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NASA NTRS1980

Atmospheric microwave refractivity and refraction

The atmospheric refractivity can be expressed as a function of temperature, pressure, water vapor content, and operating frequency. Based on twenty-year meteorological data, statistics of the atmospheric refractivity were obtained. These statistics were used to estimate the variation of dispersion, attenuation, and refraction effects on microwave and millimeter wave signals propagating along atmospheric paths. Bending angle, elevation angle error, and range error were also developed for an exponentially tapered, spherical atmosphere.

Yu, E.↗

NASA NTRS2004

The Cryogenic, High-Accuracy, Refraction Measuring System (CHARMS): A New Facility for Cryogenic Infrared through Vacuum Far-Ultraviolet Refractive Index Measurements

The optical designs of future NASA infrared (IR) missions and instruments, such as the James Webb Space Telescope's (JWST) Near-Mixed Camera (NIRCam), will rely on accurate knowledge of the index of refraction of various IR optical materials at cryogenic temperatures. To meet this need, we have developed a Cryogenic, High-Accuracy Refraction Measuring System (CHARMS). In this paper we discuss the completion of the design and construction of CHARMS as well as the engineering details that constrained the final design and hardware implementation. In addition, we will present our first light, cryogenic, IR index of refraction data for LiF, BaF2, and CaF2, and compare our results to previously published data for these materials.

Frey, Bradley J.↗

NASA NTRS2020

Testing Densities and Refractive Indices of Extraterrestrial Ice Components Using Molecular Structures - Organic Compounds and Molar Refractions

The use of infrared spectra to determine molecular abundances of icy astronomical objects and to study their chemistry requires laboratory measurements of reference spectra and related quantities, such as the index of refraction (n) and density (p) of candidate ices. Here we present new n and p measurements on ices involving over 30 C-, H-, and O-containing compounds, both acyclic and cyclic, representing seven chemical families. We examine the results in a way that is rare in the astrochemical literature, namely one in which data from an ice formed from molecules of a particular chemical family are compared to measurements on another member of the same family, such as of a homologous series or a pair of isomers. Apart from the intrinsic usefulness of the n and data, a structure-based comparison can help establish trends and identify possibly spurious results. As liquid-phase data sometimes are used in low-temperature astrochemical work in the absence of solid-phase measurements, we compare our new ice results to those for the corresponding room-temperature liquids. We emphasize the use of our n and p data to compute the molar refraction (RM) for each of our ices, and how the resulting RM values compare to those expected from molecular structures. The use of calculated RM values and measured n values to calculate ice densities, in the absence of direct measurements, is also addressed.

Hudson, Reggie L.↗

DOE OSTI2021

Talbot-Lau x-ray deflectometer: Refraction-based HEDP imaging diagnostic

Talbot-Lau x-ray interferometry has been implemented to map electron density gradients in High Energy Density Physics (HEDP) experiments. X-ray backlighter targets have been evaluated for Talbot-Lau X-ray Deflectometry (TXD). Cu foils, wires, and sphere targets have been irradiated by 10–150 J, 8–30 ps laser pulses, while two pulsed-power generators (∼350 kA, 350 ns and ∼200 kA, 150 ns) have driven Cu wire, hybrid, and laser-cut x-pinches. A plasma ablation front generated by the Omega EP laser was imaged for the first time through TXD for densities >1023 cm−3. Backlighter optimization in combination with x-ray CCD, image plates, and x-ray film has been assessed in terms of spatial resolution and interferometer contrast for accurate plasma characterization through TXD in pulsed-power and high-intensity laser environments. The results obtained thus far demonstrate the potential of TXD as a powerful diagnostic for HEDP.

Valdivia, M. P.↗

NASA NTRS2000

Retrieving the Vertical Structure of the Effective Aerosol Complex Index of Refraction from a Combination of Aerosol in Situ and Remote Sensing Measurements During TARFOX

The largest uncertainty in estimates of the effects of atmospheric aerosols on climate stems from uncertainties in the determination of their microphysical properties, including the aerosol complex index of refraction, which in turn determines their optical properties. A novel technique is used to estimate the aerosol complex index of refraction in distinct vertical layers from a combination of aerosol in situ size distribution and remote sensing measurements during the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). In particular, aerosol backscatter measurements using the NASA Langley LASE (Lidar Atmospheric Sensing Experiment) instrument and in situ aerosol size distribution data are utilized to derive vertical profiles of the "effective" aerosol complex index of refraction at 815 nm (i.e., the refractive index that would provide the same backscatter signal in a forward calculation on the basis of the measured in situ particle size distributions for homogeneous, spherical aerosols). A sensitivity study shows that this method yields small errors in the retrieved aerosol refractive indices, provided the errors in the lidar-derived aerosol backscatter are less than 30% and random in nature. Absolute errors in the estimated aerosol refractive indices are generally less than 0.04 for the real part and can be as much as 0.042 for the imaginary part in the case of a 30% error in the lidar-derived aerosol backscatter. The measurements of aerosol optical depth from the NASA Ames Airborne Tracking Sunphotometer (AATS-6) are successfully incorporated into the new technique and help constrain the retrieved aerosol refractive indices. An application of the technique to two TARFOX case studies yields the occurrence of vertical layers of distinct aerosol refractive indices. Values of the estimated complex aerosol refractive index range from 1.33 to 1.45 for the real part and 0.001 to 0.008 for the imaginary part. The methodology devised in this study provides, for the first time, a complete set of vertically resolved aerosol size distribution and refractive index data. yielding the vertical distribution of aerosol optical properties required for the determination of aerosol-induced radiative flux changes.

Redemann, J.↗

NASA NTRS2000

Retrieving the Vertical Structure of the Effective Aerosol Complex Index of Refraction from a Combination of Aerosol in Situ and Remote Sensing Measurements During TARFOX

The largest uncertainty in estimates of the effects of atmospheric aerosols on climate stems from uncertainties in the determination of their microphysical properties, including the aerosol complex index of refraction, which in turn determines their optical properties. A novel technique is used to estimate the aerosol complex index of refraction in distinct vertical layers from a combination of aerosol in situ size distribution and remote sensing measurements during the Tropospheric Aerosol Radiative Forcing Observational Experiment (TARFOX). In particular, aerosol backscatter measurements using the NASA Langley LASE (Lidar Atmospheric Sensing Experiment) instrument and in situ aerosol size distribution data are utilized to derive vertical profiles of the 'effective' aerosol complex index of refraction at 815 nm (i.e., the refractive index that would provide the same backscatter signal in a forward calculation on the basis of the measured in situ particle size distributions for homogeneous, spherical aerosols). A sensitivity study shows that this method yields small errors in the retrieved aerosol refractive indices, provided the errors in the lidar derived aerosol backscatter are less than 30% and random in nature. Absolute errors in the estimated aerosol refractive indices are generally less than 0.04 for the real part and can be as much as 0.042 for the imaginary part in the case of a 30% error in the lidar-derived aerosol backscatter. The measurements of aerosol optical depth from the NASA Ames Airborne Tracking Sunphotometer (AATS-6) are successfully incorporated into the new technique and help constrain the retrieved aerosol refractive indices. An application of the technique to two TARFOX case studies yields the occurrence of vertical layers of distinct aerosol refractive indices. Values of the estimated complex aerosol refractive index range from 1.33 to 1.45 for the real part and 0.001 to 0.008 for the imaginary part. The methodology devised in this study provides, for the first time a complete set of vertically resolved aerosol size distribution and refractive index data, yielding the vertical distribution of aerosol optical properties required for the determination of aersol-induced radiative flux changes

Redemann, J.↗

NASA NTRS1977

Measurement of the Specific Refractivities of CF4 and C2F6

In order to relate the measured fringe shift of an interferometer to density, the relation between density rho and refractive index n must be known. For gases where the refractive index is close to unity, this relation between density and refractive index is very closely approximated by (n - 1) = K rho where K is the specific refractivity, or the Gladstone-Dale constant. The specific refractivity, which is weakly dependent on wavelength and temperature, is readily available for a number of common test gases such as N2 and air. For more unique test gases such as CF4 and C2F6 for which refractive index data at optical wavelengths is not readily available, the constants can be estimated from the atomic refractivities of carbon and fluorine. In order to verify this estimation, a two-beam interferometer was used to experimentally determine the specific refractivities of CF4 and C2F6. This data was required for holographic interferometric measurements made at the Langley Hypersonic CF4 Tunnel. A Twyman-Green interferometer with a He-Ne laser light source of vacuum wavelength lambda equal to 633 nm was used to measure the constants. One beam of the two-beam interferometer passed through an optical cell of known inside length l which could be evacuated and slowly filled with the test gas to a density of 7.2 kg/cu m for CF4 or 5.7 kg/cu m for C2F6. If the refractive index (and hence density) is constant along the optical path through the cell, the fringe shift M and density change Delta rho are related M = 2Kl Delta rho/lambda for the double pass interferometer. Thus K can be determined by measuring the fringe shift as the density is changed. The output of a photodiode used to detect the fringe shift was recorded on a strip chart recorder. The rate of pressure increase of the test gas in the cell was controlled such that the fringes shifted at a rate of 0.5 to 1 fringe per sec. The pressure in the test cell was measured with a high accuracy quartz crystal pressure transducer and recorded approximately every 20 fringe peaks. The temperature of the cell was measured with a thermocouple and recorded at the start, midpoint, and end of each test.

Burner, A. W.↗

NASA NTRS2022

Employing Relaxed Smoothness Constraints on Imaginary Part of Refractive Index in AERONET Aerosol Retrieval Algorithm

In the Aerosol Robotic Network (AERONET) retrieval algorithm, smoothness constraints on the imaginary part of the refractive index provide control of retrieved spectral dependence of aerosol absorption by preventing the inversion code from fitting the noise in optical measurements and thus avoiding unrealistic oscillations of retrievals with wavelength. The history of implementation of the smoothness constraints in the AERONET retrieval algorithm is discussed. It is shown that the latest version of the smoothness constraints on the imaginary part of refractive index, termed standard and employed by Version 3 of the retrieval algorithm, should be modified to account for strong variability of light absorption by brown-carbon-containing aerosols in UV through mid-visible parts of the solar spectrum. In Version 3 strong spectral constraints were imposed at high values of the Ångström exponent (440–870 nm) since black carbon was assumed to be the primary absorber, while the constraints became increasingly relaxed as aerosol exponent deceased to allow for wavelength dependence of absorption for dust aerosols. The new version of the smoothness constraints on the imaginary part of the refractive index assigns different weights to different pairs of wavelengths, which are the same for all values of the Ångström exponent. For example, in the case of four-wavelength input, the weights assigned to short-wavelength pairs (440–675, 675–870 nm) are small so that smoothness constraints do not suppress natural spectral variability of the imaginary part of the refractive index. At longer wavelengths (870–1020 nm), however, the weight is 10 times higher to provide additional constraints on the imaginary part of refractive index retrievals of aerosols with a high Ångström exponent due to low sensitivity to aerosol absorption for longer channels at relatively low aerosol optical depths. The effect of applying the new version of smoothness constraints, termed relaxed, on retrievals of single-scattering albedo is analyzed for case studies of different aerosol types: black- and brown-carbon-containing fine mode aerosols, mineral dust coarse mode aerosols, and urban industrial fine mode aerosol. It is shown that for brown-carbon-containing aerosols employing the relaxed smoothness constraints resulted in significant reduction in retrieved single-scattering albedo and spectral residual errors (compared to standard) at the short wavelengths. For example, biomass burning smoke cases showed a reduction in single-scattering albedo and spectral residual error at 380 nm of ∼ 0.033 and ∼ 17 %, respectively, for the Rexburg site and ∼ 0.04 and ∼ 12.7 % for the Rimrock site, both AERONET sites in Idaho, USA. For a site with very high levels of black-carbon-containing aerosols (Mongu, Zambia), the effect of modification in the smoothness constraints was minor. For mineral dust aerosols at small Ångström exponent values (Mezaira site, UAE), the spectral constraint on the imaginary part of the refractive index was already relaxed in Version 3; therefore the new relaxed constraint results in minimal change. In the case of weakly absorbing urban industrial aerosols at the GSFC site, there are significant changes in retrieved single-scattering albedo using relaxed assumption, especially reductions at longer wavelengths: ∼ 0.016 and ∼ 0.02 at 875 and 1020 nm, respectively, for 440 nm aerosol optical depth (AOD) ∼ 0.3. The modification of smoothness constraints on the imaginary part of the refractive index has a minor effect on retrievals of other aerosol parameters such as the real part of the refractive index and parameters of the aerosol size distribution. The implementation of the relaxed smoothness constraints on the imaginary part of the refractive index in the next version of the AERONET inversion algorithm will produce significant impacts at some sites in short wavelength channels (380 and 440 nm) for some biomass burning smoke cases with significant brown carbon content and possibly in mid-visible channels (500 and 675 nm) to near-infrared channels (870 to 1020 nm) for some urban industrial aerosol types. However, most differences in single-scattering albedo retrievals between those applying the new relaxed constraint and the standard constraint will be within the uncertainty of the single-scattering albedo retrievals, depending on the level of aerosol optical depth, Ångström exponent, brown carbon content and wavelength.

Aliaksandr Siniuk↗

DOE OSTI2023

Refractivity Observations from Radar Phase Measurements: The 22 May 2002 Dryline Case during IHOP Project

The dryline, often associated with the development of severe storms in the Southern Great Plains of the United States of America, is a boundary layer phenomenon that occurs when a warm and moist air mass from the Gulf of Mexico meets a hot and dry air mass from the southwest desert area. An accurate knowledge of the water vapor spatio-temporal variability in the lower part of the atmosphere is crucial for a better understanding of the evolution of the dryline. The tropospheric refractivity, directly related to water vapor content, is a proxy for the water vapor content of the troposphere. It has already been demonstrated that the refractivity and the refractivity vertical gradient can be jointly estimated from radar phase measurements. In fact, it has been shown that using kriging interpolation techniques, accurate refractivity maps within the coverage area of the radar can be obtained with high temporal resolution. In this paper, a detailed analysis of the time series of radar-based refractivity maps obtained during a dryline that occurred on the afternoon of 22 May 2002 during the International H 2 O Project is presented. Comparisons between the time series of radar refractivity maps, obtained with the NCAR S-Pol radar, and the refractivity measurements derived from automatic ground-based weather stations and the AERI instrument, placed at different locations within the coverage area of the NCAR S-Pol radar, demonstrate the accuracy of radar refractivity estimates even for highly variable conditions, both in time and space, in the troposphere. Correlation coefficients higher than 0.95 are obtained in all weather station locations. Regarding the RMSE, errors less than 6 N-units are obtained for all cases, being even as low as 2.92 N-units at some locations.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1976

The prediction of zenith range refraction from surface measurements of meteorological parameters

In the last two decades, increasingly sophisticated deep space missions have placed correspondingly stringent requirements on navigational accuracy. As part of the effort to increase navigational accuracy, and hence the quality of radiometric data, much effort has been expended in an attempt to understand and compute the tropospheric effect on range (and hence range rate) data. The general approach adopted has been that of computing a zenith range refraction, and then mapping this refraction to any arbitrary elevation angle via an empirically derived function of elevation. The prediction of zenith range refraction derived from surface measurements of meteorological parameters is presented. Refractivity is separated into wet (water vapor pressure) and dry (atmospheric pressure) components. The integration of dry refractivity is shown to be exact. Attempts to integrate wet refractivity directly prove ineffective; however, several empirical models developed by the author and other researchers at JPL are discussed. The best current wet refraction model is here considered to be a separate day/night model, which is proportional to surface water vapor pressure and inversely proportional to surface temperature. Methods are suggested that might improve the accuracy of the wet range refraction model.

Berman, A. L.↗

NASA NTRS1990

Predicted and measured boundary layer refraction for advanced turboprop propeller noise

Currently, boundary layer refraction presents a limitation to the measurement of forward arc propeller noise measured on an acoustic plate in the NASA Lewis 8- by 6-Foot Supersonic Wind Tunnel. The use of a validated boundary layer refraction model to adjust the data could remove this limitation. An existing boundary layer refraction model is used to predict the refraction for cases where boundary layer refraction was measured. In general, the model exhibits the same qualitative behavior as the measured refraction. However, the prediction method does not show quantitative agreement with the data. In general, it overpredicts the amount of refraction for the far forward angles at axial Mach number of 0.85 and 0.80 and underpredicts the refraction at axial Mach numbers of 0.75 and 0.70. A more complete propeller source description is suggested as a way to improve the prediction method.

Dittmar, James H.↗

NASA NTRS2004

Design of Amphoteric Refraction Models Using WAVICA and RAYICA

The phenomenon of refraction of light is due to refractive index mismatches in two different media. However, to achieve this effect, a finite reflection loss is inevitable. A recent finding presented a unique type of interface, ferroelastic materials, that enables refraction without any reflection for either an electron or a light beam. This property is called total refraction. The same type of interface that yields total refraction can also yield amphoteric refraction, where the index of refraction can be either positive or negative depending on the incident angle. This interface could potentially be used to steer light without reflections which could have major applications in high power optics. My goal this summer is to first familiarize myself with the Mathematica software, especially the Wavica and Rayica packages. I will then model the amphoteric refraction by either modifying the Wavica and Rayica packages or using the built-in functions in these packages.

Su, Richard↗

NASA NTRS1992

Effect of Index of Refraction on Radiation Characteristics in a Heated Absorbing, Emitting, and Scattering Layer

The index of refraction can considerably influence the temperature distribution and radiative heat flow in semitransparent materials such as some ceramics. For external radiant heating, the refractive index influences the amount of energy transmitted into the interior of the material. Emission within a material depends on the square of its refractive index, and hence this emission can be many times that for a biackbody radiating into a vacuum. Since radiation exiting through an interface into a vacuum cannot exceed that of a blackbody, there is extensive reflection at the internal surface of an interface, mostly by total internal reflection. This redistributes energy within the layer and tends to make its temperature distribution more uniform. The purpose of the present analysis is to show that, for radiative equilibrium in a gray layer with diffuse interfaces, the temperature distribution and radiative heat flux for any index of refraction can be obtained very simply from the results for an index of refraction of unity. For the situation studied here, the layer is subjected to external radiative heating incident on each of its surfaces. The material emits, absorbs, and isotropically scatters radiation. For simplicity the index of refraction is unity in the medium surrounding the layer. The surfaces of the layer are assumed diffuse. This is probably a reasonable approximation for a ceramic layer that has not been polished. When transmitted radiation or radiation emitted from the interior reaches the inner surface of an interface, the radiation is diffused and some of it thereby placed into angular directions for which there is total internal reflection. This provides a trapping effect for retaining energy within the layer and tends to equalize its temperature distribution. An analysis of temperature distributions in absorbing-emitting layers, including index of refraction effects, was developed by Gardon (1958) to predict cooling and heat treating of glass plates. The interfaces were optically smooth; the resulting specular reflections were computed from the Fresnel reflection laws. This provides a somewhat different behavior than for diffuse interfaces. A similar application was for heating that occurs in a window of a re-entry vehicle (Fowle et al., 1969). A number of recent papers (Rokhsaz and Dougherty, 1989; Ping and Lallemand, 1989; Crosbie and Shieh, 1990) further examined the effects of Fresnel boundary reflections and nonunity refractive index. Other examples of analyses of both steady and transient heat transfer to single or multiple plane layers (Amlin and Korpela, 1979; Tarshis et al., 1969) have used diffuse assumptions at the interfaces as in the present study

Siegel, R.↗

DOE OSTI2021

Probing the ultrafast gain and refractive index dynamics of a VECSEL

Typically, strong gain saturation and gain dynamics play a crucial role in semiconductor laser mode-locking. While there have been several investigations of the ultrafast gain dynamics in vertical-external-cavity surface-emitting lasers (VECSELs), little is known about the associated refractive index changes. Yet, such refractive index changes do not only have a profound impact on the pulse formation process leading to self-phase modulation, which needs to be compensated by dispersion, but they are also of particular relevance for assessing the feasibility of Kerr-lens mode-locking of VECSELs. Here, we measure both refractive index as well as gain dynamics of a VECSEL chip using the ultrafast beam deflection method. We find that, in contrast to the gain dynamics, the refractive index dynamics is dominated by an instantaneous (100 fs) and a very slow component (100 ps). The time-resolved measurement of nonlinear refraction allows us to predict a pulse-length dependent, effective nonlinear refractive index n 2,eff , which is shown to be negative and on the order of 10 -16 m 2 =W for short pulse lengths (100 fs). It becomes positive for large excitation fluences and large pulse lengths (few ps). These results agree with some previous reports of self-mode-locked VECSELs for which the cavity design and pulse properties determine sign and strength of the nonlinear refractive index when assuming Kerr-lens mode-locking.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Time-refraction optics with single cycle modulation

Abstract We present an experimental study of optical time-refraction caused by time-interfaces as short as a single optical cycle. Specifically, we study the propagation of a probe pulse through a sample undergoing a large refractive index change induced by an intense modulator pulse. In these systems, increasing the refractive index abruptly leads to time-refraction where the spectrum of all the waves propagating in the medium is red-shifted, and subsequently blue-shifted when the refractive index relaxes back to its original value. We observe these phenomena in the single-cycle regime. Moreover, by shortening the temporal width of the modulator to ∼5–6 fs, we observe that the rise time of the red-shift associated with time-refraction is proportionally shorter. The experiments are carried out in transparent conducting oxides acting as epsilon-near-zero materials. These observations raise multiple questions on the fundamental physics occurring within such ultrashort time frames, and open the way for experimenting with photonic time-crystals, generated by periodic ultrafast changes to the refractive index, in the near future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Joint Inversion of Surface Electrical Resistivity Tomography and Seismic Refraction Data between the 200 Areas

Geologic stratigraphy on the Hanford Site influences groundwater and contaminant migration through the aquifer system and the vadose zone. The current geologic framework model (GFM) relies heavily on a sparse distribution of borehole data in some locations to map geologic contacts and hydrologic properties in the subsurface. Non-invasive geophysical methods such as electrical resistivity tomography (ERT), transient electromagnetic surveying, and seismic imaging are being used at Hanford to map subsurface structure in areas with limited well observations. This is to develop and mature the capability of geophysical methods to aid in GFM refinement, to identify regions of subsurface complexity, and for optimal well siting. A joint inversion of co-located seismic refraction and ERT data was carried out for data collected on a ~2.3-km profile between the 200 Areas on the Hanford Site. While ERT and seismic refraction images have sensitivity to overlapping physical properties (porosity, moisture content, lithology), the resolution and physics used to acquire each of these datasets are different and therefore information can be different or mutually complementary. Performing a joint inversion provides a reasonable option for a coherent, coupled interpretation for mutually complementary datasets. Between the 200 Areas, there are few boreholes to interpret the geologic framework model, and these data sets were obtained to provide a first line of evidence toward identifying stratigraphic structure. The seismic refraction and ERT data were independently inverted during fiscal year 2022 and broadly showed a two-layer structure with a trough-like feature that is ~1 km wide and upwards of 150 m deep. The depth of the trough feature was greater in the ERT image compared to the seismic image, which indicated a maximum depth of approximately 110 m. The objective of the joint inversion described in this report was to invert the seismic refraction and ERT data together while constraining the ERT image to be structurally similar to the seismic refraction image. The approach was applied using the geophysical inverse modeling program E4D, which has the capability to invert first-arrival times from seismic refraction data and ERT resistances using a “cross-gradient” constraint. The application of cross-gradient constraints with different weights produces ERT models that show a high degree of similarity within the upper 100 m (above ~120 m elevation). None of the ERT models show an improved structural similarity to the seismic result; therefore, it is recommended that further attempts to jointly interpret these models focus on petrophysics and image resolution. Petrophysical measurements of core samples would improve knowledge of what drives the ERT response in this region and, along with downhole geophysical measurements, could be used to “ground truth” the surface-based geophysical results. Image resolution studies would provide insight into which regions of the inverted images are reliable and which regions are poorly constrained.

58 GEOSCIENCES↗

NASA NTRS1980

Measurement of the specific refractivities of CF4 and C2F6

In order to relate the measured fringe shift of an interferometer to the density of a medium, the relation between density and refractive index, which is expressed by the specific refractivity, must be known. In the present paper, the specific refractivities of the wind tunnel test gases CF4 and C2F6 are determined in order to verify estimations based on the atomic refractivities of carbon and fluorine. A Twyman-Green two-beam interferometer with a 633-nm He-Ne laser light source was used to measure the specific refractivity as a function of fringe shift as the density of the gas was changed. Values of 0.122 and 0.131 cu cm/g were obtained for CF4 and C2F6 respectively at a temperature of 300 K, which are within 1% of the values computed from the atomic refractivities.

Burner, A. W.↗

NASA NTRS1983

Calculations of atmospheric refraction for spacecraft remote-sensing applications

Analytical solutions to the refraction integrals appropriate for ray trajectories along slant paths through the atmosphere are derived in this paper. This type of geometry is commonly encountered in remote-sensing applications utilizing an occultation technique. The solutions are obtained by evaluating higher-order terms from expansion of the refraction integral and are dependent on the vertical temperature distributions. Refraction parameters such as total refraction angles, air masses, and path lengths can be accurately computed. It is also shown that the method can be used for computing refraction parameters in astronomical refraction geometry for large zenith angles.

Chu, W. P.↗