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High-accuracy spacecraft tracking requires tropospheric modeling which is generally scaled by either estimated or measured values of surface refractivity. This report summarizes the results of a worldwide surface-refractivity test conducted in 1968 in support of the Apollo program. The results are directly applicable to all NASA radio-tracking systems.
The effect of omitting the parallactic refraction correction for satellite optical observations in the determination of station coordinates is analyzed for a large satellite data distribution. A significant error effect is seen in station heights. A geodetic satellite data distribution of 23 close earth satellites, containing 30,000 optical observations obtained by 13 principal Baker-Nunn camera sites, is employed. This distribution was used in a preliminary Goddard Earth Model (GEM 1) for the determination of the gravity field of the earth and geocentric tracking station locations. The parallactic refraction correction is modeled as an error on the above satellite data and a least squares adjustment for station locations is obtained for each of the 13 Baker-Nunn sites. Results show an average station height shift of +8 meters with a dispersion of plus or minus 0.7 meters for individual sites. Station latitude and longitude shifts amounted to less than a meter. Similar results are obtained from a theoretical method employing a probability distribution for the satellite optical observations.
A formula for correcting laser measurements of satellite range for the effect of atmospheric refraction is given. The corrections apply above 10 deg elevation to satellites whose heights exceed 70 km. The meteorological measurements required are the temperature, pressure, and relative humidity of the air at the laser site at the time of satellite pass. The accuracy of the formula was tested by comparison with corrections obtained by ray-tracing radiosonde profiles. The standard deviation of the difference between the refractive retardation given by the formula and that calculated by ray-tracing was less than about 0.04% of the retardation or about 0.5 cm at 10 deg elevation, decreasing to 0.04 cm near zenith.
A determination is presented of the ionospheric refraction correction requirements for the Goddard range and range rate (GRARR) S-band, modified S-band, very high frequency (VHF), and modified VHF systems. The relation ships within these four systems are analyzed to show that the refraction corrections are the same for all four systems and to clarify the group and phase nature of these corrections. The analysis is simplified by recognizing that the range rate is equivalent to a carrier phase range change measurement. The equation for the range errors are given.
A study was conducted of an alternate method for storage and use of bathymetry data in the Langley Research Center and Virginia Institute of Marine Science mid-Atlantic continental-shelf wave-refraction computer program. The regional bathymetry array was divided into 105 indexed modules which can be read individually into memory in a nonsequential manner from a peripheral file using special random-access subroutines. In running a sample refraction case, a 75-percent decrease in program field length was achieved by using the random-access storage method in comparison with the conventional method of total regional array storage. This field-length decrease was accompanied by a comparative 5-percent increase in central processing time and a 477-percent increase in the number of operating-system calls. A comparative Langley Research Center computer system cost savings of 68 percent was achieved by using the random-access storage method.
It is demonstrated that the scattering ratio-principle originally restricted to exact forward and exact backward scattering, and to values of the size parameter and of the product (refractive index x size parameter) less than 0.8 has a much wider applicability. After relaxing these stringent conditions, it is also shown that this principle can be retained as the basis of an experimental technique for retrieving the mean effective size and refractive index of transparent atmospheric particulates.
Mariner 9 ultraviolet spectrometer observations of the 1971 dust clouds obscuring the surface of Mars have been analyzed by matching the observed dust phase function with Mie scattering calculations for size distributions of homogeneous and isotropic material. Preliminary results indicate an effective particle radius of not less than 0.2. The real component of the index of refraction is not less than 1.8 at both 268 and 305 nm; corresponding values for the imagery component are 0.02 and 0.01. These values are consistent with those found by Mead (1970) for the visible and near-visible wavelengths. The refractive index and the absorption coefficient increase rapidly with decreasing wavelength in going from the visible to the ultraviolet, indicating the presence of an ultraviolet absorption band which may shield organisms from ultraviolet irradiation.
Experimental scattering results using a microwave analog technique are described. Artificially constructed axially symmetric spheres with a graphite-like fine-layered composite structure and anisotropic refractive indices were employed to aid high-precision measurements of forward scattering under stable conditions (temperature, physical dimensions, electronic conditions) and to facilitate studies of the extinction and polarization of light by graphite particles in interstellar space. A theoretical approximation utilizing Mie theory for spheres with suitable orientation-dependent refractive indices is applied to account for changes in the complex forward-scattering amplitudes and phase in response to target orientation. The methods are extended to the full range of scattering angles, from the forward direction continuously to about 165 deg and at 180 deg. Agreement between experiment and prediction is close when the symmetry axis is parallel to the polarization.
A method for determining the refractive index profile of thick phase gratings in linear electrooptic crystals is presented. This method also determines the effective photovoltaic electric field and the relative contributions of diffusion and drift during hologram recording. The method requires only a knowledge of the modulation ratio during hologram recording and the fundamental and the higher-order diffraction efficiencies of the grating. As an illustration of the method, the refractive index profile, the effective photovoltaic field, and the relative contributions of diffusion and drift are determined from experimental measurements for a lithium niobate holographic grating.
The Langley Research Center and Virginia Institute of Marine Science wave refraction computer model was applied to the Baltimore Canyon region of the mid-Atlantic continental shelf. Wave refraction diagrams for a wide range of normally expected wave periods and directions were computed by using three bottom topography approximation techniques: quadratic least squares, cubic least squares, and constrained bicubic interpolation. Mathematical or physical interpretation of certain features appearing in the computed diagrams is discussed.
The previously derived DSN Radio Frequency Angular Tropospheric Refraction Model contained an assumption which was subsequently seen to be at a variance with the theoretical basis of angular refraction. The modification necessary to correct the model is minor in that the value of a constant is changed.
A ground station network tracked a high altitude spacecraft which in turn tracked a low orbiting satellite. Orbit data are relayed back to the ground stations. A refraction study was performed on this configuration to compute ionospheric and tropospheric refraction effects along the satellite and ground links.
The effects of tropospheric and ionospheric refraction errors are analyzed for the GEOS-C altimeter project in terms of their resultant effects on C-band orbits and the altimeter measurement itself. Operational procedures using surface meteorological measurements at ground stations and monthly means for ocean surface conditions are assumed, with no corrections made for ionospheric effects. Effects on the orbit height due to tropospheric errors are approximately 15 cm for single pass short arcs (such as for calibration) and 10 cm for global orbits of one revolution. Orbit height errors due to neglect of the ionosphere have an amplitude of approximately 40 cm when the orbits are determined from C-band range data with predominantly daylight tracking. Altimeter measurement errors are approximately 10 cm due to residual tropospheric refraction correction errors. Ionospheric effects on the altimeter range measurement are also on the order of 10 cm during the GEOS-C launch and early operation period.
The effects of departures from the spherical symmetry assumption are investigated by describing the refractivity profile on the earth's surface as a generalized function of the surface coordinates. Aspects of satellite ranging geometry are considered and the representation of the true group refractivity of the atmosphere at any point on the earth's surface is discussed. Surface meteorological data obtained from a few east coast weather stations are analyzed to obtain typical values of the higher order bias terms.
The optical performance of a virtual image display system is evaluated. Observation of a two-element (unachromatized doublet) refractive system led to the conclusion that the major source of image degradation was lateral chromatic aberration. This conclusion was verified by computer analysis of the system. The lateral chromatic aberration is given in terms of the resolution of the phosphor dots on a standard shadow mask color cathode ray tube. Single wavelength considerations include: astigmatism, apparent image distance from the observer, binocular disparities and differences of angular magnification of the images presented to each of the observer's eyes. Where practical, these results are related to the performance of the human eye. All these techniques are applied to the previously mentioned doublet and a triplet refractive system. The triplet provides a 50-percent reduction in lateral chromatic aberration which was the design goal. Distortion was also reduced to a minimum over the field of view. The methods used in the design of the triplet are presented along with a method of relating classical aberration curves to image distance and binocular disparity.
The feasibility of recovering parameters from one-way range rate between two earth orbiting spacecraft during occultation of the tracking signal by the earth's lower atmosphere. The tracking data is inverted by an integral transformation (Abel transform) to obtain a vertical refractivity profile above the point of closest approach of the ray connecting the satellites. Pressure and temperature distributions can be obtained from values of dry refractivity using the hydrostatic equation and perfect gas law. Two methods are investigated for recovering pressure and temperature parameters. Results show that recovery is much more sensitive to satellite velocity errors than to satellite position errors. An error analysis is performed. An example is given demonstrating recovery of parameters from radio occultation data obtained during satellite-to-satellite tracking of Nimbus 6 by the ATS 6 satellite.
Four separable effects of atmospheric turbulence on average refraction angles in occultation experiments are derived from a simplified analysis, and related to more general formulations by B. S. Haugstad. The major contributors are shown to be due to gradients in height of the strength of the turbulence, and the sense of the resulting changes in refraction angles is explained in terms of Fermat's principle. Because the results of analyses of such gradient effects by W. B. Hubbard and J. R. Jokipii are expressed in other ways, a special effort is made to compare all of the predictions on a common basis. We conclude that there are fundamental differences, and use arguments based on energy conservation and Fermat's principle to help characterize the discrepancies.
The technique proposed by Fymat (1976) for retrieving the complex refractive index of atmospheric aerosols using narrowband spectral transmission ratios, taken within an overall narrow spectral interval, is investigated in the case of modelled polydispersions of rural, maritime-continental, maritime-sea spray and meteoric dust aerosols. It is confirmed that for not too broad size distributions most of the information comes from a narrow size range of 'active' aerosols so that, under these circumstances, the refractive index components can indeed be retrieved essentially independently of the size distribution. For 0.1% accurate data in three colors, the technique can provide the real and imaginary components of the index respectively within 0.07% and 0.3% accuracy.