Error Propagation from Integral Moments and Spectral Derivatives of Stokes Profiles to Magnetic Observables
Abstract
We aim to derive convenient analytic estimations of magnetic inference errors, which can be used to inform and facilitate the creation of the science-traceability matrix of a polarimetric instrument. In order to do this, we study the general problem of the propagation of Poissonian noise in polarized light signals to derived data products of the Stokes profiles, namely integral moments of arbitrary orders and spectral derivatives of the intensity. In particular, we derive the errors on the longitudinal and transversal projections of the magnetic field inferred from the weak-field approximation (WFA) of the Zeeman effect. The propagated errors on magnetic inference are traced back to the signal- to-noise ratio (SNR) of the observations. The results can be used to quantify the contributions of different environmental and instrumental conditions (spectral line width, spectral resolution, line spread function, stray light) to the overall error on the inferred quantities. Our tests indicate that the integral-moment method of inference is comparable to the local derivative in a predictable way.
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BibTeX
@misc{casini2026error,
title = {{Error Propagation from Integral Moments and Spectral Derivatives of Stokes Profiles to Magnetic Observables}},
author = {Roberto Casini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.32948},
eprint = {2609.32948},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32948},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Error Propagation from Integral Moments and Spectral Derivatives of Stokes Profiles to Magnetic Observables
AU - Roberto Casini
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2609.32948
UR - https://arxiv.org/abs/2609.32948
AB - We aim to derive convenient analytic estimations of magnetic inference errors, which can be used to inform and facilitate the creation of the science-traceability matrix of a polarimetric instrument. In order to do this, we study the general problem of the propagation of Poissonian noise in polarized light signals to derived data products of the Stokes profiles, namely integral moments of arbitrary orders and spectral derivatives of the intensity. In particular, we derive the errors on the longitudinal and transversal projections of the magnetic field inferred from the weak-field approximation (WFA) of the Zeeman effect. The propagated errors on magnetic inference are traced back to the signal- to-noise ratio (SNR) of the observations. The results can be used to quantify the contributions of different environmental and instrumental conditions (spectral line width, spectral resolution, line spread function, stray light) to the overall error on the inferred quantities. Our tests indicate that the integral-moment method of inference is comparable to the local derivative in a predictable way.
ER -