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In observations, it is important to deproject the two fundamental quantitiescharacterizing a bar, i.e., its length ($a$) and ellipticity ($e$), to face-onvalues before any careful analyses. However, systematic estimation on theuncertainties of the commonly used deprojection methods is still lacking.Simulated galaxies are well suited in this study. We project two simulatedbarred galaxies onto a 2D plane with different bar orientations and diskinclination angles ($i$). Bar properties are measured and deprojected with thepopular deprojection methods in the literature. Generally speaking,deprojection uncertainties increase with increasing $i$. All the deprojectionmethods behave badly when $i$ is larger than $60^\circ$, due to verticalthickness of the bar. Thus, future statistical studies of barred galaxiesshould exclude galaxies more inclined than $60^\circ$. At moderate inclinationangles ($i\leq60^\circ$), 2D deprojection methods (analytical and imagestretching) and Fourier-based methods (Fourier decomposition and bar-interbarcontrast) perform reasonably well with uncertainties $\sim10\%$ in both the barlength and ellipticity. Whereas the uncertainties of the 1D analyticaldeprojection can be as high as $100\%$ in certain extreme case.  We find that different bar measurement methods show systematic differences inthe deprojection uncertainties. We further discuss the deprojection uncertaintyfactors with the emphasis on the most important one, i.e., the 3D structure ofthe bar itself. We construct two triaxial toy bar models that can qualitativelyreproduce the results of the 1D and 2D analytical deprojections; they confirmthat the vertical thickness of the bar is the main source of uncertainties.

Uncertainties in the Deprojection of the Observed Bar Properties