Introduction

Fringe stopping prior to cross-correlation allows longer visibility integration times without introducing de-correlation, which in turn allows the size of the correlator output products to be substantially reduced.  The new correlator for the MWA, "MWAX", was designed from the outset to include pre-correlation fringe stopping.  However, it was not supported in the first operational release and users were required to perform phase corrections post-correlation within Birli.  Fringe stopping is currently available for all observations by request and its use is encouraged. Feedback is especially welcome at this stage in the commissioning process.

Background

The fringe stopping process involves applying virtual signal delays to compensate for varying path delays between tiles during an observation. The major advantage of this approach to geometric corrections is that it is performed prior to cross-correlation, integration and averaging. Prior to fringe stopping, many of the observation modes available to MWA users involving long integration times or broad frequency averaging would have resulted in unacceptable geometric errors, as downstream processing tools require relatively fine-grained data to perform corrections effectively - especially at longer baselines, where the rate of fringe rotation is higher. Short integration times and fine frequency resolution both have a large impact on the size of the visibility data produced in a given observation, without necessarily improving the scientific usefulness of the data - typically, most of this resolution is averaged away in the final data products. Fringe stopping allows users to make use of long integration times and broad frequency averaging, without sacrificing the quality of the data. Smaller data volumes are easier to manage, store and process, and longer observations that may have produced prohibitively large volumes of data in the past may be feasible with fringe stopping.

We encourage all MWA users to test this new capability for any observations in the first observing semester of 2023. Starting in the second observing semester of 2023, fringe stopping will be the default mode for all MWA observations. Observations without fringe stopping will continue to be supported on an opt-out basis.

Usage

Fringe stopping is available on an opt-in basis for any observation during the first observing semester of 2023. Users may request fringe stopping at the time of scheduling, or at any time prior to the start of the observation. There is no change to how observation data is delivered and no software changes are required to use it, apart from that you should not tell Birli to apply geometric corrections to a fringe-stopping observation. By default, Birli will detect whether an observation was made with fringe-stopping, and geometric corrections will not be run unless explicitly specified at the command line or selected in ASVO.

Fringe stopping is available for voltage-capture (VCS) observations. In this case, the voltage data files will have whole-sample delays applied to each RF channel and fractional delay metadata will be populated in the file headers. Voltage data files are also upgraded to allow for commensal research users accessing VCS data to selectively enable or disable fringe stopping after-the-fact, irrespective of the configuration requested for the original observation. Over the coming days, this page will be updated with a full schema for the upgraded voltage data files and software for applying/removing fringe stopping corrections.

Implementation

A technical summary of the MWAX fringe stopping implementation will be published soon as part of the forthcoming MWAX paper, a detailed description of the design and validation will be published shortly thereafter.

A (very) brief overview: when a fringe-stopping observation is scheduled, the scheduling software generates an additional data table in the metafits file sent to the correlator, containing periodically updated Az/Al values for each tile, reflecting small changes in pointing direction required during the observation period. These updated pointing directions are calculated at 4-second intervals using the astropy library and picked up where the real-time part of the fringe stopping system begins, during UDP voltage capture. For each Az/Al entry, and for each tile, a path length difference is calculated relative to the array centre, and converted to a time delay. The time delay is interpolated between the 4s reference points at a 5ms granularity, corresponding to the FFT block size in the correlator. The delay is split into a whole-sample and fractional-sample component, the latter of which corresponds to a delay shorter than the sampling period of the coarse-channelised voltage data. The whole-sample component is used to shift actual voltage samples in the data forward or back by an integer number of samples. The fractional component is stored in a metadata table in the voltage capture file, and applied by the correlator after the F-stage, in the frequency domain, as a phase rotation.

The fundamental unit of time for fringe-stopping is the sample, which at a sample rate of 1.28MHz, corresponds to about 0.7 microseconds. Delays are typically in the range of +/- 20 whole samples. The fractional component is represented in the metadata table with 32-bit floats, which we found to be sufficient. Corrections are performed by applying a phasor parameterised by a slope and offset derived with integer millisample precision from the 32-bit floating point input. The precision and range used in these calculations has been selected to accommodate corrections in a wide range of circumstances, with most observations making use of only a small fraction of the available resolution.

Diagram: Comparison of geometric corrections process for using Birli and fringe-stopping

Validation

Fringe stopping has been validated against the output of Birli and shown to produce identical results in tests involving hand-crafted data, designed to test particular aspects of its behaviour in isolation. Results on real-world data, from running fringe stopping on live observations simultaneously with Birli in a split-mode configuration, have shown fringe-stopping to perform comparably to Birli on short integration times and fine frequency averaging, and with superior results on longer integration times and coarser channel averaging.

The validation process will be described in detail in a future publication.

Diagram: Time-phase plots generated from fringe stopping (left) and Birli (right) data for 20 baselines, observing PicA with an 8s integration time.

Diagram: Time-phase plots for fringe stopping (blue) vs Birli (gold) for five baselines (rows) at increasing integration times (columns, 0.5s, 1s, 2s, 4s, 8s).

Since Birli is widely used and its results accepted, it has served as the gold standard for correctness in our fringe stopping implementation. However, since real data tends to be quite noisy in practice, we do not expect Birli and fringe stopping to produce truly identical output files. To eliminate the guesswork involved in comparing two slightly different patterns of noise, we worked on developing some simpler comparisons. 

For these hand-crafted tests, we modified voltage capture files to replace the sample data for all the RF sources, with identical copies of the data for one of them, so that the contents would be perfectly correlated, with zero phase difference at every instant and every frequency. Then, for each test case, we would create two copies. One had no fringe stopping metadata, while the other would have the same fringe stopping delays applied to the cloned voltage sources as would have been applied to the real data. Both copies were correlated offline and processed with Birli. 

When Birli sees the copy with no fringe stopping, it applies its own corrections, unaware that it is applying corrections to already perfectly in phase data. Thus, when we plot phase vs time and frequency on the output, what we see is a neat visual representation of the corrections that would have been made for the original observation. 

Likewise, for the copy with fringe stopping applied, it is being applied to data which is already in phase. Birli sees that fringe stopping is active and suppresses its usual corrections, and now we can make plots to directly compare what Birli would do, versus what fringe stopping would do. They should be the same, and indeed they are. 

Diagram: Frequency-phase plots for fringe stopping (left) vs Birli (right), using hand-crafted data to examine phase slopes at an instant in time.