\subsubsection{2MASS Extinction}
As discussed in \citet{Goodman_2009}, although it is expected that in a region as large and complicated as the Ophiuchus the gas-to-dust ratio can vary by a significant amount, the 2MASS/NICER-based extinction measurement might still be the most reliable tracer of column density amongst all the tracers presented in this paper. However, we have to treat it with extreme care, especially towards the very diffuse and very dense regions. In both cases, the uncertainty comes from the number of background stars that can be used to derive the extinction. This being said, the 2MASS extinction is used as the ``true'' extinction measurement and helps us determine the conversion from various types of density measurement (for example, the optical depth and the mass column density) to the equivalent V-band extinction.

Fig. 5 shows the distribution of the 2MASS extinction. It has a clear log-normal-like profile. \citet{Padoan_1997} point out that this log-normal-like profile is equivalent to the $\sigma(A_V)-A_V$ relation first discovered by \citet{Lada_1994}. Thoraval et al. (1997) find that this is the result of small structures below the resolution limit. 