We report a near-infrared survey of 200 arcmin2 in the cores of the rh
o Ophiuchi interstellar clouds, leading to the detection of 91 sources
. We develop a new method for estimating the luminosities of these sou
rces based on fitting of isochrones from theoretical models. Applicati
on of this method allows us to determine a luminosity function and acc
ompanying initial mass function for the cluster of young stars forming
in these clouds. The IMF extends to well below the bottom of the main
sequence (0.08 M.) with no obvious feature at the transition between
stellar and substellar masses. The power-law exponent of the IMF at lo
w stellar and substellar masses is roughly - 1.3 to - 1.1, with formal
errors of 0.2. These values are consistent with extrapolation of many
estimates of the local IMF to substellar masses. At least seven objec
ts appear to be substellar, even allowing for the largest plausible er
rors in the observations, the analysis, and the theoretical evolutiona
ry models for these sources. It therefore seems likely that brown dwar
fs form in significant numbers and that the process of cloud fragmenta
tion is not biased against substellar masses. These results indicate t
hat the widespread difficulty in finding large numbers of brown dwarfs
in older stellar populations arise from the rapid cooling and possibl
y from atmospheric absorptions that may depress the near infrared spec
tra outputs of these objects.