Introduction

Fringe stopping is a technique for implementing geometric corrections for an observation in the correlator, prior to cross-correlation allows longer visibility integration times without introducing de-correlation, integration and averaging. It is an alternative to performing geometric corrections later in the data processing pipeline, with tools such as Birli or cotter, as has been necessary for MWA observations in the past. In most cases fringe stopping is expected to be superior to traditional post-correlation geometric corrections, and it will be the default mode for MWA observations starting in the second half of 2023. It is currently available for evaluation by request, and feedback 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.

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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.

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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 - targeting a precision on the order of microsample resolution. 16-bit signed integers targeting millisample resolution were found to be insufficiently precise for fringe stopping. 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

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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.

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