Rayleigh Scattering Cross Sections Research Articles

Scattering and absorption cross sections of atmospheric gases in the ultraviolet–visible wavelength range (307–725 nm)

Abstract. Accurate Rayleigh scattering and absorption cross sections of atmospheric gases are essential for understanding the propagation of electromagnetic radiation in planetary atmospheres. Accurate extinction cross sections are also essential for calibrating high-finesse optical cavities and differential optical absorption spectroscopy and for accurate remote sensing. In this study, we measured the scattering and absorption cross sections of carbon dioxide, nitrous oxide, sulfur hexafluoride, oxygen, and methane in the continuous wavelength range of 307–725 nm using broadband cavity-enhanced spectroscopy (BBCES). The experimentally derived Rayleigh scattering cross sections for CO2, N2O, SF6, O2, and CH4 agree with refractive index-based calculations, with a difference of (0.4 ± 1.2) %, (−0.6 ± 1.1) %, (0.9 ± 1.4) %, (2.8 ± 1.2) %, and (0.9 ± 2.2) %, respectively. The O2–O2 collision-induced absorption and absorption by methane are obtained with high precision at the 0.8 nm resolution of our BBCES instrument in the 307–725 nm wavelength range. New dispersion relations for N2O, SF6, and CH4 were derived using data in the UV–vis wavelength range. This study provides dispersion relations for refractive indices, n-based Rayleigh scattering cross sections, and absorption cross sections based on more continuous and more extended wavelength ranges than available in the current literature.

Determination of Rayleigh scattering cross sections and indices of refraction for Ar, CO2, SF6, and CH4 using BBCES in the ultraviolet

Rayleigh scattering cross sections for argon, carbon dioxide, sulfur hexafluoride, and methane were measured using Broadband Cavity Enhanced Spectroscopy (BBCES) between 264 and 297 nm, extending the region of experimental cross section data available for all four gases. The experimentally derived values for Ar and CO2 are in excellent agreement with refractive index based (n-based) calculations, within 0.8% and 1.0% on average, respectively. Our measured Rayleigh scattering cross sections for SF6 and CH4, however, suggest that n-based calculations for these gases should be revised. We derive new dispersion relations for SF6 and CH4, incorporating data from this study and from our previous work at 333–363 nm, to provide improved indices of refraction and n-based Rayleigh scattering cross sections.

Quantification of nitrous acid (HONO) and nitrogen dioxide (NO<sub>2</sub>) in ambient air by broadband cavity-enhanced absorption spectroscopy (IBBCEAS) between 361 and 388 nm

Abstract. This work describes an incoherent broadband cavity-enhanced absorption spectroscopy (IBBCEAS) instrument for quantification of HONO and NO2 mixing ratios in ambient air. The instrument is operated in the near-ultraviolet spectral region between 361 and 388 nm. The mirror reflectivity and optical cavity transmission function were determined from the optical extinction observed when sampling air and helium. To verify the accuracy of this approach, Rayleigh scattering cross sections of nitrogen and argon were measured and found to be in quantitative agreement with literature values. The mirror reflectivity exceeded 99.98 %, at its maximum near 373 nm, resulting in an absorption path length of 6 km from a 1 m long optical cavity. The instrument precision was assessed through Allan variance analyses and showed minimum deviations of ±58 and ±210 pptv (1σ) for HONO and NO2, respectively, at an optimum acquisition time of 5 min. Measurements of HONO and NO2 mixing ratios in laboratory-generated mixtures by IBBCEAS were compared to thermal dissociation cavity ring-down spectroscopy (TD-CRDS) data and agreed within combined experimental uncertainties. Sample ambient air data collected in Calgary are presented.

Rayleigh scattering cross sections of argon, carbon dioxide, sulfur hexafluoride, and methane in the UV-A region using Broadband Cavity Enhanced Spectroscopy

Accurate Rayleigh scattering cross sections are important for understanding the propagation of electromagnetic radiation in planetary atmospheres and for calibrating mirror reflectivity in high finesse optical cavities. In this study, we used Broadband Cavity Enhanced Spectroscopy (BBCES) to measure Rayleigh scattering cross sections for argon, carbon dioxide, sulfur hexafluoride, and methane between 333 and 363 nm, extending the region of available UV measurements for all four gases. Comparison of our results with refractive index based (n-based) calculations demonstrates excellent agreement for Ar and CO2, within 0.2% and 1.0% on average, respectively. For SF6, our mean Rayleigh scattering cross sections are lower by 2.2% on average relative to the n-based calculation and lie outside the 1-σ measurement uncertainty; however, the results still fall within our 2-σ uncertainty. The measured Rayleigh scattering cross sections for CH4 are in substantial disagreement (22%) with those calculated from the most recent n-based values in the literature and lie far outside our mean 1-σ uncertainty of 1.6%. Extrapolation of several older index of refraction measurements from visible wavelengths to the UV yields better agreement with our results for CH4, but the agreement is still generally outside our 1-σ measurement uncertainty. Use of the dispersion relation derived in this work provides significantly improved Rayleigh scattering cross sections for CH4 in the UV-A spectral region.

A broadband cavity-enhanced spectrometer for atmospheric trace gas measurements and Rayleigh scattering cross sections in the cyan region (470–540 nm)

Abstract. An incoherent broadband cavity-enhanced absorption spectroscopy (IBBCEAS) instrument for quantification of atmospheric trace gases that absorb in the cyan region of the electromagnetic spectrum (470 to 540 nm), including NO2 and I2, is described. The instrument uses a light-emitting diode coupled to a 1 m optical cavity consisting of a pair of mirrors in stable resonator configuration. Transmitted light is monitored using a grating spectrometer and charge-coupled device array detector. The average mirror reflectivity was determined from the N2∕He and Ar∕He ratios of scattering coefficients and was ∼99.98 % at its maximum, yielding an effective optical path length of 6.3 km. Cross sections of N2, O2, air, Ar, CO2, and CH4 scattering and of O4 absorption were measured and agree with literature values within the measurement uncertainty. Trace gas mixing ratios were retrieved using the spectral fitting software DOASIS (DOAS intelligent system) from 480 to 535 nm. Under laboratory conditions, the 60 s, 1σ measurement precisions were ±124 and ±44 pptv for NO2 and I2, respectively. The IBBCEAS instrument sampled ambient air in Ucluelet, BC, Canada, in July 2015. IBBCEAS retrievals agreed with independent measurements of NO2 by blue diode laser cavity ring-down spectroscopy (r2=0.975), but ambient I2 concentrations were below the detection limit.

Rayleigh scattering of 66Dy-K X-rays in elements with 22 ≤ Z ≤ 90

Rayleigh scattering differential cross sections for the 45.2keV (66Dy Kα2), 46.0keV (66Dy Kα1) and 52.1keV (66Dy Kβ1,3) X-rays have been measured at 139° in 44 elements with 22 ≤ Z ≤ 90. The measurements were performed using a radiation source consisting of an annular 66Dy foil excited by the 59.54keV γ-ray photons from 241Am radioactive source. Intensity of the incident photons along with other geometrical factors were determined by measuring the isotropically emitted K X-ray yields from targets and knowledge of the corresponding K X-ray fluorescence cross sections. The measured Rayleigh scattering cross sections are compared with those based on various form factor formalisms and the state-of-the-art S-matrix calculations to differentiate between their relative efficacies. The scattering cross sections based on the modified form factor (MF) formalism exhibit large deviations for the elements with electron binding energies in vicinity of the incident photon energy, and these deviations smooth out on inclusion of the anomalous scattering factors (ASFs) to the MF values. The cross sections based on the MF after including ASF's are found to be on an average higher by ~ 8% as compared to the measured ones. The S-matrix values exhibit in general good agreement with the measured cross sections for the elements with 22 ≤ Z ≤ 90.

Measurement of large angle Rayleigh scattering cross sections for 39.5, 40.1 and 45.4 keV photons in elements with 26 ≤ Z ≤ 83

The present work reports Rayleigh scattering cross section measurements for the 39.5keV (Sm- Kα2), 40.1keV (Sm-Kα1) and 45.4keV (Sm-Kβ1,3) X-ray photons in 35 elements with 26 ≤ Z ≤ 83 at backward angle of 139°. The scattering measurements were performed in reflection mode geometrical set up involving a secondary photon source consisting of Samarium (62Sm) target excited by the 59.54keV γ-rays from the 241Am radioactive source. The scattered photons were detected using a low energy germanium (LEGe) detector. The product of detector efficiency, intensity of incident photons and other geometrical factors were determined by measuring the K X-ray yields from targets with 47 ≤ Z ≤ 59 and knowledge of the respective K X-ray fluorescence cross sections. The measured cross sections are compared with the theoretical cross sections based on the modified form factor (MF) formalisms and the second-order S-matrix approach. The experimental results demonstrate large deviations from the MF values for the elements with K shell binding energy (BK) in vicinity of the incident photon energy (Ein), which smooth out with inclusion of the anomalous scattering factors (ASFs). The S-matrix values, in general, agree with the measured cross sections for all the elements under investigation.

In situ Characterization of Nanoparticles Using Rayleigh Scattering

We report a theoretical analysis showing that Rayleigh scattering could be used to monitor the growth of nanoparticles under arc discharge conditions. We compute the Rayleigh scattering cross sections of the nanoparticles by combining light scattering theory for gas-particle mixtures with calculations of the dynamic electronic polarizability of the nanoparticles. We find that the resolution of the Rayleigh scattering probe is adequate to detect nanoparticles as small as C60 at the expected concentrations of synthesis conditions in the arc periphery. Larger asymmetric nanoparticles would yield brighter signals, making possible to follow the evolution of the growing nanoparticle population from the evolution of the scattered intensity. Observable spectral features include characteristic resonant behaviour, shape-dependent depolarization ratio, and mass-dependent line shape. Direct observation of nanoparticles in the early stages of growth with unobtrusive laser probes should give insight on the particle formation mechanisms and may lead to better-controlled synthesis protocols.

Heat Dissipation of Resonant Absorption in Metal Nanoparticle-Polymer Films Described at Particle Separation Near Resonant Wavelength

Polymer films containing plasmonic nanostructures are of increasing interest for development of responsive energy, sensing, and therapeutic systems. The present work evaluates heat dissipated from power absorbed by resonant gold (Au) nanoparticles (NP) with negligible Rayleigh scattering cross sections randomly dispersed in polydimethylsiloxane (PDMS) films. Finite element analysis (FEA) of heat transport was coordinated with characterization of resonant absorption by Mie theory and coupled dipole approximation (CDA). At AuNP particle separation greater than resonant wavelength, correspondence was observed between measured and CDA-predicted optical absorption and FEA-derived power dissipation. At AuNP particle separation less than resonant wavelength, measured extinction increased relative to predicted values, while FEA-derived power dissipation remained comparable to CDA-predicted power absorption before lagging observed extinguished power at higher AuNP content and resulting particle separation. Effects of isolated particles, for example, scattering, and particle-particle interactions, for example, multiple scattering, aggregation on observed optothermal activity were evaluated. These complementary approaches to distinguish contributions to resonant heat dissipation from isolated particle absorption and interparticle interactions support design and adaptive control of thermoplasmonic materials for a variety of implementations.

UV-Vis Ratiometric Resonance Synchronous Spectroscopy for Determination of Nanoparticle and Molecular Optical Cross Sections.

Demonstrated herein is a UV-vis Ratiometric Resonance Synchronous Spectroscopic (R2S2, pronounced as "R-two-S-two" for simplicity) technique where the R2S2 spectrum is obtained by dividing the resonance synchronous spectrum of a NP-containing solution by the solvent resonance synchronous spectrum. Combined with conventional UV-vis measurements, this R2S2 method enables experimental quantification of the absolute optical cross sections for a wide range of molecular and nanoparticle (NP) materials that range optically from pure photon absorbers or scatterers to simultaneous photon absorbers and scatterers, simultaneous photon absorbers and emitters, and all the way to simultaneous photon absorbers, scatterers, and emitters in the UV-vis wavelength region. Example applications of this R2S2 method were demonstrated for quantifying the Rayleigh scattering cross sections of solvents including water and toluene, absorption and resonance light scattering cross sections for plasmonic gold nanoparticles, and absorption, scattering, and on-resonance fluorescence cross sections for semiconductor quantum dots (Qdots). On-resonance fluorescence quantum yields were quantified for the model molecular fluorophore Eosin Y and fluorescent Qdots CdSe and CdSe/ZnS. The insights and methodology presented in this work should be of broad significance in physical and biological science research that involves photon/matter interactions.

Rayleigh scattering cross-section measurements of nitrogen, argon, oxygen and air

Knowledge about Rayleigh scattering cross sections is relevant to predictions about radiative transfer in the atmosphere, and needed to calibrate the reflectivity of mirrors that are used in high-finesse optical cavities to measure atmospheric trace gases and aerosols. In this work we have measured the absolute Rayleigh scattering cross-section of nitrogen at 405.8 and 532.2nm using cavity ring-down spectroscopy (CRDS). Further, multi-spectral measurements of the scattering cross-sections of argon, oxygen and air are presented relative to that of nitrogen from 350 to 660nm using Broadband Cavity Enhanced Spectroscopy (BBCES). The reported measurements agree with refractive index based theory within 0.2±0.4%, and have an absolute accuracy of better than 1.3%. Our measurements expand the spectral range over which Rayleigh scattering cross section measurements of argon, oxygen and air are available at near-ultraviolet wavelengths. The expressions used to represent the Rayleigh scattering cross-section in the literature are evaluated to assess how uncertainties affect quantities measured by cavity enhanced absorption spectroscopic (CEAS) techniques. We conclude that Rayleigh scattering cross sections calculated from theory provide accurate data within very low error bounds, and are suited well to calibrate CEAS measurements of atmospheric trace gases and aerosols.

Near-infrared Rayleigh scattering of SF6

Cavity ring-down measurements have been performed on sulphur hexafluoride, in order to determine the extinction in the pressure range from 0 to 20 bar at 20°C (293 K), by using a tunable continuous wave distributed feedback diode laser emitting around 1180 nm. The cavity loss rate has been found to have both a linear dependence and a quadratic dependence on the gas density. While the linear component has been identified with the Rayleigh scattering, the quadratic component is likely due to collision-induced processes. The Rayleigh scattering cross section at 1180 nm has been determined as (1.25 ± 0.18) × 10−27 cm2 and has been compared with Rayleigh scattering cross sections measured in the deep-ultraviolet and visible spectral region.

Verification of TG‐61 dose for synchrotron‐produced monochromatic x‐ray beams using fluence‐normalized MCNP5 calculations

Ion chamber dosimetry is being used to calibrate dose for cell irradiations designed to investigate photoactivated Auger electron therapy at the Louisiana State University Center for Advanced Microstructures and Devices (CAMD) synchrotron facility. This study performed a dosimetry intercomparison for synchrotron-produced monochromatic x-ray beams at 25 and 35 keV. Ion chamber depth-dose measurements in a polymethylmethacrylate (PMMA) phantom were compared with the product of MCNP5 Monte Carlo calculations of dose per fluence and measured incident fluence. Monochromatic beams of 25 and 35 keV were generated on the tomography beamline at CAMD. A cylindrical, air-equivalent ion chamber was used to measure the ionization created in a 10 × 10 × 10-cm(3) PMMA phantom for depths from 0.6 to 7.7 cm. The American Association of Physicists in Medicine TG-61 protocol was applied to convert measured ionization into dose. Photon fluence was determined using a NaI detector to make scattering measurements of the beam from a thin polyethylene target at angles 30°-60°. Differential Compton and Rayleigh scattering cross sections obtained from xraylib, an ANSI C library for x-ray-matter interactions, were applied to derive the incident fluence. MCNP5 simulations of the irradiation geometry provided the dose deposition per photon fluence as a function of depth in the phantom. At 25 keV the fluence-normalized MCNP5 dose overestimated the ion-chamber measured dose by an average of 7.2 ± 3.0%-2.1 ± 3.0% for PMMA depths from 0.6 to 7.7 cm, respectively. At 35 keV the fluence-normalized MCNP5 dose underestimated the ion-chamber measured dose by an average of 1.0 ± 3.4%-2.5 ± 3.4%, respectively. These results showed that TG-61 ion chamber dosimetry, used to calibrate dose output for cell irradiations, agreed with fluence-normalized MCNP5 calculations to within approximately 7% and 3% at 25 and 35 keV, respectively.

SU-E-T-101: Dosimetry Intercomparison for a Synchrotron-Produced Monochromatic X-Ray Beam.

This study performed a dosimetry intercomparison for synchrotron-produced monochromatic x-ray beams. Ion chamber depth-dose measurements in a polymethylmethacrylate (PMMA) phantom were compared with the product of MCNP5 Monte Carlo calculations of dose per fluence and measured incident fluence at 25 and 35 keV. The ion chamber measurements are being used to calibrate dose output for cell irradiations designed to investigate photoactivated Auger electron therapy at the LSU Center for Advanced Microstructures and Devices (CAMD) synchrotron facility. Monochromatic beams of 25 and 35 keV were generated on the tomography beamline at CAMD. A cylindrical, air-equivalent ion chamber was used to measure the ionization created in a 10×10×10-cm3 PMMA phantom at depths of 0.6 - 7.7 cm. AAPM TG-61 protocol was applied to convert measured ionization into dose. MCNP5 simulations of the irradiation geometry were performed to determine the dose deposition per photon fluence in the phantom. Photon fluence was determined using a NaI detector to make scattering measurements of the beam from a polyethylene target at angles 15 - 60 degrees. Differential Compton and Rayleigh scattering cross sections were used to derive the incident fluence. At 35 keV dose measurements for equal exposures determined using the MCNP5-fluence results underestimated those of the ion chamber by 1.8 - 4.8% for PMMA depths from 0.6 - 7.7 cm, respectively. At 25 keV there was an overestimate of 6.6 - 1.9%. These results show that TG-61 ion chamber dosimetry, used to calibrate the dose output for the cell irradiations, is accurate within approximately 7% for beam energies 25-35 keV. This research was supported by contract W81XWH-10-1-0005 awarded by The U.S. Army Research Acquisition Activity, 820 Chandler Street, Fort Detrick, MD 21702-5014. This report does not necessarily reflect the position or policy of the Government, and no official endorsement should be inferred.

Calculation of the total Rayleigh scattering cross sections of photons in the energy range of 30–50 keV for Nb and Mo elements

The total Rayleigh scattering cross sections are calculated in the energy range of 30–50 keV using the modified relativistic form factors (MRFF), non-relativistic form factors (NFF), and relativistic form factors (RFF). Numerical calculations are made for energies above the K-threshold comparisons, for medium- Z elements (Nb and Mo), primarily at small momentum transfers. The integration range is divided into intervals using a modified formula to take into account the smaller scattering angles. The calculated cross sections based on MRFF, NFF, and RFF are presented and compared with the tabulated theoretical values. It is found that the values calculated using the NFF and RFF are smaller than the tabulated values with a ratio of 3–7%. It is also observed that the smallest total Rayleigh scattering cross section values are obtained using the MRFF.

Elastic scattering of gamma rays and X-rays

Studies of elastic gamma ray scattering were pursued independently by the groups of Prof. Ghose and the author for several decades in spite of somewhat meagre support. Several techniques for such studies developed by the two groups and some of the results obtained in the energy range from tens of keV to about 1.5 MeV are described briefly. The theoretical background necessary for understanding these results is also outlined. The results showed the importance of Modified Relativistic Form Factor (MRFF) approximation in the explanation of atomic Rayleigh scattering cross sections in the small angle regime and the necessity for an inclusion of real Delbrück scattering amplitudes at large scattering angles. Dispersion corrections to form factor amplitudes or the so-called anomalous scattering factors are shown to be needed at photon energies close to electron binding energy thresholds. A few promising future extensions of such studies are indicated at the end.

Delbrück contribution in the elastic scattering of1.115−MeVphotons

Differential cross sections for the elastic scattering of 1.115-MeV photons from tungsten (Z=74) and lead (Z=82) have been measured at angles ranging from 30 deg. to 135 deg., using a high purity coaxial germanium detector. The experimental results are compared with S-matrix theoretical calculations of Rayleigh scattering cross sections, which also include contributions arising from the nuclear Thomson amplitudes and the Delbrueck amplitude in lowest order Born approximation. The present experimental data at 1.115 MeV indicates that Delbrueck amplitudes calculated with lowest-order Born approximation, when combined with S-matrix Rayleigh scattering amplitudes, are sufficient, as has previously been observed at 1.332 MeV for a number of high-Z elements, and at 1.121 MeV and 1.173 MeV for Z=92. This result for Z=74 and Z=82 at 1.115 MeV provides further confirmation that the Delbrueck amplitudes calculated with lowest-order Born approximation are sufficient for energies at and below 1.332 MeV, in contrast to the situation at 2.754 MeV where Coulomb corrections to the Delbrueck amplitudes are significant for high-Z elements.

Rayleigh scattering cross sections of combustion species at 266, 355, and 532 nm for thermometry applications

Rayleigh scattering cross sections are measured for nine combustion species (Ar, N2, O2, CO2, CO, H2, H2O, CH4, and C3H8) at wavelengths of 266, 355, and 532 nm and at temperatures ranging from 295 to 1525 K. Experimental results show that, as laser wavelengths become shorter, polarization effects become important and the depolarization ratio of the combustion species must be accounted for in the calculation of the Rayleigh scattering cross section. Temperature effects on the scattering cross section are also measured. Only a small temperature dependence is measured for cross sections at 355 nm, resulting in a 2-8% increase in cross section at temperatures of 1500 K. This temperature dependence increases slightly for measurements at 266 nm, resulting in a 5-11% increase in cross sections at temperatures of 1450 K.

Rayleigh scattering cross sections of O2 at wavelengths longer than 180 nm

Rayleigh scattering of solar radiation by oxygen molecules is an important contributor to the photon flux in the atmosphere at wavelengths longer than the threshold for direct photodissociation of O2 near 180 nm. We carry out detailed calculations of Rayleigh scattering cross sections of O2 at wavelengths from 180 to 205 nm in the region of the discrete Schumann‐Runge band system. The cross sections contain numerous resonance structures, whose characteristics we identify. Beyond 205 nm we show that the cross sections diminish rapidly before taking up the known variation as the inverse fourth power of the wavelength at long wavelengths. We present detailed results for cross sections for scattering by O2 in individual rotational levels of the ground vibrational state sufficient to allow the calculation of the Rayleigh scattering cross sections at atmospheric temperatures.

X-RAY SCATTERING CROSS SECTIONS FOR MOLECULES, PLASTICS, TISSUES, AND FEW BIOLOGICAL MATERIALS

Compton and Rayleigh scattering cross sections for bone, bakelite, polycarbonate, nylon, lucite, polystyrene, polyethylene, water, glycogen, fat, calcium hydroxyapatite and protein are calculated for various monoenergetic Kα X-ray energies covering the angular region from 0 to 180° using non-relativistic, relativistic, relativistic modified and molecular form factors and the non-relativistic incoherent scattering function. The scattered radiation from these materials will be very useful to develop a semianalytic model to investigate the potential applications of X-ray scatter imaging. The scatter model can be used as a tool for designing and optimizing X-ray imaging system. However, one particular area of interest is in Monte Carlo simulation of photon transport in applications to medical physics and radiography.