  We present a 3-dimensional matched filtering approach for the blind search of
faint emission-line sources in integral-field spectroscopic datasets. The
filter is designed to account for the spectrally rapidly varying background
noise due to the telluric air glow spectrum. A software implementation of this
matched filtering search is implemented in an updated version of the Line
Source Detection Cataloguing tool (LSDCat2.0). Using public data from the
MUSE-Wide survey we show how the new filter design provides higher detection
significances for faint emission line sources buried in between atmospheric
[OH]-bands at $\lambda \gtrsim 7000$\,\AA{}. We also show how, for a given
source parameterisation, the selection function of the improved algorithm can
be derived analytically from the variances of the data. We verify this analytic
solution against source insertion and recovery experiments in the recently
released dataset of the MUSE eXtreme Deep Field (MXDF). We then illustrate how
the selection function has to be re-scaled for 3D emission line source profiles
that are not fully congruent with the template. This procedure alleviates the
construction of realistic selection functions by removing the need for
computationally cumbersome source insertion and recovery experiments.
