We have completed an optical spectroscopic survey of an unbiased, extinction-limited sample of candidate young stars covering 1.3 square degrees of the Rho Ophiuchi star forming region. While infrared, X-ray, and optical surveys of the cloud have identified many young stellar objects (YSOs), these surveys are biased towards particular stages of stellar evolution and are not optimal for studies of the disk frequency and initial mass function.We have obtained over 300 optical spectra to help identify 135 association members based on the presence of H-alpha in emission, lithium absorption, X-ray emission, a mid-infrared excess, a common proper motion, reflection nebulosity, and/or extinction considerations. Spectral types along with R and I band photometry were used to derive effective temperatures and bolometric luminosities for association members to compare with theoretical tracks and isochrones for pre-main-sequence stars. An average age of 3.1 Myr is derived for this population which is intermediate between that of objects embedded in the cloud core of Rho Ophiuchi and low mass stars in the Upper Scorpius subgroup. Consistent with this age we find a circumstellar disk frequency of 27% plus or minus 5%. We also constructed an initial mass function for an extinction-limited sample of 123 YSOs (A_v less than or equal to 8 mag), which is consistent with the field star initial mass function for YSOs with masses > 0.2 M_sun. There may be a deficit of brown dwarfs but this result relies on completeness corrections and requires confirmation.
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