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Full Characterisation of the Polarisation Primary Beam of the GRAO 32-m Telescope

Theophilus Ansah-Narh, Nia Imara, Benedicta Woode, Joseph Bremang Tandoh, Emmanuel Proven Adzri, Diana Klutse, Evaristus Uzochukwu Iyida

arXiv:2609.08700v1astro-ph.IMeess.SPmath-phmath.MPphysics.comp-phphysics.ins-det

TL;DR

A unified direction-dependent account of beam leakage and polarization-recovery conditioning had not been reported for the GRAO 32-m. Full-wave electromagnetic simulations and a Jones–Mueller framework show that the telescope’s polarimetric response varies across the beam rather than being captured by one scalar coefficient.

  • Problem

    A unified treatment of direction-dependent beam response, Stokes leakage, and polarisation-recovery conditioning is uncommon, leaving the GRAO 32-m without such a full-beam characterisation.

    Source: §1 · p. 2

  • Method

    The study uses full-wave electromagnetic simulations and a Jones–Mueller framework to characterize the GRAO 32-m response across the primary beam.

    Source: §1 · p. 2

  • Results

    The GRAO 32-m polarimetric response is intrinsically direction-dependent and cannot be fully represented by a single scalar beam or calibration coefficient.

    Source: §7 · p. 19

  • Takeaways & Limitations

    An on-axis calibration cannot in general remove leakage from emission observed through other beam positions, including in extended-source and raster-scan observations.

    Source: §6 · p. 18

    The results are an intrinsic electromagnetic reference for the nominal configuration; receiver and signal-chain effects, pointing, alignment, atmospheric, temporal, and physical-model uncertainties are not represented.

    Source: §6 · p. 18

Abstract

from arXiv · show

Direction-dependent instrumental polarisation is a major systematic limitation in high-fidelity single-dish radio polarimetry, yet a unified characterisation of beam leakage and the conditioning of polarisation recovery is lacking for the Ghana Radio Astronomy Observatory (GRAO) 32-m telescope. We aim to establish a quantitative, direction-dependent polarimetric beam model at 5.0 and 6.7 GHz. High-resolution \texttt{GRASP} electromagnetic simulations of the nominal telescope configuration are used to derive the full complex Jones response and corresponding Mueller matrices, from which beam shape, beam squint, instrumental Stokes leakage, and intrinsic cross-polarisation ratio (IXR) are evaluated across the primary beam. The Stokes $I$ beams have half-power beam widths of $396.4$ and $295.3$ arcsec at 5.0 and 6.7 GHz, respectively, with main-beam efficiencies of $56.4$ and $55.6$ per cent. At 5.0 GHz, the circular-polarisation beam squint is $9.96$ arcsec ($2.5$ per cent of the HPBW), whereas no statistically significant squint is detected at 6.7 GHz. Leakage from Stokes $I$ into linear polarisation remains below $0.1$ per cent within the half-power beam but increases substantially towards the sidelobes. IXR reaches approximately $80$ dB on axis and decreases with angular offset. These results establish the intrinsic electromagnetic polarimetric response of the GRAO 32-m telescope and provide a quantitative baseline for direction-dependent calibration and subsequent observational validation.

1 INTRODUCTION

Single-dish polarimetry requires a direction-dependent account of the telescope’s matrix response, but the GRAO 32-m lacked a unified characterization of leakage and polarization-recovery conditioning. This study combines Jones, Mueller, leakage, beam-squint, and IXR analyses to establish an electromagnetic baseline.

1 INTRODUCTION

  • Direction-dependent antenna response couples Stokes parameters, producing spurious signals that can mimic or obscure weak astrophysical polarisation.The response varies across the beam, so a scalar beam or constant leakage term is insufficient.Source: §1 · p. 1
  • Prior beam studies often report leakage or cross-polarisation without assessing the stability of polarization inversion across the primary beam.Similar leakage levels can still correspond to different sensitivities to noise and calibration errors when Jones-matrix conditioning differs.Source: §1 · p. 2
  • The GRAO 32-m had prior electromagnetic studies of total-power performance, but its Jones and Mueller responses, leakage, squint, and conditioning had not been examined together.Spatially resolved IXR is also less commonly included in single-dish primary-beam characterizations.Source: §1 · p. 2
  • The study derives direction-dependent Jones and Mueller responses at 5 and 6.7 GHz to quantify beam responses, squint, Stokes leakage, and IXR.It presents these field-, Stokes-, and conditioning-level metrics as an intrinsic electromagnetic baseline for later observational calibration and validation.Source: §1 · p. 2

2.1 GRAO 32-m Telescope

The GRAO 32-m is a refurbished, steerable telescope in Ghana, configured with shaped Cassegrain optics and a beam-waveguide. Its 5.0 and 6.7 GHz receivers motivate the modeled frequency cases.

2.1 GRAO 32-m Telescope

  • The fully steerable 32-m telescope at Kutunse, Ghana, serves as a single-dish facility and an African VLBI Network station.Its location provides access to a large fraction of the celestial sphere.Source: §2.1 · pp. 2–3
  • Originally built as a telecommunications ground station, the antenna was converted for astronomy and VLBI through structural, mechanical, receiver, control, software, and timing upgrades.Photogrammetry and microwave holography assessed subreflector alignment and primary-reflector deformation.Source: §2.1 · p. 3
  • The telescope uses shaped Cassegrain reflectors and four beam-waveguide mirrors to route radiation to a stationary receiver cabin.The primary reflector is 32 m in diameter, with an approximately 0.32 f/D ratio.Source: §2.1 · p. 3
  • The C-band receiver configurations centered near 5.0 and 6.7 GHz provide representative cases for the beam analysis.The receiver architecture supports dual circular polarisation; 6.7 GHz is used for the 6668.518 MHz Class II methanol maser transition.Source: §2.1 · p. 3

2.2 Electromagnetic Model and GRASP Configuration

The electromagnetic model uses GRASP to calculate the GRAO telescope’s direction-dependent far-field response at 5.0 and 6.7 GHz. It retains the nominal optical configuration and processes sampled fields for polarimetric analysis.

2.2 Electromagnetic Model and GRASP Configuration

  • GRASP models the telescope’s principal optical features and calculates its direction-dependent far-field response at 5.0 and 6.7 GHz.The resulting electromagnetic fields feed the subsequent polarimetric formulation.Source: §2.2 · p. 3

2.2.1 Reflector Geometry and Surface Representation

  • The reflector model retains the shaped primary and secondary geometries, telescope dimensions, relative positions, and beam-waveguide geometry in a segmented surface mesh.The mesh resolves electromagnetic variation at the highest modeled frequency and incorporates the specified 1.88 mm RMS primary surface accuracy.Source: §2.2.1 · p. 3

2.2.2 Feed Illumination

  • The feed illumination sets the amplitude and phase distribution incident on the subreflector, affecting primary illumination, spillover, sidelobes, and the far field.The same feed excitation is retained at both frequencies, and is propagated through the reflector and beam-waveguide geometry.Source: §2.2.2 · pp. 3–4

2.2.3 Support Structures and Electromagnetic Blockage

  • The model includes the subreflector support and four primary support struts, which can cause blockage, diffraction, and azimuth-dependent sidelobe structure.These structures are represented by their nominal geometry rather than by an ideal rotationally symmetric model.Source: §2.2.3 · p. 4

2.2.4 Surface Accuracy and Alignment Assumptions

  • The reference simulations use nominal reflector, beam-waveguide, and feed alignment without additional surface deformations or mechanical offsets.The computed response therefore represents the specified nominal configuration.Source: §2.2.4 · p. 4

2.2.5 Physical Optics and Physical Theory of Diffraction

  • Physical optics models currents on the conducting reflectors, while physical theory of diffraction adds contributions from edges and other significant discontinuities.The combined PO–PTD calculation is applied consistently at both frequencies and retains off-axis and sidelobe response.Source: §2.2.5 · p. 4

2.2.6 Angular Sampling of the Electromagnetic Response

  • The far-field response is sampled over θ = 0°–3° in 0.015° steps and φ = 0°–360° in 1° steps, covering the principal beam and first sidelobe.This angular sampling is distinct from the reflector-surface mesh; the four complex field responses at each direction are retained for later processing.Source: §2.2.6 · p. 4

3 POLARISATION THEORY AND METRICS

The framework preserves the direction-dependent complex field response and links it to Stokes observables. It uses Jones and Mueller matrices alongside beam, leakage, and conditioning metrics to describe polarimetric performance.

3.1 Jones matrix beam representation

  • The Jones matrix maps the incident electric field to the output field at each sky direction, retaining amplitude and phase information.Its diagonal entries are co-polar voltage patterns; its off-diagonal entries describe cross-polar coupling.Source: §3.1 · pp. 4–5

3.2 Mueller matrix formulation for a single dish

  • The Mueller matrix maps the Jones response into Stokes space, with its elements arising from bilinear combinations of complex Jones components.Its first row gives total-power response, including intensity-to-polarisation leakage; off-diagonal entries describe Stokes coupling and distinct diagonal terms describe Q, U, and V beam patterns.Source: §3.2 · p. 5

3.3 Instrumental polarisation metrics

  • Beamwidth, squint, cross-polarisation, and intensity-to-linear-polarisation leakage summarize different aspects of beam response.The leakage metric represents fractional spurious linear polarisation from an unpolarised source and depends on Jones-element magnitudes and relative phases.Source: §3.3 · p. 6

3.4 Intrinsic Cross-Polarisation Ratio (IXR)

  • IXR expresses Jones-matrix conditioning on a polarimetry-oriented scale; it transforms the condition number rather than providing an independent conditioning measure.Higher IXR corresponds to better conditioning, while ill-conditioning increases sensitivity of polarisation reconstruction to noise and instrumental errors.Source: §3.4 · p. 6
  • IXR characterizes intrinsic direction- and frequency-dependent response, not the performance of a particular calibration algorithm.It is derived from the Jones-matrix singular values and complements leakage metrics by describing inversion stability.Source: §3.4 · p. 6

4 DATA PROCESSING

The processing converts simulated Jones fields into direction-dependent Mueller and polarimetric products while retaining the complex field through interpolation. The resulting beam representations show structured, non-scalar responses away from boresight.

4 DATA PROCESSING

  • The workflow transforms GRASP Jones patterns from linear to circular basis, maps them to a tangent plane, and derives direction-dependent Mueller matrices and metrics.The circular-basis transformation is applied pointwise across the angular grid.Source: §4 · pp. 6–7

4.1 Tangent-Plane Mapping and Interpolation

  • Linear versus cubic interpolation differed by less than 0.1% in amplitude, 0.01 rad RMS phase, 0.01 dB in IXR, and 0.0001% in leakage.The finer target grid is a resampling and adds no intrinsic angular information beyond the native GRASP solution.Source: §4.1 · p. 7

4.2 Mueller Matrix Construction and Polarimetric Metrics

  • IXR was evaluated via Jones-matrix SVD, with a minimum-singular-value bound preventing numerical failure near singular directions.Stokes beams, leakage maps, and IXR distributions were derived from direction-dependent Mueller matrices without smoothing or empirical fitting.Source: §4.2 · p. 8

4.3 Jones and Mueller Beam Representations

  • Structured off-diagonal Mueller terms show a non-scalar response away from boresight, while cross-polar phase winding and off-axis growth contrast with co-polar behavior.The Jones amplitude and phase patterns vary with frequency and angular direction across the beam.Source: §4.3 · pp. 8, 10, Figure 3 · p. 9, Figure 2 · p. 9

5 RESULTS AND ANALYSIS

The simulated beam is well-conditioned on axis but polarimetric performance degrades with angular offset, especially toward the sidelobes. Beam squint, cross-polar response, and Mueller leakage vary across the field, motivating direction-dependent rather than global characterisation.

5 RESULTS AND ANALYSIS

  • Cross-polar power rises from a near-null at boresight to the −70 to −80 dB range near the half-power beam width, then increases toward the sidelobes.The cross-polar beams form a four-lobed pattern, while their phase has abrupt transitions and wrapping absent from power-only descriptions.Source: Figure 5 · p. 11, §5 · p. 12, Figure 9 · p. 15
  • Combined linear instrumental polarisation stays below 0.5 per cent within the half-power beam width, while I→Q and I→U leakage reaches 10^-2 to 10^-3 near the plotted field edge.Leakage forms ring-like structures that trace the total-power beam sidelobes.Source: §5 · p. 14, Figure 11 · p. 16
  • IXR reaches ∼80 dB on axis and falls to ∼25–30 dB near the first sidelobe; mean IXR is higher at 6.7 GHz across the central beam.The regional statistics also show increasing variability toward and beyond the half-power boundary.Source: §5 · p. 15
  • HPBWs are 396.4 arcsec at 5.0 GHz and 295.3 arcsec at 6.7 GHz, with main-beam efficiencies of 0.564 and 0.556, respectively.The 5.0 GHz circular-polarisation squint is 9.96 arcsec (2.5 per cent of HPBW); at 6.7 GHz it is unresolved below 7.03 arcsec.Source: §5 · pp. 11, 16
  • The RHCP and LHCP beam centres are displaced by 9.96 arcsec at 5.0 GHz, a 2.5 per cent HPBW offset that contributes to off-axis leakage and poorer conditioning.No resolvable displacement is obtained at 6.7 GHz at the map's 7.03 arcsec per pixel sampling.Source: §5 · pp. 13, 16
  • The present HPBWs and first-sidelobe levels closely match Venter & Bolli (2018), providing an independent consistency check on the electromagnetic model.The present model gives HPBWs of 0.1101° and 0.0820° and first sidelobe levels of approximately −15.4 and −15.6 dB.Source: §5 · pp. 16–17

6 DISCUSSION

The GRAO 32-m polarimetric response varies across the primary beam, so on-axis characterisation or a single leakage coefficient cannot describe it. The discussion connects this spatial variation to calibration, polarisation recovery, and the limits of the simulated model.

6 DISCUSSION

  • The telescope’s polarimetric response is intrinsically direction dependent, so a single leakage coefficient or on-axis characterisation is inadequate.Beam structure, polarisation coupling, and matrix conditioning describe complementary aspects of that response.Source: §6 · pp. 17, 19
  • Changing field-response amplitudes and phases away from boresight increase coupling between polarisation states, making the response spatial rather than fixed at the receiver.Differential displacement of circular-polarisation beams can also map source structure into apparent polarisation during extended-source or scanning observations.Source: §6 · p. 18
  • Off-axis Jones and Mueller response must be considered in calibration, especially for extended sources and mapping that sample different beam positions.An on-axis calibration cannot in general remove leakage observed through other parts of the beam.Source: §6 · pp. 18–19
  • IXR measures inversion stability rather than leakage magnitude, and its decline off axis makes polarisation recovery more sensitive to response uncertainty and measurement noise.A favourable on-axis response does not imply uniform conditioning across the field.Source: §6 · p. 18
  • Published telescope results do not support a simple numerical ranking because studies use different metrics and characterise different stages of the instrumental chain.The passage recommends metric-, frequency-, and calibration-matched comparisons.Source: §6 · p. 18
  • Cross-polarisation predictions are harder to validate than dominant diagonal Jones terms because small absolute differences in weak responses can mean large relative differences.Good co-polar agreement alone does not establish cross-polarisation or polarimetric-purity accuracy.Source: §6 · p. 18
  • The simulations represent the intrinsic electromagnetic response of the adopted configuration, not the full realised on-sky response.Receiver gain and phase, pointing, alignment, atmospheric and temporal effects, and physical-model uncertainties are not included.Source: §6 · p. 18
  • The absence of on-sky measurements defines the study’s scope; commissioning observations can test the predicted response and bridge it to end-to-end calibration.Such measurements can identify contributions from the realised receiver, telescope configuration, and observing conditions.Source: §6 · pp. 18–19

7 CONCLUSION

The study establishes a direction-dependent polarimetric beam characterisation for the GRAO 32-m using full-wave electromagnetic simulations and a Jones–Mueller framework. Its model is an intrinsic reference for the adopted configuration and a basis for future calibration and validation.

7 CONCLUSION

  • The study uses full-wave simulations and a unified Jones–Mueller framework to characterise the GRAO 32-m beam across the primary beam.The framework preserves complex polarisation response from electromagnetic fields through to Stokes-space observables.Source: §7 · p. 19
  • The GRAO 32-m polarimetric response is direction dependent and cannot be fully represented by a scalar beam or calibration coefficient.The Jones and Mueller representations treat beam shape, polarisation coupling, and matrix conditioning together.Source: §7 · p. 19
  • The model is an intrinsic electromagnetic reference for the adopted configuration, not a complete account of realised on-sky performance.Commissioning measurements can validate the response and distinguish beam behaviour from receiver, observing-system, and operational effects.Source: §7 · p. 19

FUNDING

The work was conducted through a GAEC–GSSTI and UCSC collaborative framework and received support from the GRAO–UCSC Astronomy Development Project and a France–Ghana bilateral program.

FUNDING

  • The research was conducted under a memorandum of understanding between GAEC, through GSSTI, and the Regents of the University of California on behalf of UCSC.Source: FUNDING · p. 19
  • Financial support came from the GRAO–UCSC Astronomy Development Project and the France–Ghana bilateral program under FEF–Initiative Africa.The bilateral program was coordinated by the French Ministry for Europe and Foreign Affairs and implemented through the French Embassy in Ghana.Source: FUNDING · p. 19
  • GSSTI provided institutional resources and computational facilities.Source: FUNDING · p. 19

DATA AVAILABILITY

The study’s data and analysis scripts derive from GRASP electromagnetic simulations of the GRAO 32-m telescope and are available to qualified researchers on reasonable request.

DATA AVAILABILITY

  • The data underlying the article come from electromagnetic simulations of the GRAO 32-m telescope conducted using GRASP.Source: DATA AVAILABILITY · p. 19
  • The simulation data and associated analysis scripts will be made available to qualified researchers upon reasonable request to the corresponding author.Source: DATA AVAILABILITY · p. 19
  • The authors state that no proprietary or confidential information is included.Source: DATA AVAILABILITY · p. 19
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