  The European Space Agency mission Gaia has published with its second data
release (DR2) a catalogue of photometric measurements for more than 1.3 billion
astronomical objects in three passbands. The precision of the measurements in
these passbands, denoted G, G_BP, and G_RP, reaches down to the milli-magnitude
level. The scientific exploitation of this data set requires precise knowledge
on the response curves of the three passbands. This work aims to improve the
exploitation of the photometric data by deriving an improved set of response
curves for the three passbands, allowing for an accurate computation of
synthetic Gaia photometry. This is achieved by formulating the problem of
passband determination in a functional analytic formalism, and linking the
photometric measurements with four observational, one empirical and one
theoretical spectral library. We present response curves for G, G_BP, and G_RP
that differ from the previously published curves, and which provide a better
agreement between synthetic Gaia photometry and Gaia observations.
