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Photodissociation regions (PDRs) are parts of the ISM consisting of predominantly neutral gas, located at the interface between H II regions and molecular clouds. The physical conditions within these regions show variations on very short spatial scales, and therefore PDRs constitute ideal laboratories for investigating the properties and evolution of dust grains. We have mapped IC 63 at high resolution from the UV to the NIR (275 nm to 1.6 $\mu$m), using the Hubble Space Telescope WFC3. Using a Bayesian SED fitting tool, we simultaneously derive a set of stellar ($T_\text{eff}$, $\log(g)$, distance) and extinction ($A_V$, $R_V$) parameters for 520 background stars. We present maps of $A_V$ and $R_V$ with a resolution of 25 arcsec based on these results. The extinction properties vary across the PDR, with values for $A_V$ between 0.5 and 1.4 mag, and a decreasing trend in $R_V$, going from 3.7 at the front of the nebula to values as low as 2.5 further in. This provides evidence for evolution of the dust optical properties. We fit two modified blackbodies to the MIR and FIR SED, obtained by combining the $A_V$ map with data from Spitzer and Herschel. We derive effective temperatures (30 K and 227 K) and the ratio of opacities at 160 $\mu$m to V band $\kappa_{160} / \kappa_V$ ($7.0 \times 10^{-4}$ and $2.9 \times 10^{-9}$) for the two dust populations. Similar fits to individual pixels show spatial variations of $\kappa_{160} / \kappa_{V}$. The analysis of our HST data, combined with these Spitzer and Herschel data, provides the first panchromatic view of dust within a PDR., Comment: 28 pages, 20 figures, accepted for publication in The Astrophysical Journal