Imaging from STIX visibility amplitudes

Abstract

Aims. This study is aimed at providing the first demonstration of STIX Fourier-transform X-ray imaging using semi-calibrated (amplitude-only) visibility data acquired during Solar Orbiter's cruise phase. Methods. We used a parametric imaging approach whereby STIX visibility amplitudes are fitted by means of two non-linear optimization methods: a fast meta-heuristic technique inspired by social behavior and a Bayesian Monte Carlo sampling method that, although slower, provides a better way of quantifying the uncertainties. Results. When applied to a set of solar flare visibility amplitudes recorded by STIX on November 18, 2020, the two parametric methods provide very coherent results. The analysis also demonstrates the ability of STIX to reconstruct data at a high time resolution and, from a spectral viewpoint, it shows the reliability of a double-source scenario that is consistent with a thermal versus nonthermal interpretation. Conclusions. In this preliminary analysis of STIX imaging based only on visibility amplitudes, we formulate the imaging problem as a non-linear parametric issue addressed by means of two high-performance optimization techniques that both show the ability to sample the parametric space in an effective fashion, thus avoiding any local minima.

First hard X-ray imaging results by Solar Orbiter STIX

“…The results provided by these five approaches have been compared with the ones provided by a visibility amplitude fitting method based on Particle Swarm Optimization (PSO). Amplitude fitting, which has been validated in a previously published paper by Massa et al (2021), was an intermediate approach to extract imaging information from STIX observations before the phase calibration reached a satisfactory level. With the phase calibration now available, this method is essentially obsolete.…”

“…As a consequence, STIX is a Fourier-based imager that provides 30 samples of the Fourier transform of the incoming photon flux, termed visibilities, and STIX images at different photon energies can be reconstructed by means of algorithms for the inversion of the Fourier transform from limited data (Piana et al 2022;Perracchione et al 2021). A first version of the calibration of STIX visibility amplitudes became available in Spring 2021, and a demonstration of STIX imaging capabilities using these semicalibrated visibilities has been obtained by using parametric approaches (Massa et al 2021). Since then, the calibration of both amplitude and phase of STIX visibilities has been carried out for the 24 coarsest sub-collimators labeled from 3a through 10c, where the number refers to the detector resolution and the letter a, b, or c refers to the orientation of the grids (see Table 2 in Krucker et al 2020).…”

Forward-fitting STIX visibilities

“…Specifically, at each iteration, the location of each particle is updated based on its velocity at the previous iteration, the best position visited by the particle since the beginning of the iterative process and the global best position visited by the whole swarm. For details on the implementation of this procedure we refer the reader to Section 3 in Massa et al (2021).…”

“…The result of our analysis is that, when the number of available visibilities is so small as in the case for the ESA space telescope, there are significant experimental conditions where the use of AMOEBA for optimization provides unreliable parameter estimation. Therefore, here we describe the performances of a different minimization approach, based on a biology-inspired strategy (Wahde 2008;Liu et al 2011) that has been used for fitting STIX visibility amplitudes when fully calibrated visibilities were not yet available (Massa et al 2021). In the present paper this strategy is applied for the first time to fully calibrated visibilities and its performances are compared with the ones of simplex optimization in the case of several data sets made of both synthetic and experimental STIX visibilities.…”

First Hard X-Ray Imaging Results by Solar Orbiter STIX

“…As a consequence, STIX is a Fourier-based imager that provides 30 angular Fourier components of the X-ray source termed visibilities , and STIX images at different photon energies can be reconstructed utilizing algorithms for the inversion of the Fourier transform from limited data (Piana et al., 2022 ; Perracchione, Massone, and Piana, 2021 ). A first version of the calibration of STIX visibility amplitudes became available in spring 2021, and a demonstration of STIX imaging capabilities using these semi-calibrated visibilities has been obtained by parametric approaches (Massa et al., 2021 ). Since then, the calibration of both amplitude and phase of STIX visibilities has been carried out for the 24 coarsest sub-collimators labeled from 3a through 10c, where the number refers to the detector resolution and the letter a, b, or c refers to the orientation of the grids (see Table 2 in Krucker et al., 2020 ).…”