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The newly commissioned University of New South Wales Infrared Fabry-Perot (UNSWIRF) has been used to image molecular hydrogen emission at 2.12 and 2.25 μm in the reflection nebula Parsamyan 18. P 18 is known to exhibit low values of the (1-0)/(2-1) S(1) ratio, suggestive of UV-pumped fluorescence rather than thermal excitation by shocks. Our line ratio mapping reveals the full extent of this fluorescent emission from extended arc-like features, as well as a more concentrated thermal component in regions closer to the central exciting star. We show that the emission morphology, line fluxes and gas density are consistent with the predictions of photodissociation region (PDR) theory. Those regions with the highest intrinsic 1-0 S(1) intensities also tend to show the highest (1-0)/(2-1) S(1) line ratios. Furthermore, variations in the line ratio can be attributed to intrinsic fluctuations in the incident radiation field and/or the gas density, through the self-shielding action of H2. An isolated knot of emission discovered just outside P 18, and having both an unusually high (1-0)/(2-1) S(1) ratio and relative velocity, provides additional evidence for an outflow source associated with P 18.