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NASA NTRS2008

Frequency-Tuneable Pre-Stabilized Lasers for LISA via Sideband Locking

Laser frequency noise mitigation is one of the most challenging aspects of the LISA interferometric measurement system. The unstabilized frequency fluctuations must be suppressed by roughly twelve orders of magnitude in order to achieve a stability sufficient for gravitational wave detection. This enormous suppression will be achieved through a combination of stabilization and common-mode rejection. The stabilization component will itself be achieved in two stages: pre-stabilization to a local optical cavity followed by arm-locking to some combination of the inter-spacecraft distances. In order for these two stabilization stages to work simultaneously, the lock-point of the pre-stabilization loop must be frequency tunable. The current baseline stabilization technique, locking to an optical cavity, does not provide tunability between cavity resonance, which are typically spaced by 100s of MHz. Here we present a modification to the traditional Pound-Drever-Hall cavity locking technique that allows the laser to be locked to a cavity resonance with an adjustable frequency offset. This technique requires no modifications to the optical cavity itself, thus preserving the stability of the frequency reference. We present measurements of the system stability, demonstrating that the pre-stabilization level satisfies LISA requirements. We also present a demonstration of a phase-lock loop which utilizes the tunable sideband locking technique as a pre-stabilizations tage. The performance of the pre-stabilized phase-lock-loop indicates that the tunable sideband technique will meet the requirements as an actuator for arm-locking in LISA.

Thorpe, James Ira↗
NASA NTRS2006

Picometer Level Modeling of a Shared Vertex Double Corner Cube in the Space Interferometry Mission Kite Testbed

The Space Interferometry Mission (SIM) is a microarcsecond interferometric space telescope that requires picometer level precision measurements of its truss and interferometer baselines. Single-gauge metrology errors due to non-ideal physical characteristics of corner cubes reduce the angular measurement capability of the science instrument. Specifically, the non-common vertex error (NCVE) of a shared vertex, double corner cube introduces micrometer level single-gauge errors in addition to errors due to dihedral angles and reflection phase shifts. A modified SIM Kite Testbed containing an articulating double corner cube is modeled and the results are compared to the experimental testbed data. The results confirm modeling capability and viability of calibration techniques.

metrology↗
NASA NTRS2008

Direct-View Multi-Point Two-Component Interferometric Rayleigh Scattering Velocimeter

This paper describes an instantaneous velocity measurement system based on the Doppler shift of elastically scattered laser light from gas molecules (Rayleigh scattering) relative to an incident laser. The system uses a pulsed laser as the light source, direct-viewing optics to collect the scattered light, an interferometer to analyze spectrally the scattered light mixed with the incident laser light, and a CCD camera to capture the resulting interferogram. The system is capable of simultaneous, spatially (approximately 0.2 mm(exp 3)) and temporally (approximately 40 ns) resolved, multiple point measurements of two orthogonal components of flow velocity in the presence of background scattered light, acoustic noise and vibrations, and flow particulates. Measurements in a large-scale axi-symmetric Mach 1.6 H2-air combustion-heated jet running at a flow sensible enthalpy specific to Mach 5.5 hypersonic flight are performed to demonstrate the technique. The measurements are compared with CFD calculations using a finite-volume discretization of the Favre-averaged Navier-Stokes equations (VULCAN code).

Bivolaru, Daniel↗
NASA NTRS1985

Optical interferometry in fluid dynamics research

Optical interferometry techniques have been applied to the investigation of transonic airfoil flow fields in large-scale wind tunnels. Holographic interferometry techniques were used in the study of two-dimensional symmetric NACA 64A010 and Douglas Aircraft Company DSMA671 supercritical airfoil performance in the NASA Ames 2 ft x 2 ft transonic wind tunnel. Quantitative data obtained from the interferograms were compared to the surface pressure data. The excellent agreement obtained verified the accuracy of the flow visualization and demonstrated the potential for acquiring quantitative scalar results. Measurements of the inviscid flow speed and the boundary layer and wake velocity profiles were extracted from the interferograms and compared to laser Doppler velocimeter measurements. These results were also in good agreement. A method for acquiring real-time interferometric data in large-scale facilities was developed. This method, based on the point diffraction interferometer, was successfully tested in the Ames 2 ft x 2 ft transonic wind tunnel. The holographic and real-time interferometry methods were applied to the investigations of circulation control airfoils utilizing the Coanda effect. These results revealed the details of the jet interaction with the trailing edge boundary layer and the other parameters affecting the lift augmentation.

Bachalo, W. D.↗
NASA NTRS2022

Measurement of Surface Deformation Related to the December 2018 Mt. Etna Eruption Using Time-Series Interferometry and Magma Modeling for Hazard Zone Mapping

Mount Etna has erupted several times since it was first formed. Recently, Mount Etna began erupting again over 24–27 December 2018. Because it erupts frequently, Mount Etna should be observed on a frequent basis. From June 2018 to October 2019, 34 and 56 interferometric synthetic aperture radar (InSAR) images were acquired from the ascending and descending tracks of the Sentinel-1 satellite, respectively. We employed the Stanford Method for Persistent Scatterers (StaMPS) and a refined small baseline subset (SBAS) InSAR method to produce a surface deformation time-series map. In the time-series analysis, the phase signal remained unaltered with time. The Okada model was then applied to the result to generate a modeled interferogram, and the Q-LavHA program was run to generate a lava flow prediction model. A direct comparison of the results showed that Persistent Scatterers Interferometry (PSI)-StaMPS and the refined SBAS technique were comparable in terms of the displacement pattern, with slightly different velocity values obtained for individual points. In particular, a velocity range of −25 to 21 cm/yr was obtained from PSI-StaMPS, whereas a range of −30 to 25 cm/yr was obtained from the refined SBAS method. Upon computation of the vertical and east-west displacement components based on ascending and descending track data using both methods, deformation velocities of 51.5 and 52.5 cm/yr in the westerly direction on the western flank of Mount Etna were obtained from PSI-StaMPS and the refined SBAS method, respectively, whereas on the eastern flank, deformation toward the east was estimated to occur at a velocity of 50.1 or 54.2 cm/yr, respectively. PSIStaMPS estimated a vertical deformation velocity of −5.3 to 18.3 cm/yr, whereas the refined SBAS method produced a velocity range of approximately −7 to 19 cm/yr. The interferogram obtained via Okada modeling showed two fault sources in the 2018 Mount Etna eruption and a total volume change of approximately 12.39 × 10 6 m 3 . From the modeling results, a lava flow prediction model was generated using the Q-LavHA program. The approaches described in this study can be used by government officials, authorities, and other decision-makers to monitor and assess the risk of volcanic activity in the region.

Suci Ramayanti↗
NASA NTRS2006

Simultaneous CARS and Interferometric Rayleigh Scattering

This paper reports for the first time the combination of a dual-pump coherent anti-Stokes Raman scattering system with an interferometric Rayleigh scattering system (CARS - IRS) to provide time-resolved simultaneous measurement of multiple properties in combustion flows. The system uses spectrally narrow green (seeded Nd:YAG at 532 nm) and yellow (552.9 nm) pump beams and a spectrally-broad red (607 nm) beam as the Stokes beam. A spectrometer and a planar Fabry-Perot interferometer used in the imaging mode are used to record the spectrally broad CARS spectra and the spontaneous Rayleigh scattering spectra, respectively. Time-resolved simultaneous measurement of temperature, absolute mole fractions of N2, O2, and H2, and two components of velocity in a Hencken burner flame were performed to demonstrate the technique.

Bivolaru, Daniel↗
NASA NTRS2004

Mid-IR interferometric nulling for TPF

By the middle of 2006, the Interferometry Technology development program for NASA’s Terrestrial Planet Finder (TPF) Mission has the goal of demonstrating deep and stable interferometric nulling of broadband Mid-IR thermal radiation under conditions that are traceable to the expected on-orbit conditions. Specifically, the task is to demonstrate null levels of 10 to the negative 6 power, with a 50% BW centered at 10 um, with null stabilities of 10 to the negative 7 power all at cryogenic temperatures for observational periods of a couple of hours. The Achromatic Nulling activity at JPL addresses this concern in two testbeds: the warm nulling testbed and the cryonulling testbed. The warm nulling testbed will demonstrate the physics of nulling broadband thermal sources in an environment that is conducive to efficient research. We’ll explore nulling techniques, optical-mechanical alignment methods, motion control, and path-length metrology for a single beam interferometer, as well as preliminary planet detection techniques. Ultimate nulling capabilities under conditions that are more flight-like will be demonstrated in cryogenic nulling testbed. Knowledge gained from operation at room temperature will be applied to the cryongenic experiment where we face the additional challenges of extreme temperatures, cryongenic actuators, component survivability and fluxes that are within an order of magnitude of expected flux levels on orbit. Concurrently, we will develop a low flux mid-IR camera that will allow us to measure the nulls at these faint photon fluxes. This talk will review this development activity and will include recent nulling experimental results and plans for future work.

Vasisht, Gautam↗
NASA NTRS2005

SAR Interferometry as a Tool for Monitoring Coastal Changes in the Nile River Delta of Egypt

The Nile River Delta is experiencing rapid rates of coastal change. The rate of both coastal retreat and accretion in the Eastern Nile Delta requires regular, accurate detection and measurement. Current techniques used to monitor coastal changes in the delta are point measurements and, thus, they provide a spatially limited view of the ongoing coastal changes. SAR interferometry can provide measurements of subtle coastal change at a significantly improved spatial resolution and over large areas (100 sq km). Using data provided by the ERS-1&2 satellites, monitoring can be accomplished as frequently as every 35 days when needed. Radar interferometry is employed in this study to detect segments of erosion and accretion during the 1993-2000 period. The average rates of erosion and accretion in the Eastern Nile Delta are measured to be -11.64 m/yr and +5.12 m/yr, respectively. The results of this interferometric study can be used effectively for coastal zone management and integrated sustainable development for the Nile River Delta.

Aly, Mohamed H.↗
NASA NTRS1993

High angular resolution measurements of Algol

Algol (Beta Per) is an extensively studied triple system which includes an eclipsing pair. Using long baseline optical interferometry, the AB-C system of Algol has had its geometric and physical parameters determined with higher resolution and accuracy than obtained with other techniques. The orbital elements are determined, without the use of spectroscopic data, as follows: P = 680.05 d +/- 0.06 d, T = JD 2,446,931.4 +/- 1.5, e = 0.225 +/- 0.005, a-double-prime = 94.61 +/- 0.22 mas, i = 83.98 deg +/- 0.09 deg, omega = 310.29 deg +/- 0.08 deg, and Omega = 312.26 deg +/- 0.13 deg. The distance to Algol is determined as 28.2 +/- 0.8 pc. The absolute magnitude of the C component is 2.86 +/- 0.46 mag, and its mass is 1.50 +/- 0.11 solar mass. The observational results indicate the difference of the inclinations between the eclipsing pair and the wide pair to be within 1.6 deg. For the first time, the eclipsing of the close pair was observed interferometrically, and the results compare well with those from photometry.

Pan, Xiaopei↗
NASA NTRS2014

Ultra-Wideband, Dual-Polarized, Beam-Steering P-Band Array Antenna

A dual-polarized, wide-bandwidth (200 MHz for one polarization, 100 MHz for the orthogonal polarization) antenna array at P-band was designed to be driven by NASA's EcoSAR digital beam former. EcoSAR requires two wide P-band antenna arrays mounted on the wings of an aircraft, each capable of steering its main beam up to 35deg off-boresight, allowing the twin radar beams to be steered at angles to the flight path. The science requirements are mainly for dual-polarization capability and a wide bandwidth of operation of up to 200 MHz if possible, but at least 100 MHz with high polarization port isolation and low cross-polarization. The novel design geometry can be scaled with minor modifications up to about four times higher or down to about half the current design frequencies for any application requiring a dual-polarized, wide-bandwidth steerable antenna array. EcoSAR is an airborne interferometric P-band synthetic aperture radar (SAR) research application for studying two- and three-dimensional fine-scale measurements of terrestrial ecosystem structure and biomass, which will ultimately aid in the broader study of the carbon cycle and climate change. The two 2×8 element Pband antenna arrays required by the system will be separated by a baseline of about 25 m, allowing for interferometry measurements. The wide 100-to- 200-MHz bandwidth dual-polarized beams employed will allow the determination of the amount of biomass and even tree height on the ground. To reduce the size of the patches along the boresight dimension in order to fit them into the available space, two techniques were employed. One technique is to add slots along the edges of each patch where the main electric currents are expected to flow, and the other technique is to bend the central part of the patch away from the ground plane. The latter also facilitates higher mechanical rigidity. The high port isolation of more than 40 dB was achieved by employing a highly symmetrical feed mechanism for each pair of elements: three apertures coupling to the patch elements were placed along the two symmetry lines of the antenna element pair. Two apertures were used in tandem to excite two of the stacked patch elements for one polarization; the other was used to excite one element from one side and the other element from the other side, opposite in phase, taking care of the remaining polarization. The apertures narrow down to a small gap where they are excited by a crossing microstrip line to prevent any asymmetrical excitation of the two sides of the aperture gap, minimizing port-to-port coupling. Using patches that are non-planar leads to higher mechanical rigidity and smaller patch sizes to fit into the available space. Aperture coupling minimizes direct metal-to-metal connections. Using an aperture coupling feed mechanism results in a feed network for two antenna elements with a total of three feed points, plus one simple in-phase combiner to reduce it to two ports. It greatly reduces the complexity of the alternative, but more conventional, way of feeding a pair of two dual-polarized elements with high port isolation.

duToit, Cornelis↗
NASA NTRS1986

Pulsed mononode dye laser developed for a geophysical application

Following the extension of the lidar technique in the study of the atmosphere, the necessity of having a high power pulsed laser beam with a narrowed bandwidth and the possibility of selecting a particular wavelength within a certain spectral region arises. With the collaboration of others, a laser cavity using the multiwave Fizeau wedge (MWFW) was developed. Using the classical method of beam amplification with the aid of different stages, a new pulsed dye laser device was designed. The originality resides in the use of reflecting properties of the MFWF. Locally a plan wave coming with a particular angular incidence is reflected with a greater than unity coefficient; this is the consequence of the wedge angle which doubles the participation of every ray in the interferometric process. This dye laser operation and advantages are discussed. The feasibility of different geophysical applications envisageable with this laser is discussed.

Jegou, J. P.↗
NASA NTRS1992

Subnanosecond GPS-based clock synchronization and precision deep-space tracking

Interferometric spacecraft tracking is accomplished by the Deep Space Network (DSN) by comparing the arrival time of electromagnetic spacecraft signals at ground antennas separated by baselines on the order of 8000 km. Clock synchronization errors within and between DSN stations directly impact the attainable tracking accuracy, with a 0.3-nsec error in clock synchronization resulting in an 11-nrad angular position error. This level of synchronization is currently achieved by observing a quasar which is angularly close to the spacecraft just after the spacecraft observations. By determining the differential arrival times of the random quasar signal at the stations, clock offsets and propagation delays within the atmosphere and within the DSN stations are calibrated. Recent developments in time transfer techniques may allow medium accuracy (50-100 nrad) spacecraft tracking without near-simultaneous quasar-based calibrations. Solutions are presented for a worldwide network of Global Positioning System (GPS) receivers in which the formal errors for DSN clock offset parameters are less than 0.5 nsec. Comparisons of clock rate offsets derived from GPS measurements and from very long baseline interferometry (VLBI), as well as the examination of clock closure, suggest that these formal errors are a realistic measure of GPS-based clock offset precision and accuracy. Incorporating GPS-based clock synchronization measurements into a spacecraft differential ranging system would allow tracking without near-simultaneous quasar observations. The impact on individual spacecraft navigation-error sources due to elimination of quasar-based calibrations is presented. System implementation, including calibration of station electronic delays, is discussed.

Dunn, C. E.↗
NASA NTRS1991

Sub-nanosecond clock synchronization and precision deep space tracking

Interferometric spacecraft tracking is accomplished at the NASA Deep Space Network (DSN) by comparing the arrival time of electromagnetic spacecraft signals to ground antennas separated by baselines on the order of 8000 km. Clock synchronization errors within and between DSN stations directly impact the attainable tracking accuracy, with a 0.3 ns error in clock synchronization resulting in an 11 nrad angular position error. This level of synchronization is currently achieved by observing a quasar which is angularly close to the spacecraft just after the spacecraft observations. By determining the differential arrival times of the random quasar signal at the stations, clock synchronization and propagation delays within the atmosphere and within the DSN stations are calibrated. Recent developments in time transfer techniques may allow medium accuracy (50-100 nrad) spacecraft observations without near-simultaneous quasar-based calibrations. Solutions are presented for a global network of GPS receivers in which the formal errors in clock offset parameters are less than 0.5 ns. Comparisons of clock rate offsets derived from GPS measurements and from very long baseline interferometry and the examination of clock closure suggest that these formal errors are a realistic measure of GPS-based clock offset precision and accuracy. Incorporating GPS-based clock synchronization measurements into a spacecraft differential ranging system would allow tracking without near-simultaneous quasar observations. The impact on individual spacecraft navigation error sources due to elimination of quasar-based calibrations is presented. System implementation, including calibration of station electronic delays, is discussed.

Charles Dunn↗
NASA NTRS2005

Stroboscopic Interferometer for Measuring Mirror Vibrations

Stroboscopic interferometry is a technique for measuring the modes of vibration of mirrors that are lightweight and, therefore, unavoidably flexible. The technique was conceived especially for modal characterization of lightweight focusing mirror segments to be deployed in outer space; however, the technique can be applied to lightweight mirrors designed for use on Earth as well as the modal investigation of other optical and mechanical structures. To determine the modal structure of vibration of a mirror, it is necessary to excite the mirror by applying a force that varies periodically with time at a controllable frequency. The excitation can utilize sinusoidal, square, triangular, or even asynchronous waveforms. Because vibrational modes occur at specific resonant frequencies, it is necessary to perform synchronous measurements and sweep the frequency to locate the significant resonant modes. For a given mode it is possible to step the phase of data acquisition in order to capture the modal behavior over a single cycle of the resonant frequency. In order to measure interferometrically the vibrational response of the mirror at a given frequency, an interferometer must be suitably aligned with the mirror and adjustably phase-locked with the excitation signal. As in conventional stroboscopic photography, the basic idea in stroboscopic interferometry is to capture an image of the shape of a moving object (in this case, the vibrating mirror) at a specified instant of time in the vibration cycle. Adjusting the phase difference over a full cycle causes the interference fringes to vary over the full range of motion for the mode at the excitation frequency. The interference-fringe pattern is recorded as a function of the phase difference, and, from the resulting data, the surface shape of the mirror for the given mode is extracted. In addition to the interferometer and the mirror to be tested, the equipment needed for stroboscopic interferometry includes an arbitrary-function generator (that is, a signal generator), an oscilloscope, a trigger filter, and an advanced charge-coupled-device (CCD) camera. The optical components are positioned to form a pupil image of the mirror under test on the CCD chip, so that the interference pattern representative of the instantaneous mirror shape is imaged on the CCD chip.

Stahl, H. Philip↗
NASA NTRS2013

Interferometric Meteor Head Echo Observations using the Southern Argentina Agile Meteor Radar (SAAMER)

A radar meteor echo is the radar scattering signature from the free-electrons in a plasma trail generated by entry of extraterrestrial particles into the atmosphere. Three categories of scattering mechanisms exist: specular, nonspecular trails, and head-echoes. Generally, there are two types of radars utilized to detect meteors. Traditional VHF meteor radars (often called all-sky1radars) primarily detect the specular reflection of meteor trails traveling perpendicular to the line of sight of the scattering trail, while High Power and Large Aperture (HPLA) radars efficiently detect meteor head-echoes and, in some cases, non-specular trails. The fact that head-echo measurements can be performed only with HPLA radars limits these studies in several ways. HPLA radars are very sensitive instruments constraining the studies to the lower masses, and these observations cannot be performed continuously because they take place at national observatories with limited allocated observing time. These drawbacks can be addressed by developing head echo observing techniques with modified all-sky meteor radars. In addition, the fact that the simultaneous detection of all different scattering mechanisms can be made with the same instrument, rather than requiring assorted different classes of radars, can help clarify observed differences between the different methodologies. In this study, we demonstrate that such concurrent observations are now possible, enabled by the enhanced design of the Southern Argentina Agile Meteor Radar (SAAMER) deployed at the Estacion Astronomica Rio Grande (EARG) in Tierra del Fuego, Argentina. The results presented here are derived from observations performed over a period of 12 days in August 2011, and include meteoroid dynamical parameter distributions, radiants and estimated masses. Overall, the SAAMER's head echo detections appear to be produced by larger particles than those which have been studied thus far using this technique.

SPECULAR↗
NASA NTRS2019

Comprehensive Severe Weather Impact Assessment and Monitoring using Synthetic Aperture Radar and Auxiliary Data

Remote sensing datasets, particularly acquired by Synthetic Aperture Radar (SAR) sensors, have become increasingly important in severe weather disaster impact studies given their ability to observe the Earth largely irrespective of weather and sunlight conditions. The reliability of existing SAR change detection products applied on a pair of SAR images is constrained by the limitation of current methods to differentiate and classify disaster specific changes from anthropogenic surface alterations. Moreover, the inherent properties of the sensors, variations in SAR backscatter due to changes in surface conditions, and other factors exacerbate these limitations. We proposed a novel procedure expanding on earlier SAR-based change detection methods to exclude anthropogenic alterations and other sources of ambiguity that might lead to inaccurate mapping of the impacts of severe weather disasters. We applied the proposed procedure that is based on long term interferometric and amplitude-based change detection analyses of Sentinel- 1 SAR imagery to two study sites recently impacted by severe weather disasters (Flooding post severe weather events in urban centers; Hailstorm damage on crops). For the first case study, Sentinel-1 SLC scenes from two flood events in the Houston area (April 2016 flooding event and Hurricane Harvey of August-September 2017) were used to construct a flood map depicting areas repeatedly affected by the flood. Pixels with consistent coherence values in the pre-disaster coherence stack were retained for comparison with the pre- and post-disaster coherence stack and pixels with significant decline (greater than 60%) in coherence values were retained in the final flood map. The findings of the applied technique were calibrated and validated through datasets from NOAA/NWS Service storm reports, aerial imaging (NOAA and Civil Air Patrol), Federal Emergency Management Agency (FEMA) reporting, and targeted collections of NASA’s L-band UAVSAR data. Findings and products derived from the adopted methodology can be useful in disaster response and mitigation activities.

Gebremichael, Esayas↗
NASA NTRS2007

Radar Interferometer for Topographic Mapping of Glaciers and Ice Sheets

A report discusses Ka-band (35-GHz) radar for mapping the surface topography of glaciers and ice sheets at high spatial resolution and high vertical accuracy, independent of cloud cover, with a swath-width of 70 km. The system is a single- pass, single-platform interferometric synthetic aperture radar (InSAR) with an 8-mm wavelength, which minimizes snow penetration while remaining relatively impervious to atmospheric attenuation. As exhibited by the lower frequency SRTM (Shuttle Radar Topography Mission) AirSAR and GeoSAR systems, an InSAR measures topography using two antennas separated by a baseline in the cross-track direction, to view the same region on the ground. The interferometric combination of data received allows the system to resolve the pathlength difference from the illuminated area to the antennas to a fraction of a wavelength. From the interferometric phase, the height of the target area can be estimated. This means an InSAR system is capable of providing not only the position of each image point in along-track and slant range as with a traditional SAR but also the height of that point through interferometry. Although the evolution of InSAR to a millimeter-wave center frequency maximizes the interferometric accuracy from a given baseline length, the high frequency also creates a fundamental problem of swath coverage versus signal-to-noise ratio. While the length of SAR antennas is typically fixed by mass and stowage or deployment constraints, the width is constrained by the desired illuminated swath width. As the across-track beam width which sets the swath size is proportional to the wavelength, a fixed swath size equates to a smaller antenna as the frequency is increased. This loss of antenna size reduces the two-way antenna gain to the second power, drastically reducing the signal-to-noise ratio of the SAR system. This fundamental constraint of high-frequency SAR systems is addressed by applying digital beam-forming (DBF) techniques to synthesize multiple simultaneous receive beams in elevation while maintaining a broad transmit illumination. Through this technique, a high antenna gain on receive is preserved, thereby reducing the required transmit power and thus enabling high-frequency SARs and high-precision InSAR from a single spacecraft.

Moller, Delwyn K.↗
NASA NTRS1973

Applications of radio interferometry to navigation

Radio astronomy experiments have demonstrated the feasibility of making precise position measurements using interferometry techniques. The application of this method to navigation and marine geodesy is discussed, and comparisons are made with existing navigation systems. The very long baseline technique, with a master station, can use either an artificial satellite or natural sources as position references; a high-speed data link is required. A completely ship-borne system is shown to be feasible, at the cost of poorer sensitivity for natural sources. A comparison of Doppler, delay and phase-track modes of operating a very long baseline configuration is made, as that between instantaneous measurements and those where a source can be tracked from horizon to transit. Geometric limitations in latitude and longitude coverage are discussed. The characteristics of natural radio sources, their flux, distribution on the sky, and apparent size are shown to provide a limit on position measurements precision. The atmosphere and frequency standard used both contribute to position measurement uncertainty by affecting interferometric phase.

Knowles, S. H.↗