VLBA Observational Status Summary 2018A

This sub-section describes the instrumentation that collects and amplifies radio-frequency (RF) radiation from a source, converts, and transmits it to the station control building.  Napier et al. (1994) includes further information on most of the following aspects.

The antenna brings the RF signals to a focus at one of ten feeds.  The main reflector is a 25-m diameter shaped figure of revolution with a focal-length-to-diameter ratio of 0.354.   A 3.5-m diameter Cassegrain subreflector with a shaped asymmetric figure is used at observing wavelengths shorter than 30 cm, while the prime focus is used at longer wavelengths.  The antenna features a wheel-and-track mount, with an advanced-design reflector support structure.  Antenna motions are relatively rapid for an antenna of this size, to facilitate rapid source changes: 30° per minute in elevation and 90° per minute in azimuth.

The feed couples free-space electromagnetic waves into waveguides for transmission to the receiver system. Feeds at observing wavelengths shorter than 30 cm are located on a ring at the offset Cassegrain focus, and are selected by rotation of the subreflector with a maximum transition time of about 20 seconds. A frequency-selective dichroic system enables simultaneous 13/4-cm observations. The 90- and 50-cm feeds are crossed dipoles mounted on the subreflector near prime focus; simultaneous 90/50-cm observations are possible.

The polarizer extracts orthogonal circularly-polarized signals, which are routed separately to dual receivers.  In receiver wavelength bands shorter than 30 cm, the polarizer is cooled to cryogenic temperatures.

The receiver amplifies the signal. Most VLBA receivers use HFET (Heterostructure Field Effect Transistor) amplifiers at a physical temperature of 15 K, but the 90- and 50-cm receivers use GaAsFETs (Gallium Arsenide FETs) at room temperature. All receivers produce dual-polarization outputs, in opposite hands of circular polarization.

The IF converter mixes the receiver output signals with the first LO generated by a front end synthesizer. Two IF bands between 512 and 1024 MHz are output by each converter, one in each sense of circular polarization. The same LO signal is used for mixing with both polarizations in most cases. However, the 4 cm IF converter has a special mode that allows both output signals to be connected to the RCP output of the receiver and to use separate LO signals, thereby allowing the use of spanned bandwidths exceeding 512 MHz. Also, the 90 cm and 50 cm signals are combined and transmitted on the same IFs. The 50 cm signals are not frequency converted, while the 90 cm signals are upconverted to 827 MHz before output.

Four IF cables, designated A, B, C, D, carry the IF signals from the antenna vertex room to the station control building. Normally only two IFs are in use at a time, with the signals from each IF converter transmitted via A and C, or B and D; by convention, RCP is normally carried by IFs A and B, and LCP by C and D. However, several 4-IF configurations are available for special cases. These include dual-polarization observations at two arbitrary frequencies anywhere within the 4-8 GHz range of the new 6-cm receiver, and combinations of dual IF outputs from both the 13- and 4-cm receivers (using the dichroic system described in the paragraph on feeds above).  Either of these configurations can be activated simply by specifying the desired frequencies and polarizations.  The 4-cm receiver also supports a 3-IF configuration, with a second first LO available for RCP signals; this mode requires that the SCHED setup include the 'dualx' parameter.

Essential auxiliary instrumentation, required to make simultaneous observations feasible at VLBA stations separated by thousands of kilometers, is described in this sub-section.

A hydrogen maser provides an ultra-stable frequency reference at each VLBA station.  Its standard signals, at 100 MHz and 5 MHz, and multiplied versions thereof, are used throughout the station electronics, both in the antenna and in the station building.

The front end synthesizer generates reference signals to convert the receiver output from RF to IF, with lock points at (n× 500) ± 100 MHz (for n an integer).  Output frequencies range between 2.1 and 15.9 GHz. There are 3 such synthesizers, each of which is locked to the maser. One synthesizer is used for most frequency bands, but two are used at 1 cm, at 7 mm, 3 mm, and for the 4 cm wideband mode.

VLBA stations support several different types of calibration measurements.

Two calibration signals are injected near the beginning of the primary data path, and detected elsewhere in the VLBA system, with derived corrections applied in data analysis:

The switched-noise system injects well calibrated, broadband noise, switched on-off in a 50% duty cycle at 80 Hz.  This noise signal is synchronously detected in the RDBE, to provide a time-tagged system-temperature table that is delivered with the primary fringe visibility data.  Application of these measurements for amplitude calibration is discussed separately.

The pulse-cal system injects a series of pulses at intervals of 1.0 or 0.2 microseconds, to generate monochromatic, phase-stable tones, spaced at multiples of 1 MHz or 5 MHz.  The tones are detected in the VLBA DiFX correlator.  Application of these measurements for phase calibration is discussed separately.

There is also a round trip cable calibration scheme that monitors the length of the signal cables, to enable corrections for temperature and pointing induced variations.

The RDBE replaces much of the VLBA's original analog signal processing in the station control building.  The baseband converters, in particular, are eliminated by sampling directly from the IF outputs of each station's receivers, with 8-bit precision.  All subsequent processing is performed digitally.  For clarity in the following descriptions, two items of essential VLBA terminology are defined here:

An "IF" refers to one of a maximum of four 512-MHz wide intermediate-frequency analog signals transmitted from the receiver(s) to the RDBE.  Most receivers provide two IFs, in opposite circular polarizations.  However, four IFs are available to support specialized observing modes at some wavelengths: two dual-polarization pairs, at arbitrary frequencies within the full range of the new 6-cm receiver; or from different receivers in 13/4-cm or 90/50-cm dual-receiver operation.

A "channel" refers to a single contiguous frequency range (of any bandwidth), observed in a single polarization, that is sampled, filtered, and recorded as a separate entity.  This approach is essential for the VLBA, where capabilities are fundamentally limited by the overall data-transmission bandwidth.

'RDBE' is an acronym for "ROACH Digital Backend''.  ROACH, in turn, refers to the FPGA-based central signal processing board ("Reconfigurable Open Architecture Computing Hardware'') that was developed in a collaboration among NRAO, the South African KAT project, and the Collaboration for Astronomy Signal Processing and Electronics Research (CASPER) at UC Berkeley.  In addition to the ROACH, the RDBE includes an input analog level control module, a sampler developed by CASPER, and a synthesizer board which generates the 1024-MHz sample clock. RDBEs accept two 512-1024 MHz IF inputs, and deliver packetized output via a 10G Ethernet interface.  Each VLBA station is equipped with two RDBE units.

Currently, two separate "observing systems" are available within the VLBA's RDBE.  Inputs to either data system can come from any of the four VLBA IFs.  Some suggestions for choosing between the observing systems follow the functional outlines below.

PFB:  The polyphase filterbank digital signal-processing algorithm produces sixteen fixed-bandwidth 32-MHz channels within a single RDBE unit.  Channels can be selected flexibly between two input IFs, and can be placed at 32-MHz steps along the entire IF frequency range. Some typical selection modes include [a] a compact dual-polarization configuration of eight contiguous 32-MHz channels at matching frequencies in each polarization; [b] a spanned-band dual-polarization configuration, with eight 32-MHz channel pairs spaced every 64 MHz; and [c] a single-polarization configuration of 16 channels, contiguous across the entire width of one IF.  (In case [c], one end channel will not lie within the IF band, and does not produce usable data.)  The selected channels are requantized at two bits per Nyquist sample and output in a packetized stream at a total data rate of 2048 Mbps (referred to subsequently as "2 Gbps'').

DDC:  The digital downconverter algorithm supports a wide range of bandwidths.  A total of 1, 2, or 4 channels can be processed within a single RDBE unit; 4 or 8 channels are available using both RDBEs.  Available bandwidths range downward from 128 MHz to 1 MHz in binary steps; recording rate limitations restrict the 128-MHz bandwidth to a maximum of 4 channels.  All channels must use the same bandwidth within an observing scan.  Channels can be selected flexibly among up to four input IFs, and in either sideband.  Tuning of individual channels can be set in steps of 15.625 kHz, although 250-kHz steps are recommended when compatibility with legacy systems is required.  Channels may not cross IF zone boundaries at 640 and 896 MHz.  Each channel is requantized at two bits per Nyquist sample and output in a packetized stream, at a total data rate ranging from 4 to 2048 Mbps (subsequently "2 Gbps").

Suggestions for Observing System Selection: Wideband science will be possible using either the PFB observing system, at its fixed 2048 Mbps data rate, or the DDC system at 2048 Mbps or lower rates.  Both systems provide output at two bits per Nyquist sample.  The primary instrumental differences are in the numbers and bandwidths of channels, and in the channel passbands.  The PFB's many narrower channels may be advantageous in avoiding spectral ranges impacted by interference, particularly in the 18-cm band.  On the other hand, the smaller number of wider-band channels available in the DDC may simplify data analysis in some cases. Digital logic capacity of the RDBE limits the PFB's signal processing to fewer filter taps for each of its 16 channels than for the 4-channel DDC system, so that the DDC's passbands cut off significantly more sharply.

Spectroscopic and other narrow-band observations will generally be best supported by the DDC system, which incorporates scientifically equivalent counterparts for all modes of the VLBA legacy system, and extends these to wider bandwidths.  Even extremely narrow bands can be accommodated by observing at 1 MHz bandwidth and selecting a narrower range using the DiFX correlator's spectral zoom mode.

Most VLBA receivers produce only two IFs, in opposite polarizations, but some receivers support four-IF modes, such as dual-polarization dual-frequency. The four-IF capability of the DDC allows these modes to be exploited.

Conversion of Legacy Schedules to RDBE/DDC: A separate web page describes the relatively straightforward conversion of SCHED “keyin” files applicable to the VLBA's legacy data system, to use the DDC system instead.   Explanations of the "scientifically equivalent" modes referred to above are included.  It is designed primarily for users with some VLBA experience.

A software-based network switch, purchased from XCube Research and Development, is an essential element of the data path at each VLBA station.  Its primary functions are to merge the packet streams from each of the two RDBE units into a single stream that is sent to the Mark 5C recorder, and to regulate the timing of these packets so as not to overflow the Mark 5C's input buffer.

Other switching and real-time data analysis functions may be added as part of future developments.  A phase-cal detection capability is currently under test.

The VLBA's data transmission system comprises the recorder units at the stations, playback units at the correlator, and the magnetic disk modules that are shipped between those units.  The Mark 5C recording system was developed jointly by NRAO, Haystack Observatory, and Conduant Corporation.  It closely resembles the Mark 5A version used previously by the VLBA, and the Mark 5B used at some other observatories.  In particular, identical disk modules are used.  However, Mark 5C is a packet-based system, which allows a more straightforward functionality than its predecessors.   It simply records the payload of each 10G Ethernet packet originating in the RDBE, without imposing any special recording format.  All formatting of the observed data — most essentially, the precision time tag — is internal to the packet payloads, which are transmitted directly from recorder to playback by the Mark 5C system.  Mark 5B formatting is used internally by the RDBE's PFB personality, but the newer VLBI Data Interchange Format (VDIF) is used in the DDC personality.

Each Mark 5C unit accommodates two removable modules, each in turn comprising eight commercial disk drives.  As used on the VLBA, these modules are recorded sequentially at a maximum rate of 2 Gbps, matching the current maximum RDBE output rate.  Available recording media are expected to support the highest data rates for approximately half of all observing hours.

Further information on the Mark 5C system is available in the Sensitivity Upgrade memo series, and in the Haystack Mark 5 series.

The correlator is situated in the SOC, at the end of the data path.  Its role is to reproduce the signals recorded at the VLBA stations and any others involved in the observation, and to combine them in two-station baseline pairs, to yield the visibility function which is the fundamental measurement produced by the VLBA.  VLBA observations are processed using the DiFX software correlator. DiFX was developed at Swinburne University in Melbourne, Australia (Deller et al. 2007), and adapted to the VLBA operational environment by NRAO staff (Brisken 2008).  Subsequent references to "DiFX" apply specifically only to this VLBA implementation.

We encourage users to include the following text in the Acknowledgments section of any publication arising from VLBA observations made since December 2009:

This work made use of the DiFX software correlator developed at Swinburne University of Technology as part of the Australian Major National Research Facilities program.

... and to cite the following paper by the developers: Deller, et al. 2011, PASP, 123, 275.

Software correlation has become feasible in recent years, and is especially well suited to applications like VLBI with bandwidth-limited data-transmission systems and non-realtime processing. Among its several advantageous aspects are: (1) flexible allocation of processing resources to support correlation of varying numbers of stations, frequency and time resolution, and various special processing modes, with no fundamental fixed limits other than the finite performance of the processing cluster; (2) optimization of resource usage to minimize processing time; (3) integration of control and processing functions; (4) continuously scalable, incremental upgrade paths; and (5) relatively straightforward implementation of special modes and tests. These and other virtues of software correlation are discussed in more detail by Deller et al. (2007).

Despite the absence of fixed limits cited in item (1) above, guidelines have been established for the extremes of spectral resolution, integration period, and output rate, for routine DiFX processing, as specified in the appropriate sections below. Exceptions will be considered for proposals including a sufficiently compelling scientific justification.

The VLBA DiFX correlator is not configured to process data from a single antenna, nor is a multi-station autocorrelation-only mode available.

Operation of DiFX is governed primarily by an observation description in VEX format (currently vex1.5).  This format is used for both station and correlator control functions in a number of VLBI arrays, and VLBA program SCHED (Walker 2011) has been producing it for many years.

DiFX only accepts data on Mark5 disk modules, as recorded by a Mark5A, Mark5B, Mark5B+ or Mark5C recorder.  It can process data in a variety of formats including VLBA, Mark4, and Mark5B.  Support for VDIF format is currently incomplete but includes those versions created by the VLBA RDBE and the VLA WIDAR correlator.  Modes recorded at EVN stations are also thought to be fully supported.

Correlator output is written according to the FITS Interferometry Data Interchange Convention (Greisen 2009).  In addition to the fundamental visibility function measurements and associated meta-data, the FITS files include amplitude and phase calibration measurements, weather data, and editing flags, all derived from data logged at the observing stations.  An up-to-date release of AIPS is required to handle DiFX data properly.

Conversion of DiFX correlator output to the Mark 4 format that is used primarily in analysis of geodetic observations is also available.  To enable this additional output, a SCHED parameter CORDFMT=MARK4 should be specified.

DiFX allows quite flexible selection of the desired number of "spectral points" spanning each individual data channel.  Any number that can be factored as 2ⁿ · 5^m can be specified, subject to these limitation:

• A maximum of 4096 points per channel, for routine DiFX processing.
• A total of 132,096, summed over all channels and polarization products, for compatibility with AIPS.
• A minimum spectral resolution of 2 Hz.

The number of spectral points must be the same for all data channels at any given time, although multiple passes are possible with different sets of channels. The actual spectral resolution obtained, and statistical independence of the spectral points, depends on subsequent smoothing and other processing.

DiFX also supports "spectral zooming'', selection of a subset of correlated spectral points from any or all data channels.  Only the selected spectral points are included in the output dataset.  This capability is of value mainly in maser studies, where a recorded data channel may be much wider than the maser emission in two main categories of observations:  (1) Maser astrometry with in-beam continuum calibrators.  Wideband observing is required for maximum sensitivity on the calibrators, while zooming allows high spectral resolution at the frequencies where maser emission appears.  (2) Multiple maser transitions.  When wideband data channels are used to cover a large number of widely separated maser transitions, spectral zooming allows the empty portions of high-resolution spectrum to be discarded.

Spectral zooming does not work with mixed sideband observing, this can happen for HSA or global observations where some telescopes require upper sideband and others require lower sideband.  In proposing observations that will use spectral zooming, the required number of spectral points before zooming should be specified in the Proposal Submission Tool.  Currently, the location and width of the "zoom" bands must be communicated directly to VLBA operations before correlation.

DiFX accommodates a nearly continuous range of correlator integration periods over the range of practical interest. Individual integrations are quantized in multiples of the indivisible internal FFT interval, which is equal to the number of spectral points requested, divided by the data channel bandwidth.

For most cases, with low to moderate spectral resolution, and/or wide data channels, the FFT intervals are fairly short, and it is straightforward to find an integration period in any desired range that is an optimal integral multiple of the FFT interval. ("Optimal'' refers here to the performance of DiFX.)  Extreme cases of very high spectral resolution (many spectral points across a narrow data channel - resolution of less than about 100 Hz) imply FFT intervals long enough that only limited choices of integral multiples are available.

For flexibility in these situations (although the option exists in all cases), integration periods other than an integral multiple of the FFT interval can be approximated, in a long-term mean, by an appropriate sequence of nearby optimal integral multiples. In this case, output records are time-tagged as if correlated with exactly the requested period.

SCHED accepts an additional parameter so that users can indicate that the requested integration period is to be implemented exactly, as described above. Otherwise, the nearest optimal integral multiple of the FFT interval is passed to the correlator.

The field of view in VLBI observations is very small, around 10^-4 of the primary antenna beam area. This restricted interferometer beam arises in the correlation process from smearing at positions away from the correlation phase center, due to averaging in time (with, typically, a 2-second period) and/or across bandwidth ("chromatic aberration'' over, typically, 0.5 MHz spectral resolution). Thus, imaging of targets that are widely spaced in the primary beam requires multiple processing passes in typical correlator implementations. If the visibilities are maintained at high time and frequency resolution, it is possible to perform a u-v shift after correlation, essentially repointing the correlated dataset to a new phase center. However, this approach would require prohibitively large visibility datasets.

DiFX implements multiple u-v shifts inside the correlator, to generate as many phase centers as are necessary, in a single correlation pass. The output consists of one dataset of normal size for each phase center. This mode consumes around three times the correlator resources of a normal continuum correlation, due to the need for finer frequency resolution before the u-v shift, but the additional cost is only weakly dependent on the number of phase centers. For reasonable spectral and temporal resolution requirements (for example, adequate for smearing < 10% at the 50% contour of the VLBA primary beam), 200 phase centers require only 20% more correlator time than 2 phase centers. Extremely high spectral and/or temporal resolution (e.g. for shifts even closer to the edge of the primary beam) carry a higher overhead per additional phase center. This mode thus should be requested only for imaging of three or more sources within any single antenna pointing.  The correlator output rate expands proportionally to the number of phase centers.

Correlator memory limits the product of baselines, spectral points, and phase centers for one correlator pass.  The current limit is approximately 600 phase centers for the 10 element VLBA at 2 Gbps record rate (512 MHz polarization-summed bandwidth).   An unlimited number of phase centers can ultimately be achieved in multiple correlation passes, however.

Multiple phase-center correlation is requested in the NRAO Proposal Submission Tool by setting the "Number of Fields'' item in the resource section to the maximum number of phase centers required for any antenna pointing specified in a given resource. The requested spectral resolution and integration time should correspond to the desired initial number of spectral points per data channel (required to minimize bandwidth smearing) and the desired integration between u-v shifts (to minimize time smearing).  A resulting expanded output data rate that exceeds the current limit, as well as any required multiple passes, must be justified specifically in the proposal.

SCHED includes facilities to support specification of the actual phase center locations to be used in correlation.

For more details on wide-field imaging techniques, see Bridle & Schwab (1999), and Garrett et al. (1999).

Correlation parameters should result in an output rate less than 10 MBytes per second (of observing time) for routine DiFX processing; higher rates may be considered if required and adequately justified. Observers should ensure that their data-analysis facilities can handle the dataset volumes that will result from the correlation parameters they specify.

An approximate parametrization of the output rate is given by

\[R = 4 \cdot \frac{N_{\rm stn} \cdot (N_{\rm stn}+1) \cdot N_{\rm sbb} \cdot N_{\rm spc}}{T_{\rm int}}\cdot N_{\rm ppb} \cdot N_{\rm phc} \cdot p\]

where the rate \(R\) is in Byte/s;

\( N_{\rm stn} , \; N_{\rm sbb} , \; N_{\rm spc} \) are the numbers of observing stations, data channels, and spectral points per data channel, respectively;

\(T_{\rm int}\) is the correlator integration period;

\(N_{\rm ppb}\) is the number of pulsar phase bins;  and

\(N_{\rm phc}\) is the number of phase centers.

The polarization factor \(p=1\) for single-polar, or dual-polar parallel-hand output;  or \(p=2\) for cross-polar, four-Stokes processing.

Output data rates are also estimated by SCHED.

VLBI fringe phases are much more difficult to deal with than fringe amplitudes.  If the a priori correlator model assumed for VLBI correlation is particularly poor, then the fringe phase can wind so rapidly in both time (the fringe rate) and in frequency (the delay) that no fringes will be found within the finite fringe rate and delay windows examined during correlation.  Reasons for a poor a priori correlator model include source position and station location errors, atmospheric (tropospheric and ionospheric) propagation effects, and the behavior of the independent clocks at each station.  Users observing sources with poorly known positions should plan to refine the positions first on another instrument.  To allow accurate location of any previously unknown antennas and to allow VLBA staff to conduct periodic monitoring of clock drifts, each user should include one or more "fringe finder" sources which are strong, compact, and have accurately known positions.  Consult Markowitz & Wurnig (1998) to select a fringe finder for observations between between 20 cm and 7 mm; your choice will depend on your wavelengths but J0555+3948=DA193, J0927+3902=4C39.25, J1642+3948=3C345, and J2253+1608=3C454.3 are generally reliable in the range 13 cm to 2 cm.  In addition, at 90 and 50 cm we recommend either J1331+3030=3C286 or J2253+1608=3C454.3.  Fringe-finder positions, used by default by VLBA program SCHED (Walker 2011) and the VLBA correlator, are given in the standard source catalog available as an ancillary file with SCHED.

Fringe phases should be coherent across the entire set of channels produced by each RDBE.  Correction of phase offsets between the two RDBEs at each station, and/or between the oppositely polarized signal channels, can be determined using the "phase cal'' or "pulse cal'' system (Thompson 1995).   In conjunction with the LO cable length measuring system, this system can also be used to measure changes in the delays through the cables and electronics which must be removed for accurate geodetic and astrometric observations.

The phase cal system consists of a pulse generator and a sine-wave detector.  The interval between the pulses can be either 0.2 or 1 microsecond.  They are injected into the signal path at the receivers and serve to define the delay reference point for astrometry.  The pulses appear in the spectrum as a "comb'' of very narrow, weak spectral lines at integral multiples of 1 or 5 MHz.  The phases of one or more of these lines are measured by the detector, logged as a function of time, and delivered in a PC table.

AIPS tasks can load and apply the PC data.  However, some VLBA observers may still want to use a strong compact source to do a "manual'' phase cal if necessary (Diamond 1995).  Spectral line users will not want the pulse cal comb to appear in their observations, and should ensure that their observing schedules both disable the pulse cal generators and include observations suitable for a manual phase cal.   Manual phase calibration also is likely to be necessary for non-VLBA stations that have no tone generators or detectors, and in VLBA observations at 3 mm, where the VLBA receivers have no pulse calibration tones.

After correlation and application of the pulse calibration, the phases on a VLBA target source still can exhibit high residual fringe rates and delays.  Before imaging, these residuals should be removed to permit data averaging in time and, for a continuum source, in frequency.  The process of finding these residuals is referred to as fringe fitting.   Before fringe fitting, it is recommended to edit the data based on the a priori edit information provided for VLBA stations.  Such editing data are delivered in the FG table.  The old baseline-based fringe search methods have been replaced by more powerful global fringe search techniques (Cotton 1995a; Diamond 1995).  Global fringe fitting is simply a generalization of the phase self-calibration technique, as during a global fringe fit the difference between model phases and measured phases are minimized by solving for the station-based instrumental phase, its time slope (the fringe rate), and its frequency slope (the delay).  Global fringe fitting in AIPS is done with the program FRING or associated procedures.  If the VLBA target source is a spectral line source or is too weak to fringe fit on itself, then residual fringe rates and delays can be found on an adjacent strong continuum source and applied to the VLBA target source in a phase-referencing technique.

VLBA delays do tend to be very stable (1 to a few ns) during observations at higher frequencies where the ionospheric variations are limited.  Thus one, or a small number, of high SNR fringe fits on strong fringe finders may provide superior results for delay, over trying to fit weaker sources.  The phases will still need to be corrected, but that can be done with self-calibration or a phase-only fringe fit.

After fringe-fitting and averaging, VLBA visibility amplitudes should be inspected and obviously discrepant points removed (Diamond 1995; Walker 1995b).  Usually such editing is done interactively using tasks in AIPS or the Caltech program Difmap (Shepherd 1997).  VLBA correlator output data also includes flags derived from monitor data output in an FG table, containing information such as off-source flags for the stations during slews to another source.

Even after global fringe fitting, averaging, and editing, the phases on a VLBA target source can still vary rapidly with time.  Most of these variations are due to inadequate removal of station-based atmospheric phases, but some variations also can be caused by an inadequate model of the source structure during fringe fitting.   If the VLBA target source is sufficiently strong and if absolute positional information is not needed, then it is possible to reduce these phase fluctuations by looping through cycles of Fourier transform imaging and deconvolution, combined with phase self-calibration in a time interval shorter than that used for the fringe fit (Cornwell 1995; Walker 1995b; Cornwell & Fomalont 1999).  Fourier transform imaging is straightforward (Briggs, Schwab, & Sramek 1999), and done with AIPS task IMAGR or the Caltech program Difmap (Shepherd 1997).  The resulting VLBI images are deconvolved to rid them of substantial sidelobes arising from relatively sparse sampling of the u-v plane (Cornwell, Braun, & Briggs 1999).  Such deconvolution is achieved with AIPS tasks based on the CLEAN or Maximum Entropy methods or with the Caltech program Difmap.

Phase self-calibration just involves minimizing the difference between observed phases and model phases based on a trial image, by solving for station-based instrumental phases (Cornwell 1995; Walker 1995b; Cornwell & Fomalont 1999).  After removal of these instrumental phases, the improved visibilities are used to generate an improved set of model phases, usually based on a new deconvolved trial image.  This process is iterated several times until the phase variations are substantially reduced.  The method is then generalized to allow estimation and removal of complex instrumental antenna gains, leading to further image improvement.  Both phase and complex self-calibration can be accomplished using AIPS task CALIB or with the Caltech program Difmap.  Self-calibration should only be done if the VLBA target source is detected with sufficient signal-to-noise in the self-calibration time interval (otherwise, fake sources can be generated!), and if absolute positional information is not needed.

The useful field of view in VLBI images can be limited by finite bandwidth, integration time, and non-coplanar baselines (Wrobel 1995; Cotton 1999b; Bridle & Schwab 1999; Perley 1999b). Measures of image correctness -- image fidelity and dynamic range -- are discussed by Walker (1995a) and Perley (1999a).

If the VLBA target source is not sufficiently strong for self-calibration or if absolute positional information is needed but geodetic techniques are not used, then VLBA phase referenced observations must be employed (Beasley & Conway 1995).  Currently, 63% of all VLBA observations employ phase referencing.  Wrobel et al. (2000) recommend strategies for phase referencing with the VLBA, covering the proposal, observation, and correlation stages.  A VLBA phase reference source should be observed frequently and be within a few degrees of the VLBA target region, otherwise differential atmospheric (tropospheric and ionospheric) propagation effects will prevent accurate phase transfer.  VLBA users can draw candidate phase calibrators from the source catalog distributed with SCHED, which contains over 7000 sources.  Easy searching for the nearest calibrators is available online through the VLBA Calibrator Survey (Beasley et al. 2002).  Most of these candidate phase calibrators now have positional uncertainties below 1 mas.

Calibration of atmospheric effects for either imaging or astrometric observations can be improved by the use of multiple phase calibrators that enable multi-parameter solutions for phase effects in the atmosphere.  See AIPS Memos 110 (task DELZN, Mioduszewski 2004) and 111 (task ATMCA, Fomalont & Kogan 2005), available from the AIPS home page, for further information.

Walker & Chatterjee (1999) have investigated ionospheric corrections using GPS based ionospheric models.  Such corrections can be of significant benefit for even the highest frequencies on the VLBA.  These corrections may be made with the AIPS task TECOR, as described in AIPS Cookbook Appendix C (NRAO 2006), or the procedure VLBATECR.  In addition, it is strongly recommended that the most accurate Earth-Orientation values be applied to the calibration, since correlation may have taken place before final values were available; this may be done with AIPS task CLCOR or more easily with the AIPS procedure VLBAEOPS.

The rapid motion of VLBA antennas often can lead to very short time intervals for the slew between target source and phase reference source, and some data may be associated with the wrong source.  Users should be alert for visibility points of very low amplitude at the beginnings of scans.

In VLBA polarimetric observations, channels are assigned in pairs to opposite hands of circular polarization at each frequency.  Typical "impurities" of the antenna feeds are about 3% for the center of most VLBA bands and degrade toward the band edges and away from the pointing center in the image plane.  Without any polarization calibration, an unpolarized source will appear to be polarized at the 2% level.  Furthermore, without calibration of the RCP-LCP phase difference, the polarization angle is undetermined.  With a modest investment of time spent on calibrators and some increased effort in the calibration process, the instrumental polarization can be reduced to less than 0.5%.

To permit calibration of the feed impurities (sometime also called "leakage" or "D-terms"), VLBA users should include observations of a strong (≈ 1 Jy) calibration source, preferably one with little structure.  This source should be observed during at least 5 scans covering a wide range (> 100 degrees) of parallactic angle, with each scan lasting for several minutes.  The electric vector polarization angle (EVPA) of the calibrator will appear to rotate in the sky with parallactic angle while the instrumental contribution stays constant.  Some popular calibrator choices are J0555+3948=DA193 and J1407+2827=OQ208, although either or both may be inappropriate for a given frequency or an assigned observing time.  Fortunately, many calibrators satisfying the above criteria are available.

A viable alternative approach to measuring polarization leakage is to use an unpolarized calibrator source.  This can be done with a single scan.

The wide channel bandwidths now available may make it necessary to apply frequency-dependent instrumental polarization corrections.  Most VLBI calibrators are resolved, and the usual AIPS tool for solving for instrumental polarization using resolved sources, LPCAL, does not handle this frequency dependence.  Procedures are being tested for dealing with this issue.  They are likely to involve making polarization images based on the best LPCAL results, using them to divide the data, then using the frequency dependence capability in PCAL to do the rest.

To set the absolute EVPA on the sky, it is necessary to determine the phase difference between RCP and LCP.  For VLBA users at frequencies of 5 GHz and above, the best method for EVPA calibration is to observe one or two of the compact sources that are being monitored with the VLA; see the VLA/VLBA Polarization Calibration Page (Taylor & Myers 2000).  At 1.6 GHz it may be preferable to observe a source with a stable, long-lived jet component with known polarization properties.  At frequencies of 5 GHz and below one can use J0521+1638=3C138 (Cotton et al. 1997a), J1331+3030=3C286 (Cotton et al. 1997b), J1829+4844=3C380 (Taylor 1998), or J1902+3159=3C395 (Taylor 2000). At 8 GHz and above one may use J1256-0547=3C279 (Taylor 1998) or J2136+0041=2134+004 (Taylor 2000), although beware that some of these jet components do change on timescales of months to years.  It will be necessary to image the EVPA calibrator in Stokes I, Q, and U, and  to determine the appropriate correction to apply.  Thus it is recommended to obtain 2 to 4 scans, each scan lasting at least 3 minutes, over as wide a range in hour angle as is practical.

To permit calibration of the RCP-LCP delays, VLBA users should include a 2-minute observation of a very strong (≈ 10 Jy) calibration source.  While 3C279 is a good choice for this delay calibration, any very strong fringe-finder will suffice.

Post-processing steps include amplitude calibration; fringe-fitting; solving for the RCP-LCP delay; self-calibration and Stokes I image formation; instrumental polarization calibration; setting the absolute position angle of electric vectors on the sky; and correction for ionospheric Faraday rotation, if necessary (Cotton 1995b, 1999a; Kemball 1999).  All these post-processing steps can currently be done in AIPS, as can the polarization self-calibration technique described by Leppänen, Zensus, & Diamond (1995).

Diamond (1995) and Reid (1995, 1999) describe the special requirements for data acquisition, correlation, and post-processing of spectroscopic VLBI observations.  The transition rest frequency, approximate velocity, and velocity width for the line target must be known in order to set the observing frequency and bandwidth correctly.  The schedule should include observations of one or more strong continuum sources to be used for fringe-finding, "manual" phase calibration, and bandpass calibration.  In addition, scans of a continuum source reasonably close to the line target should be scheduled, for use in delay and fringe-rate calibration.  The pulse cal generators should be disabled.

Post-processing steps include performing Doppler corrections for the Earth's orbital motion (a correction for Earth rotation is not necessary for VLBA observations since station-based fringe rotation is applied in the correlator); amplitude calibration using single-antenna spectra; fringe fitting the continuum calibrators and applying the results to the line target; referencing phases to a strong spectral feature in the line source itself; deciding whether to use normal synthesis imaging or fringe rate mapping; and then forming a spectral line cube.  All these post-processing steps can be done in AIPS.

Data reduction techniques for VLBI spectral line polarimetry are discussed by Kemball, Diamond, & Cotton (1995) and Kemball (1999).

All special processing required for pulsar observations is supported within the correlator.  Details of the available gating and binning options, and their impact on the output data rate, are presented in the pulsar modes and output rate subsections of the DiFX section, respectively.

In the interest of enhancing VLBI sensitivity and/or angular resolution, several inter-observatory agreements have been established to support combinations of the VLBA with other radio telescopes.  This section describes the observing capabilities of each of these combinations.

The HSA comprises the VLBA, phased Very Large Array (VLA), Green Bank Telescope (GBT), Effelsberg, and Arecibo telescopes, and subsets thereof.  All of these are equipped with instrumentation compatible with the VLBA observing capabilites described in the Station Signal Processing section.  VLBI observations combining the VLBA with any one or more of the other four HSA stations can be requested in a single HSA proposal.  Proposal deadlines for the HSA coincide with those for the VLBA alone, as described in Section 15.  Further information on "Observing with the High Sensitivity Array" is available in a separate document.

• The VLA is available as a single phased array ("Y27"; no subarrays) with two independently-tunable subband pairs, one polarization pair (RCP+LCP) in the A0/C0 basebands and the other (RCP+LCP) in the B0/D0 basebands.  Setups also matching the VLBA PFB and DDC (4- and 8-channel) observing systems are available on the VLA.  The VLA must be set up to match the VLBA; mixed modes are not allowed.

Bandwidths must be uniform across the entire VLBI array, and throughout the entire duration of the observation.  In particular, VLA phasing and VLBI observing must be carried out at the same bandwidth.  Subband bandwidths of 16 MHz and wider are available as a general capability.  Bandwidths narrower than 16 MHz may work if the source is strong enough, but are expected to be of limited use, have not been tested, and are available only on a shared-risk basis.

Two adjunct documents: VLBI at the VLA and Guide to Observing with the VLBA: HSA/GMVA/Global VLBI, discuss the available phased-VLA capabilities, and provide instructions for their use.

• The GBT, like the VLBA, transitioned to a new partnership arrangement as of semester 2017A.  Time available for VLBI on the GBT has been reduced compared to earlier observing semesters due to this change.  Proposers should only include the GBT in the proposal if it is essential for the science and if it is clearly justified in the text.

The GBT is frequency agile (with some limitations) at all its bands.

The GBT's 6 cm receiver is similar to the VLBA's new system, but does differ in converting to circular polarization at ambient temperature.  Tests have seen substantial polarization leakage between the RCP and LCP channels. Proposals to use this receiver will be considered only for total-intensity observations.  Such proposals should request full dual-polarization modes for both observation and correlation, and careful calibration of the leakage terms should be included in the data analysis.

Proposals including the GBT in an HSA observation must include time to set up the telescope (pointing, focus, etc.) prior to the start of the observation. This can take 0.5-1 hour depending on the frequency.

Further information on use of the GBT may be found in Section 5.7 and Chapter 7 of the GBT Proposer's Guide, in the GBT Observer's Guide, and in the VLBI at the GBT page.

• The Effelsberg telescope supports both of the VLBA observing systems, and is frequency agile at 5 GHz and above.

Further information on use of Effelsberg is available at the Effelsberg HSA page.

• The Arecibo 305-m telescope is currently available only with the PFB observing system.  An RSRO project is encouraged to help qualify the 4-channel DDC observing system at Arecibo.

The telescope operates at frequencies up to 10 GHz, and  can observe between declinations of -1 and +38 degrees, with transits ranging up to 2.75 hours at 18.5 degrees.

Further information on use of Arecibo is available in The VLBI Guide at Arecibo and The New Users Guide.

The GMVA observes at 3mm wavelength, using 8 VLBA stations, GBT, Effelsberg, Pico Veleta, Onsala, Metsaehovi, Yebes, and Korean VLBI Network (KVN) telescopes. (The VLBA stations in high-humidity locations at HN and SC are not equipped with 3mm receivers.)

The European part of the GMVA is coordinated by the Max-Planck-Institut für Radioastronomie (MPIfR), which hosts the main GMVA website.  Proposal deadlines for the GMVA coincide with those for the VLBA alone, as described in Section 15.  Observations are block-scheduled in two sessions per year, typically in April-May and September-October, and correlated at the MPIfR in Bonn.

In GMVA observations, all telescopes operate at their highest possible bandwidth.  Currently, this is a 2 Gbps data rate in all cases except at the KVN telescopes, which operate in a compatible 1 Gbps mode.

The EVN is a VLBI network of stations operated by an international consortium of institutes (Schilizzi 1995).  The EVN home page provides access to the EVN User's Guide.  Included in the guide is an EVN Status Table, giving details of current observing capabilities of all EVN stations; and the EVN Call for Proposals, which specifies EVN session dates and the wavelengths to be observed.

The EVN provides proposal, review, and scheduling mechanisms for such programs, and conducts regular sessions of several weeks throughout the year to carry out these observations.  Unlike the VLBA, HSA, and GMVA, the EVN operates on a trimester cycle, with proposal deadlines on February 1, June 1, and October 1.

Proposals requesting the EVN in combination with the VLBA or other affiliates are classified as "Global cm VLBI".  EVN and Global cm VLBI proposals must be prepared and submitted to the EVN using the EVN's NorthStar Tool.  Approved observations will be carried out during EVN sessions.