On Identifying and Mitigating Bias in Inferred Measurements for Solar Vector Magnetic-Field Data

The problem of bias, meaning over- or under-estimation, of the component perpendicular to the line-of-sight [ $B_{\perp }$ ] in vector magnetic-field maps is discussed. Previous works on this topic have illustrated that the problem exists; here we perform novel investigations to quantify the bias, fully understand its source(s), and provide mitigation strategies. First, we develop quantitative metrics to measure the $B_{\perp }$ bias and quantify the effect in both local (physical) and native image-plane components. Second, we test and evaluate different options available to inversions and different data sources, to systematically characterize the impacts of these choices, including explicitly accounting for the magnetic fill fraction [ $ff$ ]. Third, we deploy a simple model to test how noise and different models of the bias may manifest. From these three investigations we find that while the bias is dominantly present in under-resolved structures, it is also present in strong-field, pixel-filling structures. Noise in the spectropolarimetric data can exacerbate the problem, but it is not the primary cause of the bias. We show that fitting $ff$ explicitly provides significant mitigation, but that other considerations such as the choice of ${\chi }^2$ -weights and optimization algorithms can impact the results as well. Finally, we demonstrate a straightforward "quick fix" that can be applied post facto but prior to solving the ${180}^{\circ }$ ambiguity in $B_{\perp }$ , and which may be useful when global-scale structures are, e.g., used for model boundary input. The conclusions of this work support the deployment of inversion codes that explicitly fit $ff$ or, as with the new SyntHIA neural-net, that are trained on data that did so.