VLBA > VLBA Observational Status Summary 2013A

# 1. Introduction

This document summarizes the current observational capabilities of NRAO's Very Long Baseline Array (VLBA) instrument. The VLBA is an array of ten 25-m diameter antennas at stations distributed over United States territory (Napier et al. 1994; Napier 1995). It is the first astronomical array dedicated to observations using the technique of Very Long Baseline Interferometry (VLBI), which was pioneered in the 1960s. The VLBA offers (1) in absentia, year-round station and correlator operation; (2) station locations selected to optimize u-v plane coverage; (3) ten observing bands at wavelengths ranging from 90 cm to 3 mm (two stations are not equipped at 3 mm); (4) rapid, automated selection of receivers and of frequencies within a given receiver; and (5) integrated data flow from acquisition to correlation to post-processing. VLBA observations can acquire simultaneous dual circular polarizations from any single receiver or from receiver pairs at 13/4 cm or 90/50 cm. The VLBA is operated remotely from the Pete V. Domenici Science Operations Center (SOC, formerly known as the Array Operations Center) in Socorro, New Mexico.

Broad overviews of the kinds of astronomical research possible with the VLBA are presented in the conference proceedings edited by Zensus, Taylor, & Wrobel (1998), and the VLBA 10th anniversary proceedings (Romney & Reid 2005). Recommended reading for users new to the VLBA includes a short VLBI overview (Walker 1999b) and a short guide for novice users of the VLBA (Ulvestad 2004).

This document's primary intent is to provide, in concise form, the minimal information needed to formulate technically sound proposals requesting VLBA resources. Secondary aims are to describe some of the subtleties of data reduction and telescope scheduling, and to list relevant software and documentation. It is updated synchronously with the NRAO calls for proposals, or more often when required by major changes.  The current version is available at  https://science.nrao.edu/facilities/vlba/docs/manuals/oss .

Requests for information beyond the scope of this document should be directed to the NRAO Helpdesk.

# 2. New Developments

This edition of the Observational Status Summary includes descriptions of two new instrumental developments that will radically enhance the VLBA's capabilities.

1. 2-Gbps Continuum Bandwidth: New technologies for digital signal processing, data recording, and correlation, have made possible an expansion of the VLBA's continuum bandwidth to 256 MHz per polarization. This corresponds to a recorded data rate of 2 Gigabits per second (Gbps), a 16-fold increase over the sustainable rate of 128 Megabits per second that was available when the VLBA was inaugurated, and 4 times the current standard data rate. The signal/noise ratio in a typical continuum observation will be improved by factors of 2-4.

Overviews of the new wideband instrumentation are presented in sections on the ROACH Digital Backend and Mark 5C Recorder. More detailed information is available in the Sensitivity Upgrade memo series.  Questions can be submitted via the NRAO Helpdesk.

2. Wideband 6-cm Receiver: The VLBA's original 6 cm receivers are being replaced with substantially upgraded systems based on the EVLA design.  An expanded tuning range, covering 3.9 - 7.9 GHz, will enable observations of the 6.7-GHz methanol maser line, and reduced system noise will enhance continuum sensitivity by about 35%.  This receiver system supports a full 4-IF data-transmission configuration, allowing dual-polarization observations at two widely separated frequencies in the overall range.

Installations of upgraded receivers, and the accompanying new feeds, have been completed at eight stations.  Full ten-station operation is scheduled to become available in August 2012.

Preliminary information on the new receiver system's performance is incorporated in the "Receiver Frequency Ranges & Performance" table elsewhere in this document.   An NRAO eNews article (Walker & Hayward 2011) presents a comprehensive description of the new receiver and its first light in November 2011.

# 3. Antenna Sites

Table 1 gives the geographic locations of the ten stations comprising the VLBA, ordered from East through West.  All locations are based on the WGS84 ellipsoid used by the GPS system, with Earth radius $a=6378.137\: \rm{km}$ and flattening $1/f=298.257223563$.

See Napier (1995) for further site information.

 North West Latitude Longitude Elevation Code Location [° ′ ″] [ ° ′ ″] [m] Saint Croix, VI 17:45:23.68 64:35:01.07 16 SC Hancock, NH 42:56:00.99 71:59:11.69 296 HN North Liberty, IA 41:46:17.13 91:34:26.88 222 NL Fort Davis, TX 30:38:06.11 103:56:41.34 1606 FD Los Alamos, NM 35:46:30.45 106:14:44.15 1962 LA Pie Town, NM 34:18:03.61 108:07:09.06 2365 PT Kitt Peak, AZ 31:57:22.70 111:36:44.72 1902 KP Owens Valley, CA 37:13:53.95 118:16:37.37 1196 OV Brewster, WA 48:07:52.42 119:40:59.80 250 BR Mauna Kea, HI 19:48:04.97 155:27:19.81 3763 MK

Several other radio telescopes often participate in VLBI observing in conjunction with the VLBA.   A High Sensitivity Array (HSA) currently comprises the VLBA, Karl G. Jansky Very Large Array (VLA), and Robert C. Byrd Green Bank Telescope (GBT) -- all NRAO facilities, plus Arecibo (operated by the National Astronomy and Ionosphere Center), and Effelsberg (operated by the Max-Planck-Institut für Radioastronomie).   Elsewhere we present a more detailed description of the HSA; locations of the HSA telescopes are listed in Table 2 HSA observing proposals are addressed on a separate page of this document.

The phased VLA is rejoining the HSA in observing semester 2013A, after a three-year gap during construction of the EVLA.  A limited set of modes will be available initially.

The VLBA joins with the European VLBI Network (EVN) in a global cm-wave VLBI network during EVN sessions, and with networks of geodetic stations during global campaigns.  Proposals for these and other, less frequent worldwide collaborative observations are addressed on a separate page of this document.

 North West Latitude Longitude Elevation Code Location [° ′ ″] [ ° ′ ″] [m] VLA, NM 34:04:43.75 107:37:05.91 2115 Y27 Green Bank, WV 38:25:59.24 79:50:23.41 807 GB Arecibo, PR 18:20:36.60 66:45:11.10 497 AR Effelsberg, Germany 50:31:30 −6:53:00.3 319 EB

# 4. Frequency Bands & Performance

The nominal frequency ranges for VLBA receiver systems are shown in Table 3.  Actual frequency ranges are broader; consult the measurements reported by Hronek & Walker (1996) for details.  Updates on frequency-dependent performance across VLBA bands is available at http://www.vlba.nrao.edu/cgi-bin/wbd_dir.pl.  These actual ranges may be especially important for avoiding radio frequency interference (RFI), and for programs involving extragalactic spectral lines, rotation measures (Cotton 1995b; Kemball 1999), and multi-frequency synthesis (Conway & Sault 1995; Sault & Conway 1999).

 [1] [2] [3] [4] [5] [6] [7] Receiver Nominal Typical Center Typical Baseline Image Band Frequency Zenith Frequency Peak Sensitivity Sensitivity Designation Range SEFD for SEFD Gain ΔS2048,2m ΔIm2048,8h [GHz] [Jy] [GHz] [K Jy-1] [mJy] [μJy beam-1] 90 cm 0.312 - 0.342 2227 0.326 0.097 (g)  29 (i)  196 50 cm (a) 0.596 - 0.626 2216 0.611 0.088 (g)  81 (j)  553 21 cm (b) 1.35 - 1.75 296 1.438 0.096 1.0 9 18 cm (b) 1.35 - 1.75 303 1.658 0.100 1.0 10 13 cm (c) 2.15 - 2.35 322 2.275 0.093 1.1 10 13 cm (c,d) 2.15 - 2.35 337 2.275 0.090 1.1 11 6 cm (*) 3.9 - 7.9 210 4.990 0.120 0.7 7 4 cm 8.0 - 8.8 307 8.425 0.113 1.0 10 4 cm (d) 8.0 - 8.8 407 8.425 0.106 1.3 13 2 cm 12.0 - 15.4 550 15.369 0.104 1.8 17 1 cm (e) 21.7 - 24.1 502 22.236 0.107 1.7 16 1 cm (e) 21.7 - 24.1 441 23.799 0.107 1.5 14 7 mm 41.0 - 45.0 1436 43.174 0.078 (g)    7 45 3 mm (f) 80.0 - 90.0 4000 86.2 0.025 (h)  26 (k)  224
Notes:
(a) User-selectable filters available to restrict frequencies to 608.2-613.8 MHz.
(b) Different ranges within the same 20 cm receiver.
(c) Filters at NL, LA, and OV restrict frequencies to 2200-2400 MHz.
(d) Using 13/4 cm dichroic.
(e) Different ranges within the same 1 cm receiver. Continuum performance is better at 23.8 GHz, away from the water line.
(f) See Table 4 for individual station details.
(g) Fringe-fit interval 1 minute.     (h) Fringe-fit interval 30 seconds.
(i) Data rate 256 Mbps.                 (j) Data rate 32 Mbps.
(k) 8-station array; 4-hour integration.

(*) These receivers are being upgraded substantially; this table now shows the performance of the new systems.  Additional information on the upgraded receivers, including the current installation schedule, can be found in the New Developments section.

Also shown in Table 3 are parameters characterizing the performance of a typical VLBA station for the various frequency bands.  Columns [3] and [5] give typical VLBA system-equivalent-flux-density (SEFD) values at zenith and opacity-corrected peak gains, respectively.  These are means over measurements in both polarization at all ten antennas, at the frequencies in column [4].

The typical zenith SEFD can be combined with the aggregate recorded data rate and appropriate integration times to estimate the root-mean-square (RMS) noise level on a single VLBA baseline, and in a VLBA image.  Characteristic values tabulated in columns [6] and [7] are computed assuming, for most cases, the VLBA's upgraded 2-Gbps recording rate for continuum observations;  a typical fringe-fit interval of 2 minutes; and a total on-source integration time of 8 hours.  Exceptions, indicated in the table notes, apply to the fringe-fit intervals at the lowest and highest frequency bands, where shorter intervals are often required; for the recording rate limits imposed by the available RF bandwidth at the lowest frequency bands; and for most parameters at the extreme 3-mm band.  Performance may be worse than the tabulated estimates on some baselines due to poor primary or subreflector surfaces or poor atmospheric conditions.

 Antenna Nominal Typical Typical Typical Baseline Frequency Zenith Peak Zenith Sensitivity Range SEFD Gain Tsys ΔS512,30s [GHz] [Jy] [K Jy-1] [K] [mJy] BR 80.0 - 90.0 3500 0.039 135 28. NL 80.0 - 96.0 4900 0.055 270 33. FD 80.0 - 96.0 3600 0.034 120 28. LA 80.0 - 90.0 3100 0.051 160 … PT 80.0 - 96.0 4100 0.024 100 28. KP 80.0 - 96.0 4600 0.025 110 30. OV 80.0 - 96.0 5800 0.020 100 33. MK 80.0 - 96.0 4100 0.023 100 28.

The 3 mm band extends beyond the design specification for the VLBA antenna, and is challenging for the panel-setting accuracy of the primary reflectors, the figure of the subreflectors, and the pointing of the antennas. In addition, performance in this band is highly dependent on weather conditions. Table 4 gives the approximate current performance at 86 GHz for each antenna, as well as the RMS noise in 30 seconds (at 2 Gbps) on a baseline to LA, which is one of the most sensitive3 mm antennas.

# 5.1. Primary Signal Path

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 all frequencies above 1 GHz, while the prime focus is used at lower frequencies.  The antenna features a wheel-and-track mount, with an advanced-design reflector support structure.  Antenna motions, designed to facilitate rapid source changes, are at 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 bands above 1 GHz 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 dichroic system enables simultaneous 2.3/8.4 GHz observations. The 330 and 610 MHz feeds are crossed dipoles mounted on the subreflector near prime focus; simultaneous 330/610 MHz observations are possible.

The polarizer extracts orthogonal circularly-polarized signals, which are routed separately to dual receiver channels. For receivers above 1 GHz, the polarizer is cooled to cryogenic temperatures.

The receiver amplifies the signal. Most VLBA receivers are HFETs (Heterostructure Field Effect Transistors) at a physical temperature of 15 K, but the 90 cm and 50 cm receivers are GaAsFETs (Gallium Arsenide FETs) at room temperature. Each receiver has 2 channels, in opposite circular polarizations. The 1 cm, 7 mm, and 3 mm receivers also perform an initial frequency down conversion.

The IF converter mixes the receiver output signals with the first LO generated by a front end synthesizer. Two signals between 512 and 1024 MHz are output by each IF converter, one for 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, and D, carry the IF signals from the antenna vertex room to the station control building. Normally only two cables 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, switching is available to support other configurations needed for special cases. These include dual-band dual-polarization modes that use all four IFs, and in particular, the capability of the new C-band receiver for dual-polarization observations at two frequencies anywhere within its 4-8 GHz range.

# 5.2. Frequency and Time Standard

Essential auxiliary instrumentation, required to make simultaneous observations feasible at VLBA stations separated by, typically, 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 the reference signals used to convert the receiver output from RF to IF. The lock points are at (n× 500) ± 100 MHz, where n is an integer. The synthesizer output frequency is 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.

# 5.3. Calibration Signals

VLBA stations support several different types of calibration measurements.

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

The switched-noise system injects well calibrated, broadband noise, switched at 80 Hz in a 50% duty-cycle square wave.  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 at frequency intervals of 1 MHz or 5 MHz.  The tones are detected currently in the VLBA DiFX correlator, and eventually will be available from the RDBE. 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.

# 5.4. Roach Digital Backend (RDBE)

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 the station's received signals from the 512-1024 MHz IFs, with 8-bit precision.  All subsequent processing is performed digitally.

'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 that generates the 1024-MHz sample clock.  Each RDBE accepts two 512-1024 MHz inputs, and delivers packetized output to the Mark 5C recording system via a 10G Ethernet interface.

Two separate FPGA "personalities" are currently available within the VLBA's RDBE:

PFB:  The RDBE's initial personality, in regular use for scientific observations since 2012 February 19, implements a polyphase filterbank (PFB) signal-processing algorithm.  It produces sixteen fixed-bandwidth 32-MHz sub-bands, which can be selected flexibly between two input IFs (typically equivalent to polarizations), and 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 sub-bands at matching frequencies in each polarization; (b) a spanned-band dual-polarization configuration, with eight 32-MHz sub-bands spaced every 64 MHz in each polarization; and (c) a single-polarization configuration of 16 sub-bands, contiguous across the entire width of one IF.  The selected sub-bands are requantized at two bits per sample and transmitted to the recording system, at a total data rate of 2.048 Gbps (referred to subsequently as "2 Gbps'').  An important auxiliary function, detection of the switched broadband noise calibration signal, is also supported by the PFB.

DDC: Newer FPGA firmware, still under development, implements a digital downconverter (DDC) algorithm.  The current version, available for scientific use on a shared-risk basis, supports 1, 2, or 4 sub-bands with equal bandwidths of 64 or 128 MHz.  Sub-bands can be selected flexibly between two input IFs (typically equivalent to polarizations), and in either sideband.  Tuning of individual sub-bands within the input IFs can be set in steps of 15.625 kHz, although 250-kHz steps are recommended when compatibility with legacy systems is required.  Sub-bands may not cross IF zone boundaries at 640 and 896 MHz.  Each sub-band is requantized at two bits per sample and transmitted to the recording system, at a total data rates ranging from 256 Mbps to 2 Gbps.  The DDC also incorporates an advanced switched-noise detection methodology.

Development of the DDC firmware continues, toward its primary goal of supporting narrowband spectroscopic observations.  Current specifications limit the narrowest bandwidth to 1 MHz due to formatting restrictions.  However, with the DiFX correlator's high spectral resolution and spectral zoom capabilities, much narrower effective bandwidths can be achieved.

Two RDBE units are required at each VLBA station to provide adequate signal processing capacity for all anticipated applications, including four-IF and/or 8-sub-band observing modes.  The first set of RDBEs has been in regular use on the VLBA since mid-2011; fabrication of the second set is nearing completion.

Further information on the RDBE is available in the Sensitivity Upgrade memo series.

# 5.5. Mark 5C Recorder

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 new Mark 5C 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 functionally more straightforward than its predecessors.   It simply records the payload of each 10G Ethernet packet received from the RDBE without imposing any special recording format.  All formatting of the observed data -- most essentially, the precision time tags -- is internal to the packet payloads, which are transmitted directly from recorder to playback by the Mark 5C system.  Initially, Mark 5B format is being used internally, for compatibility with some existing correlators.  An eventual transition is planned to the VLBI Data Interchange Format (VDIF).

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.  Modules of 16-TB capacity, intended to suffice for recording a majority of VLBA observations at the 2-Gbps data rate, were procured with funding awarded through NSF's MRI-R2 program.  Unfortunately, commissioning tests of the 2-Gbps capability encountered unacceptably high failure rates in these modules, which limit the throughput currently achievable in wideband observations.

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

# 6.1. Introduction

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).

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 Swinburne University of Technology software correlator, developed as part of the Australian Major National Research Facilities Programme and operated under licence.

... and to cite the following recent 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, NRAO has established guidelines 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.

DiFX processes 2-bit samples with substantially greater efficiency than 1-bit samples over double the bandwidth, basically because only half as many samples must be correlated.  Since these two cases have nearly equivalent baseline sensitivity, a specific justification is also required for proposals requesting the wider-bandwidth, 1-bit mode.

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

DiFX processes input data recorded in Mark 5A, Mark 5B, and the new Mark 5C formats.  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, derived from data logged at the VLBA stations (Ulvestad 1999).  AIPS release 31DEC08 or later is required to handle DiFX data properly.

For observing semester 2013A, a recent upgrade provides conversion of DiFX correlator output to the Mark 4 format that is used primarily in analysis of geodetic observations.  To enable this additional output, a SCHED parameter CORDFMT=MARK4 should be specified.

# 6.2. Spectral Resolution

DiFX currently supports powers-of-2 numbers of spectral points spanning each individual sub-band, up to 4096 for routine DiFX processing, and up to 32,768 if required and adequately justified.  (The latter limit is the maximum resolution currently supported by AIPS.)   Oversampled data (essential for extremely high spectral resolution with the original VLBA instrumentation, but no longer necessary) can be decimated appropriately. Currently, both the number of spectral points, and the oversampling factor, must be the same for all sub-bands at any given time, although multiple passes are possible with different sets of sub-bands. 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 channels from any or all sub-bands.  Only the selected channels are included in the output dataset.  This capability will be of value mainly in maser studies, where the recorded band 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 wide bands 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.

In proposing observations that will use spectral zooming, the required number of channels before zooming should be specified in the Proposal Submission Tool.  Currently, the location and width of the "zoom" sub-bands must be communicated directly to VLBA operations before correlation.

# 6.3. Integration Period

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 sub-band bandwidth.

For most cases, with low to moderate spectral resolution, and/or wide sub-bands, 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 sub-band - 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 now 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.

# 6.4. Multiple Phase Centers

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 due to averaging in time (with, typically, a 2-second period) and/or across bandwidth ("chromatic aberration'' over, typically, 0.5 MHz spectral resolution), at positions away from the correlation phase center. 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 output data rate must be justified if it exceeds the current limit.

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 frequency channels per sub-band (required to minimize bandwidth smearing) and the desired integration between u-v shifts (to minimize time smearing).  SCHED includes facilities to support specification of the actual phase center locations.

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

# 6.5. Output Rate

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

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

where the rate $R$ is in Byte/s;

$N_{\rm stn} , \; N_{\rm sbb} , \; N_{\rm spc}$ are the numbers of observing stations, sub-bands, and spectral channels per sub-band, respectively;

$T_{\rm int}$ is the correlator integration period;   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.

# 7. Angular Resolution & u-v Coverage

Table 5 gives the maximum lengths ($B^{\rm km}_{\rm max}$) for each of the VLBA's 45 internal baselines as well as the baselines to HSA telescopes. A measure of the corresponding resolution ($\theta_{\rm HPBW}$) in milliarcseconds (mas) is

$$\theta_{\rm HPBW} \sim 2063 \times \frac{\lambda^{\rm cm}}{B^{\rm km}_{\rm max}} \; {\rm mas}$$

where $\lambda^{\rm cm}$ is the receiver wavelength in cm (Wrobel 1995). A uniformly weighted image made from a long u-v plane track will have a synthesized beam with a slightly narrower minor axis.

 SC HN NL FD LA PT KP OV BR MK EB AR GB Y27 SC ... 2853 3645 4143 4458 4579 4839 5460 5767 8611 6822 238 2708 4532 HN 2853 ... 1611 3105 3006 3226 3623 3885 3657 7502 5602 2748 829 3198 NL 3645 1611 ... 1654 1432 1663 2075 2328 2300 6156 6734 3461 1064 1640 FD 4143 3105 1654 ... 608 564 744 1508 2345 5134 8084 3922 2354 515 LA 4458 3006 1432 608 ... 236 652 1088 1757 4970 7831 4246 2344 226 PT 4579 3226 1663 564 236 ... 417 973 1806 4795 8014 4365 2551 52 KP 4839 3623 2075 744 652 417 ... 845 1913 4466 8321 4623 2939 441 OV 5460 3885 2328 1508 1088 973 845 ... 1214 4015 8203 5255 3323 1025 BR 5767 3657 2300 2345 1757 1806 1913 1214 ... 4398 7441 5585 3326 1849 MK 8611 7502 6156 5134 4970 4795 4466 4015 4398 ... 10328 8434 7028 4835 EB 6822 5602 6734 8084 7831 8014 8321 8203 7441 10328 ... 6911 6335 8008 AR 238 2748 3461 3922 4246 4365 4623 5255 5585 8434 6911 ... 2545 4317 GB 2708 829 1064 2354 2344 2551 2939 3323 3326 7028 6335 2545 ... 2516 Y27 4532 3198 1640 515 226 52 441 1025 1849 4835 8008 4317 2516 ...

Values of $\theta_{\rm HPBW}$ for the longest VLBA baseline, at the center frequencies of the standard observing bands (Table 3), are shown in Table 6. The longest VLBA baseline at 3 mm is currently that between MK and NL, which is about 30% shorter than the longest baseline at lower frequencies.

 Observing band [cm]: 90 50 21 18 13 6 4 2 1 0.7 0.3 $\theta_{\rm HPBW}$ [mas]: 22 12 5 4.3 3.2 1.4 0.85 0.47 0.32 0.17 0.12

Customized plots of the u-v plane coverage with the VLBA and/or other VLBI stations can be generated by NRAO program SCHED (Walker 2011).

# 8. Baseline Sensitivity

Baseline sensitivity is the RMS thermal noise (ΔS) in the visibility amplitude in a single polarization on a single baseline.  Adequate baseline sensitivity is required for VLBI fringe fitting.  Baseline sensitivities between VLBA antennas, for typical observing parameters, are listed in column [6] of the "Receiver Frequency Ranges & Performance" table.

Alternatively, the baseline sensitivity for two identical antennas, in the weak source limit, can be calculated using the formula (Walker 1995a; Wrobel & Walker 1999):

$$\Delta S = {\rm SEFD} / [\eta_s \cdot ( 2 \cdot \Delta \nu \cdot \tau_{\rm ff} ) ^{1/2} ] \; {\rm Jy}$$

SEFD or "system equivalent flux density" is the system noise expressed in Janskys.  $\eta_s \le 1 \ \$ accounts for the VLBI system inefficiency (primarily quantization in the data recording).  Kogan (1995b) provides the combination of scaling factors and inefficiencies appropriate for VLBA visibility data.  The bandwidth in Hz is $\Delta\nu$.  For a continuum target, use the sub-band width or the full recorded bandwidth, depending on the fringe-fitting mode; for a line target, use the sub-band width divided by the number of spectral points across the sub-band.  $\tau_{\rm ff}$ is the fringe-fit interval in seconds, which should be less than or about equal to the coherence time.

Moran & Dhawan (1995) discuss expected coherence times.   The actual coherence time appropriate for a given observation can be estimated using observed fringe amplitude data on an appropriately strong and compact source.

For non-identical antennas 1 and 2, SEFD can be replaced by the geometric mean $\sqrt{{\rm SEFD}_1 \times {\rm SEFD}_2}$.

Approximately equal baseline sensitivities can be obtained using either 1-bit (2-level) or 2-bit (4-level) quantization at a constant overall bit rate.  For 2-bit sampling relative to the 1-bit case, halving the bandwidth is closely compensated by an increase in ηs of nearly $\sqrt{2}$.   Since the DiFX correlator processes 2-bit samples with substantially greater efficiency, 1-bit sampling must be justified in the proposal.

# 9. Image Sensitivity

Image sensitivity is the RMS thermal noise (ΔIm) expected in a single-polarization image.   Image sensitivities for the 10-station VLBA, for typical observing parameters, are listed in column [7] of the "Receiver Frequency Ranges & Performance" table.

Alternatively, the image sensitivity for a homogeneous array with natural weighting can be calculated using the following formula (Wrobel 1995; Wrobel & Walker 1999).

$$\Delta I_m = {\rm SEFD} / [\eta_s \cdot ( N \cdot (N-1) \cdot \Delta \nu \cdot t_{\rm int} ) ^{1/2} ] \; \rm{Jy\; beam^{-1}}$$

Parameters SEFD, $\eta_s$, and $\Delta\nu$ are the same as those used in computing baseline sensitivity, $N$ is the number of observing stations, and $t_{\rm int}$ is the total integration time on source in seconds.

The expression for image noise becomes rather more complicated for a heterogeneous array such as the HSA, and may depend quite strongly on the data weighting that is chosen in imaging.   The EVN sensitivity calculator provides a convenient estimate.   For example, the RMS noise at 22 GHz for the 10-station VLBA in a 1-hr integration is reduced by a factor between 4 and 5 by adding the GBT and the phased VLA.

If simultaneous dual polarization data are available with the above value of ΔIm per polarization, then for an image of Stokes I, Q, U, or V,

$$\Delta I = \Delta Q = \Delta U = \Delta V = \frac{\Delta I_m}{\sqrt{2}}$$

For a polarized intensity image of $P = \sqrt{Q^2 + U^2}$

$$\Delta P = 0.655 \times \Delta Q = 0.655 \times \Delta U$$

It is sometimes useful to express $\Delta I_m$ in terms of an RMS brightness temperature in Kelvins ($\Delta T_B$) measured within the synthesized beam.  An approximate formula for a single-polarization image is

$$\Delta T_b \sim 320 \times \Delta I_m \times (B^{\rm km}_{\rm max})^2 \; {\rm K}$$

where $B^{\rm km}_{\rm max}$ is as in Table 5.

# 10. Calibration Transfer

Data necessary to perform accurate calibration for the VLBA are supplied as part of the correlator output files, and will appear as extension tables within the AIPS datasets created by task FITLD.  These tables include GC (gain), TY (system temperature), and WX (weather) tables for amplitude calibration, PC (pulse-cal) tables for system phase calibration, and FG (flag) tables for editing.

For non-VLBA stations, some or all of these tables may be missing, since relevant measurements are not available at the time of correlation.  For example, for the HSA, GC and TY information are available for most stations, except that calibration of the phased VLA requires additional information about the flux density of at least one source.  Flag (FG) tables for non-VLBA stations generally are absent or only partially complete, lacking information about antenna off-source times.  However, the "flag" file that is written by program SCHED (Walker 2011) is quite good at predicting the on-source times for the HSA stations.   In using this file as an input to AIPS task UVFLG, it is recommended that all entries for the ten VLBA stations be deleted.   The FG table supplied with the correlator output files includes the actual on-source times for these antennas, obtained directly from VLBA monitor data.   For further information on applying calibrations, see Appendix C of the AIPS Cookbook (NRAO staff, 2006) or the relevant AIPS HELP files.

# 11. Amplitude Calibration

Traditional calibration of VLBI fringe amplitudes for continuum sources requires knowing the on-source system noise in Jy (SEFD; Moran & Dhawan 1995).  System temperatures in Kelvin ($T_{\rm sys}$) are measured continuously during observations at VLBA stations, with mean values tabulated at least once per source/frequency combination or once every user-specified interval (default 2 minutes), whichever is shorter.  These $T_{\rm sys}$ values are used in fringe amplitude calibration by AIPS task APCAL, which converts $T_{\rm sys}$ to SEFD by dividing by the VLBA antenna gains in $\rm K\: Jy^{-1}$, expressed as a peak gain multiplied by a normalized "gain curve".  The latter data are based on regular monitoring of all receiver and feed combinations.  $T_{\rm sys}$ and gain values for VLBA antennas are delivered in TY and GC tables, respectively.  Single-station spectra can be used for amplitude calibration of spectral line observations.

Additional amplitude adjustments may be necessary to correct for the atmospheric opacity above an antenna, which can be significant at high frequencies (Moran & Dhawan 1995).  Leppänen (1993) describes a method for opacity adjustments.  AIPS task APCAL uses weather data from the WX table to carry out such adjustments.

Further corrections are usually applied to observations taken with 2-bit (4-level) sampling, for the effects of non-optimal setting of the quantizer voltage thresholds (Kogan 1995a).  These adjustments are usually relatively minor but can induce systematic effects.  Sampling-based calibration adjustments are determined by AIPS task ACCOR.  The combination of the antenna and quantizer calibrations may be found and applied in AIPS using the procedure VLBACALA.

Although experience with VLBA calibration shows that it probably yields fringe amplitudes accurate to 5% or less at the standard frequencies in the 1-10 GHz range, it is recommended that users observe a few amplitude calibration check sources during their VLBA program.  Such sources can be used (1) to assess the relative gains of VLBA antennas plus gain differences among sub-bands at each station; (2) to test for non-closing amplitude and phase errors; and (3) to check the correlation coefficient adjustments, provided contemporaneous source flux densities are available independent of the VLBA observations.  These calibrations are particularly important if non-VLBA stations are included in an observation, since their a priori gains and/or measured system temperatures may be much less accurate than for the well-monitored VLBA stations.  The recommended technique for this situation is to restrict the gain normalization in self-calibration to a subset of trusted stations (generally some of the VLBA stations), and to high elevations. AIPS task CALIB can do both.

The VLBA gains are measured at the center frequencies appearing in column [4] of the "Receiver Frequency Ranges & Performance" table; users observing at other frequencies may be able to improve their amplitude calibration by including brief observations, usually of their amplitude check sources, at the appropriate frequencies.  Amplitude check sources should be point-like on inner VLBA baselines.  Some popular choices in the range 13 cm to 2 cm are J0555+3948=DA193, J0854+2006=OJ287, and J1310+3220.  Other check sources may be selected from various VLBI surveys.  It might be prudent to avoid sources known to have exhibited extreme scattering events (e.g., Fiedler et al. 1994a, b).

# 12.1. Fringe Finders

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 NRAO 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 NRAO program SCHED (Walker 2011) and the VLBA correlator, are given in the standard source catalog available as an ancillary file with SCHED.

# 12.2. The Pulse Cal System

Fringe phases should be coherent across the entire set of sub-bands produced by each RDBE.  Correction of phase offsets between the two planned 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 pulse 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 is 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.

# 12.3. Fringe Fitting

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.

# 12.4. Editing

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.

# 12.5. Self-Calibration, Imaging, and Deconvolution

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).

# 12.6. Phase Referencing

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 VLBA correlator's source catalog, which is distributed with SCHED.  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 web page, for further information.

Walker & Chatterjee (1999) have investigated ionospheric corrections.  Such corrections can even be of significant benefit for frequencies as high as 5 GHz or 8 GHz (Ulvestad & Schmitt 2001).  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.  Some data may be associated with the wrong source, leading to visibility points of very low amplitude at the beginnings of scans.  Application of the AIPS program QUACK using the `TAIL' option will fix this problem.

# 13.1. Polarimetry

In VLBA polarimetric observations, sub-bands 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.

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).

# 13.2. Pulsar Observations

Pulsar observing is an expert mode of the VLBA, requiring additional understanding and effort on the part of the user.  Those willing to learn to use them can take advantage of the following enhanced capabilities supporting pulsar observations, available in the DiFX correlator:

1. Binary Gating: A simple pulse-phase driven on-off accumulation window can be specified, with "on" and "off" phases.  Such gating increases the signal to noise ratio of pulsar observations by a factor of typically 3 to 6, and can also be used to search for off-pulse emission.
2. Matched-filter Gating: If the pulse profile at the observation frequency is well understood and the pulse phase is very well predicted by the provided pulse ephemeris, additional signal to noise over binary gating can be attained by appropriately scaling the correlation coefficients as a function of pulse phase.  Depending on the pulse shape, additional gains of up to 50% in sensitivity over binary gating can be realized.
3. Pulsar Binning: This mode entails generating a separate visibility spectrum for each requested range of pulse phase.  There are no explicit limits to the number of pulse phase bins that are supported, however, data rates can become increasingly large.  Currently AIPS does not support databases with multiple phase bins.  Until post-processing support is available, a separate FITS file will be produced for each pulsar phase bin.

In all cases, the user will be responsible for providing a pulsar spin ephemeris.  Except for certain applications of mode 3, the ephemeris must be capable of predicting the absolute rotation phase of the pulsar.  Pulsar modes incur a minimum correlation-time penalty of about 50%.  High output data rates may require greater correlator resource allocations.  Details of pulsar observing, including practical aspects of using the pulsar modes, and limitations imposed by operations, are documented by Brisken (2009).

# 13.3. Spectral Line Observations

Diamond (1995) and Reid (1995, 1999) describe the special problems encountered during data acquisition, correlation, and post-processing of a spectral line program.  The spectral line user must know the transition rest frequency, the approximate velocity and velocity width for the line target, and the corresponding observing frequency and bandwidth.  The schedule should include observations of a strong continuum source to be used for fringe-finding, "manual" phase calibration, and bandpass calibration; as well as scans of a continuum source reasonably close to the line target to be used as a fringe-rate and delay calibrator.  The pulse cal generators should be disabled.

Post-processing steps include performing Doppler corrections for the Earth's rotation and orbital motion (the correction for rotation is not necessary for observations when station-based fringe rotation is applied, as is the case for the VLBA); 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; and deciding whether to do fringe rate mapping or normal synthesis imaging and then form a spectral line cube.  All these post-processing steps can currently be done in AIPS.

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

# 14.1. VLBA & HSA/EVN/Global Proposals

Since 2011, time on the VLBA and other NRAO instruments is scheduled on a semester basis, with each semester lasting six months.  Proposal deadlines are February 1 and August 1, with the February 1 proposal deadline nominally covering time to be scheduled during the following August through January, and the August 1 deadline covering time to be scheduled from February through July.

Observing proposals may specify the VLBA, or the VLBA in combination with various other VLBI arrays.  It should be noted, however, that proposals to use the European VLBI Network (EVN) and Global cm VLBI are handled by the EVN on a trimester system, with proposal submission deadlines of February 1, June 1, and October 1.  Further instructions are available on proposal preparation and submission for the various types of VLBI arrays.

1. The VLBA alone. A Call for Proposals is published in the NRAO eNews approximately two weeks in advance of each semester submission deadline.  Currently, these deadlines are 5pm (1700) Eastern Time on February 1, and August 1.   (If the deadline falls on a holiday or weekend, it is extended to the next working day.)  VLBA proposals must be prepared and submitted using the NRAO Proposal Submission Tool (PST), available via NRAO Interactive Services.

All proposals will be reviewed by a Science Review Panel (SRP) in relevant subdisciplines (e.g., solar system, stellar, galactic, extragalactic, etc.).  The SRP's comments and rating are strongly advisory to the NRAO Time Allocation Committee (TAC), and the comments of both groups are passed on to the proposers soon after each meeting of the TAC (twice yearly) and prior to the next proposal submission deadline.  A detailed description of the time allocation process is available.

Approved programs are scheduled by the VLBA scheduling officers, who may be contacted at 'schedsoc@nrao.edu'.  Ulvestad (2004) provides a short guide to using the VLBA, aimed specifically at inexperienced users but also useful to fill in knowledge gaps for more experienced users.

2. The High Sensitivity Array (HSA). The HSA comprises the VLBA in combination with the VLA, the GBT, Effelsberg, and/or Arecibo; observing time of up to 100 hours per trimester has been reserved for these observations.  Subsets of the HSA may also be requested.  All deadlines and procedures are the same as for the VLBA above.  Further information on "Observing with the High Sensitivity Array" is available in a separate document.

The phased VLA is rejoining the HSA in observing semester 2013A, after a three-year gap during construction of the EVLA.  The functionality of the VLBA's RDBE unit is supported in the VLA by various elements dispersed throughout the system; phased-array output is written directly from the WIDAR correlator to a Mark 5C recorder.  A limited set of modes will be available initially.

Arecibo only operates at frequencies up to 10 GHz, and can view sources only within 19.7° of its zenith; see http://www.naic.edu for further information about Arecibo's properties.
3. The European VLBI Network (EVN) and Global cm VLBI. The EVN consists of a VLBI network of stations operated by an international consortium of institutes (Schilizzi 1995).  The EVN home page provides access to the EVN User 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 2-3 weeks, 3 times per year, to carry out these observations.  EVN proposal deadlines are February 1, June 1, and October 1, with no allowance made for weekends.  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.  Such observations will be carried out during EVN sessions.
4. The Global 3 mm Array. This array consists of the VLBA stations outfitted with 3 mm receivers, together with Effelsberg, Pico Veleta, Plateau de Bure, Onsala, and Metsähovi.  The European part of the 3 mm Array is coordinated by the Max-Planck-Institut für Radioastronomie.  Further details, including instructions on proposal submission, are available.

The NRAO SCHED program (Walker 2011) can be used to determine the Greenwich Sidereal Time range during which the VLBI target sources are visible at various stations.  This program can also be used to evaluate the u-v plane coverage and synthesized beams provided by the selected array.

A source position service is available through NRAO to obtain accurate positions for use in correlation (Walker 1999a).  This should be requested simultaneously with the proposal, if not earlier.  Requirements for source position accuracy in correlation are discussed by Ulvestad (2004).

# 14.2. Phased VLA Modes for Semester 2013A

HSA proposals for observing semester 2013A can request the phased VLA in conjunction with the VLBA, and for processing at the Socorro DiFX correlator.  A comprehensive adjunct to the VLA Observational Status Summary, "VLBI at the VLA", discusses the available phased-VLA capabilities, and provides instructions for their use.  This sub-section of the VLBA Observational Status Summary summarizes only the specific modes available, and their compatibility between the two instruments.

Phased-array data will be limited to two VLA subband pairs, in any combination of polarizations, but with each pair in different IFs (AC and BD).  Channelizations at four different bandwidths will be available, as shown in Table 7.  Bandwidths must be uniform within each station, across the entire VLBI array, and throughout the entire duration of the observation.  At the narrower bandwidths, the two pairs of VLA channels limit the baseline sensitivity to less than can be achieved internally on the VLBA.

Table 7:  Phased-VLA / VLBA Compatibility

Phased VLAVLBA
Bandwidth Data Rate Data System Sub-bands Data Rate
[MHz]
[Mbps]

[Mbps]
128 2048 DDC 4 2048
64 1024 DDC 4 1024
32 512 PFB 16 2048
16 256 Legacy 8 512

# 14.3. Large Proposals

Proposals requesting more than 200 hours of total time on the VLBA, the HSA, or various combinations of NRAO telescopes in VLBI and non-VLBI modes, are covered under the NRAO Large Proposal Policy.

# 14.4. Director's Discretionary Time

The NRAO has established two categories of proposals for Director's Discretionary Time (DDT). DDT is limited to a maximum of 5% of the total observing time on the VLBA. All DDT proposals should be submitted using the standard NRAO procedures, using the on-line proposal tool. Proposals submitted by any other means (e.g., phone calls, e-mails, faxes, word-of-mouth) will be not be considered.

1. Target of Opportunity. Target of Opportunity (ToO) proposals are for unexpected or unpredicted phenomena such as supernovae in nearby galaxies or extreme X-ray or radio flares. ToO Proposals are evaluated rapidly, with scheduling done as quickly as possible and as warranted by the nature of the transient phenomenon. ToO Proposals are evaluated on the basis of scientific merit by the Chair of the relevant Science Review Panel and Observatory staff with the necessary scientific expertise. The technical feasibility of the proposed observations will be assessed by Observatory staff. The proprietary period for data obtained by ToO Proposals will be assessed on a case-by-case basis but will be no more than six months.
2. Exploratory Time. Exploratory Proposals are normally for requests of small amounts of time, typically a few hours or less, in response to a recent discovery, possibly to facilitate future submission of a larger proposal. In general, there will not be a need for immediate scheduling with these proposals, but they may need to be observed with the VLBA without waiting for an entire proposal cycle. The possibility that a proposer forgets about or misses a proposal deadline, or just discovered that he/she was granted time for a particular source on some other telescope, will not constitute sufficient justification for granting observing time by this process. Thus, Exploratory Proposals must include a clear description of why the proposal could not have been submitted for normal review at a previous NRAO proposal deadline, and why it should not wait for the next proposal deadline. Proposals for exploratory time will be evaluated on the basis of scientific merit by the relevant Science Review Panel. Observatory staff will assess their technical feasibility. Notification of the disposition of an Exploratory Proposal normally will be within three weeks of receipt of the proposal; some of these proposals may be put in a queue such that they may or may not be observed. The proprietary period for data obtained by Exploratory Proposals normally will be six months.

Please see https://science.nrao.edu/observing/proposal-types/directorsdiscretionarytime for further information.

# 14.5. Student Support & Dissertations

Students planning to use one or more NRAO telescopes for their PhD dissertation (particularly if more than one proposal will be required) may submit a "Plan of Dissertation Research" of no more than 1000 words with their first proposal.  This plan can be referred to in later proposals.  At a minimum it should contain a thesis time line and an estimate of the level of NRAO telescope resources needed.  The plan provides some assurance against a dissertation being impaired by an adverse review of one proposal when the full scope of the project is not seen.  The plan can be submitted via NRAO Interactive Services.  Proposers are reminded to prepare the plan comfortably in advance of the proposal deadline.

NRAO maintains a Student Observing Support program for research by students, both graduate and undergraduate, at U.S. universities and colleges.  Regular and Large proposals submitted for the VLA, VLBA, and GBT, and any combination of these telescopes, are eligible.  New applications to the program may be submitted along with new observing proposals at any proposal deadline.

# 15. Preparation for Observing

Users allocated VLBA observing time, either on fixed dates or on a dynamically-scheduled basis, will be sent instructions for preparing observing schedules.  Approximately 65% of all VLBA observations are scheduled dynamically, based on array and weather conditions predicted 1-2 days in advance.  Most VLBA observations are scheduled using the NRAO program SCHED (Walker 2011).  Help with preparing VLBA observations is available through the NRAO Helpdesk.

# 16. During Observing

Each VLBA program is run remotely from the SOC by VLBA operations.  No observing assistance by a VLBA user is expected, although VLBA operations should be able to reach the observer by telephone during the program.  As the program progresses, the array operator monitors the status of the antennas and the station data path, mainly using a compact yet comprehensive display program.  Various logging, calibration, and flagging data are automatically recorded by the monitor and control system running on the station computer at each VLBA site.  If necessary, the array operator can request local assistance from a site technician at each VLBA station.  Recorded media are automatically shipped from each VLBA station to the correlator specified by the observer.

# 17.1. AIPS

AIPS, NRAO's Astronomical Image Processing System, is a set of programs for the analysis of continuum and line observations, and is widely used with VLBA and VLBI data.  These programs are available for a wide range of computer operating systems, including various flavors of Linux and the Mac-OS/X operating system.   Extensive online internal documentation can be accessed within AIPS.  An entire chapter in the AIPS Cookbook (NRAO staff, 2007) provides useful "how-to" guidance those reducing VLBI data, including discussion of VLBA calibration transfer, space VLBI, polarimetry, and phase referencing.   Appendix C of the AIPS Cookbook provides a step-by-step guide to calibrating many types of VLBA data sets in AIPS, employing simple VLBA utilities, including calibration modifications for VLBA+VLA datasets.

A new ''frozen" version of AIPS is produced each year, and a newer version is updated and made available throughout the calendar year. Observers are encouraged to use a very recent version of AIPS, in order to keep up with ongoing  developments in VLBA instrumentation.

# 17.2. CASA

CASA (Common Astronomy Software Applications) is the new data reduction package that will be used for the EVLA and ALMA. It does not yet offer an end-to-end reduction path for VLBA data.  However, CASA does contain imaging and calibration tools that may be of use for VLBI data.

# 17.3. Difmap

Difmap (Shepherd 1997) provides editing, imaging, self-calibration, and pipelining capabilities in an interactive package.  It was developed as part of the Caltech VLBI Analysis Programs and remains widely used, although development has been frozen and continued support is limited primarily to assistance in installation.

# 18.1. General Information

VLBA users are welcome to visit the SOC to analyze the results of their observations.  Visitors to Socorro can take advantage of the NRAO Guest House.  This facility contains eight single, four double, and two two-bedroom apartments, plus a lounge/kitchen, and full laundry facilities.  The Guest House is located on the campus of New Mexico Tech (NMIMT), a short walk from the SOC.  Reservations are made through the online registration form.  Reservations must be made at least 1 week prior to your visit to the NRAO/NM, and 2 weeks notice is preferred.   Computing requirements and the level of staff assistance needed must be specified through the online form.

Students visiting for their first VLBA data reduction trip must be accompanied by their faculty advisor.   Standard NRAO travel reimbursement policy applies to VLBA data reduction trips.

# 18.2. Travel Support for Visiting the SOC

Travel support is available for U.S.-based observers to travel to NRAO to observe and/or reduce data.  Please see Travel Support for NRAO Observing Runs and Data Reduction for Non-NRAO Employees for details of eligibility and how to claim reimbursement.

# 19. Data Archive and Distribution

All output from the VLBA is maintained in the NRAO data archive.  The user(s) who proposed the observations retains a proprietary right to the data for an interval of 12 months following the end of correlation of the last observations requested in the original proposal, or a direct extension of that proposal.  Thereafter, the archived data are available to any person on request.  Data can be obtained from the archive either as multiple correlator output files, or as large FITS files with default calibrations attached.

Although the online archive is the preferred distribution path, VLBA data can also be written onto DDS-3 or -4 DAT cassettes and mailed. Initial distribution to the proposing user occurs automatically, soon after correlation is complete.

Distributed data conform to the FITS Interferometry Data Interchange Convention (Greisen 2009), which is read by AIPS task FITLD.

# 20.1. Acknowledgment to NRAO

Any papers using observational material taken with NRAO instruments (VLBA or otherwise) or papers where a significant portion of the work was done at NRAO, should include the following acknowledgment to NRAO and NSF:

The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

# 20.2. Acknowledgment for DiFX

VLBA observations are currently correlated using NRAO's implementation of the DiFX software correlator.  DiFX was developed at Swinburne University in Melbourne, Australia, and is used by NRAO under license from Swinburne.  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 Swinburne University of Technology software correlator, developed as part of the Australian Major National Research Facilities Programme and operated under licence.

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

# 20.3. Dissertations

Students whose dissertations include observations made with NRAO instruments are expected to provide copies of, or links to, their theses for inclusion and maintenance at the NRAO library. These will be catalogued and made available via the NRAO library.

# 20.4. Reprints

Given the prevalence of electronic access to the literature, NRAO will no longer pay for the purchase of reprints of published papers.

# 21. Documents and Articles

A list of documents and articles referred to in this document follows. Numerous articles from two books appear; abbreviations for these books and complete references for them are as follows:

VLBI & the VLBA = Very Long Baseline Interferometry and the VLBA, Astronomical Society of the Pacific Conference Series, Volume 82, eds. J.A. Zensus, P.J. Diamond, & P.J. Napier.

Synthesis II = Synthesis Imaging in Radio Astronomy II, Astronomical Society of the Pacific Conference Series, Volume 180, eds. G.B. Taylor, C.L. Carilli, & R.A. Perley.

1. Beasley, A.J., & Conway, J.E. 1995, in VLBI & the VLBA, p. 327
2. Beasley, A.J., Gordon, D., Peck, A.B., Petrov, L., MacMillan, D.S., Fomalont, E.B., & Ma, C. 2002, Astrophysical Journal Supplement, 141, 13
3. Bridle, A.H., & Schwab, F.R. 1999, in Synthesis II, p. 371.
4. Briggs, D.S., Schwab, F.R., & Sramek, R.A. 1999, in Synthesis II, p. 127.
5. Brisken, W. 2008, VLBA Sensitivity Upgrade Memo # 23. http://www.vlba.nrao.edu/memos/sensi/
6. Brisken, W. 2009, VLBA Sensitivity Upgrade Memo # 32. http://www.vlba.nrao.edu/memos/sensi/
7. Conway, J.E., & Sault, R.J. 1995, in VLBI & the VLBA, p. 309. http://www.cv.nrao.edu/vlbabook/
8. Cornwell, T.J. 1995, in VLBI & the VLBA, p. 39. http://www.cv.nrao.edu/vlbabook/
9. Cornwell, T.J., Braun, R., & Briggs, D.S. 1999, in Synthesis II, p. 151.
10. Cornwell, T.J., & Fomalont, E.B. 1999, in Synthesis II, p. 187.
11. Cotton, W.D. 1995a, in VLBI & the VLBA, p. 189. http://www.cv.nrao.edu/vlbabook/
12. Cotton, W.D. 1995b, in VLBI & the VLBA, p. 289. http://www.cv.nrao.edu/vlbabook/
13. Cotton, W.D. 1999a, in Synthesis II, p. 111.
14. Cotton, W.D. 1999b, in Synthesis II, p. 357.
15. Cotton, W.D., Dallacasa, D., Fanti, C., Fanti, R., Foley, A.R., Schilizzi, R.T., & Spencer, R. E. 1997a, Astronomy & Astrophysics, 325, 493.
16. Cotton, W.D., Fanti, C., Fanti, R., Dallacasa, D., Foley, A.R., Schilizzi, R.T., & Spencer, R. E. 1997b, Astronomy & Astrophysics, 325, 479.
17. Deller, A.T., Tingay, S.J., Bailes, M., & West, C. 2007, Publications of the Astronomical Society of the Pacific, 119, 318.
18. Deller, A. T., Brisken, W. F., Phillips, C. J., Morgan, J., Alef, W. Cappallo, R., Middleberg, E., Romney, J., Rotmann, H., Tingay, S. J., & Wayth, R., 2011, Publications of the Astronomical Society of the Pacific, 123, 275.
19. Diamond, P.J. 1995, in VLBI & the VLBA, p. 227.  http://www.cv.nrao.edu/vlbabook/
20. Fiedler, R., Dennison, B., Johnston, K.J., Waltman, E.B., & Simon, R.S. 1994a, Astrophysical Journal, 430, 581.
21. Fiedler, R., Pauls, T., Johnston, K.J., & Dennison, B. 1994b, Astrophysical Journal, 430, 595.
22. Fomalont, E., & Kogan, L. 2005, AIPS Memo No. 111. http://www.aips.nrao.edu/aipsdoc.html
23. Garrett, M. A., Porcas, R. W., Pedlar, A., Muxlow, T. W. B., & Garrington, S. T. 1999, New Astronomy Reviews, 43, 519.
24. Greisen, E. W. 2009, AIPS Memo 114.  http://www.aips.nrao.edu/aipsdoc.html
25. Hronek, A., & Walker, R.C. 1996, VLBA Test Memo No. 51.  https://science.nrao.edu/facilities/vlba/publications/memos/test/index/test51memo.pdf
26. Kemball, A.J. 1999, in Synthesis II, p. 499.
27. Kemball, A.J., Diamond, P.J., & Cotton, W.D. 1995, Astronomy & Astrophysics Supplement Series, 110, 383.
28. Kogan, L. 1995a, VLBA Scientific Memo No. 9. https://science.nrao.edu/facilities/vlba/publications/memos/sci/index/sci09memo.pdf
29. Kogan, L. 1995b, VLBA Scientific Memo No. 12. https://science.nrao.edu/facilities/vlba/publications/memos/sci/index/sci12memo.pdf
30. Leppänen, K.J. 1993, VLBA Scientific Memo No. 1. https://science.nrao.edu/facilities/vlba/publications/memos/sci/index/sci01memo.pdf
31. Leppänen, K.J., Zensus, J.A., & Diamond, P.J. 1995, Astronomical Journal, 110, 2479.
32. Markowitz, A., & Wurnig, J. 1998, VLBA Test Memo No. 60. http://www.aoc.nrao.edu/%7Eanalysts/vlba/ffs.html
33. Mioduszewski, A. 2004, AIPS Memo No. 110. http://www.aips.nrao.edu/aipsdoc.html
34. Moran, J.M., & Dhawan, V. 1995, in VLBI & the VLBA, p. 161. http://www.cv.nrao.edu/vlbabook/
35. Napier, P.J. 1995, in VLBI & the VLBA, p. 59. http://www.cv.nrao.edu/vlbabook/
36. Napier, P.J., Bagri, D.S., Clark, B.G., Rogers, A.E.E., Romney, J.D., Thompson, A.R., & Walker, R.C. 1994, Proc. IEEE, 82, 658.
37. NRAO staff, 2007, AIPS Cookbook. http://www.aips.nrao.edu/cook.html
38. Perley, R.A. 1999a, in Synthesis II, p. 275.
39. Perley, R.A. 1999b, in Synthesis II, p. 383.
40. Reid, M.J. 1995, in VLBI & the VLBA, p. 209. http://www.cv.nrao.edu/vlbabook/
41. Reid, M.J. 1999, in Synthesis II, p. 481.
42. Rogers, A.E.E. 1995, in VLBI & the VLBA, p. 93. http://www.cv.nrao.edu/vlbabook/
43. Romney, J.D., & Reid, M.J. 2005, Future Directions in High Resolution Astronomy, Astronomical Society of the Pacific Conference Series, Volume 340.
45. Sault, R.J., & Conway, J.E. 1999, in Synthesis II, p. 419.
46. Schilizzi, R.T. 1995, in VLBI & the VLBA, p. 397. http://www.cv.nrao.edu/vlbabook/
47. Shepherd, M.C. 1997, ADASS IV, Astronomical Society of the Pacific Conference Series, Volume 125, eds. G. Hunt & H.E. Payne, p. 77.  http://www.nrao.edu/meetings/proceedings.shtml
48. Taylor, G.B. 1998, Astrophysical Journal, 506, 637.
49. Taylor, G.B. 2000, Astrophysical Journal, 533, 95.
50. Taylor, G.B., & Myers, S.T. 2000, VLBA Scientific Memo No. 26. https://science.nrao.edu/facilities/vlba/publications/memos/sci/index/sci26memo.ps
51. Thompson, A.R. 1995, in VLBI & the VLBA, p. 73. http://www.cv.nrao.edu/vlbabook/
52. Ulvestad, J.S. 1999, VLBA Operations Memo No. 34. http://www.vlba.nrao.edu/memos/vlba/
53. Ulvestad, J.S. 2004, VLBA Scientific Memo No. 27, Version 3.0 https://science.nrao.edu/facilities/vlba/publications/memos/sci/index/sci27memo.ps
54. Ulvestad, J.S. & Schmitt 2001, VLBA Test Memo No. 68. https://science.nrao.edu/facilities/vlba/publications/memos/test/index/test68memo.pshttps://science.nrao.edu/facilities/vlba/publications/memos/test/index/test68memo.ps
55. Walker, R.C. 1995a, in VLBI & the VLBA, p. 133. http://www.cv.nrao.edu/vlbabook/
56. Walker, R.C. 1995b, in VLBI & the VLBA, p. 247. http://www.cv.nrao.edu/vlbabook/
57. Walker, R.C. 1999a, Accurate Source Position Service. http://www.vlba.nrao.edu/astro/prop/prep/positions.shtml
58. Walker, R.C. 1999b, in Synthesis II, p. 433.
59. Walker, R.C. & Chatterjee, S. 1999, VLBA Scientific Memo No. 23. https://science.nrao.edu/facilities/vlba/publications/memos/sci/index/sci23memo.ps
60. Walker, C., Durand, S., Kutz, C., & Hayward, R. 2007a, VLBA Sensitivity Upgrade Memo # 10. https://science.nrao.edu/facilities/vlba/publications/memos/sensitivity-upgrade/index/sensimemo10.pdf
61. Walker, C., Romney, J., Brisken, W., & Durand, S. 2007b, VLBA Sensitivity Upgrade Memo # 15. https://science.nrao.edu/facilities/vlba/publications/memos/sensitivity-upgrade/index/sensimemo15.pdf
62. Walker, C., Durand, S., Kutz, C., & Hayward, R. 2008, VLBA Sensitivity Upgrade Memo # 21. https://science.nrao.edu/facilities/vlba/publications/memos/sensitivity-upgrade/index/sensimemo21.pdf
63. Walker, R.C. 2011, The SCHED User Manual. http://www.aoc.nrao.edu/software/sched/
64. Walker, C., & Hayward R. 2011, NRAO eNews 4, Issue 12, 2011. https://science.nrao.edu/enews/4.12
65. Wrobel, J.M. 1995, in VLBI & the VLBA, p. 411. http://www.cv.nrao.edu/vlbabook/
66. Wrobel, J.M., & Walker, R.C. 1999, in Synthesis II, p. 171.
67. Wrobel, J.M., Walker, R.C., Benson, J.M., & Beasley, A.J. 2000, VLBA Scientific Memo No. 24. https://science.nrao.edu/facilities/vlba/publications/memos/sci/index/sci24memo.ps
68. Zensus, J.A., Taylor, G.B., & Wrobel, J.M. 1998, IAU Colloquium 164: Radio Emission from Galactic and Extragalactic Compact Sources, Astronomical Society of the Pacific Conference Series, Volume 144. http://www.nrao.edu/meetings/past.shtml

# 22. Further Information

Requests for information beyond the scope of this document should be directed to the NRAO Helpdesk

# 23. Editor's Acknowledgments

This document is the collective work of innumerable individuals who wrote and edited the text, commented on draft material, and implemented the capabilities described herein, during the 19 years since the VLBA's dedication in 1993.  We thank these many colleagues for their contributions.  J. D. Romney, current editor of the Summary, is responsible for the most recent revisions, and thus is the best contact for readers who may have questions on the material, or suggestions that would enhance the usefulness of this guide.