  Ground-based optical microlensing surveys have provided tantalising, if
inconclusive, evidence for a significant population of free-floating planets
(FFPs). Both ground and space-based facilities are being used and developed
which will be able to probe the distrubution of FFPs with much better
sensitivity. It is vital also to develop a high-precision microlensing
simulation framework to evaluate the completeness of such surveys. We present
the first signal-to-noise limited calculations of the FFP microlensing rate
using the Besancon Galactic model. The microlensing distribution towards the
Galactic centre is simulated for wide-area ground-based optical surveys such as
OGLE or MOA, a wide-area ground-based near-IR survey, and a targeted
space-based near-IR survey which could be undertaken with Euclid or WFIRST. We
present a calculation framework for the computation of the optical and
near-infrared microlensing rate and optical depth for simulated stellar
catalogues which are signal-to-noise limited, and take account of extinction,
unresolved stellar background light and finite source size effects, which can
be significant for FFPs. We find that the global ground-based I-band yield over
a central 200 deg^2 region covering the Galactic centre ranges from 20
Earth-mass FFPs year^-1 up to 3,500 year^-1 for Jupiter FFPs in the limit of
100% detection efficiency, and almost an order of magnitude larger for a K-band
survey. For ground-based surveys we find that the inclusion of finite source
and the unresolved background reveals a mass-dependent variation in the spatial
distribution of FFPs. For a space-based H-band covering 2 deg^2, the yield
depends on the target field but maximizes close to the Galactic centre with
around 76 Earth through to 1,700 Jupiter FFPs year^-1. For near-IR space-based
surveys the spatial distribution of FFPs is found to be largely insensitive to
the FFP mass scale.
