Very Long Baseline Interferometry (VLBI)

vlbi_thumbVery Long Baseline Interferometry (VLBI) is a technique being used by the United States Naval Observatory (USNO) to determine the reference frames for stars and the Earth, and to predict the variable orientation of the Earth in three-dimensional space. Knowing the celestial and terrestrial reference frames is important to the Department of Defense (DoD) in order to maintain the accuracy of the Global Positioning System (GPS) upon which much of the world depends for navigation.

GPS is a satellite-based navigation system made up of a network of 24 DoD satellites that circle the earth twice a day in very precise orbits and repeatedly transmit position and timing information to earth. GPS receivers use the timing data to determine the distances to a number of satellites and then their positions to triangulate the user's exact location. While highly accurate, this calculated location is in the reference frame of the GPS satellites. Translating to a location on the Earth (in the terrestrial reference frame) requires precise knowledge of the position and orientation of the Earth relative to the satellites, data that are determined by the Earth Orientation Parameters (EOP). The EOP give the Earth's position (the terrestrial reference frame) in the celestial reference frame (which can be translated to the GPS satellite frame). Continuous, unpredictable changes in the shape and (primarily) the orbit of the Earth require daily measurement of the EOP. Without such frequent calibration a drift of up to 20 meters in position could occur in GPS triangulations over a 2 week period.

VLBI is the only technique that can make the precise celestial position measurements required to produce meaningful EOP needed to calibrate the GPS system. The EOP are also essential for performing orbit controls of spacecraft, as well as deciding to insert or delete a leap seconds in the Coordinated Universal Time (UTC), which is the primary time standard by which the world regulates clocks. USNO provides a variety of VLBI-based data products that include positions of extragalactic radio sources that define an astrometric quasi-inertial Celestial Reference Frame (CRF), positions and velocities of radio antennas that define a VLBI-based Terrestrial Reference Frame (TRF) and the EOP that link the CRF and the TRF.

What is VLBI?

“VLBI” is an abbreviation of “Very Long Baseline Interferometry”. It is a technique used in radio astronomy where observations are made simultaneously by radio telescopes situated at distant locations on the Earth's surface. The simultaneous observations are combined in post-processing to “synthesize” a radio telescope the size of the distance between the individual elements, producing extremely high-resolution measurements of the astrometric radio source. The radio signal data received at each telescope is paired with timing information, usually from a local atomic clock, and the time differences between the arrivals of the radio waves at the separate antennas determined by correlating the signals. By using the amplitude and phase information of the correlated signal data between the many different telescopes it is possible to produce an image of the astrometric radio source.

Images of the extragalactic quasar source 0458-020 at two different frequencies, 8.4 GHz (left) and 24 GHz (right). Images were produced from VLBI data recorded and reduced at USNO through the Radio Reference Frame Image Database program. They demonstrate the varying structure of the sources as a function of observing frequency, which can affect the astrometric and geodetic measurements produced by USNO. (Image courtesy of USNO)

Exploiting data collected from multiple telescopes that are separated by very large distances is what enables VLBI to produce high resolution imagery. Since the VLBI technique measures the time differences between the arrival of radio waves at separate antennas, it can also be used “in reverse” to perform earth rotation studies, map movements of tectonic plates very precisely (within millimeters), perform various types of geodesy, and determine the position of the Earth's center in the CRF to very high accuracy.

How VLBI Works

VLBI is a geometric technique which measures the time difference in the arrival of a radio wavefront emitted by a distant astronomical radio source (typically a quasar) between at least two Earth-based radio telescopes. Knowing the time difference (τ), and the angular separation (β) between the viewpoint and the baseline between the antennas of the telescopes, the distance between the telescopes can be determined (see figure below). Because the time difference measurements are precise to a few picoseconds, VLBI determines the relative positions of the cooperating radio telescopes to a few millimeters and the positions of the radio source to a few milliarcseconds. Usually the VLBI-data are acquired over a 24 hour period on about 30 quasars in about 300 different directions. Since the radio telescopes are fixed on the rotating Earth, VLBI tracks instantaneously the orientation of the Earth in an inertial reference frame provided by the very distant quasars.

Very Long Baseline Interferometry (VLBI)

The VLBI data consists of digitized noise of the radio signal from the quasar that is transferred via fiber-optics from each telescope to USNO. The antenna signal is time-stamped with an extremely precise and stable atomic clock (usually a hydrogen maser) that is additionally locked onto a GPS time standard. This data is processed through a correlator that plays back the recorded data from all the stations simultaneously where the data are aligned and correlated by searching for the maximum of the cross-correlation-function. The timing of the playback is adjusted according to the atomic clock information associated with each data stream, and the estimated times of arrival of the radio signal at each of the telescopes. The latest known distance between the telescopes provides a first guess of the time delay for correlating the signals. If the position of the antennas is not known to sufficient accuracy or atmospheric effects are significant, fine adjustments are made until interference fringes are detected. A number of playback timings over a range of nanoseconds are usually tested until the correct timing is found. At the peak of the correlation function the amplitude and phase are determined and used to calculate a precise relative delay. The correlator output are the fringe phase and the fringe amplitude from which the delay and delay rate of the wavefront can be derived. Using the speed of light, the delay is interpreted as the location of the source on the sky and/or the orientation of the baseline in space.

By observing many sources distributed across the sky with multiple antennas distributed around the globe, one can simultaneously solve for the source positions, antenna locations, and the orientation of the Earth in space. From the VLBI data, the USNO produces estimates of the Earth orientation parameters on a regular basis. Typically, measurements of the variation in the rotation rate of the Earth (UT1-UTC) are made on a daily basis with a typical turnaround time from observation to final result in as fast as 4-5 hours. Measurements of UT1-UTC are made on a microsecond scale with these VLBI observations. In addition, 24 hour sessions are recorded twice per week to solve for the full range of EOP including: X,Y pole position, nutation, precession, and variable rotation rate. Typical turnaround times for these experiments are on the order of 2-3 days. These experiments lead to micro-arcsecond measurements of the position of the Earth’s pole, translating into centimeter accuracies.

USNO currently employs a hardware-based correlator where VLBI data is processed using purpose-built legacy equipment that is both expensive and difficult to maintain and upgrade. They are transitioning to a more flexible and efficient software-based system where the VLBI data can be processed with open source applications running on off-the-shelf, easily upgradeable hardware. Operation of the open source software currently requires that the VLBI data flow be managed via a series of time consuming command line operations by a doctoral scientist. The desire is to have an operational system where the data correlator can be easily operated via a graphical user interface (GUI) by mission operators.

How We Are Helping

CPI is currently assisting USNO in implementing a software correlator to replace the existing hardware-based correlator in the pre- and post-processing of the radio astronomy data. We are responsible for designing and developing a graphical user interface to provide monitoring and control of the software application that correlates VLBI data and reports the health and progress of associated data playback units. We are also implementing a relational database management system (RDBMS) to track the flow of data from the point at which data are received, through the correlation process, to the distribution and archiving of the final data products. The goal is to automate the data processing to simplify operation and increase efficiency.

Partial view of the graphical user interface for USNO VLBI software correlator

Further Reading

Phase Centre Determinations at GPS-Satellites with VLBI, Hayo Hase

Review of VLBI2010 Concept and General Specifications, B. Petrachenko, Natural Resources Canada (NRCan), IVS TeSpec Workshop, Bad Kötzting, Germany, March 1-2, 2012.

VLBI2010: Current and Future Requirements for Geodetic VLBI Systems, A. Neill, Report of the Working Group 3 to the IVS Directing Board, September 16, 2005