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Optimisation of calibration sources for global 21-cm experiments: the REACH case

Adarsh Kumar Dash, Dominic Anstey, Harry T. J. Bevins, Eloy de Lera Acedo, Gary Allen, Kaan Artuc, Gianni Bernardi, Martin Bucher, Steve Carey, Jean Cavillot, Ricardo Chiello, Adelicia S. Chu, Wessel Croukamp, John Cumner, Saswata Dasgupta, Dirk I. L. de Villiers, Jiten Dhandha, Aleksandra Dragovic, John A. Ely, Anastasia Fialkov, Thomas Gessey-Jones, Will J. Handley, Christian Kirkham, Girish Kulkarni, Samuel A. K. Leeney, Alessio Magro, P. Daan Meerburg, Shikhar Mittal, Daniel Molnar, Rohan S. Patel, Joe H. N. Pattison, Saurabh Pegwal, Carla M. Pieterse, Jonathan R. Pritchard, Gabriella Rajpoot, Nima Razavi-Ghods, Daniel Robins, Ian L. V. Roque, Anchal Saxena, Killian H. Scheutwinkel, Emma Shen, Peter H. Sims, Marta Spinelli, Jiacong Zhu

Abstract

The spin-flip 21-cm signal from the Cosmic Dawn and the Epoch of Reionization is an essential probe of the conditions that led to the formation of the first luminous objects in the early Universe. However, its detection remains a major challenge owing to its low strength compared to the bright foregrounds and the requirement of precise calibration of the instrument to prevent systematics that could hinder a detection or lead to false inferences. REACH (Radio Experiment for the Analysis of Cosmic Hydrogen) is a radiometer experiment designed to detect this sky-averaged signal in the frequency range of 50--130~MHz. Using a wide-beam antenna, REACH calibration relies on internal reference sources, covering a broad range of temperatures and reflection coefficients. The choice of type and number of calibrators used significantly influences the quality of the calibration. This work investigates these effects and introduces a novel method for selecting an optimal set of calibration sources. With an optimised set, we aim to reduce calibration time, thereby increasing sky integration time while preserving calibration accuracy. We explore two optimisation strategies: one applied across the full receiver band and another performed on a frequency-by-frequency basis. Finally, we demonstrate that, with a total calibration time comparable to the conventional full-calibrator set, an optimised set with fewer calibrators achieves approximately a $15~\%$ reduction in calibrated temperature noise and improved absolute calibration of the instrument. This has implications for better calibration strategies in similar radiometer experiments.

Optimisation of calibration sources for global 21-cm experiments: the REACH case

Abstract

The spin-flip 21-cm signal from the Cosmic Dawn and the Epoch of Reionization is an essential probe of the conditions that led to the formation of the first luminous objects in the early Universe. However, its detection remains a major challenge owing to its low strength compared to the bright foregrounds and the requirement of precise calibration of the instrument to prevent systematics that could hinder a detection or lead to false inferences. REACH (Radio Experiment for the Analysis of Cosmic Hydrogen) is a radiometer experiment designed to detect this sky-averaged signal in the frequency range of 50--130~MHz. Using a wide-beam antenna, REACH calibration relies on internal reference sources, covering a broad range of temperatures and reflection coefficients. The choice of type and number of calibrators used significantly influences the quality of the calibration. This work investigates these effects and introduces a novel method for selecting an optimal set of calibration sources. With an optimised set, we aim to reduce calibration time, thereby increasing sky integration time while preserving calibration accuracy. We explore two optimisation strategies: one applied across the full receiver band and another performed on a frequency-by-frequency basis. Finally, we demonstrate that, with a total calibration time comparable to the conventional full-calibrator set, an optimised set with fewer calibrators achieves approximately a reduction in calibrated temperature noise and improved absolute calibration of the instrument. This has implications for better calibration strategies in similar radiometer experiments.

Paper Structure

This paper contains 15 sections, 29 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. REACH receiver calibration overview
  3. The calibration formalism
  4. The calibration sources
  5. Noise estimation
  6. Noise-dominated noise-wave parameter
  7. Noise-less noise-wave parameter
  8. Condition numbers
  9. Application to REACH data
  10. Condition number and quality of calibration
  11. Selection of preferred calibrators
  12. Piecewise calibration
  13. Calibration results
  14. Conclusions
  15. Uncertainty calculation for noise-dominated noise-wave parameters

Figures (8)

  • Figure 1: A schematic of a simple radiometer. The antenna observes the sky at brightness temperature $T_\mathrm{sky}$. $T_\mathrm{ant}$ is the antenna temperature. The long dashed line represents the reference plane where the impedance mismatch is supposed to occur between a source and the receiver. $G_\mathrm{rec}$ and $G_\mathrm{rec}$ are the gain and noise temperature of the receiver. The calibration is performed by Dicke switching between the cold source and noise source (NS), as well as switching among the calibrators in the case of a mismatched antenna.
  • Figure 2: A Smith chart showing the reflection coefficients of the 12 calibrators used in REACH. The cold and hot loads are well matched, and their reflection coefficients are close to the centre of the plot. For reference, the antenna reflection coefficient is also plotted. The measurements are taken in the range of 50--130 MHz.
  • Figure 3: Plots for two cases of calibrator set sizes: (top) 6 sources ([cold, hot, c2r27, c2r36, c2r69, c2r91]) and (bottom) 8 sources ([cold, hot, c2r27, c2r36, c2r69, c2r91, r25, r100]). For each case, we show the X-terms (left), the respective condition number spectrum (centre) and the estimated noise-wave parameters (right). In the X-terms plots for 8 calibration sources, the magenta and grey curves correspond to the additional calibrators in the set. It must be noted that the y-axis range is different for all noise-wave parameter plots.
  • Figure 4: Calibration quality vs mean condition number plots for three validation sources with different cable lengths (top, middle and bottom rows respectively). For each validator, on the left we show the trends of standard deviation $\sigma_\mathrm{T}$ of the temperature solution and on the right, the absolute mean deviation $\left\lvert\overline{\Delta T}\right\rvert$ of the solution from the target temperature. Each point in the figure represents a different calibrator set with sizes as shown in the colour bar at the bottom. The black $\star$ shows the calibrator sets which do not include the hot source. An estimate of (minimum) theoretical noise, calculated using an 11-calibrator set in Equation \ref{['Eq:Noise_propagation_and_estimation']}, is also shown as a red dashed line in the plots on the left column for each validation source.
  • Figure 5: Top: For each validation source (y-axis), the intensity chart shows the percentage occurrence of each calibrator in the best calibrator sets with $\overline{\kappa}~\leq~53$. Bottom: A cumulative percentage occurrence of each calibrator obtained by averaging the respective column in the top chart.
  • ...and 3 more figures