2.1. Improved RACS astrometry and catalogue matching

Our offset correction that had been used in Scott et al. (Reference Scott2023) was based upon the Rapid ASKAP Continuum Survey (RACS; McConnell et al. Reference McConnell2020; Hale et al. Reference Hale2021), in particular the RACS-Low1 release (i.e. the catalogue derived from the lowest frequency ASKAP band). However, the RACS catalogue had not been astrometry corrected to account for any residual time- or direction-dependent errors between field calibrator and target scans. No phase calibration had been applied to RACS prior to imaging and self-calibration steps, and hence such errors could propagate through to the final RACS catalogue positions. As a result, systematic astrometric offsets were present in the RACS source positions and therefore also affected the field-offset calculations performed by CELEBI.

An astrometry correction for the RACS-Low1 (and later RACS-Low3, a third iteration of the full Southern sky) catalogue was derived through crossmatching with the Wide-field Infrared Survey Explorer (WISE; Wright et al. Reference Wright2010) catalogue. Full details of the methodology are described by Jaini et al. (Reference Jaini, Deller, Wang, Lenc and Glowacki2025), who demonstrated that systematic positional offsets of approximately 0.26^″–1.24^″ could be present across the sky prior to correction. After applying the corrections, the typical positional accuracy of individual RACS sources improved to ∼0.3^″ over most of the sky. These corrections can be significant enough to shift the localisation ellipse of distant (z > 0.5) FRBs onto a separate host galaxy candidate, or for nearby FRBs, shift the position on or off spiral arms. We note that localisations since and including those published by Shannon et al. (Reference Shannon2025) include astrometry corrections for RACS.

More recently, the same correction methodology has been extended to the higher-frequency RACS catalogues (RACS-Mid1 and RACS-High1; Jaini et al. Reference Jaini, Deller, Wang, Lenc, Duschene and Glowacki2026). These catalogues provide more appropriate reference frames for FRBs detected in the corresponding ASKAP observing bands, since they minimise systematic differences arising from frequency-dependent source structure or resolution. The CELEBI pipeline has therefore been updated to support these catalogues alongside RACS-Low. Currently, when RACS does not have sufficient coverage for field corrections (such as at low Galactic latitudes, or at high (>30°) declinations where the performance of ASKAP is significantly reduced), the user is able to use a different radio continuum source catalogue (e.g. VLASS; Lacy et al. Reference Lacy2020) as an option when running the pipeline – a feature not previously implemented in CELEBI.

To support these improvements, we redesigned the catalogue lookup module used to identify reference sources in each FRB field. Earlier versions queried only the RACS-Low catalogue through the CASDA TAP service. The updated system now supports RACS-Low1, RACS-Mid1, RACS-High1, and VLASS catalogues. While RACS-Low1 continues to use unified catalogues even after astrometry corrections, the mid- and high-frequency epochs are currently distributed as beam-level source lists. CELEBI therefore dynamically assembles the relevant catalogues by combining sources from the beams closest to the target position, allowing the pipeline to construct an appropriate set of reference sources for each field while maintaining consistency with the survey data products.

We also introduced an improved source-selection procedure designed to identify reliable, compact reference sources for astrometric offset calculations. Rather than simply discarding sources with multiple matches, the new method applies three filtering criteria simultaneously: (i) a compactness requirement based on the ratio of integrated to peak flux density (<1.5), (ii) a S/N threshold of >6, and (iii) an adaptive minimum separation from neighbouring sources that increases for brighter sources. This approach reduces the impact of bright or blended sources that could bias the offset estimate while still retaining faint but isolated sources suitable for astrometric measurements. For RACS-Low, where both source and Gaussian component catalogues are available, a more sophisticated heuristic is applied to remove strongly resolved sources by identifying Gaussian components with integrated flux exceeding 20% of the source flux and angular separations greater than 10 arcsec, ensuring that only compact sources are retained.

Finally, the updated CELEBI implementation includes explicit systematic uncertainty parameters for both right ascension and declination. These parameters allow the pipeline to incorporate known catalogue-level astrometric uncertainties when computing localisation offsets, providing a more realistic estimate of the final positional error budget. Together, these changes allow CELEBI to take full advantage of the improved RACS astrometry while providing a more flexible and reliable framework for identifying reference sources across multiple radio surveys.

2.2. Localisation uncertainty along the beam axes

Position errors for localised FRBs are most commonly expressed in terms of uncertainties along the axes of the celestial coordinate system in use – typically right ascension and declination – which is equivalent to an uncertainty ellipse aligned with those axes. However, since the ‘natural’ basis for the interferometric localisation errors is the coordinate system defined by the major and minor axes of the synthesised beam, the ‘true’ position uncertainty ellipse is aligned with the beam axes rather than the celestial coordinate system. We hence estimate the absolute astrometric offsets and position uncertainties along the axes of the beam.

For each reference field source, astrometric offsets projected along the beam major and minor axes are calculated using a coordinate transform given by

(1) \begin{align}\begin{split} \Delta X_{\textrm {major}} &= \Delta \textrm {RA} \: \sin {(\textrm {BPA})} + \Delta \textrm {DEC} \: \cos {(\textrm {BPA})} \\[3pt] \Delta X_{\textrm {minor}} &= \Delta \textrm {RA} \: \cos {(\textrm {BPA})} - \Delta \textrm {DEC} \: \sin {(\textrm {BPA})}, \end{split} \end{align}

where ΔRA, ΔDEC are the differences between the source coordinates in the field image and those in the reference catalogue, and BPA is the position angle (in degrees, although radians can also be used here and Equations (2)–(4)) of the (elliptical) synthesised beam associated with the field image. Uncertainties on the astrometric offset for each reference source are then estimated using the relation

(2) \begin{align}\begin{split} \delta X_{\textrm {major}}^2 &= [d_{\textrm {maj}} \: \cos {(\Delta \textrm {PA})}]^2 + [d_{\textrm {min}} \: \sin {(\Delta \textrm {PA})}]^2 + \sigma _{\textrm {ref}}^2 \\[3pt] \delta X_{\textrm {minor}}^2 &= [d_{\textrm {maj}} \: \sin {(\Delta \textrm {PA})}]^2 + [d_{\textrm {min}} \: \cos {(\Delta \textrm {PA})}]^2 + \sigma _{\textrm {ref}}^2, \end{split} \end{align}

where d _maj, d _min represent the major and minor axes of the best-fit elliptical Gaussian describing the source and ΔPA is the difference between its position angle and BPA; $\sigma$ _ref represents the position uncertainty of the source in the reference catalogue (RACS) which is treated as a circularly symmetric quantity and is significantly sub-dominant to the field image uncertainties, as RACS is considerably deeper than the 12 s field image. The inverse-variance-weighted mean of the offsets, calculated separately along the major and minor axes, represents the best estimate of the net astrometric offset and the associated uncertainties.

The error on the FRB position has three independent contributors – the statistical error on the FRB position in the image, statistical error on the offset from the reference catalogue, and systematic error associated with the reference catalogue astrometry – which are added in quadrature separately along the beam major and minor axes. The statistical error on FRB position in the image, along the synthesised beam axes, are given by

(3) \begin{align}\begin{split} \delta Stat_{\textrm {major}}^2 &= \frac {\sqrt {[D_{\textrm {maj}} \: \cos {(\delta \textrm {PA})}]^2 + [D_{\textrm {min}} \: \sin {(\delta \textrm {PA})}]^2}}{2.35 \: \textrm {SNR}} \\[4pt] \delta Stat_{\textrm {minor}}^2 &= \frac {\sqrt {[D_{\textrm {maj}} \: \sin {(\delta \textrm {PA})}]^2 + [D_{\textrm {min}} \: \cos {(\delta \textrm {PA})}]^2}}{2.35 \: \textrm {SNR}}, \end{split} \end{align}

where D _maj, D _min represent the major and minor axes of the best-fit elliptical Gaussian describing the FRB in the image and $\delta$ PA is the difference between its position angle and BPA; SNR is the image-plane S/N ratio of the FRB. The statistical errors on the offset from the reference catalogue, along the major and minor axes of the synthesised beam, are given by

\begin{align*}1.79 \: (\delta X_{\textrm {major}}, \delta X_{\textrm {minor}}) \end{align*}

where the systematic scale factor of 1.79 was empirically estimated by Day et al. (Reference Day, Deller, James, Lenc, Shivani Bhandari and Bannister2021) and incorporates systematic contributions to positional offsets for each source such as the mismatch in angular resolution and frequency between the two images being compared. The systematic astrometric uncertainty of the reference catalogue is adopted from Jaini et al. (Reference Jaini, Deller, Wang, Lenc and Glowacki2025), corresponding to 0.30^″ over most of the RACS sky and degrading slightly to 0.40^″ within the Galactic plane.

The uncertainties on the localisation of a given FRB are quoted in terms of an error ellipse with axes ( $\delta$ _major, $\delta$ _minor), oriented along the synthesised beam in the corresponding field image with a position angle defined by BPA. The projected uncertainties along RA and DEC axes are given by

(4) \begin{align}\begin{split} \delta \textrm {RA} &= \sqrt {[\delta _{\textrm {major}} \sin {(\textrm {BPA})}]^2 + [\delta _{\textrm {minor}} \cos {(\textrm {BPA})}]^2} \\[4pt] \delta \textrm {DEC} &= \sqrt {[\delta _{\textrm {major}} \cos {(\textrm {BPA})}]^2 + [\delta _{\textrm {minor}} \sin {(\textrm {BPA})}]^2}. \end{split} \end{align}

However, as shown in Figure 1, the error ellipse implied by these projected errors (from left to right 0.7^″ x 0.76^″, 1.045^″ x 1.369^″, and 0.75^″ x 0.65^″; represented by dashed cyan ellipses) does not represent the true error ellipse (ellipse major axis, minor axis, and PA of [0.89^″, 0.53^″, −39.6°], [1.513^″, 0.823^″, −30.45°], [0.81^″, 0.56^″, −57.04°]; denoted in solid yellow). For any analysis sensitive to the FRB position accuracy (e.g. the location relative to spiral sub-structure; Gordon et al. Reference Gordon2025), using the true error ellipse is recommended.Footnote ^a

Figure 1.

The projected error (dashed cyan) and true error (solid yellow) ellipses for three CRAFT FRBs. The background optical imaging span 20 arcsec across and were originally presented in Shannon et al. (Reference Shannon2025).

2.3. Matched filter imaging

The previous iteration of CELEBI (Scott et al. Reference Scott2023) made use of large boxcar filters centred on the rough position of the FRB in the voltage buffer to image and produce a localisation with (sub)arcsecond precision. The boxcar would typically be of O(10) ms wide, which for most CRAFT FRBs, having widths of O(100) $\unicode{x03BC}$ s to O(1) ms (Scott et al. Reference Scott2025), would introduce a large amount of noise. Additionally, when adding the visibilities together, further noise would be introduced if the FRB possessed complex morphology in time and/or frequency (e.g. scintillation or band-limited emission). This becomes an issue when faint FRBs are detected, especially with the recent CRACO upgrade which has increased the rate of faint FRB detections. Hence, a new process called matched filter imaging has been implemented into CELEBI.

The new imaging pipeline makes use of the HTR Stokes I power dynamic spectra to build an optimal time and frequency matched filter, which when applied will minimise the noise added when imaging the FRB. To build the matched filter, the FRB needs to be located in the HTR data, enabling the S/N ratio as a function of time and frequency to be measured. Producing this HTR data via beamforming requires an initial estimate of the FRB location, which can be provided from the CRACO detection if available, or from a default boxcar filter imaging otherwise. Once generated, the Stokes I dynamic spectrum is averaged in frequency. Then, the on-pulse window of the burst is estimated using a cutoff threshold which is some fraction of the peak sample. Time-dependent and frequency-dependent weights are then derived using the on-pulse window:

(5) \begin{align}\begin{split} & w_{t} = \frac {1}{n}\sum _{f}^{n} I(t,f)\\[2pt] & w_{f} = \frac {1}{m}\sum _{t}^{m} I(t,f) \end{split} \end{align}

where w _t and w _f are time-dependent and frequency-dependent weights, respectively, and m and n are the number of time bins and frequency channels, respectively. We note that time-dependent weights are always used for matched filter imaging, while frequency weighting is turned off by default. Frequency weighting is only switched on when the final FRB position is S/N ratio limited and the FRB has significant frequency structure (generally, is only bright in a small fraction of the bandwidth), such that applying frequency weighting leads to an appreciable gain in detection significance. Furthermore, since the HTR data products are normalised to unity variance in every frequency channel, the frequency weighting does not take into account the instrumental bandpass response. An off-pulse window is also taken for RFI subtraction. The off-pulse window is split into two equal parts and placed on either side of the on-pulse window. A guard window is then placed between the on-pulse and off-pulse windows to avoid potential signal leakage into the RFI bins. The typical width of the off-pulse window is of O(10) ms whilst the width of the guard window is of O(1) ms. This is to ensure most of the RFI being subtracted is constant in time (Scott et al. Reference Scott2023). The RFI bins, guard bins, and on-pulse bins are combined into a single matched filter binconfig file and passed to DiFX to correlate and obtain visibility data.

The time and frequency weights are applied to the visibilities separately, with the time weighting applied immediately as the data were time-scrunched (averaged to a single time bin), while the frequency weights are applied during the gridding stage when imaging the FRB. Since the FRB model at the imaging stage uses a frequency independent model for the FRB emission, the frequency weights derived in Equation (5) are used to calculate both an amplitude correction to the visibilities (required to make the FRB appear spectrally flat; Rau & Cornwell Reference Rau and Cornwell2011), and a modification to the corresponding visibility weights. Essentially, this upweights frequency ranges where the FRB is bright (even after the visibility amplitude has been scaled down) and downweights frequency ranges where it is faint (even after the visibility amplitude is scaled up). The time scrunching process generates a single visibility per frequency (and per baseline, but the baseline index is not shown here as all baselines receive the same scaling) as follows:

(6) \begin{align}V(\,f) = \frac {1/w_{f}\sum ^{n}(V(t,f) - V(\,f)_{\mathrm{RFI}})w_{d}(t,f)w_{t}}{\sum ^{n}w_{d}(t,f)w_{t}}. \end{align}

Here, w _d (t, f) are the initial visibility weights (which are derived during correlation and account for the number of data samples that have contributed to each visibility, as a function of time and frequency) and V(f)_RFI are the time averaged RFI visibilities. 1/w _f is the appropriate amplitude scaling factor to scale the FRB amplitude to a constant value as a function of frequency. The frequency-dependent visibility weights that are saved to the visibility dataset and applied in the imaging process are re-calculated to account for this frequency-dependent amplitude correction as well as the summation over time:

(7) \begin{align}w_{d}(\,f) = w_{f}^2\sum ^{n}w_{d}(t,f)w_{t}, \end{align}

which allows for the bright regions of FRB emission (where the noise is now low, due to the amplitude scaling) to be upweighted during imaging, and the faint regions (where the noise is high) to be downweighted. The result of this process is a single match-filtered visibility time bin that is then processed in the same manner described in Section 3.7.2 of Scott et al. (Reference Scott2023) to image the FRB and produce a more refined localisation. In turn, the refined localisation can then be used to ensure an optimally coherent addition of the signals from every antenna – maximising the S/N ratio – in new HTR outputs.

2.3.1. A matched filter example case: FRB 20251019A

The use of the matched filter imaging approach is particularly important for lower S/N FRBs only detected by the CRACO system, as well as high-DM FRBs which are likely at high redshift. Distant FRBs require as high a precision as possible for accurate host association. An example of such an object is FRB 20251019A, which was detected with ASKAP/CRACO at a DM of 1 277 pc cm⁻³ and localised to sub-arcsecond precision with a reported S/N of 9.9. The localisation uncertainty ellipse originally from CELEBI using 5 ms of data had a major/minor axis size of 0.727/0.575^″, while implementation of matched filter imaging (time weighting only; the FRB did not have significant frequency structure) reduced this to 0.594/0.507^″ centred on 10:08:27.454, +16:23:56.358 (reduction of 18%/12% respectively, and an unchanged PA of −38.06°).

To identify the host galaxy of FRB 20251019A, we performed a PATH (Aggarwal et al. Reference Aggarwal, Budavári, Deller, Eftekhari, James, Prochaska and Tendulkar2021) analysis on archival r-band imaging from the DESI Legacy Survey DR9 (Dey et al. Reference Dey2019). However, this analysis revealed no viable host candidates and a large posterior that the host was unseen (P(U|x) = 0.99). We obtained Keck/MOSFIRE (McLean et al. Reference McLean, McLean, Ramsay and Takami2012) imaging in J-band for a total exposure time of 1 375 s on 2026 January 15 UT (PI Davies, Program 2025B_W007). The data were reduced using the POTPyRI Footnote ^b imaging reduction pipeline. However, no host galaxy was identified at or around the FRB position to a 3 $\sigma$ limiting magnitude of J _AB > 24.4. We show the image and 1 $\sigma$ FRB localisation in Figure 2. Despite the elusiveness of the host of FRB 20251019A to date, matched filter imaging enables the best possible localisation for such FRBs and hence maximises the ability to localise currently rare high-redshift (z > 1) FRB candidates. This object, along with other currently hostless FRBs such as FRB 20210912A (Marnoch et al. Reference Marnoch2023), highlights the need for deep optical imaging for the higher redshift FRB population.

Figure 2.

The J-band Keck/MOSFIRE image of the field of FRB 20251019A. The 1 $\sigma$ FRB localisation is overlaid as a yellow ellipse; no source is visible at the FRB position to a 3 $\sigma$ limiting magnitude of J _AB $\gt$ 24.4.

2.4. Near-field imaging

Both the correlation and beamforming functions of the CELEBI pipeline require a model of the geometric propagation delay of the signal wavefront between the ASKAP antennas. By default, this is provided by the CALC package used by the DiFX software correlator, which is a highly accurate and well-tested suite of code used for astrophysical sources. However, this assumes an astrophysical source located far from the array. For near-field objects where the curvature of the signal wavefront is not negligible, a different approach to the generation of the geometric delay model is required.

For near-field objects, the DiFX delay model generation step can instead make use of the NASA SPICE toolkitFootnote ^c to produce the geometric delays used in correlation and beamforming. While DiFX has provided this functionality for some time (e.g. McCallum et al. Reference McCallum, Schunck, McCallum and McCarthy2025), the CELEBI interface prior to CRACO detections did not initially expose the ability to demand a near-field geometric model, nor the ability to provide the Two-Line Ephemeris (TLE) information needed to generate such a model. In this updated version of CELEBI, target sources can be specified as near-field objects and ephemeris information provided in order to accurately image and/or beamform such objects. For example, when CRAFT detected a nanosecond-duration radio pulse from the Relay-2 satellite (James et al. Reference James2025), this functionality was used to search for fainter pulses from the satellite during the recorded voltage download by accurately tracking the satellite for the duration of the 12 s data window.

2.5. Single polarisation processing

Data were downloaded from the ASKAP antennas by coarse channel, antenna, and polarisation in a sequential fashion, with polarisation being the slowest variable to be downloaded. Accordingly, if a voltage download is interrupted (for instance, due to a scan change which is more likely for an FRB detected during shorter calibration observations), it is possible that only data from a single polarisation (possibly for a subset of antennas) is obtained. In the initial version of CELEBI, such single polarisation datasets could only be processed for calibration and imaging through manual intervention (by trimming the calibrator voltage dataset to exactly match the obtained FRB dataset, in terms of antennas and polarisations available), while beamforming assumed dual polarisation and was completely intractable.

In this version of CELEBI, we have generalised the application of calibration solutions in both imaging and beamforming (as well as the production of Stokes data products in the beamforming pipeline) to gracefully handle single polarisation datasets, producing a pseudo-Stokes I image and pseudo-Stokes I time series (without any of the polarisation calibration described in Section 3) from the available polarisation data. This has allowed the recovery of CELEBI positions and time-series data for 3 FRBs, with two newer FRBs since Scott et al. (Reference Scott2025) to be presented in a forthcoming ASKAP data release (Dial et al. in preparation).

2.6. Deeper field imaging for offset corrections

There are two main components of fast radio transient localisation: the position of the imaged transient itself, and the offset correction based on the positions of detected field sources in the remaining voltage dump data, currently limited to 12 s of integration time. One avenue to further improve the accuracy of FRB localisation is to use a deeper image of the field from the ASKAP observation the radio transient was detected within. For instance, typical RACS pointings are ∼15 min each in length and would yield many more field sources than what is visible in 12 s (a S/N boost of 8.66). This would be particularly beneficial for any transient sources detected in a relatively ‘quiet’ part of the radio sky containing a low number of sufficiently bright radio continuum sources that can be imaged in 12 s than the number that would appear in a 15 min ASKAP integration.

However, the ASKAP hardware data and the dumped voltage-based data, as well as calibration and flagging applied to each, may not be equivalent. Hence a further correction may need to be applied when using a deeper field image from the hardware data. A separate approach that could be taken is to measure the offset of field source positions between the deeper field image and the 12 s derived field image and in turn use the deeper image for a better measurement of the offset field correction, benefiting from the larger number of sources. A proper investigation and implementation of this approach is planned in a later update to CELEBI.

3.1. Polarimetric effects

The polarisation of our radio signal is characterised by the Stokes parameters, which are expressed in terms of horizontal and vertical components E _x and E _y :

(8) \begin{align} \begin{split} I &= {|E_{x}|^{2} + |E_{y}|^{2}}\\[3pt] Q &= {|E_{y}|^{2} - |E_{x}|^{2}}\\[3pt] U &= 2{\mathrm{Re}}(E_{x}^{*}E_{y})\\[3pt] V &= 2{\mathrm{Im}}(E_{x}^{*}E_{y}), \end{split} \end{align}

where Stokes Q is negated to comply with the pulsar Stokes conventions in Van Straten et al. (Reference Van Straten, Manchester, Johnston and Reynolds2010), as the ASKAP Phased Array Feed (PAF) uses a left-handed basis (Day et al. Reference Day2020). We use a polarisation calibrator with known rest-frame polarisation fractions:

(9) \begin{align} {\bf S_{0}} = \begin{matrix} \left[\begin{matrix} Q_{{\mathrm o}}(\,f) \\[1pt] 0 \\[1pt] V_{{\mathrm o}}(\,f) \end{matrix}\right ].\end{matrix} \end{align}

The signal undergoes Faraday rotation along the LOS. This is modelled as a simple rotation $\chi$ about the (Q, U) plane (i.e. a rotation of the linear polarisation vector):

(10) \begin{align}{\bf A} = \left[\begin{matrix}{\mathrm {cos}}(2\chi ) &\quad {\mathrm{sin}}(2\chi ) &\quad 0 \\[1pt] -{\mathrm{ sin}}(2\chi ) &\quad {\mathrm {cos}}(2\chi ) &\quad 0 \\[1pt] 0 &\quad 0 &\quad 1\end{matrix}\right]. \end{align}

Once a signal reaches the ASKAP antenna, the PAF will have an angular offset $\psi$ from the sky coordinate system (Day et al. Reference Day2020), which may also be expressed as a rotation in the (Q, U) plane:

(11) \begin{align}{\bf A} = \left[\begin{matrix} {\mathrm{cos}}(2\chi + 2\psi ) &\quad {\mathrm{sin}}(2\chi + 2\psi ) &\quad 0 \\[1pt] -{\mathrm{sin}}(2\chi + 2\psi ) &\quad {\mathrm{cos}}(2\chi + 2\psi ) &\quad 0 \\[1pt] 0 &\quad 0 &\quad 1 \end{matrix} \right]. \end{align}

The electronics that separately digitise the E _x and E _y components are imperfect; as such, they introduce a slight time and phase delay ( $\tau$ , $\phi$ ) during recombination, known as polarisation leakage. This results in conversion between linear and circular polarisation, expressed as a rotation in the (U, V) plane by an angle $\theta$ :

(12) \begin{align}\begin{split} \theta & = 2\pi f\tau + \phi \\[1pt] {\bf B} & = \left[\begin{matrix} 1 &\quad 0 &\quad 0 \\[1pt] 0 & \quad {\mathrm{cos}}(\theta ) &\quad {\mathrm{sin}}(\theta ) \\[1pt] 0 &\quad -{\mathrm{sin}}(\theta ) &\quad {\mathrm{cos}}(\theta ) \end{matrix}\right]. \end{split} \end{align}

Finally, the PAF edge and corner beams are known to exhibit significant leakage, causing coupling between the E _x and E _y components. Consequently, the natural wave modes received by the antenna become slightly elliptical. The most severe cases show ∼5–10% coupling. Heiles et al. (Reference Heiles2001) formalises these instrumentation effects more generally. Here, we make the assumption that the phase angle of coupling between E _x and E _y (i.e. $\chi$ in Heiles et al. Reference Heiles2001) is 90°, which reduces the coupling to a simple rotation in the (Q, V) plane by the ellipticity angle $\alpha$ :

(13) \begin{align}{\bf C} = \left[\begin{matrix} {\mathrm{cos}}(2\alpha ) &\quad 0 &\quad {\mathrm{sin}}(2\alpha ) \\[1pt] 0 &\quad 1 &\quad 0 \\[1pt] -{\mathrm{sin}}(2\alpha ) &\quad 0 &\quad {\mathrm{cos}}(2\alpha ) \end{matrix}\right]. \end{align}

Accounting for these effects, the measured Stokes parameters ${\bf S_{m}}$ become:

(14) \begin{align}{\bf S_{m}} = {\bf B} {\bf C} {\bf A} {\bf S_{0}}. \end{align}

By default, we do not fit $\alpha$ because not all FRBs are detected in corner or edge beams where this effect is significant. Hence, this parameter is a toggle in the CELEBI implementation.

3.2. Deriving calibration solutions

Using Equation (14) we sample the full parameter space (RM, $\psi$ , $\tau$ , $\phi$ , $\alpha$ , L _offset, V _offset) to derive polarisation calibration solutions. The two additional free parameters L _offset and V _offset are sampled to account for small zeroth-order deviations in the total linear and circular polarisation fractions over different observing bands:

(15) \begin{align}\begin{split} & L_{m} \rightarrow L_{m} + L_{{\mathrm {offset}}} \\[3pt] & V_{m} \rightarrow V_{m} + V_{{\mathrm {offset}}}. \end{split} \end{align}

Using Bayesian inference with the dynesty (Dynamic nested sampling) Sampler (Speagle Reference Speagle2020) through the Bilby (Ashton et al. Reference Ashton2019) package, we maximise the log likelihood $\mathcal{L}$ _T :

(16) \begin{align}\begin{split} & \mathcal{L}_{S} = -\frac {1}{2}\sum ^{N}_{i = 1}\Bigg ({\ln}{(2\pi \sigma ^{2}_{S}) + \bigg (\frac {S-S_{m}}{\sigma _{S}}\bigg )^{2} \Bigg )} \\[3pt] & \mathcal{L}_{T} = \mathcal{L}_{Q} + \mathcal{L}_{U} + \mathcal{L}_{V}, \end{split} \end{align}

where $\sigma$ _S is the error measurement in the measured Stokes parameter S, S _m is the modelled Stokes parameters using Equation (14) and N is the number of frequency channels.

3.3. Applying calibration solutions

Applying the solutions for the polarimetric effects detailed above is trivial in (Q, U, V) space. However, these solutions must be applied when constructing the Stokes dynamic spectra, which is performed multiple times for some FRBs – such as when channelising at different frequency resolutions, applying baseline corrections or performing coherent de-dispersion. A more robust, albeit more complex, method is to apply these solutions directly to the E _x and E _y voltages after coherent beamforming.

First, the polarisation leakage corrections $\tau$ and $\phi$ are applied to the E _x voltages in the frequency domain:

(17) \begin{align} {E_{x}}(t) = \mathcal{F}^{-1}\big[{E_{x}}(\,f){e}^{-i(2\pi f\tau + \phi)}\big], \end{align}

where $\mathcal{F}$ ⁻¹ is the inverse Fourier transform. Next, the coupling between E _x and E _y (if applicable) is corrected by rotating E _x and E _y by the ellipticity angle $\alpha$ in the time domain:

(18) \begin{align}\left[\begin{matrix} {E_{x}} \\[1pt] {E_{y}} \end{matrix} \right] = \left[\begin{matrix} {\mathrm{cos}}(\alpha ) & -i{\mathrm{sin}}(\alpha ) \\[1pt] -i{\mathrm{sin}}(\alpha ) & {\mathrm{cos}}(\alpha ) \end{matrix} \right] \left[\begin{matrix} {E_{x}} \\[1pt] {E_{y}} \end{matrix} \right]. \end{align}

Finally, the PAF angular misalignment is corrected by rotating E _x and E _y by $\psi$ :

(19) \begin{align}\left[\begin{matrix} {E_{x}} \\[1pt] {E_{y}} \end{matrix}\right] = \left[\begin{matrix}{\mathrm{cos}}(\psi ) & -{\mathrm{sin}}(\psi ) \\[1pt] {\mathrm{sin}}(\psi ) & {\mathrm{cos}}(\psi ) \end{matrix}\right] \left[\begin{matrix} {E_{x}} \\[1pt] {E_{y}} \end{matrix}\right]. \end{align}

Note that this is an inverse rotation, since we are correcting the physical rotational offset.

3.4. Polarisation calibrators

Two sources are used for polarisation calibration: J0835-4510 and J1644-4559 (hereafter Vela and 1644, respectively). Similarly to Scott et al. (Reference Scott2023), we model 1644 using a second order polynomial:

(20) \begin{align}\begin{split} & L_{{\mathrm o}} = -1.31\times 10^{-8}f^{2} + 1.76\times 10^{-4}f - 3.18\times 10^{-2} \\[3pt] & V_{{\mathrm o}} = 3.19\times 10^{-8}f^{2} -1.82\times 10^{-6}f -1.2\times 10^{-2}, \end{split} \end{align}

where f is the channel frequency in MHz. While 1644 is well behaved across the mid–high ASKAP bands (f > 1 GHz), two properties hinder calibration at lower frequencies. (1) The long rotation period and limited ASKAP voltage buffer allow only a small number of pulses to be folded, limiting the S/N. (2) A large scattering timescale causes the pulse profile to broaden significantly, depolarising the burst. Thus, caution is required when using 1644 at low frequencies.

Figure 3.

Summary of Vela observations from 26 December 2020 to 4 December 2024 zoomed using the UWL receiver. The spectra are zoomed in on the ASKAP observing band. Top Panel: The linear polarisation fraction from the UWL observations are shown in black; the different shades of black are used to differentiate the 15 observations. The red dashed line shows the best fit for L/I using a third order polynomial. Bottom Panel: The circular polarisation fraction. The red dashed line shows the best fit for V/I using a hyperbolic tangent function.

For Vela, we provide two models. The first assumes a flat spectrum where L _o = 0.95 and V _o = − 0.05 (Scott et al. Reference Scott2023), as used in recent CRAFT publications (Bera et al. Reference Bera2024; Dial et al. Reference Dial2025; Scott et al. Reference Scott2025). The second model uses Ultra wideband Low (UWL) observations of Vela with the Murriyang (Parkes) telescope (Hobbs et al. Reference Hobbs2020). UWL observations of Vela from December 2020 to December 2024 were reduced using PSRCHIVE (Hotan et al. Reference Hotan, van Straten and Manchester2004), including RFI flagging, bandpass calibration and de-dispersion. The Stokes dynamic spectra were then dumped from the archive files and an additional incoherent de-dispersion search was used to maximise the S/N in the Stokes I time-series profile. We integrated ∼160 $\unicode{x03BC}$ s of data around the pulse peak to obtain 1 MHz channelised Stokes I, Q, U, and V spectra. Figure 3 shows the results for the linear and circular polarisation fractions over the 15 UWL observations. Across the ASKAP observing band (700–1 800 MHz), L/I and V/I are relatively stable over the 4 year dataset. Based on these results, we developed empirical models of L/I and V/I using a third order polynomial and a hyperbolic tangent function respectively:

(21) \begin{align}\begin{split} & L_{{\mathrm o}} = 5.62\times 10^{-12}f^{3} -4.51\times 10^{-8}f^{2}+8.24\times 10^{-5}f \\[3pt] & \qquad +9.18\times 10^{-1} \\[3pt] & V_{{\mathrm o}} = 2.91\times 10^{-2}\tanh (\!-8.62\times 10^{-3}(\,f + 5.16\times 10^{-2})) \\[3pt] & \qquad + 1.23\times 10^{3}, \end{split} \end{align}

where tanh is defined in Abramowitz & Stegun (Reference Abramowitz and Stegun1972). The difference between the two models is only a few percent; by default, we use the flat-spectrum model.

We use FRB 20230708A to demonstrate the new pipeline using Vela as the calibrator with a flat-spectrum model; the details of the detection and offline processing are already published (Dial et al. Reference Dial2025). Before deriving the calibration solutions we ensure the Stokes dynamic spectra of the calibrator are properly de-dispersed. The calibrator voltages are already de-dispersed coherently at this stage (Scott et al. Reference Scott2023); for Vela a nominal DM of 67.97 pc cm⁻³ is used. However, the DM of Vela is known to change by ∼0.2 pc cm⁻³ yr⁻¹. Therefore, we perform a second stage of incoherent dedispersion using ΔDM. A number of trial ΔDMs are performed, and the highest S/N is used as input to derive the calibration solutions.

Figure 4.

Top panel: The measures Stokes Q, U, and V spectra of Vela and the derived polarisation calibration models shown in the bold dashed lines. Middle panel: The Vela Stokes spectra after the polarisation corrections have been applied and the intrinsic Vela model shown in the bold dashed lines. Bottom panel: Best fit for the polarisation leakage.

Figure 4. Long description

The image contains three line graphs. Panel A: The top panel shows the measures of Stokes Q, U, and V spectra of Vela and the derived polarisation calibration models. The x-axis represents frequency in MHz, and the y-axis represents X/I. The data series are represented by dashed lines in orange for Q, green for U, and blue for V. Panel B: The middle panel displays the Vela Stokes spectra after the polarisation corrections have been applied and the intrinsic Vela model shown in the bold dashed lines. The x-axis represents frequency in MHz, and the y-axis represents X/I. The data series are represented by dashed lines in orange for Q, green for U, and blue for V. Panel C: The bottom panel shows the best fit for the polarisation leakage. The x-axis represents frequency in MHz, and the y-axis represents theta leakage in radians. The data points are represented by black squares, and the best fit line is shown in red.

Figure 4 shows the fitted calibration solutions using Vela. These solutions were applied to the voltages of FRB 20230708A. We used the ILEX Footnote ^d software package to process the voltages and obtain the Stokes spectra that are shown in Figure 5. Although the deviations in the observed Vela polarisation are on the order of a few % when compared to the intrinsic model, the changes in L/I and V/I can be significant, which illustrates the importance of performing proper polarisation calibration.

Figure 5.

Stokes linear polarisation (top panel) and circular polarisation (bottom panel) for FRB20230708A with the applied polarisation calibration solutions (darker lines) and without (fainter lines). The spectra were obtained by integrating over the first bright component of the burst (see Dial et al. Reference Dial2025).

We investigated the effects of beam offset on these solutions. For offsets up to 0.5 degrees (which is the case for most FRBs), deviations from the Vela model remain within a few percent. However, for bursts detected at large offsets (>1°), beam morphology begins to drastically affect the measured polarisation. The current modelling cannot fully capture these effects as evidenced by the strong oscillations in L/I and V/I seen in Figure 6.

Figure 6.

Stokes linear and circular polarisation fractions for FRB20240210A with a beam offset of 1.71 degrees.

4.1. Structure maximisation – a SHRINE for CELEBI

The observed DM of an FRB is important to accurately measure. Dedispersing the FRB signal is particularly key to properly investigate the temporal and polarised properties of the wide range of burst structures (as demonstrated in Scott et al. Reference Scott2025), as studies on FRB pulses are sensitive to the assumed value of DM used. There are two main approaches: a S/N ratio maximising DM value, or one that maximises structure (e.g. Caleb et al. Reference Caleb2020; Platts et al. Reference Platts2021). Sutinjo et al. (Reference Sutinjo2023) introduced a smoothing filter method and structure maximisation method (the vector norm or ‘2-norm’, $\sqrt {\Sigma (d/dt)^{2}}$ ) which included a calculation of the uncertainty of the structure parameter. The approach used by Sutinjo et al. (Reference Sutinjo2023) was in turn developed into a separate package and applied to derive the reported DM values for the CRAFT ICS (incoherent sum survey) catalogue (Shannon et al. Reference Shannon2025). These DM values were also used for the presented CRAFT HTR FRB pulses analysed by Scott et al. (Reference Scott2025).

Due to the data processing workflow of CELEBI in localising the FRB from voltage data, extracting an HTR dataset using the localisation, and then refining the localisation based on improved DM and matched filtering before repeating the HTR step, this process was built into the CELEBI code directly. However, as this structure maximisation approach to the DM can be employed in FRB datasets outside of those obtained through CRAFT, the code for deriving structure maximising DM, as well as S/N maximised values of DM, has additionally been made publicly available. The SHRINE package (Structure maximisation of High-time Resolution Intensity profiles with No-nonsense Errors) can be found at https://github.com/marcinglowacki/SHRINE.

4.2. Profile-based scientific workflow management

To facilitate the deployment of CELEBI on distributed supercomputing infrastructure, the Nextflow workflow management system is employed (Di et al. Reference Di, Paolo, Floden, Barja, Palumbo and Notredame2017). The CELEBI pipeline is specified using Nextflow as a directed acyclic graph of tasks, each of which is specified with a Python or Bash script. Each task is associated with a list of input and output files, as well as a list of global, workflow-level parameters that the task depends on, such as the number of antennas or the observation duration. Nextflow automatically handles the scheduling of CELEBI’s tasks on the nodes of the supercomputing infrastructure and the management of files transiting between tasks and nodes.

Experience gained from the first version of CELEBI revealed inefficiencies in Nextflow’s resource management. In particular, the application developer is responsible for specifying the resources reserved for each task, such as the number of CPU cores, the amount of memory reserved, or the duration of the allocated time slot. These specifications were usually based on rough task requirement estimates, resulting in static over-provisioning of execution time by 94% and memory footprints by 89% for a typical CELEBI execution. This over-provisioning is partly due to the configuration-dependent nature of the time and memory requirements of tasks, which causes developers to set large reservations that are compatible with any pipeline configuration. Consequently, the latency of the pipeline on a shared supercomputing infrastructure deteriorates as the allocation of unnecessarily large tasks is less likely to happen quickly.

To allocate resources more effectively for CELEBI’s tasks, an analysis of prior execution traces can be used to build a configuration-dependent resource allocation model (Desnos et al. in preparation).Footnote ^e Each execution of the Nextflow pipeline generates execution traces containing resource monitoring data for each task. These execution traces are obtained from multiple runs of the input pipeline with different configurations. Configuration-dependent prediction models for memory and execution time are then constructed from these execution traces using statistical and machine learning methods, such as ANOVA (ANalysis Of VAriance) and symbolic regressions. These models can then be used to generate new configurations for future pipeline executions, where the resource requirements for each task are based on these prediction models. Using this approach with 3 $\sigma$ safety margins to avoid task failures due to insufficient allocated resources, over-provisioning of task execution time is reduced to 33%, and memory over-provisioning to 23%, with CELEBI. On the shared OzSTAR infrastructure, these finer task granularities lead to a substantial reduction (∼30–60%) in the wall-time latency of the pipeline in uncontrolled conditions with a varying supercomputer workload, thanks to faster scheduling of smaller tasks (while also helping the OzSTAR queue to be scheduled more efficiently).

4.3. Software container environment

The previous version of CELEBI was dependent upon specific software dependencies and operating system (OS) of nodes on the OzSTAR (Optical & X-ray Supercomputing for Theoretical Astronomical Research) supercomputing facility.Footnote ^f In 2023, a change of the OS of OzSTAR to match a newer Ngarrgu Tindebeek (NT) machine was coupled with new system libraries and software modules. This system upgrade was incompatible with the original version of CELEBI. In order to address this, avoid issues from any other future changes in OS or system libraries and ensure CELEBI could operate on other supercomputers, we opted to adapt CELEBI to a containerised system. Installation of the container henceforth is the only prerequisite with regard to software for CELEBI to be able to function. Special thanks to Astronomy Data and Computing Services (ADACS) is given for their help with this process, alongside error handling and optimisation improvements to CELEBI (typical improvement in run-time by over a factor of two).

The software container CELEBI now uses was developed through Docker and can be loaded either locally or on a supercomputer with Docker installed. The container includes an installation of the Astronomical Image Processing System (AIPS), a previously difficult component to install and vital dependency of CELEBI. Other dependencies of CELEBI captured in the container include the correlator program Distributed FX (DiFX; Deller et al. Reference Deller, Tingay, Bailes and West2007, Reference Deller2011), the Very Long Baseline Interferometry (VLBI) scheduling program SCHED, and Common Astronomy Software Applications (CASA; CASA Team et al. 2022). The container is maintained and is publicly available on GitHub: https://github.com/marcinglowacki/celebi-container.