  Progress in understanding star formation requires detailed observational
constraints on the initial conditions, i.e. dense clumps and cores in giant
molecular clouds that are on the verge of gravitational instability. Such
structures have been studied by their extinction of Near-Infrared (NIR) and,
more recently, Mid-Infrared (MIR) background light. It has been somewhat more
of a surprise to find that there are regions that appear as dark shadows at
Far-Infrared (FIR) wavelengths as long as $\sim$100$\mu m$. Here we develop
analysis methods of FIR images from Spitzer-MIPS and Herschel-PACS that allow
quantitative measurements of cloud mass surface density, $\Sigma$. The method
builds upon that developed for MIR extinction mapping (MIREX) (Butler and Tan
2012), in particular involving a search for independent saturated, i.e. very
opaque, regions that allow measurement of the foreground intensity. We focus on
three massive starless core/clumps in IRDC G028.37+00.07, deriving mass surface
density maps from 3.5 to 70$\mu m$. A by-product of this analysis is
measurement of the spectral energy distribution of the diffuse foreground
emission. The lower opacity at 70$\mu m$ allows us to probe to higher $\Sigma$
values, up to $\sim1\:{\rm{g\:cm}^{-2}}$ in the densest parts of the
core/clumps. Comparison of the $\Sigma$ maps at different wavelengths
constrains the shape of the MIR-FIR dust opacity law in IRDCs. We find it is
most consistent with the thick ice mantle models of Ossenkopf and Henning
(1994). There is tentative evidence for grain ice mantle growth as one goes
from lower to higher $\Sigma$ regions.
