This is the first of a series of investigations into far-IR characteristics of 11 planetary nebulae (PNs) under the Herschel Space Observatory Open Time 1 program, Herschel Planetary Nebula Survey (HerPlaNS). Using the HerPlaNS data set, we look into the PN energetics and variations of the physical conditions within the target nebulae. In the present work, we provide an overview of the survey, data acquisition and processing, and resulting data products. We perform (1) PACS/SPIRE broadband imaging to determine the spatial distribution of the cold dust component in the target PNs and (2) PACS/SPIRE spectral-energy-distribution (SED) and line spectroscopy to determine the spatial distribution of the gas component in the target PNs. For the case of NGC 6781, the broadband maps confirm the nearly pole-on barrel structure of the amorphous carbon-richdust shell and the surrounding halo having temperatures of 26-40 K. The PACS/SPIRE multi-position spectra show spatial variations of far-IR lines that reflect the physical stratification of the nebula. We demonstrate that spatially-resolved far-IR line diagnostics yield the (T_e, n_e) profiles, from which distributions of ionized, atomic, and molecular gases can be determined. Direct comparison of the dust and gas column mass maps constrained by the HerPlaNS data allows to construct an empirical gas-to-dust mass ratio map, which shows a range of ratios with the median of 195+-110. The present analysis yields estimates of the total mass of the shell to be 0.86 M_sun, consisting of 0.54 M_sun of ionized gas, 0.12 M_sun of atomic gas, 0.2 M_sun of molecular gas, and 4 x 10^-3 M_sun of dust grains. These estimates also suggest that the central star of about 1.5 M_sun initial mass is terminating its PN evolution onto the white dwarf cooling track.
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