phase-shifted to center the field-of-view on the centroid of the source. The data are then radially binned into bins of equal width. To test the robustness of the $uv$-plane fitting against the $uv$-bin size, we vary the $uv$-bin size from 5 to 50 k$\lambda$.

We fit each $uv$-plane dataset with (1) a single Gaussian profile, (2) two Gaussian components to investigate the possibility of having compact, bright \[\] emission embedded in an extended, low surface-brightness component; (3) a combination of a single Gaussian profile and a constant term, corresponding to a point-source in the image plane. To determine whether the two-component model significantly improves the goodness-of-fit compared to the one-component model, we compare the two models using the F-test [@Bevington1969]. The single-component model is preferred for the continuum emission in ALESS 49.1 and \[\] emission in ALESS 57.1, independently of the $uv$-bin size. We will address the robustness of the inferred $R_{1/2}$ in Section \[subsec:mock\_data\]. The two-component model is strongly ($p>0.95$) preferred for the \[\] emission in ALESS 49.1 and the continuum emission in ALESS 57.1. We do not find the Gaussian $+$ constant-term (point-source) model to be preferred over the single-Gaussian model for any dataset considered. The best-fitting values 