  The OTELO survey is a very deep, blind exploration of a selected region of
the Extended Groth Strip and is designed for finding emission-line sources
(ELSs). The survey design, observations, data reduction, astrometry, and
photometry, as well as the correlation with ancillary data used to obtain a
final catalogue, including photo-z estimates and a preliminary selection of
ELS, were described in a previous contribution. Here, we aim to determine the
main properties and luminosity function (LF) of the [O III] ELS sample of OTELO
as a scientific demonstration of its capabilities, advantages, and
complementarity with respect to other surveys. The selection and analysis
procedures of ELS candidates obtained using tunable filter (TF) pseudo-spectra
are described. We performed simulations in the parameter space of the survey to
obtain emission-line detection probabilities. Relevant characteristics of [O
III] emitters and the LF([O III]), including the main selection biases and
uncertainties, are presented. A total of 184 sources were confirmed as [O III]
emitters at a mean redshift z=0.83. The minimum detectable line flux and
equivalent width (EW) in this ELS sample are $\sim$5 $\times$ 10$^{-19}$ erg
s$^{-1}$ cm$^{2}$ and $\sim$6 \AA, respectively. We are able to constrain the
faint-end slope ($\alpha = -1.03\pm0.08$) of the observed LF([O III]) at
z=0.83. This LF reaches values that are approximately ten times lower than
those from other surveys. The vast majority (84\%) of the morphologically
classified [O III] ELSs are disc-like sources, and 87\% of this sample is
comprised of galaxies with stellar masses of M$_\star$ $<$ 10$^{10}$
M$_{\odot}$.
