  To investigate the universality hypothesis of the initial mass function in
the substellar regime, the population of the rho Ophiuchi molecular cloud is
analysed by including a new sample of low-mass spectroscopically confirmed
members. To that end, we have conducted a large spectroscopic follow-up of
young substellar candidates uncovered in our previous photometric survey. The
spectral types and extinction were derived for a newly found population of
substellar objects, and its masses estimated by comparison to evolutionary
models. A thoroughly literature search was conducted to provide an up-to-date
census of the cluster, which was then used to derive the luminosity and mass
functions, as well as the ratio of brown dwarfs to stars in the cluster. These
results were then compared to other young clusters. It is shown that the study
of the substellar population of the rho Ophiuchi molecular cloud is hampered
only by the high extinction in the cluster ruling out an apparent paucity of
brown dwarfs. The discovery of 16 new members of rho Ophiuchi, 13 of them in
the substellar regime, reveals the low-mass end of its population and shows the
success of our photometric candidate selection with the WIRCam survey. The
study of the brown dwarf population of the cluster reveals a high disk fraction
of 76 (+5-8)%. Taking the characteristic peak mass of the derived mass function
and the ratio of brown dwarfs to stars into account, we conclude that the mass
function of rho Ophiuchi is similar to other nearby young clusters.
