We present broad band imaging observations obtained with the ``peak up imagers of the Spitzer Space Telescope Infrared Spectrograph (IRS) at wavelengths of 16micron and 22micron for a number of sources detected primarily at submillimeter wavelengths, which are believed to be at high, though undetermined, redshift. We targeted 11 sources originally detected by SCUBA and 5 submillimeter sources detected at 1.2mm by MAMBO. Two optically discovered quasars with z>6 were also observed to determine if there is detectable dust emission at such high redshifts. Seven of the submillimeter sources and both high-redshift quasars were detected, and upper limits of about ~50microJy apply to the remainder. Using their mid-/far-IR colors, we demonstrate that all of the submillimeter sources are at z>1.4. The mid-IR colors for two of our detections and three of our strong upper limits suggest that these galaxies must be at z>2.5. We also introduce a technique for estimating redshifts and source characteristics based only on the ratio of fluxes in the 16micron and 22micron images.
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