  The aim of this study is to demonstrate how the logarithmic millimeter
continuum gradient observed using the Atacama Large Millimeter/submillimeter
Array (ALMA) may be used to estimate optical thickness in the solar atmosphere.
We discuss how using multi-wavelength millimeter measurements can refine plasma
analysis through knowledge of the absorption mechanisms. Here we use sub-band
observations from the publicly available science verification (SV) data, whilst
our methodology will also be applicable to regular ALMA data. The spectral
resolving capacity of ALMA SV data is tested using the enhancement coincident
with an X-ray Bright Point (XBP) and from a plasmoid ejection event near active
region NOAA12470 observed in Band 3 (84-116 GHz) on 17/12/2015. We compute the
interferometric brightness temperature light-curve for both features at each of
the four constituent sub-bands to find the logarithmic millimetre spectrum. We
compared the observed logarithmic spectral gradient with the derived
relationship with optical thickness for an isothermal plasma to estimate the
structure's optical thicknesses. We conclude, within 90% confidence, that the
stationary enhancement has an optical thickness between $0.02 \leq \tau \leq
2.78$, and that the moving enhancement has $0.11 \leq \tau \leq 2.78$, thus
both lie near to the transition between optically thin and thick plasma at 100
GHz. From these estimates, isothermal plasmas with typical Band 3 background
brightness temperatures would be expected to have electron temperatures of
$\sim 7370 - 15300$ K for the stationary enhancement and between $\sim 7440 -
9560$ K for the moving enhancement, thus demonstrating the benefit of sub-band
ALMA spectral analysis.
