Euclid. Properties and performance of the NISP signal estimator

TL;DR

The paper analyzes the NISP onboard signal estimator for Euclid, evaluating biases, variances, and the quality factor using Monte Carlo simulations and early flight data. It revisits the likelihood-based estimator with a diagonal covariance and derives corrections for high-flux constant bias and an improved variance estimator, while validating Gaussian assumptions and the folding behavior at low flux. A dedicated discussion on Data Processing Approximation (DPA) shows that using detector-averaged parameters introduces small, well-characterized biases that are largely negligible for science, though space weather can produce QF outliers. Flight data broadly agree with simulations, enabling leading-order corrections and demonstrating the QF’s usefulness for data quality control, including cosmic-ray identification. The results have practical implications for the reliability of flux measurements and the robustness of online data processing in space-based NIR surveys.

Abstract

The Euclid spacecraft, located at the second Lagrangian point of the Sun-Earth system, hosts the Near-Infrared Spectrometer and Photometer (NISP) instrument. NISP is equipped with a mosaic of 16 HgCdTe-based detectors to acquire near-infrared photometric and spectroscopic data. To meet the spacecraft's constraints on computational resources and telemetry bandwidth, the near-infrared signal is processed onboard via a dedicated hardware-software architecture designed to fulfil the stringent Euclid's data-quality requirements. A custom application software, running on the two NISP data processing units, implements the NISP signal estimator: an ad-hoc algorithm which delivers accurate flux measurements and simultaneously estimates the quality of signal estimation through the quality factor parameter. This paper investigates the properties of the NISP signal estimator by evaluating its performance during the early flight operations of the NISP instrument. First, we revisit the assumptions on which the inference of the near-infrared signal is based and investigate the origin of the main systematics of the signal estimator through Monte Carlo simulations. Then, we test the flight performance of the NISP signal estimator. Results indicate a systematic bias lower than 0.01 e/s for 99% of the NISP pixel array, well within the noise budget of the estimated signal. We also derive an analytical expression for the variance of the NISP signal estimator, demonstrating its validity, particularly when the covariance matrix is not pre-computed. Finally, we provide a robust statistical framework to interpret the QF parameter, analyse its dependence on the signal estimator bias, and show its sensitivity to cosmic ray hits on NISP detectors. Our findings corroborate previous results on the NISP signal estimator and suggest a leading-order correction based on the agreement between flight data and simulations.

Figures (9)

• Figure 1: Top panels: Bias of the signal estimator. Bottom panel: QF values. Left panels: Bias as function of $n_{\rm g}$ for $n_{\rm f}=16$, $n_{\rm d}=11$, and $\sigma_R=13\,{\rm e}^{-}$ in the case where $f_{\rm 0} > f_{\rm f}$ (no folding effect). For $f = f_{\rm 0}$ (green squares) for which the off-diagonal entries of the variance matrix are null, the bias is perfectly predicted by the analytical formula (dashed lines) from Eq. (\ref{['eq:bias']}) for the signal, and Eq. (\ref{['eq:QFbias']}) for the QF. For $f<f_{\rm 0}$ (light green triangles), the theoretical prediction underestimates the bias. For $f>f_{\rm 0}$ (dark green dots) the theoretical prediction overestimates the bias. Right panels: bias of the signal estimator as a function of flux in spectroscopic readout mode. The flux values $f_{\rm 0}$ are indicated by vertical lines for each of the readout noise values. The $f_{\rm f}=0.1\,{\rm e}^{-}\,{\rm s}^{-1}$ flux value, above which the folding contribution is negligible, is indicated by a grey dash-dot-dotted vertical line. Positive contribution of the $D_{ij}$ to the covariance matrix for $f > f_{\rm 0}$ translates in the measured signal bias lower than the analytical formula, while negative contribution of the $D_{ij}$ translates in the measured signal bias higher than the analytical formula. For $f \gg f_{\rm 0}$ and $f \gg f_{\rm f}$, the bias does not depend on flux. Similar results are obtained in photometric readout mode.
• Figure 2: Left panel: Ratio of the off-diagonal terms $D_{ij}$ to the diagonal terms $D_{ii}$ in the covariance matrix of group differences as a function of flux for three different readout noise values. The flux values $f_{\rm 0}$ for which $D_{ij} = 0$ are indicated by vertical lines for each $\sigma_{\sfont R}$ value. Right panel: Flux $f_{\rm 0}$, defined in Eq. (\ref{['eq:f0']}), plotted as function of the pixel's readout noise $\sigma_{\sfont R}$. The horizontal line indicates the limiting flux $f_{\rm f}$ defined in Sect. \ref{['sec:gfolding']} for no folding distribution at any $\sigma_{\sfont R}$ in spectroscopic readout mode.
• Figure 3: Probability that no more than 10% of $\Delta G$ fall below the folding point $-\beta$ in spectroscopic readout mode. The contribution is negligible for all readout noise values for flux higher than $f_{\rm f}=0.1\,{\rm e}^{-} {\rm s}^{-1}$. For typical NISP pixels with readout noise $\sigma_{\sfont R}=13\,{\rm e}^{-}$, the folding contribution is negligible for the entire range of fluxes. A similar result holds for the photometric readout mode.
• Figure 4: Left panel: Variance estimator $\rho^{2}[\hat{g}]$ defined in Eq. (\ref{['eq:var_def']}) compared to the observed dispersion of the $\hat{g}[\Delta \vec{G}]_{n_{\rm g}}$ values. The theoretical estimate is in perfect agreement with the observed value for $f>0.5\,{\rm e}^{-} {\rm s}^{-1}$, independently of the readout noise and readout mode. Right panel: QF variance normalised to $2(n_{\rm g}-2)$ as function of flux in spectroscopic readout mode.
• Figure 5: DPA induced bias to the signal estimator $\hat{g}[\Delta \vec{G}]_{n_{\rm g}}$ (top panels) and to the QF (bottom panels). For each value of the pixel simulated readout noise $\sigma_{\sfont R}$, we have chosen the specific flux value $f=f_{\rm0}$ for which the off-diagonal terms in the covariance matrix vanish and the theoretical bias model conforms to the simulated values (thick solid lines). Additionally, for each $\sigma_{\sfont R}$ we perform simulations for $f=\frac{f_{\rm0}}{2}$ (dashed lines) and $f=2f_0$ (dotted lines). Left panels: Bias due to $\Delta \sigma_{\sfont R}$. The shaded areas correspond to the typical case of possible values of $-3 < \Delta \sigma_{\sfont R}<6$ as 99% of pixels are in this range of $\Delta \sigma_{\sfont R}$ -- see Sect. \ref{['sec:flight_performance_sig']}. Typical pixel has a readout noise $\sigma_{\sfont R}\approx 13\,{\rm e}^{-}$ and is represented by orange lines. Right panels: Bias due to $\Delta f_{\rm e}$. The shaded area corresponds to the typical dispersion of gain values.