technology development for a space flight infrared heterodyne spectrometer will be described.

Kostiuk, Theodor↗
NASA NTRS2002

Effect of Wind Velocity on Flame Spread in Microgravity

A three-dimensional, time-dependent model is developed describing ignition and subsequent transition to flame spread over a thermally thin cellulosic sheet heated by external radiation in a microgravity environment. A low Mach number approximation to the Navier Stokes equations with global reaction rate equations describing combustion in the gas phase and the condensed phase is numerically solved. The effects of a slow external wind (1-20 cm/s) on flame transition are studied in an atmosphere of 35% oxygen concentration. The ignition is initiated at the center part of the sample by generating a line-shape flame along the width of the sample. The calculated results are compared with data obtained in the 10s drop tower. Numerical results exhibit flame quenching at a wind speed of 1.0 cm/s, two localized flames propagating upstream along the sample edges at 1.5 cm/s, a single line-shape flame front at 5.0 cm/s, three flames structure observed at 10.0 cm/s (consisting of a single line-shape flame propagating upstream and two localized flames propagating downstream along sample edges) and followed by two line-shape flames (one propagating upstream and another propagating downstream) at 20.0 cm/s. These observations qualitatively compare with experimental data. Three-dimensional visualization of the observed flame complex, fuel concentration contours, oxygen and reaction rate isosurfaces, convective and diffusive mass flux are used to obtain a detailed understanding of the controlling mechanism, Physical arguments based on lateral diffusive flux of oxygen, fuel depletion, oxygen shadow of the flame and heat release rate are constructed to explain the various observed flame shapes.

Prasad, Kuldeep↗
NASA NTRS1977

ESR studies of the slow tumbling of vanadyl spin probes in nematic liquid crystals

ESR line shapes that are appropriate for slowly tumbling vanadyl spin probes in viscous nematic liquid crystals were calculated by the stochastic Liouville method. Because of the symmetry possessed by vanadyl, the analysis and interpretation of these line shapes was simplified considerably. Spectral line shapes agreed well with experimental spectra of VOAcAc in the nematic liquid crystal Phase V and BEPC. Deviations from Brownian rotational diffusion were noted. A slowly fluctuating torque analysis yielded good agreement with the experimental spectra.

Eastman, M. P.↗
NASA NTRS2012

Pulsed Lidar Measurements of Atmospheric CO2 Column Absorption in the ASCENDS 2011 Airborne Campaign

We have previously demonstrated an efficient pulsed, wavelength-resolved IPDA lidar technique for measuring the tropospheric CO2 concentrations as a candidate for NASA's ASCENDS mission. Our team participated in the 2010 ASCENDS airborne campaigns we flew airborne version of the CO2 and O2 lidar on the NASA DC-8. The CO2 lidar measures the atmospheric backscatter profiles and shape of the 1572.33 nm absorption line using 250 mW average laser power, 30 wavelength samples per scan and 300 scans per second. Most flights had 5-6 altitude steps to greater than 12 km, and clear CO2 line shapes were observed at all altitudes. Our post-flight analysis estimated the Iidar range and pulse energies at each wavelength every second. We then solved for the best-fit CO2 absorption line shape, and calculated the Differential Optical Depth (DOD) at the line peak. We compared these to CO2 DODs calculated from spectroscopy based on HITRAN 2008 and the conditions from airborne in-situ readings. Analysis of the 2010 measurements over the Pacific Ocean and Lamont OK shows the expected -linear change of the peak DOD with altitude. For measurements at altitudes greater than 6 km the random errors were approximately 0.3 ppm for 80 sec averaging times. After the 2010 flights we improved the airborne lidar's scan uniformity, calibration and receiver sensitivity. Our team participated in the seven ASCENDS science flights during late July and August 2011. These flights were made over a wide variety of surface and cloud conditions near the US, including over the central valley of California, over several mountain ranges, over both broken and solid stratus cloud deck over the Pacific Ocean, snow patches on mountain tops, over thin and broken clouds above the US Southwest and Iowa, and over forests near the WLEF tower in Wisconsin. Analyses show the retrievals of lidar range and CO2 column absorption, as wen as estimates of CO2 mixing ratio worked well when measuring over topography with rapidly changing height and reflectivity, through thin clouds and to stratus cloud tops. For regions where the CO2 concentration was relatively constant, the measured CO2 absorption profile (averaged for 50 sec) matched the predicted profile to better than 1% RMS error for all flight altitudes. For 1 & 10 second averaging, the scatter in the retrievals was limited by signal shot noise (i.e. the sigual photon count). Analysis to date shows the decrease in CO2 due to vegetation when flying easterward over the Great Plains as well as the increase in CO2 concentration in the vicinity ofthe coal-fired power plant in New Mexico. Examples of these and other results will be presented.

Abshire, James B.↗
NASA NTRS1992

Solar O I 1304-A triplet line profiles

Estimates were made of the full-disk line profiles of the solar O I resonant triplet at 1304 A, using data from the SMM and the Orbiting Solar Observatory 8 for the time period 1975-1985. The observed line profiles are parameterized using a nonlinear least squares fit of the data by a simple empirical representation of the general line shape. The derived full-disk line shape parameters may be used, in combination with an appropriate value for the line-integrated full-disk solar flux, in the analysis of planetary or cometary O I 1304-A observations under any solar conditions.

Gladstone, G. R.↗
NASA NTRS1983

Line broadening in multiphoton processes with a resonant intermediate transition

It is found that the line width of the excitation spectrum for multiphoton ionization is broadened much more severely than the cascade fluorescence originating from the resonant intermediate level. These results derive from the mutual effects of the ionizing and resonating transitions, which are not properly accounted for in perturbative treatments. In general, the ionization line shape can be expressed as the sum of two Lorentzian components, each with different degrees of broadening. This line shape reduces to that of the resonating transition in the limit of vanishing intensities. Moreover, the fluorescence line shape may also exhibit a second component whose amplitude may become important under certain conditions.

Wang, C. C.↗