Tied-array beam flatfielding

Abstract

Context. Multi-element phased-array radio telescopes use digital beamforming to widen their field-of-view with numerous tied-array beams (TABs). These beams share bandpass variations and radio frequency interference (RFI). Yet, most pulsar and transient pipelines process each beam independently, ignoring shared spatial information. This leads to many RFI-dominated false positives that require extensive later sifting. Aims. We exploit multi-beam spatial information to stabilize bandpasses, suppress red noise and broad-band RFI, and drastically reduce false positives without degrading genuine astrophysical signals. Methods. We derive tied-array gain against residual phase dispersion, showing off-beam sources converge to the incoherent limit. Using chi-squared statistics, we analyze dividing a TAB by a beam-averaged reference and quantify the necessary smoothing. We test these predictions using LOFAR high-band antenna voltages (PSR B0329+54), simulations, and LOTAAS survey data (PSR J0250+5854). Results. Off-beam sources contribute nearly uniform power across beams once primary-beam effects are handled. Dividing by a smoothed multi-beam reference yields flatter dynamic spectra and equal or higher pulse signal-to-noise ratios compared to incoherent subtraction. Applied to LOTAAS data, this "beam flatfielding" cuts single-pulse false triggers by a factor of ~200 while preserving profile morphology and peak S/N. Conclusions. Beam flatfielding is a computationally cheap, simple post-beamforming step. For current and future multi-beam facilities, it provides stable bandpasses, closer-to-Gaussian noise statistics, and drastically fewer false positives, easing downstream classification without sacrificing sensitivity.

Figures (12)

• Figure 1: Normalized array gain as a function of rms phase error $\sigma_\delta$ for $N_a=20$, comparing uniform (dashed blue) and Gaussian (solid orange) phase distributions. The response is normalized by $N_a^2$ to show the transition from the fully coherent limit ($=1$) to the incoherent limit ($=1/N_a$).
• Figure 2: Normalized to unity tied-array response along a one-dimensional cut in right ascension through the PSR B0329+54 pointing. The central maximum marks the target beam. Red dots indicate the null beams with the lowest normalized response, which are used to construct the null-beam reference. The dotted horizontal line marks the incoherent-power reference level $1/N_a = 1/12 \approx 0.083$ for this 12-sub-station Superterp setup.
• Figure 3: Single-pulse dynamic spectra and time series for PSR B0329+54 after dedispersion to DM$=26.75$ pc cm$^{-3}$. The x-axis shows time across the full displayed segment ($503$ ms), which contains one bright pulse. Top row: smoothed target beam (left), smoothed average of the 48 null beams (centre), and smoothed incoherent beam (right). Bottom row: target beam after null division (left) and incoherent subtraction (right). In each panel the lower sub-plot shows the dynamic spectrum and the upper sub-plot the frequency-averaged time series with the robust S/N estimate of Eq. \ref{['eq:robust_snr']}. The plotted frequency range is $142.676$-$143.054$ MHz. The target-beam panels use a time/frequency resolution of $0.328$ ms and $12.2$ kHz; the null-beam average and incoherent reference are smoothed to $1.31$ ms and $12.2$ kHz before applying beam flatfielding. For the configuration shown here, null-division gives a slightly higher robust S/N than incoherent subtraction ($9.1$ versus $8.8$) and suppresses the broad RFI patch in the lower-right more cleanly. As shown below, the relative performance depends on the amount of null-beam averaging and smoothing.
• Figure 4: Probability density functions of normalized intensity for null and incoherent beams measured in off-pulse regions. The raw null beam (blue solid) follows the expected $\chi^2$ distribution with 4 degrees of freedom, showing a wide tail and enhanced probability near zero that makes it unsuitable as a divisor. Temporal smoothing by $N_t=4$ (orange dashed) and $N_t=12$ (green dash-dot) samples progressively narrows the distribution via the Central Limit Theorem. The incoherent beam (gray filled) sums 12 independent sub-stations and exhibits a naturally narrow Gaussian-like distribution; dotted lines show the corresponding theoretical curves. Smoothing by $N_t=12$ reduces the null-beam variance by $2.8\times$, bringing it close to the incoherent case.
• Figure 5: Null-division vs. incoherent-subtraction regimes. The colour scale shows the ratio of pulsar S/N obtained with null division to that obtained with incoherent subtraction, as a function of null-beam smoothing factor and the number of null beams averaged. Blue indicates higher S/N for incoherent subtraction at low averaging; as smoothing and the null beam count increase, the ratio rises toward and above unity because null-division avoids self-subtraction and better suppresses broad RFI.