\subsubsection{IRIS Two-point Fit of Dust Thermal Emission}
The basic method we use to derive the dust temperature and column density from the IRIS 60 and 100 $\mu$m flux densities follows \citet{Arce_1999} and \citet{Schnee_2005}. The dust temperature is determined by the ratio of flux densities at 60 and 100 $\mu$m. We then calculate the column density by estimating the opacity along each line of sight. This calculation depends on the values of two parameters: the emissivity spectral index and the conversion factor between the optical depth at 100 $\mu$m and the extinction.

The modified blackbody equation is used to model the dust thermal emission at mid/far-infrared wavelengths. It assumes that each line of sight has a uniform temperature and a uniform volume density, and that the material along the line of sight is in local thermal equilibrium (LTE). After accounting for radiative transfer along the line of sight, the modified blackbody equation can be written as the blackbody equation modified by a power-law emissivity spectral index. At the dust temperature $T_d$, we have the modified blackbody equation:

\begin{equation}
F_\lambda = B_\lambda(T_d)\,(1-\exp{(-\tau)})
\end{equation}

The optical depth $\tau$ can be written in terms of a power-law emissivity, which depends on the wavelength: $\tau = N_d\,\alpha\,\lambda^{-\beta}$ (\citet{Schnee_2005}), where $N_d$ represents the column density of dust grains, $\alpha$ is the constant that relates the flux to the optical depth of the dust, and $\beta$ is the emissivity spectral index. In the optically thin limit, we can calculate the flux from:

\begin{equation}
F_\lambda = B_\lambda(T_d)\,N_d\,\alpha\,\lambda^{-\beta}
\end{equation}

Here we have measurements in IRAS band 3 (60 $\mu$m) and band 4 (100 $\mu$m). To derive the column density, we first calculate the dust temperature from the modified blackbody equation. We can write the ratio of the flux densities at 60 $\mu$m and 100 $\mu$m as:

\begin{equation}
R = \frac{F_{60}}{F_{100}} = 0.6^{-(3+\beta)}\,\frac{\exp{(hc/\lambda_{60}kT)}-1}{\exp{(hc/\lambda_{100}kT)}-1}
\end{equation}

Once a reasonable value of $\beta$ is given, we can calculate the dust temperature. From there, we calculate the optical depth at 100 $\mu$m, assuming again that the lines of sight are optically thin.

\begin{equation}
\tau_{100} = \frac{F_{100}}{B_{100}(T_d)}
\end{equation}

We then convert the 100 $\mu$m optical depth to the V-band extinction using

\begin{equation}
A_V = X\,\tau_{100}
\end{equation}

The V-band extinction provides an estimate of the column density. Here we follow the discussion in \citet{Goodman_2009} and use the 2MASS extinction map as the ``true'' extinction measurement (with limits discussed in \S 4.1.1) to fit for a conversion factor $X$. The equivalent V-band extinction can be further converted to the column density.

Previous works have shown that the dust thermal emission at mid/far-infrared wavelengths is dominantly contributed by Big Grains (BGs; \citet{Stepnik_2003}). However, at wavelengths less than 100 $\mu$m, the observed flux density contains a significant amount of emission from Very Small Grains (VSGs), which we can no longer describe with a simple modified blackbody equation. \citet{Schnee_2008} examine the contribution of VSGs and finds that not only does a large amount of emission at mid-infrared wavelengths come from the VSGs, but also the contribution of VSGs varies systematically with $T_d$ and $N_d$. In the Perseus cloud, the contribution of VSGs at 60 $\mu$m ranges from 77 to 83 \%. We adopt a modification factor of 0.2 to account for the ``true'' thermal emission from the BGs at 60 $\mu$m, which we can model with the modified blackbody equation.

In addition to the uncertainty in the VSG contribution of emission at 60 $\mu$m, there is another uncertainty caused by the emissivity spectral index $\beta$. First we note that the modified blackbody equation assumes a single temperature and volume density for each line of sight. \citet{Shetty_2009} point out that the variation in temperature along the line of sight can affect the shape of the observed SED, even when each dust grain is in local thermal equilibrium and emits according to the blackbody equation. The result is that the modified blackbody equation can no longer recover the shape of SEDs, and that the emissivity spectral index in the empirical power law varies from one line of sight to another. \citet{Kelly_2012} further address that making $\beta$ a free parameter in the calculation does not solve this problem. Any errors in the data from observations and/or calibration will cause the derived $T_d$ and $\beta$ from the modified blackbody equation to show an artificial anti-correlation. This is because some degree of redundancy exists between increasing $T_d$ and decreasing $\beta$ (and vice versa) when we cannot measure the exact SED without any uncertainty. This false anti-correlation has led many works to assume the anti-correlation \emph{a priori} in their derivation (including \citet{Schnee_2005}, but not \citet{Schnee_2008}). For us to derive the dust temperature and column density from the IRIS 60 and 100 $\mu$m, the same trend between $T_d$ and $\beta$ forces us to use a single value for $\beta$ throughout the entire region, due to the lack of data points to fit $T_d$, $N_d$, $\beta$, and the conversion factor $X$ simultaneously. We assume $\beta = 2$ empirically from observations of cold regions (T \< 35 K; \citet{Dupac_2001}) and leave the discussion of temperature variation and the effects of noise to \S 4.2, where we enjoy the wealth of data from Herschel observations.

Fig. 2 and 3 show the equivalent V-band extinction and temperature from the calculation described above. Fig. 4 shows the distribution of the IRIS-based V-band extinction against that based on 2MASS/NICER after the data editing described in \S 3.4. We see from Fig. 4 that there are sub-populations within this distribution. Linking the data with the pixel positions on the sky makes it clear that these sub-populations correspond to different parts of the cloud. Fig. 6 shows this linked data view using the entire dataset without any editing. The dominance of data points along the 1-1 line is from the main cloud, including most of L1729, L1712 to the east and L1688 around the cluster. Points sitting slightly above the 1-1 line are mostly from around the ``shell'' region. Another population that corresponds to the ``northern streamer'' (L1755 and L1765) can be identified when we include the entire data set. The existence of ``sub-populations'' on the plot of $A_V$-$A_V$ hints at the fact that the conversion factor $X$ is different for different regions. Similar results have been reported in \citet{Pineda_2008} for the CO-based extinction. This result was not seen in \citet{Schnee_2005} due to their cropping and smoothing. We adopt the smoothing of a 3' beam, instead of the 5' beam used in \citet{Schnee_2005} and include the very east end of the Ophiuchus cloud. Both the smoothing and cropping adopted in this paper increase the possibility of including more pixels with divergent physical properties.

Fig. 5 presents the distribution of the IRIS-based extinction, which seems askew from the log-normal profile of the 2MASS extinction. This is the result of uncertainties in both the VSG emission and the emissivity spectral index $\beta$. The uncertainty in the amount of VSG emission at 60 $\mu$m affects the determination of $T_d$ using the ratio of flux densities at 60 and 100 $\mu$m. On the other hand, fixing $\beta$ = 2 affects both $T_d$ and $\tau_{100}$, and thus the column density. It is difficult to disentangle these two effects, which again were not seen in \citet{Schnee_2005} (and subsequently \citet{Goodman_2009}) due to the cropping, the smoothing and their \emph{a priori} assumption about the anti-correlation bewteen $\beta$ and $T_d$. 