Uncertainties in the Deprojection of the Observed Bar Properties
  In observations, it is important to deproject the two fundamental quantities
characterizing a bar, i.e., its length ($a$) and ellipticity ($e$), to face-on
values before any careful analyses. However, systematic estimation on the
uncertainties of the commonly used deprojection methods is still lacking.
Simulated galaxies are well suited in this study. We project two simulated
barred galaxies onto a 2D plane with different bar orientations and disk
inclination angles ($i$). Bar properties are measured and deprojected with the
popular deprojection methods in the literature. Generally speaking,
deprojection uncertainties increase with increasing $i$. All the deprojection
methods behave badly when $i$ is larger than $60^\circ$, due to vertical
thickness of the bar. Thus, future statistical studies of barred galaxies
should exclude galaxies more inclined than $60^\circ$. At moderate inclination
angles ($i\leq60^\circ$), 2D deprojection methods (analytical and image
stretching) and Fourier-based methods (Fourier decomposition and bar-interbar
contrast) perform reasonably well with uncertainties $\sim10\%$ in both the bar
length and ellipticity. Whereas the uncertainties of the 1D analytical
deprojection can be as high as $100\%$ in certain extreme case.
  We find that different bar measurement methods show systematic differences in
the deprojection uncertainties. We further discuss the deprojection uncertainty
factors with the emphasis on the most important one, i.e., the 3D structure of
the bar itself. We construct two triaxial toy bar models that can qualitatively
reproduce the results of the 1D and 2D analytical deprojections; they confirm
that the vertical thickness of the bar is the main source of uncertainties.
