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Using the 16$\mu$m peakup imager on the Infrared Spectrograph (IRS) onSpitzer, we present a serendipitous survey of 0.0392 deg$^{2}$ within the areaof the NOAO Deep Wide Field Survey in Bootes. Combining our results with theavailable Multiband Imaging Photometer for Spitzer (MIPS) 24$\mu$m survey ofthis area, we produce a catalog of 150 16$\mu$m sources brighter than 0.18 mJy(3$\sigma$) for which we derive measures or limits on the 16/24$\mu$m colors.Such colors are especially useful in determining redshifts for sources whosemid infrared spectra contain strong emission or absorption features thatcharacterize these colors as a function of redshift. We find that the 9.7$\mu$msilicate absorption feature in Ultraluminous Infrared Galaxies (ULIRGs) resultsin sources brighter at 16$\mu$m than at 24$\mu$m at z $\sim$ 1--1.8 by at least20%. With a threshold flux ratio of 1.2, restricting our analysis to $>5\sigma$detections at 16$\mu$m, and using a $3\sigma$ limit on 24$\mu$m non-detections,the number of silicate-absorbed ULIRG candidates is 36. This defines a strongupper limit of $\sim$920 sources deg$^{-2}$, on the population ofsilicate-absorbed ULIRGs at z $\sim$ 1--1.8. This source count is about half ofthe total number of sources predicted at z $\sim$ 1--2 by variousphenomenological models. We note that the high 16/24$\mu$m colors measuredcannot be reproduced by any of the mid-IR spectral energy distributions assumedby these models, which points to the strong limitations currently affecting ourphenomenological and theoretical understanding of infrared galaxy evolution.Comment: Accepted for Publication in Astrophysical Journal Letters 4 pages, 2  figures, 1 tabl

Identifying Silicate-absorbed ULIRGs at z ~ 1-2 in the Bootes Field Using the Spitzer IRS