Example of a synthetic pseudo-spectrum of an [O III] λ4959,5007 source as seen by OTELO. Upper panel: synthetic spectrum (in red) with arbitrary flux density consisting of a flat continuum plus two emission lines with Gaussian profiles (FWHM = 2 Å) modelling the [O III] doublet at z = 0.835, with Poissonian noise added. The grey dotted curves represent the Airy instrumental profiles of the OTELO RTF scan. These individual profiles can be synthesised into a custom filter response (green curve), which is useful to obtain an integrated IB flux. Lower panel: pseudo-spectrum obtained from the convolution of the synthetic spectrum in the upper panel with these Airy profiles, mimicking the OTELO data. The blue short-dashed line represents the 2σ_med,  c level above the median flux or pseudo-continuum (blue long-dashed line) defined in the main text. Flux density between both spectra differs by a factor equal to the effective passband δλ_e of an RTF slice.