Tied-array beam flatfielding

Modern multi-element phased-array radio telescopes use digital beamforming to form tens to hundreds of tied-array beams from the same input voltages. These beams therefore share bandpass structure, gain variations, and radio-frequency interference (RFI); however, most pulsar and fast-transient searches still process each beam separately before candidate classification. We exploited the spatial redundancy of multi-beam observations to stabilize bandpasses, suppress red noise and broadband RFI, and reduce false positives without degrading genuine astrophysical signals. We derived the expected tied-array gain as a function of residual phase dispersion and show how off-target sources converge toward the incoherent limit. Using chi-squared noise statistics, we analyzed division of a tied-array beam (TAB) by a smoothed beam-averaged reference. We tested the method using raw LOFAR high-band antenna (HBA) voltages of PSR B0329+54, simulations, and LOFAR Tied-Array All-Sky Survey (LOTAAS) data of PSR J0250+5854. Once the residual phases decorrelate, outer TABs converge to the incoherent limit set by the effective number of contributing stations, and off-target sources contribute nearly uniform power across beams after primary-beam effects are accounted for. A smoothed null-beam or multi-beam reference provides a stable divisor, yielding flatter dynamic spectra and an equal or higher pulse signal-to-noise ratio (S/N) than incoherent subtraction. In LOTAAS data for PSR J0250+5854, beam flatfielding reduces off-dispersion-measure single-pulse triggers by a factor of about 200 while preserving the folded profile morphology. Beam flatfielding is a post-beamforming operation that requires no additional hardware and little computation. For current and future multi-beam facilities, especially for large phased-array or tied-array mosaics, it offers a direct route to more stable bandpasses, closer-to-Gaussian noise statistics, and order-of-magnitude reductions in downstream classification load at fixed sensitivity.