We present the results of far-infrared imaging of extended regions around three bipolar preplanetary nebulae, AFGL 2688, OH 231.8+4.2, and IRAS 16342-3814, at 70 and 160 μm with the MIPS instrument on the Spitzer Space Telescope. After a careful subtraction of the point-spread function of the central star from these images, we place constraints on the existence of extended shells and thus on the mass outflow rates as a function of radial distance from these stars. We find no apparent extended emission in AFGL 2688 and OH 231.8+4.2 beyond 100'' from the central source. In the case of AFGL 2688, this result is inconsistent with a previous report of two extended dust shells made on the basis of ISO observations. We derive upper limits of 2.1 × 10-7 and 1.0 × 10-7 M⊙ yr-1 for the dust mass-loss rates of AFGL 2688 and OH 231.8, respectively, at 200'' from each source. In contrast to these two sources, IRAS 16342-3814 does show extended emission at both wavelengths, which can be interpreted as a very large dust shell with a radius of ~400'' and a thickness of ~100'', corresponding to 4 and 1 pc, respectively, at a distance of 2 kpc. However, this enhanced emission may also be Galactic cirrus; better azimuthal coverage is necessary for confirmation of a shell. If the extended emission is a shell, it can be modeled, with some assumptions about its dust properties, as enhanced mass outflow at a dust mass outflow rate of 1.5 × 10-6 M⊙ yr-1 superimposed on a steady outflow with a dust mass outflow rate of 1.5 × 10-7 M⊙ yr-1. Because of the size of the possible shell, it is likely that this shell has swept up a substantial mass of interstellar gas during its expansion, so these estimates are upper limits to the stellar mass-loss rate. We find a constant color temperature of 32 K throughout the circumstellar envelope of IRAS 16342-3814, which is consistent with heating by the interstellar radiation field.
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