9.5 Calibration strategy

If you have multiple frequency IDs in your data, you may want to separate the data for different FREQID before performing any calibration. Use UVCOP to do this and take advantage of the opportunity to delete data flagged by the correlator with FLAGVER=1. You no longer need to re-run INDXR on the output files. Again there is a procedure to do this for you:

VLBAFIX will normally be run after loading the data.

We can now begin the process of calibrating VLBI data. As the calibration process proceeds, both amplitude and phase corrections are incorporated into the CL tables. VLBI correlator output is in terms of dimensionless “correlation coefficients.” To convert to Janskys, large amplitude correction factors have to be entered into the CL tables. In addition, phase correction factors must be entered into the CL table to correct for phase offsets and ramps as functions of frequency and time. These corrections must be made so that the data can be averaged over frequency and time without loss of coherence. The process of determining the phase corrections is known as “fringe-fitting” in VLBI; see §9.5.7.

In order to calibrate the absolute phase of their data, VLBI users use either “phase-referencing” or “self-calibration”. If the self-calibration route is chosen, then the phase derivatives with respect to time and frequency are calibrated and the absolute phases are normally left uncalibrated. Then self-calibration methods are then used to generate images (see §9.7). For phase-referencing, an absolute-phase calibration is done using an external calibrator. Phase-referencing in VLBI is similar to, but slightly more complicated than, phase calibration on the VLA. In general terms, phase-referencing VLBI data is accomplished by similar methods as used for VLA data in ; be sure to read §9.5.1.2 and §9.5.7.4 for details on how to calibrate phase-referenced observations.

For astrometric data reduction methods in the reader is referred to the guide to  astrometric data reduction available from within  by typing HELP ASTROMET.

Optimum fringe-fitting results are obtained if amplitudes are calibrated first, since, in this case, the data will be weighted appropriately (the  task FIXWT may be used to adjust the weights in the data to reflect the scatter of the actual data). We therefore describe the process of amplitude calibration first in §9.5.4.6. Then, in §9.5.7, we describe the calibration of residual phase using “fringe-fitting” techniques. Note however, that for observations of strong sources or observations using only VLBA antennas (where, particularly at centimeter wavelengths, the sensitivities on all baselines are roughly the same), the order of the two calibration steps may be reversed.

9.5.1 Incremental calibration philosophy

The general strategy adopted by  for calibration is, starting with the lowest version of the CL table, to incorporate step-by-step amplitude and phase corrections for a number of different effects. At each stage either an existing CL table is modified or a new version is created from a lower version by a task which applies a certain type of calibration. Note that the actual visibilities are not changed until you are satisfied that you have the best possible calibration file; at this point the task SPLIT can be used to apply the calibration information of the best CL table to the data. However at each point along the way the effect of a particular CL table on the data can be viewed using POSSM or VPLOT by setting DOCAL=1 and GAINUSE equal to the chosen CL table. Since many CL tables may be produced in the course of calibrating a VLBI data set it is important to keep a note of which effects are included in each one. Ideally one should delete CL tables which are judged incorrect and ensure that the accumulated corrections lie in the highest numbered CL table. It is suggested that version 1 of the CL table, as produced by FITLD, be copied to CL version 2 using TACOP before any calibration is begun, and that CL version 2 be used as the starting point in the calibration sequence. An effort is made within  to insure that CL version 1 is not deleted inadvertently. If this does occur however it can be re-generated using task INDXR (described in §9.3.1.6). (Note that INDXR cannot re-generate some types of information, e.g., the phase-cals inserted by the MKIII correlator so that it is important to try to preserve the first CL table.) The task TASAV can be used to back up your tables by copying all of them to a dummy file containing no data. This can be used to save a “snapshot” of the tables at various points in your data processing for insurance purposes. The tables can be copied back into your data file if necessary using TACOP.

You can also use the verb HINOTE to add comments into the history file. This can be very useful for check-pointing progress during calibration.

When you are ready to apply the calibrations, you run either SPLIT or SPLAT. Both tasks can average data in the spectral domain if appropriate. SPLAT can also time-average the data and produces multi-source data sets on output if requested.

9.5.1.1 Smoothing and applying corrections in SN and CL tables

The various stages of calibration described below produce SN tables which are then used to create CL tables using CLCAL. The ancillary tasks SNCOR, SNSMO, SNEDT, and CLCOR can be used to modify the SN and CL tables directly. It is important to choose the proper methods of interpolation in these tasks.

SN tables can be smoothed using tasks SNEDT and SNSMO before being used to update CL tables using CLCAL. SNSMO uses superior smoothing methods to those available in CLCAL and should always be used to do any smoothing of VLBI data, i.e., data with non-zero delays and rates. The adverb DOBLANK now controls which data are actually altered by the smoothing; use it carefully.

Typical inputs for SNSMO would be:

Typical inputs for CLCAL would be:

Note well that SNVER=0 means here to combine the solutions from all SN tables, GAINVER=0 means to apply the solutions to the highest numbered CL table and GAINUSE=0 means to write a new CL table. If two SN tables contain two similar attempts at finding corrections and SNVER=0 then, effectively, CLCAL will be inconsistent in applying the solutions from these two tables. Basically, CLCAL simply concatenates all SN tables and then merges apparently identical records (same time and antenna) to eliminate blanked solutions and to complain about otherwise non-identical solutions.

The parameters INTERPOL and SAMPTYPE allow the user to choose between several different methods of smoothing the SN files followed by interpolation to the times in the CL table. Use EXPLAIN CLCAL  C R to view all the options. The default interpolation option is INTERPOL = ’2PT’, in which the SN table is linearly interpolated between the measurements in the SN table. Using SAMPTYPE = ’BOX’ causes the SN table to be smoothed with a boxcar function before being interpolated onto the CL table. The smoothing times for delay, rate etc. are specified in parameter BPARM. DOBLANK controls how both failed and good solutions are handled when smoothing. DOBLANK ≥ 0 replaces failed solutions with smoothed ones, while DOBLANK ≤ 0 replaces good solutions with smoothed ones. However it is recommended that SN smoothing be done prior to CLCAL using task SNSMO. When smoothing delays, use the new SMOTYPE = ’VLDE’ method whenever the IFs have been grouped to find single solutions (APARM(5)> 0 in FRING) across multiple IFs. Be sure to set NPIECE to indicate how many groups of IFs were used in FRING, e.g., 1 for a multi-band delay, 2 for a delay for IFs 1 — Nif∕2 amd a delay for IFs Nif∕2 + 1 — Nif.

With good quality data, the INTERPOL = ’AMBG’ option should work well. Note, however, that this option uses the SN solutions immediately before and after a CL entry to make the interpolation and it uses any SN solution found for any source specified in CALSOUR. Therefore, if CALSOUR is left blank (allowing all sources) and delay and rate solutions were significantly different for different sources, then inappropriate solutions may be applied for a few minutes before or after a source change.

One way of avoiding this problem is to run CLCAL with INTERPOL = ’AMBG’ several times, once for each source, setting both SOURCES and CALSOUR to the name of the desired source with all other inputs remaining unchanged. Another way of avoiding the problem is to use INTERPOL = ’SELF’. In this option, only solutions found on a given source are used to calibrate that source and the SN table entries closest in time for that source are used with interpolation. This is not as good as doing multiple runs with the INTERPOL = ’AMBG’ option because there can be jumps in phase at points equidistant from two SN table entries.

If there are bad SN solutions, INTERPOL = ’POLY’ is used to fit a polynomial to the rate solutions and then integrate this polynomial to determine the phase corrections to be entered into the CL table.

A final note on CLCAL. It is sometimes the case that a priori information is not available for all antennas in a single format. For example, you may have system temperature information for VLBA antennas in your SN version 2 table and for non-VLBA antennas in SN version 3. You can merge this information by running CLCAL twice with the same GAINVER and GAINUSE; each time you should explicitly set the SN version number and list the antennas to be processed using the ANTENNAS adverb. If you leave the ANTENNAS adverb blank, the final CL table will contain information only for antennas present in the last SN table processed. Note that you must use OPCODE = ’CALI’ when building up a CL table in pieces.

9.5.1.2 Running CLCAL for phase referencing observations

In particular, this example illustrates how to set the inputs for CLCAL for the specific case when phase corrections determined for the cal source ’J1636-16’ are to be transferred to the target source ’P1643-12’ in a phase referencing experiment:

It’s a good idea to always apply the calibration information to both the cal and target sources when running CLCAL for phase-referencing observations. This allows you to monitor the cal source data to check the progress of the phase calibration procedure.

9.5.2 Processing observing log and calibration information

As of 1 April 1999, the VLBA correlator provides calibration transfer information, as described in §9.3.1.2 for VLBA antennas. Experiments correlated after November 2003 also have full calibration transfer for the VLA, the GBT, Arecibo and the Bonn 100m. Consequently, you can skip §9.5.2 entirely unless you have data from non-VLBA telescopes (e.g., the VLA before November 2003, Space, other European telescope) or other correlators or you wish to process the log files manually for other reasons.

This section describes the processing of external calibration information, as supplied in ASCII log files. The information that may be used by  includes T_sys or related total power measurements, edit flags as written by the tracking stations or on-line monitor control system, weather information, and pulse-calibration data. These external data can be read into  by tasks ANTAB, UVFLG, APCAL, and PCLOD respectively, as described in §9.5.2.3, §9.5.3, §9.5.4.6 and §9.5.4.3.

You should have received information about where to obtain your calibration data. VLBA calibration log files may be obtained by ftp as described below. Similar calibration files for other participating antennas and VSOP should be obtained from the appropriate sites.

9.5.2.1 Automatic formatting of VLBA and VLBA-like log files

For VLBA antennas, the external calibration file for a given experiment can be downloaded from

The external calibration file, if suitably close to the standard VLBA format, concatenated with the gain curve file, can be automatically subdivided and re-formatted to comply with  requirements using task VLOG. Typical inputs would be:

A sequence of output text files will be created in the specified ($FITS here) directory named BZ199.* with suffixes:

1. .TSYS: T_sys calibration data, including gain curves, suitable for direct use by ANTAB. An INDEX record is constructed for each frequency ID if possible. If no match can be made to the FQ data, a warning message is printed and the INDEX keyword is omitted; the INDEX keyword must then be inserted by hand (see the HELP file for ANTAB). Gain curve entries for the frequency and time range in the uv data are copied to this output file. It is recommended to insert T_sys values at the end of scans immediately before source changes to avoid interpolation problems for sources of greatly differing flux density or use INTERPOL = ’SELF’ in CLCAL. Occasionally spurious data from previous observing runs or system start-up files will end up in the .TSYS file and must be edited out by hand.
2. .FLAG: Flag data, suitable for direct use by UVFLG. In the older format “antennas=vlba_xx” the appropriate antenna and day numbers are inserted.
3. .WX: Weather data, as used by APCAL if performing an opacity solution. This file is altered to conform with APCAL requirements (e.g., WEATHER keyword) and lines with bad entries (*) are commented out.
4. .PCAL: Pulse-calibration data, for input to PCLOD. No editing is performed.

Files with suffixes .SCAN and .MKIII contain scan summaries and MkIII information and are for information purposes only.

9.5.2.2 Manual formatting of log files

Partitioning of the calibration file can and must be done by hand if the calibration file format is sufficiently distinct from the standard VLBA format or, possibly, if it contains multiple frequency bands. If your observation used non-VLBA antennas, you will need to edit the calibration text file manually to add any log information supplied for these antennas. The necessary steps are as follows:

Extract the flagging and T_sys information from the calibration text file. You will also need to append gain curves to the T_sys file. Try EXPLAIN ANTAB to see an example file in the proper format. The parameter TIMEOFF should be set to zero for each station since both flag information and data are stored with UTC times. The keyword DTIMRANG is also supported which pads each flagged time interval to insure that even very short flag intervals are applied.

While older VLBA format calibration files were supplied with the ANTENNA keyword, newer VLBA format calibration files are supplied with the ANT_NAME keyword. In the former case, the file should be edited to insert the antenna numbers as listed in the AN table (use PRTAN on your  file to find these) and the absolute day numbers must be replaced by relative day numbers with respect to the  reference date. In the latter case, no adjustments to either day numbers or antenna numbers are necessary.

9.5.2.3 Loading calibration log information

The calibration information in the external text files such as T_sys and gain curve measurements are read into TY and GC tables using ANTAB. These tables are then used by APCAL to generate an amplitude solution (SN) table, allowing an optional solution for atmospheric opacity. The user is advised to read the ANTAB help file closely and check the syntax of the text file carefully.

The INDEX keyword is used to assign the tabulated T_sys data to individual  IF channels and polarizations. Up-to-date information on the usage of the INDEX keyword may be found by typing EXPLAIN ANTAB. Be careful to match up the proper polarization labels for the tabulated T_sys information. The frequency and polarization association for each IF channel in the  file can be compared (use LISTR with OPTYPE = ’SCAN’ or LISUN) with that at the head of the calibration text file.

The CONTROL group at the head of the calibration file is used only to specify a default index mapping. If the IF channel orders in the calibration file and the uv file are identical it is not required.

Source flux densities are not specified in the ANTAB input file. If source flux densities are required by APCAL, the source (SU) table will be searched. Use SETJY to insert flux densities if necessary.

The parameter TIMEOFF in the input file adds a time offset to the all entries. Non-VLBA stations sometimes measure the system temperature between, rather than during, scans causing ANTAB to be unable to match the measurements with the source and frequency ID. The ANTAB input parameter OFFSET serves the same purpose, but is more successful since the scan times are expanded at both ends.

ANTAB permits specification of IF-dependent and tabulated gains; the format description may be found by typing EXPLAIN ANTAB.

ANTAB can be run multiple times to append to the same TY and GC tables. Also, calibration files from separate antennas (e.g., VLA) which have T_sys data tabulated in a different format can be concatenated and processed in one run. In this case the INDEX keyword must be specified for each antenna to fix the data format.

Note that ANTAB will (usually) ignore calibration data for which there are no corresponding uv data (see the help file for ANTAB). There is one exception however: calibration data for an antenna that does not appear in the AN table will cause ANTAB to fail. If ANTAB quits under such circumstances, you have two choices. You can edit the calibration text file, removing all reference to the missing antennas; or you can use the input adverb SPARM to specify explicitly the names of antennas for which there are calibration data, but which do not appear in the AN table.

*** The use of SPARM is no substitute for careful inspection of the calibration text files. ***

Having created the input text file, typical inputs for ANTAB would be:

PRTLEV = 2 will echo the calibration file as it is processed, which can be useful in locating format errors.

9.5.2.4 Generating VLA amplitude calibration with VLAMP

Before February 2013, the VLA’s a priori calibration was done with calibration files, named xxxxxcal.y.gz (stored in gzipped format). These were obtained from the same server and disk directory as for VLBA files. This VLA file started with an explanatory preamble, including minor editing instructions. See §C.11 for more detailed instructions.

After February 2013 and the advent of the phased-EVLA, either an ANTAB style file was provided to the observer or the calibration information is in the data file. This calibration information is generated using the EVLA switched power (SY table, see §4.3.15), the known gain curve (GC table), and the first CL table using the task VLAMP. Sometimes there are problems with the values in the SY, GC, and/or CL tables and the observer might want to recreate the amplitude calibration of the phased-EVLA after editing one or more of them. To do this the phased-EVLA only data (not the VLBI data) must be loaded into  with BDF2AIPS, see §4.1.1. Then the SY and/or GC tables can be edited. For instructions on how to edit or smooth the SY table see §4.3.15. Then run VLAMP, which will create an output text file that can be loaded into the VLBI data with ANTAB. Typical inputs for VLAMP would be:

The RUN file and procedure named DOVLAMP can be used to run the full process, reading the data into  with BDF2AIPS, smoothing and applying the SY tables with TYSMO and TYAPL, correcting standard calibration source amplitudes with special usage of CALIB and CLCAL, and finally running VLAMP to produce the needed file for ANTAB.

9.5.3 Data editing

Before proceeding to calibrate, you should first flag any obviously bad data. In summary, initial editing is based on the flagging information supplied by the on-line antenna monitor systems, which is applied using UVFLG. This information may be extracted to a .FLAG file as outlined in the previous section or subsequent editing based on the station report logs, or elevation limits can also be performed using UVFLG. Finally, graphical editing tasks such as EDITR and IBLED may be used for interactive baseline-based editing. In both single- and multi-source data formats, flagging information is stored in the FG table instead of being used to discard data directly. One may also undo a flag operation using OPCODEs ’UFLG’, ’REAS’, and ’WILD’ in UVFLG. Note that this operation works only when the operation being undone is in the current flag table. (Note that many tasks delete fully flagged data when copying a data set.)

To edit uv data by reading a text file listing periods of known errors (e.g., the .FLAG text file created by VLOG) run UVFLG with the following inputs:

This will generate a FG table with entries read from $MYVLB:BC25CAL.FLAG.

To edit uv data based on elevation limits, UVFLG can be used with input parameters:

This will generate FG table flagging time ranges that fall between the specified elevation limits.

Note that in both of these examples, the flagging information is incorporated into a FG table instead of “irrevocably” deleting your data. In order to apply these flags, you must set FLAGVER to the appropriate FG table version.

Another editing task which may be useful is QUACK, which can edit the selected portion of the scan at its beginning and/or end. This might be needed because (at non-VLBA antennas) the telescopes were still slewing or system temperature measurements were being made. The first 20 seconds or so of a scan, for baselines to the VLA, are often unusable while the VLA correlator phases up at the new source position. The first second or so after a scan may also need to be flagged (OPCODE ’TAIL’) since some antennas may not leave the previous source promptly, leaving bad data marked good. QUACK can be used to flag specific antennas for these and other reasons.

Tasks EDITA and EDITR can be used to inspect and edit the data interactively. IBLED is no longer of much use except for its ability to display the degree of coherence in the data. These tasks are similar in many respects to TVFLG, but are more suited to interferometers with small numbers of baselines. It is also possible to use TVFLG to perform your editing although the TV display is somewhat confusing on sparse arrays of data, especially if there is significant source structure. Read §4.3.5 through §4.3.11 and §5.5 for more details on the editing of data. Also VPLOT may be used to edit data which deviates excessively from the mean amplitude over a specified averaging interval; see HELP VPLOT  C R for details. Task WIPER is a dangerous but powerful editing tool as well.

The task DEFLG generates a flag table to delete data having coherence less than a user-specified limit. It must be run only on sources that should be strongly coherent although it may be used to flag data from other sources in between the strong-source scans. The task SNFLG is also used to flag data whenever the phase jumps in an SN or CL table are excessive on a baseline-by-baseline basis.

The VLBA correlator may produce a lot of samples which it knows to be bad and which are flagged by the transferred flag table. For this reason alone, or if you also flag a noticeable fraction of the data set, you may wish to run UVCOP to discard the flagged data to conserve disk space and processing time.

9.5.4 Amplitude and instrumental delay calibration

We now advocate a new amplitude calibration strategy base on VLBA Scientific memo #37 (Walker 2015). This strategy interleaves classic a priori calibration with instrumental delay and bandpass calibration to improve the amplitude calibration of data from the new Roach Digital Backend (RDBE) on the VLBA (see the VLBA Observations Status Summary for a description of the RDBE and VLBA Scientific Memo #37 for a discussion of amplitude problems with the RDBE). With data from before the RDBE you can use either the old or new strategy.

9.5.4.1 Parallactic angle correction

The RCP and LCP feeds on each antenna will rotate in position angle with respect to the source during the course of the observation for alt-az antennas (which probably constitute a majority of the antennas in your observation). Since this rotation is a simple geometric effect, it can be corrected by adjusting the phases without looking at the data. This correction must be performed before any phase calibration which actually examines the data is executed. This correction is important for polarization and phase-referencing observations, so it should probably be applied to all cases.. Task CLCOR is used for this purpose; see §9.5.4.1.

There is a procedure which assists you in running CLCOR to correct phases for parallactic angle:

VLBAPANG should be run before applying any other phase corrections.

9.5.4.2 Digital sampler bias corrections for VLBA correlator data

The voltage threshold levels in the digital samplers at the antennas may differ from their optimum theoretical values and this may vary from antenna to antenna and from polarization to polarization. This sampler bias, which is usually significant only in two-bit quantization, introduces an antenna/polarization-based amplitude offset. In full polarization observations this appears as an amplitude offset between RR and LL. The cross-correlation amplitudes may be corrected if the auto-correlation spectra have been measured. See VLBA Scientific Memo No. 9 (1995, “Effect of digitizers errors on the cross and auto correlation response of an FX correlator”, by L. Kogan). Task ACCOR can be used to remove these digital sampler biases from VLBA correlator data, if FITLD was run with DIGICOR = 0, 1, or 2. ACCOR corrects these offsets by examining the autocorrelation spectra. You can check your autocorrelation data with task ACIMG which makes an image cube with axes of frequency, time, and antenna number. Use the image display options describe in Chapter 6 to inspect the image. There may be data that needs flagging. Since ACCOR computes the necessary correction by examining the total-power spectra, it must be run immediately after FITLD in the sense that nothing else should be run that actually modifies the total-power spectra directly. Although ACCOR ignores any SN or CL tables that are present, it is essential to correct for the sampler biases before performing any a posteriori calibration, e.g., fringe-fitting or self-calibration. If the ACCOR gain factors deviate from unity, there may be overall scaling or b-factor errors. For 2-bit quantization, however, the amplitude offsets for the VLBA correlator are typically of order 5 - 10%, but values as high as 20% have been observed.

For one-bit quantization, no significant sampler bias correction is expected. Nonetheless, it is recommended that ACCOR be run on one-bit data as a consistency check. VLBACCOR is a procedure which runs ACCOR, smooths the results with SNSMO, and applies the solutions using CLCAL. Typical inputs would be:

VLBACCOR will normally be run after “fixing” the the data with VLBAFIX (if needed). Use this procedure only on data from the VLBA correlator.

If you do not want to use VLBACCOR, typical inputs to ACCOR for this correction would be:

The correction factors were expected to be fairly stable over time, but they have been found to vary over times less than an hour. With a solution interval of a few minutes, such as the two minutes indicated here, it is well to examine the solution (SN) table generated by ACCOR using SNPLT for any bad points or inconsistent values. One approach is to inspect the SN table and then run SNSMO with clipping to get rid of discrepant points. Alternatively, the interactive table editing task SNEDT can be used.

9.5.4.3 Instrumental phase corrections

If you run POSSM on a short (≈ 1 minute) section of data on a strong calibrator using the inputs described in §9.4.2 and set DOCAL = -1  C R, you will see that each individual IF channel has its own independent phase offset and its own phase gradient against frequency. These phase offsets and instrumental “single-band delays” are caused by passage of the signal through the electronics of the VLBA baseband converters (or MkIII/MkIV video converter units). The VLBA system can inject narrow band signals (“phase-cals”) into the data recorded at each antenna from which the IF channel phase offsets, and the instrumental single-band delays, can be determined.

For those antennas for which phase-cal measurements are available, task PCCOR can be used to incorporate the phase-cals into an SN table. (see §9.5.4.3). If you have other antennas for which phase-cal measurements are not available, you can run CLCAL using the OPCODE=’CALP’ option to incorporate the incomplete SN table information loaded by PCCOR without throwing away data for the antennas with missing phase-cal information.

If external phase-calibration data (pulse cals) are not available then directly fringe-fitting a short scan of data to measure the phase and single-band delay offsets may be applicable under limited circumstances (see §9.5.4.4). Even when phase-calibration information is available, performing a manual phase-cal can be a good idea to confirm that the IF-dependent delays and phases have been successfully estimated and removed. One good check is to inspect the data using POSSM at times different from the time used to determine the manual phase calibration. Note that time-dependent delays may still be seen because of low elevation and ionospheric effects.

As of 1 April 1999, the VLBA correlator is capable of transferring phase-cal information directly to a PC table for some antennas. For other antennas, the phase-cal information may be read into the PC table using the task PCLOD. Type EXPLAIN PCLOD for further information. If you are unsure whether your VLBI data has phase-cal information, use IMHEAD to list the extension tables and look for a PC extension.

Phase-calibration data in a PC table can be used by task PCCOR to generate an SN table which corrects for the single-band instrumental phase and delay offsets (note that PCCOR uses two phase-cals in each IF). A short calibrator scan must be specified to be used by PCCOR to resolve any 2π phase ambiguities in the phase-calibration data. The specified time range must include at least one PC table entry for each antenna appearing in the PC table. Having resolved the 2π phase ambiguities, PCCOR uses the whole PC table to calculate entries in an SN table for all times (not just the TIMERANG used to resolve the ambiguities). The procedure VLBAPCOR runs PCCOR, FRING (if needed because of missing pulse-cals for some antennas), and CLCAL for you. Inputs are:

This should be done after the sampler correction (VLBACCOR) and before the complex bandpass, The CALP option requires the data in the specified TIMERANG to include strong fringes for those antennas lacking phase-cal data.

Running the tasks individually, typical inputs to PCCOR are:

The resulting solution table is applied using CLCAL. If you are missing phase-cal information for some antennas, you must use the ’CALP’ mode of CLCAL; this mode allows calibration information for some antennas to be incorporated into the CL table while passing other antennas through without modification. Examine the corrected data using POSSM to determine if the instrumental phase and delay offsets between the IF channels have been removed correctly.

To check that the applied phase-cals are valid, run POSSM on a short section of data containing a strong source setting DOCAL = 1, GAINUSE to the version number of the CL table containing the phase-cal calibration, and APARM(9) = 1 to place all IFs on the same plot. The phase as a function of frequency on each baseline should be smoothly varying, with no sharp jumps between different IF channels. There may be an overall linear gradient with frequency due to residual delay errors. Unless these conditions hold for all baselines, you should proceed to §9.5.4.4.

The DiFX correlator has the capability of writing a large number (1 per MHz typically) of pulse cals into each IF.  can handle this with new tasks PCFLG (flags PC data with a SPFLG-like TV display), PCEDT (flags PC data with a BPEDT-like TV graphical display), PCPLT (plots PC table data all antennas with one time per page or all times with one antenna per page), PCASS (finds amplitude bandpass), and PCFIT (fits delays and phases to PC data, writing an SN table of the changes in these as a function of time). PCLOD can now read PCAL files written by DiFX. Other tasks include PCAVG to average pulse-cal tables in time and PCRMS to edit pulse-cal tables automatically from internal statistics. POSSM can also now plot PC table data (APARM(8) = 9. This package of routines remains experimental, but it has been shown do good things with the data. It is now documented in  Memo 123.¹ New tasks in 31DEC21 include VLBSY to read VLBA total power files, VLBCD to read noise tube values from a VLBA cal file, PCABL to copy cable cal values from the old PC table to ones created by PCLOD, and PCDIV to scale pulse-cal amplitudes by the system temperatures.

9.5.4.4 “Manual” instrumental phase corrections

If your file does not have phase-cal information, or if these phase-cals do not successfully remove frequency phase offsets, you can use observations of a bright calibrator source and the task FRING to correct for these effects. If you attempted phase-cal calibration, it is best to avoid possible confusion by first deleting any partial or erroneous phase-cal information that already exists. Using CLCOR:

If you have large known delay offsets you may also wish to run CLCOR using OPCODE=’SBDL’ to shift the center of the fringe search window.

If you have a known clock offset, as may be common for an SVLBI data set, you may wish to run CLCOR with OPCODE = ’CLOC’ and CLCORPRM = 0, offset, 0, 0, 0, 0, 1, 0.

Now you can determine the manual phase correction for one or two strong calibrator scans for which all the antennas are present using VLBAMPCL. Task BSCAN may be used to select the scan(s) to be used at this stage. VLBAMPCL runs FRING and CLCAL once or twice, depending on whether one or two scans are used. Choose a scan with strong fringes to all antennas; if none exists, find a second scan that has strong fringes to the antennas missing from the first. Note that if you use 2 scans the REFANT must have good fringes in both scans. Typical inputs are:

If you wish to run FRING separately, you can determine the phase offsets/single band delays by running FRING on a short section of calibrator data where all or most of the antennas are present. Suitable inputs for FRING for this purpose are shown below; for more details of some of the FRING input parameters see §9.5.7.7. Note that it is simplest to choose a single short section of data within a single scan using TIMERANG and to set SOLINT equal to the scan length so that a single solution is achieved. The interval chosen must be less than than an atmospheric coherence time, but long enough that high signal-to-noise is achieved. At centimeter wavelengths with Jansky-level calibrators, solution intervals of a few minutes will work well. For example:

If there was no single scan where all the antennas were present, you can run FRING again for another scan setting REFANT to be one of the antennas found in the first run (the same REFANT would be best) and ANTENNAS to this antenna plus all of the antennas not found in the first run. FRING will generate a new SN table each time; be careful to keep track of which SN tables you wish to use.

The phase solutions in the SN table(s) are interpolated onto a calibration or CL table using task CLCAL as described in §9.5.1.1. To apply the calibrator solutions to the other sources in the data file, set CALSOUR to the calibrator source used when running FRING (in the example above, CALSOUR  ’0954+658’) and set SOURCES = ’ ’ for all sources. Also, set REFANT to whatever was used when running FRING. If multiple runs of FRING were required, you can set SNVER=0 so that all SN tables are combined before being applied ; if you do this, you must first be careful to delete all SN tables except those generated by FRING. Or you can run CLCAL multiple times specifying each SN table in turn, with the specific antenna numbers, while keeping the same CL table versions.

To check the output CL table, run POSSM for the scan used for the FRING solution with DOCAL = 1 and GAINUSE = 3 (i.e., the output CL table from the CLCAL above). The phase should be flat as a function of frequency on all baselines, although it may not be centered on zero. Run POSSM on another scan containing a strong calibrator to check that the assumption of constant IF phase offset holds.

9.5.4.5 Bandpass calibration

Full bandpass response calibration should be performed for all observations. It is suggested that integrating over a variable bandpass function is one of the most significant sources of non-closing errors in continuum VLBI data. By calibrating the bandpass before averaging over frequency, these effects can be avoided. In VLBA test observations, a dynamic range of 28,000:1 was achieved on the source DA193 (Briggs et al. 1994, VLBA Memo No 697A, “High Dynamic Range Imaging with the VLBA”) after applying bandpass calibration.

Bandpass calibration is carried out using the task BPASS using either the auto- or cross-correlation data. The output is a BP or bandpass table. For this amplitude calibration scheme the cross-correlation (complex) bandpass must be used. The derived bandpass solutions can be plotted using POSSM by setting APARM(8)=2. The effect of applying these bandpass solutions to your data can also be viewed using POSSM by setting DOBAND=1 and BPVER. An example of the inputs to produce bandpass spectra from the cross-correlation data would be:

Be careful with the adverb SMOOTH. If you smooth, or do not smooth, the data while finding a bandpass solution, then you must apply the same SMOOTH adverb values whenever you apply that bandpass solution to the data. The only exception is that you may smooth the data after applying the bandpass solution with SMOOTH(1) values 5 through 8 when you did no smoothing in BPASS.

This will produce a BP table containing the antenna-based bandpass functions to be applied to the data. You should check your results very carefully. The BP tables can be plotted with POSSM or printed with PRTAB. Note that this task merely creates a BP table. To use this BP table, set BPVER and DOBAND as described in §4.3.8 when running any later  tasks.

Note, if your bandpass calibrator is not stable or strong enough during the observation (your bandpass calibrator data should have a better S/N than the data you’re trying to correct with the bandpass), you could consider using the phase reference source (if there is one) and use SOLINT = -1 (include all scans to make one bandpass solution). If the bandpass calibrator is strong enough, but the average phase varies through the scan, then divide each record by “channel 0” by setting BPASSPRM(5) = -1 to adjust phase only. You should select a range of channels that have similar phases to be averaged as channel 0 using adverb ICHANSEL

The normalization of the bandpass correction can be checked by running ACSCL after BPASS. This task is a version of ACCOR which applies the current calibration tables to the data before forcing the autocorrelations to unity. Be sure to set DOBAND to apply the bandpass by your preferred method. ACSCL will write an SN table with amplitude corrections which should be very close to one. Apply that table with CLCAL. However if you run VLBAAMP, ACSCL and CLCAL will be run for you, see §9.5.4.6.

The interactive data editing task BPEDT lets one flag visibility data based on bad bandpass solutions. It can edit the BP table instead and even interpolate over the flagged values. It is a graphical editor much like EDITR and EDITA except that it displays bandpass solutions as a function of spectral channel. It is a quick way to check your bandpass table and, if necessary, to flag bad channels in your calibration source. If you do generate new data flags, you should run BPASS over again to generate a corrected BP table. Set BPASSPRM(9) = 1 to interpolate over any fully flagged channels. For really large BP tables, you may wish to use BPFLG instead after determining clip levels with BPEDT although BPEDT has been made much faster for such BP tables.

9.5.4.6 Continuum amplitude calibration

After bandpass calibration is determined, the auto-correlations can be slightly offset from unity. To correct this offset ACSCL can be run, applying all the previous amplitude and bandpass calibration. Described below is a procedure that is part of VLBAUTIL called VLBAAMP that runs ACSCL as well as the final amplitude calibration steps.

The TY table can be examined using SNPLT with OPTYPE=’TSYS’ or ’TANT’ or LISTR with OPTYPE=’GAIN’; the GC table is examined with PRTAB. SNEDT may also be used to inspect the TY table and even used to delete or smooth some of the measurements. SNRMS may be used to examine statistics of the TY table. TYSMO can be used to delete discrepant system temperatures and replace the bad and/or good values with time-smoothed values. Note, however, that anomalously high system temperatures may indicate possible bad data (e.g., due to weather) rather than bad measurements of the system temperature. On occasion, RFI in some IFs can render the values for those IFs in the TY table unusable. Task TYCOP will copy TY data between IFs and polarizations in a variety of ways in an attempt to replace the bad data with something reasonable even if not exactly correct for that antenna and IF. Note that flagging bad uv data will not change the appearance of the TY table since no flags are applied in plotting this table. EDITA may also be used to examine the TY data interactively and, if bad system temperatures are found, to flag the associated uv data. (This task does flag displayed T_sys when the data are flagged.) Tasks UVCOP and SPLAT will apply a flag table not only to the uv data, but also to the TY and SN tables. APCAL can then be used to derive an amplitude calibration (SN) table.

Atmospheric opacity becomes significant at high frequencies (≥ 15 GHz). APCAL can fit for an opacity correction, if needed, using weather information and system temperature. The weather information can be taken from the WX table by setting INVERS (after October 7, 2003) or loaded from disk by setting CALIN. In order to have APCAL fit for opacity set OPCODE to ’GRID’, ’OPAC’ or ’LESQ’ and DOFIT to 1 (both of these are necessary for an opacity fit). OPCODE ’GRID’ and ’OPAC’ need an initial guess for the receiver temperature (TRECVR and zenith opacity (TAU0). APCAL will estimate the initial guesses from the data if TRECVR and/or TAU0 are 0. If OPCODE is set to ’GRID’, ’OPAC’ or ’LESQ’ and DOFIT ≤ 0 then the opacity correction is applied using the provided TRECVR. This is a good option if you have a reliable measurement of the receiver temperature. In 31DEC20, use OPCODE ’PLOT’ to plot the data against the solution you wish to apply to make sure it is reasonable. The fits are fairly robust, but the plots that APCAL makes should be examined. Note: a large number of bad Tsys values can make the fits unreliable. APCAL will warn you if fits appear to be incorrect. The procedure VLBAAMP runs ACSCL, smooths the results with SNSMO, runs APCAL, and applies the solutions using CLCAL.:

VLBAAMP will normally be run after correcting the bandpass and loading any gain curves or system temperature data for non-VLBA antennas using ANTAB.

If you have not used VLBAAMP and do not want to correct for atmospheric opacity, typical inputs to APCAL are:

If atmospheric opacity correction is desired, set the following inputs as well as the above:

The resulting solution (SN) table can be smoothed and clipped using SNSMO and applied using CLCAL as described in §9.5.1.1). Substantial smoothing of the TY table (task TYSMO), especially for VLBA-only observations, is not generally recommended since variations of the system temperature often reflect a real response to the weather. Note, however, that TYSMO is very useful for removing bad system temperatures before they are applied. Smoothing can be useful for data from the phased-VLA, when the amplitude calibration information reflects low signal-to-noise. For non-VLBA antennas, it is important to check with SNEDT that the TY information is associated with the correct source and SNEDT can be used to delete occasional bad system temperature measurements before they are applied to the data. When opacities are fit, APCAL generates plots of the receiver temperature versus zenith angle and the opacity versus time. APCAL will warn you about bad fits, but the plots should be checked for problems with the data or the fits.

On occasion, it has been noted that plots of system temperature show unreasonable variation between IFs. This suggests that the T_cal values may have systematic errors as a function of frequency. APCAL has an option to bring the T_sys values into better agreement with either their average or with a user-chosen IF, thought to be probably accurate. APARM(6) > 0 selects this function while APARM(7) may be used to specify a specific IF to calibrate the others. Note that a single value is used for each antenna/IF over all times.

The DiFX correlator in now capable of correlating multiple phase-stopping positions within a single antenna beam (pointing position). There is task called CLVLB designed to apply corrections to a CL table (writing a new one) for the offset of phase-stopping and pointing position. The task has internal tables for the beam shape and squint of the VLBA antennas and can take user input for these parameters for other antennas. This is a new task and should be used with caution — early results with it were less than satisfying — although the corrections it applies are certainly in the right direction.

9.5.5 Spectral-line Doppler correction

Normally, when observing, you will have kept the frequency constant throughout the run for ease of observing. Therefore, although your data will have the same frequency, the center velocity of your spectrum will change with time and the spectral-line signals will wander backwards and forwards through the spectrum. To ensure that the velocity is constant throughout the data you should run SETJY and then CVEL. The VLBA correlator compensates for the revolution of the antennas relative to the center of the Earth. In this case, the only movement which CVEL should compensate is the rotation of the antennas together with the Earth around the Sun. This movement should be the same for all antennas and gives a smaller effect than the rotation relative to the center of the Earth. Nonetheless, CVEL is required for the VLBA correlator at least to be able to compare observations made at different times. Without CVEL such comparisons will show the velocity shift of the Earth’s orbit about the Sun.

SETJY will insert the velocity information required in the SU table:

Then run CVEL:

After applying the BP table, CVEL will not copy it to the output file to protect you from applying it twice. Although CVEL allows you to select which sources are to be shifted, the BP table, if DOBAND is set appropriately, will be applied to all sources found.

9.5.6 Spectral-line amplitude calibration

The calibration strategy suggested in  for spectral-line VLBI data utilizes the total-power spectra method described in Lecture 12 of VLBI, Techniques and Applications, eds. Felli and Spencer, published by Kluwer Academic Publisher, 1988. The continuum method using T_sys values (see §9.5.4.6) can also be used. The first step is to generate a so-called template spectrum. This is a high quality spectrum from the most sensitive antenna in the array that has been corrected for the effects of the bandpass filter. For example:

You should then run ACFIT to do a least-squares fit of the template total-power spectrum to the total-power spectra of all other antennas and to write the resulting time-dependent amplitude gain correction factors into an SN table.

ACFIT will generate an SN table, which has to be applied to the CL table. If needed, run SNSMO to smooth the amplitude correction factors determined by ACFIT before running CLCAL. A 30-minute smoothing interval for SNSMO (set using CPARM 0.5,0) should be sufficient.

9.5.7 Phase calibration

After carrying out amplitude calibration, the remaining calibration steps involve correcting the phase between the different integration periods. This will allow averaging of the data over both frequency and time without loss of coherence. The phase offsets may be corrected using a priori ‘phase-cal’ measurements if available and/or by directly fitting to the data.

After removing instrumental phase offsets from each IF, the data will in general still contain frequency and time dependent phase variations. The purpose of “fringe-fitting” is to determine these phase errors and then remove them from the data.

The primary  task for fringe-fitting is FRING. This task estimates time variable station-based delays (phase derivatives wrt frequency) and rates (phase derivatives wrt time) using a self-calibration-like algorithm. Once these delays and rates are determined, the task CLCAL is used to produce the phase correction that should be applied to each integration period and spectral channel to correct for delay and rate effects. This use of FRING and CLCAL is discussed in detail in §9.5.7.7. Two alternatives to FRING are the tasks BLING and BLAPP and the experimental version of FRING named KRING. BLING and BLAPP are discussed briefly in §9.5.7.8. KRING provides a superset of the functionality in FRING with numerous enhancements such as: the use of extremely small scratch files, a parsimonious use of memory, possible solution extrapolation both backwards and forwards in time and a rationalized definition of SNR. For more information about KRING, type HELP KRING from within AIPS. When fringe-fitting to many small scans, KRING can be substantially slower than FRING. When fringe-fitting data sets with large numbers of spectral channels and long solution intervals, KRING can be substantially faster than FRING.

The process of fringe-fitting, and then interpolating the solutions using CLCAL, can be a very time consuming process. For this reason it is probably wise to run through the fringe-fitting procedure described in §9.5.7.7 on a small amount of data first (say 30 minutes’ worth) before attempting to process the whole data set. This is especially true if this is your first time processing multi-IF, multi-channel VLBI data. It is probably simplest to use UVCOP to copy out a short time range of data from your main file and to work only on this initially. Doing so also avoids the possible confusion of having many versions of extension tables. Note that, if your spectral channels are narrow, the use of the CHINC parameter can speed up FRING.

9.5.7.1 Special considerations: SVLBI

The existing fringe-fitting tasks within  have been enhanced to improve their performance when dealing with SVLBI data. In addition, several new tasks have been written to address problems specific to SVLBI fringe-fitting. The primary SVLBI fringe-fitting tasks in  are BLING and FRING and are discussed in §9.5.7.7–§9.5.7.9. The tasks COHER and FRPLT, described in §9.4.6 and §9.4.7, may be of particular interest when reducing SVLBI data.

There may be delay discontinuities in the recorded data for a variety of reasons such as tracking station handoffs, clock glitches, etc. The recommended method for dealing with such discontinuities is to force scan boundaries at such events. The task INDXR can be used to generate a new NX table with scan boundaries at desired locations using an input text file. In practice, either INDXR will do the right thing by design, or your P.I. information letter should have contained instructions on how to construct a text file in the proper format for INDXR.

A new task, OBEDT, is available which allows selection of specific orbital parameter ranges, through the creation of an output flag (FG) table. This can be used to constrain initial fringe searching.

SVLBI data often contain tracking passes three or four hours in length, for which fringes are mostly (or wholly) not apparent. Typically, the space-ground baselines will have the highest correlation coefficients near perigee, when those baselines are shortest. However, the imperfectly known orbit will cause high fringe rates and short coherence times. Near apogee, the coherence time is longer, and may be limited by the atmosphere above the ground telescopes, but the correlated flux also is much lower. Sometimes, it may be possible to find fringes for only 15 or 20 minutes, but that’s better than nothing.

If no fringes are seen anywhere during a tracking pass, a useful trick is to set APARM(7) = 0.01 to let through the highest SNR for each solution interval, and set DPARM(5) = 1 to turn off the least squares solution. Then run FRING for an entire tracking pass, and use SNPLT with OPTYP = ’DELA’ and OPTYP = ’RATE’ to look for repeating values (usually easier to see in delay than in rate). Also, make plots with OPTYP = ’SNR’ to see if slightly higher SNRs are found at a time when there seems to be some consistency in delay values. It may be necessary to try this process with several values of SOLINT in order to arrive at a guess for the fringe location. Use VPLOT to plot uv distance versus time for the space-ground baselines, then search using the TIMERANG and REFANT that provide the shortest projected baselines. Another possibility is to set REFANT = ANTNUM(’MK’), since the atmospheric coherence time should be longest at Mauna Kea, and increase SOLINT to a fairly large value in hopes something will show up. (Note, however, that a large SOLINT with a wide-open search window in delay and rate may require a large-memory computer or great inefficiency due to page faulting.)

If fringes are found somewhere, use CLCOR to center the fringes (see §9.5.4.4), then run FRING again with small delay and rate windows (e.g., DPARM(2) = 200 to 400 and DPARM(3) = 40 to 80 at 1.6 GHz, or ~ 200 at 5 GHz). Set low SNR thresholds with APARM(7) = 3.5, and turn the least-squares solutions back on with DPARM(5)=0. Usually, it’s best to turn on the exhaustive antenna search with APARM(9) = 1, since only a few space-ground baselines may show fringes. It can be helpful to use SEARCH to order the search from shortest to longest space-ground baselines.

It generally doesn’t work well to use one tracking station to predict the results of another, because clock initialization offsets are typically relatively large and have unrelated errors, and fringe-rate errors also may be unrelated.

9.5.7.2 Special considerations: spectral-line

Delay and fringe-rate calibration of spectral-line VLBI data must be handled differently. The residual delay cannot be estimated from the source itself because, due to the very nature of the source, the delay is a rapidly varying function of frequency. The continuum calibrator, observed for this purpose, is first used to determine residual delays and fringe-rates which are then applied to the spectral-line source. A suitable channel or range of spectral-line channels “on-source” is then used to determine the residual fringe-rates. It is very important to note that in some situations, the residual fringe-rates determined from the calibrator may not be applicable to the line source because the fringe-rate residuals towards the two sources may be quite distinct. In such situations, the residual fringe-rates determined from the continuum source should not be applied to the line source. See §9.5.7.10 for more details.

9.5.7.3 Special considerations: polarization

In addition to phase calibrating the LL and RR data separately, for polarization data the R-L phase and delay offsets must also be determined. This is outlined in §9.5.7.11. After fringe-fitting, all parallel-hand fringe solutions need to be re-referenced to the same antenna.

9.5.7.4 Special considerations: phase-referencing

The process of phase referencing for VLBI data is conceptually very simple. Unfortunately, the technical difficulties in conducting a successful phase-referencing observation are primarily in setting up the schedule. So by the time you get around to reading this section, your project is either guaranteed to succeed or guaranteed to fail, depending upon how well your observations were designed. See the lecture by A. Beasley and J. Conway in “VLBI and the VLBA”, 1995, (ASP), and VLBA Scientific Memo No. 24 (2000, by J. Wrobel, C. Walker, J. Benson, and A. Beasley) for more details on how to design phase-referencing observations.

In “phase referencing,” the phase calibration for your target source is derived from a calibrator, or phase referencing, source observed for that purpose. First, you apply any available a priori phase-cals to both the target and cal source. Next, you fringe-fit, self-calibrate, and/or hybrid-map the cal source — whatever is needed to complete the phase calibration for that source. Finally, you apply the phase corrections so determined to the target source. In practice this is done by specifying the target as well as the cal source in the SOURCES adverb list whenever an SN table containing phase corrections for the cal source is applied using CLCAL. See §9.5.1.2 for a specific example of how to run CLCAL to transfer phase corrections determined using a cal source to a target source.

Certain “instrumental” corrections such as those for unmodeled zenith delay may have subtle but significant effects on phase referencing. See §9.5.7.5 for a discussion.

You can perform a “hybrid” form of phase referencing in some instances. It may be that your target source is too weak for initial fringe-fitting. In this case, you can fringe-fit the cal source data to determine the phase corrections to be applied to the target source data. Then, after averaging in frequency, the target source data may have adequate signal-to-noise to allow rate corrections to be determined for it by fringe-fitting. In this mode, you may or may not wish to zero the rate corrections determined on the cal source. If the cal source is “far” from the target source, the rate corrections may do more harm than good for the target source and should be zero’ed. On the other hand, your target source may be entirely too weak to fringe-fit on at all. In this case, you must rely on determining the phase corrections solely using your cal source.

If you are attempting phase-referenced astrometry, you may have a target source that is brighter than your cal source(s). In this case, you simply fringe-fit on the target source and transfer the solutions to the cal source(s). Be careful, if your goal is to extract absolute positional information, not to independently self-calibrate the cal and target sources.

9.5.7.5 Correcting for atmospheric delays

VLBI correlators remove some estimate of the non-dispersive atmospheric delay at the elevation and frequency of the observation from the data. These a priori models are usually fairly good, but careful observations can improve upon them.  offers a number of options to deal with this problem. DELZN uses multi-band delay (see §9.5.7.6) in an SN table to fit for the zenith tropospheric delay and the clocks as a function of time. It works best if the observations include data on a variety of calibrators well distributed around the sky. DELZN applies a correction to a CL table or writes a file to disk with zenith atmospheric delays and possibly clock offsets that can be used by CLCOR, OPCODE=’ATMO’ to correct a CL table. The second option is for the situation where the data used by DELZN is in a different file from the data that needs to be corrected.

To correct an attached CL table, the typical inputs for DELZN would be:

This will generate a CL table and several PL files that show the data and the fitted model. You are strongly encouraged to examine these.

To create an output file rather than correct a CL table use the same inputs as above except:

Again, you are advised to examine the resulting plot files which show both the data and the fitted model. The output file can be read in with CLCOR (OPCODE=’ATMO’; INFILE=’MYVLB:BZ199.DELZN’) to correct a CL table.

There is another task designed to deal with the effects of zenith delay in phase-referencing observations. Phases for the target source in phase referencing are corrected by the phases at the calibrator which usually is at a different elevation. Task DFCOR is a special version of CLCOR which applies the ’ATMO’ operation to correct the CL table for the difference in elevation between the target source and adjacent calibration sources without applying the full atmospheric delay correction.

If the SN table contains dispersions as well as multi-band delays, DELZN may also be run to fit a zenith angle model to the dispersions (OPTYPE = ’DISP’). Like the ’MDEL’ operation, the zenith and time function found by DELZN can be applied to a CL table or written to a text file for later application by CLCOR with OPCODE = ’DISP’.

9.5.7.6 Finding multi-band delays

For astrometric and geodetic experiments and to use DELZN (see §9.5.7.5), the multi-band delay must be determined. The multi-band delay is the delay caused by errors in the station positions and the difference between the correlator model and reality for clocks and the troposphere. The multi-band delay is best determined over IFs which are widely spaced in the frequency band. After the instrumental phases have been corrected (§9.5.4.3–§9.5.4.4), the multi-band delay can be determined in one of two ways. For strong sources do a global fringe fit as described in §9.5.7.7 setting APARM(5)=0, and then run MBDLY on the resulting SN table.

Typical inputs for MBDLY would be:

This will produce a new SN table with the MBDELAY columns filled in.

For weak sources, use APARM= 2 0 0 1 1 in FRING. This averages each IF and fits a multi-band delay across them. Note that this does not solve for single-band delays, unlike the previous method. This will also produce a new SN table with the MBDELAY columns filled in.

Note that MBDLY can fit the single-band delays for a multi-band delay plus a dispersion (phase varies with wavelength rather than frequency) with OPTYPE = ’DISP’. FRING can do a very similar fit, after finding the single-band delays, if you set APARM(10) = 1. Wide bandwidth observations at low frequencies may benefit from this.

9.5.7.7 Antenna-based fringe-fitting

To see an example of the residual phase errors in your data, use POSSM to view the phase on a short calibrator scan (at some time other than that used to solve for the phase-offsets in §9.5.4.4). In general, there will be a gradient in phase between the IFs (due to the “multi-band” delay) and also small gradients within each IF (caused by small residual “single-band” delays). These time-variable phase gradients are mainly due to inaccuracies in the geometrical time delays that the correlator assumed for the time of arrival of the wavefront at each antenna. These inaccuracies arise from propagation effects through the troposphere and ionosphere, inaccurate Earth geometry, etc. and give phase errors which are proportional to frequency. Such phase errors prevent integration of the data over frequency (or cause a loss of coherence if you do). Similarly, VPLOT will show, on any single IF and spectral channel, phases which change rapidly with time. Again, these are due to unavoidable inaccuracies in the correlator model; such large “phase rates” prevent integration over time. Both of these points are illustrated in Figure 9.1.

You will want to run FRING to correct for these residual rates. You can help these tasks by making sure that the reference pixel in frequency is in the center of the band (Nchan/2+1 is best). Use task CENTR or any of the tasks with the FQCENTER adverb to fix data sets for which this is not true.

FRING and KRING use a global fringe-fitting algorithm described by Schwab and Cotton, 1983, Astron. J., 88, 688. Unfortunately, these are large and complicated tasks. The procedure VLBAFRNG is available to simplify access to FRING and VLBAKRNG access to KRING. Versions of these procedures for phase-referencing experiments are called VLBAFRGP and VLBAKRGP. For all these procedures, if the SOURCES adverb is set, then CLCAL is run once to apply the results of FRING (or KRING) for each source in SOURCES. For the phase-referencing procedures (VLBAFRGP and VLBAKRGP), any source that is in the SOURCES list that is not in the CALSOUR list will be phase referenced to the first source in the CALSOUR list. Note that, if every source in the SOURCES list occurs in the CALSOUR list, VLBAFRNG and VLBAKRNG will run identically to VLBAFRGP and VLBAKRGP, respectively. If the SOURCES list is empty, VLBAFRNG and VLBAKRNG will run CLCAL once over all sources, while VLBAFRGP and VLBAKRGP will run CLCAL once referencing all the sources to the first source in CALSOUR. These procedures will produce new (highest numbered) SN and CL tables.

Sample inputs for procedure VLBAKRNG are:

Procedure VLBAKRGP sets the same adverbs as VLBAKRNG except

VLBAFRNG and VLBAFRGP are identical except there is no OPCODE (it is equivalent to DPARM(8)) and DPARM(4) and DPARM(7) in FRING are the same as CPARM(1) and CPARM(8) in KRING, respectively. Also note the different use of SEARCH in FRING and KRING.

Suitable inputs for the fringe-fitting task FRING are, in detail: