  Stars are born in dense cores of molecular clouds. The core mass function
(CMF), which is the mass distribution of dense cores, is important for
understanding the stellar initial mass function (IMF). We obtained 350 $\mu$m
dust continuum data using the SHARC-II camera at the Caltech Submillimeter
Observatory (CSO) telescope. A 350 $\mu$m map covering 0.25 ${deg}^{2}$ of the
Ophiuchus molecular cloud was created by mosaicing 56 separate scans. The CSO
telescope had an angular resolution of 9 $^{\prime\prime}$, corresponding to
$1.2\times {10}^{3}\ $AU at the distance of the Ophiuchus molecular cloud (131
pc). The data was reduced using the Comprehensive Reduction Utility for
SHARC-II (CRUSH). The flux density map was analyzed using the GaussClumps
algorithm, within which 75 cores has been identified. We used the Spitzer c2d
catalogs to separate the cores into 63 starless cores and 12 protostellar
cores. By locating Jeans instabilities, 55 prestellar cores (a subcategory of
starless cores) were also identified. The excitation temperatures, which were
derived from FCRAO ${}^{12}$CO data, help to improve the accuracy of the masses
of the cores. We adopted a Monte Carlo approach to analyze the CMF with two
types of functional forms; power law and log-normal. The whole and prestellar
CMF are both well fitted by a log-normal distribution, with $\mu
=-1.18\pm0.10,\ \sigma =0.58\pm0.05$ and $\mu =1.40\pm0.10,\ \sigma
=0.50\pm0.05$ respectively. This finding suggests that turbulence influences
the evolution of the Ophiuchus molecular cloud.
