Polarisation Performance of Offset Phase Antennas: A Study for FARSIDE

TL;DR

This work analyzes how offset phase centers between orthogonal dipoles in FARSIDE, a proposed lunar farside low‑frequency interferometer, affect polarization response and imaging quality. It deploys a Muller‑matrix framework built on FEKO beam models over regolith and a GLEAM‑based sky to quantify direction‑dependent leakage, finding substantial Stokes leakage into Q and V, with V leakage amplified by dipole offsets. The study shows that leakage can elevate V/I to the percent level in some regimes and presents a calibration‑based offset correction that mitigates much of this leakage, though perfect recovery depends on accurate beam, offset and PSF knowledge. These results guide deployment strategies, tolerances, and calibration requirements for lunar low‑frequency interferometry and demonstrate a generalizable pipeline for evaluating similar systems. The findings have practical impact for enabling high‑fidelity Stokes measurements essential for detecting exoplanet ECM emissions and probing the Dark Ages signal with FARSIDE.

Abstract

Several radio telescopes have been planned or proposed to be deployed on the Lunar farside in the coming years. These will observe the unexplored ultra-long wavelengths of the electromagnetic spectrum from the lunar farside's unique radio-quiet and ionosphere-free environment. One such lunar radio array is the NASA-funded concept - the Farside Array for Radio Science Investigations of the Dark Ages and Exoplanets (FARSIDE). FARSIDE will operate over 100~kHz to 40~MHz with 128 spatially non-co-located orthogonal pairs of antenna nodes distributed over a 12 X 12 km area in a four-arm spiral configuration. Being on the lunar farside, this radio interferometer will be deployed by tele-operated rovers. The rover deployment mode could lead to a phase offset between each of the two orthogonally polarised antenna elements in the array, which are typically co-located. In this paper, we quantify the effects of such antenna phase offsets on the polarisation response and imaging performance of the lunar radio array. Modelling and analysing the FARSIDE dipole beams with and without offset, we find the latter leads to additional leakages into Stokes U and V corresponding to Muller matrix terms of M2(0,1,2,3) and M3(0,1,2,3). Using a custom simulation pipeline to incorporate all four Stokes beams of spatially co-located and non-co-located dipoles, we produce visibilities and simulated images for the GLEAM (GaLactic and Extragalactic All-sky MWA) sky model through the FARSIDE array. We find that for a pure Stokes I input sky, the output image maximum Stokes V/I flux ratio for the offset case has increased to 2.5% versus 0.05% for the co-located case. The additional Stokes V needs to be corrected since the detection of Electron Cyclotron Maser (ECM) emissions from exoplanets requires high-fidelity Stokes V measurements.

Figures (14)

• Figure 1: An artist's rendering of the four arm spiral configuration of the FARSIDE array on the lunar surface. At the centre of the array is the base station with the communication antenna, fuel tank, central processing unit with correlators and the main power supply. Each of the four spiral arms, will have 32 antenna nodes consisting of two dipoles and a receiver. Also shown are the four two-wheeled rovers that will deploy the tethers containing the antenna nodes. The inset image shows the path taken by the rover to lay out the embedded dipole antennas with the 90-degree bend at each antenna node. The phase centres of the dipoles are indicated by the red dots.
• Figure 2: A sketch detailing the deployment configuration for a single antenna node of FARSIDE. The tether from the previous antenna node leads up to one of the dipoles (X-dipole). Then, the rover turns 90${^\circ}$ and lays out the orthogonal dipole (Y-dipole), carrying the tether over to the location of the next node.
• Figure 3: A schematic highlighting the difference between the spatially co-located and non co-located dipoles in a 2 element interferometer. The offset between the phase centres results in an additional delay($\tau_o$) between the X and Y combinations of each antenna pair. Additional corrections are needed when cross-correlating data from different antennas.
• Figure 4: Simulation of the dipole phase centres of the FARSIDE spiral arm array layout. Each arm has 32 pairs of dual-polarised dipoles. The green phase centres are offset from the black by 50 m in the X and Y directions. The top panel shows the top view of the complete layout spanning over 12 km in the X and Y extents. The bottom panel shows the inner $3\times3$ km of the layout and a closer look at the offsets between the X- and Y- dipoles in each antenna node.
• Figure 5: [a,b] Snapshot uv-coverage at 2 MHz of the four arm spiral array layout for zenith pointing. [a] uv-coverage for the XX and YY baselines and [b] shows uv-sampling for the XY baselines of the antenna pairs. [c,d] Normalised 2D Point Spread Functions (PSF) of the FARSIDE spiral arm layout with and without offset. [e] Azimuthally-averaged PSF versus elevation angle for the XX/YY and XY sets of baselines of the FARSIDE spiral arm layout plotted for three characteristic frequencies within the operating bandwidth.