  We present a method to estimate and map the two-dimensional distribution of
dust extinction in the late-type spiral galaxy NGC 959 from the theoretical and
observed flux ratio of optical V and mid-IR (MIR) 3.6 micron images. Our method
is applicable to both young and old stellar populations for a range of
metallicities, and is not restricted to lines-of-sight toward star-formation
(SF) regions. We explore this method using a pixel-based analysis on images of
NGC 959 obtained in the V-band at the Vatican Advanced Technology Telescope
(VATT) and at 3.6 micron (L-band) with Spitzer/IRAC. We present the original
and extinction corrected GALEX far-UV (FUV) and near-UV (NUV) images, as well
as optical UBVR images of NGC 959. While the dust lanes are not clearly evident
at GALEX resolution, our dust map clearly traces the dust that can be seen
silhouetted against the galaxy's disk in the high-resolution HST images of NGC
959. The advantages of our method are: (1) it only depends on two relatively
common broadband images in the optical V-band and in the MIR at 3.6 micron (but
adding a near-UV band improves its fidelity); and (2) it is able to map the
two-dimensional spatial distribution of dust within a galaxy. This powerful
tool could be used to measure the detailed distribution of dust extinction
within higher redshift galaxies to be observed with, e.g., the HST/WFC3
(optical--near-IR) and JWST (mid-IR), and to distinguish properties of dust
within galaxy bulges, spiral arms, and inter-arm regions.
