  Interstellar dust is a key element in our understanding of the interstellar
medium and star formation. The manner in which dust populations evolve with the
excitation and the physical conditions is a first step in the comprehension of
the evolution of inter- stellar dust. Within the framework of the Evolution of
interstellar dust Herschel key program, we have acquired PACS and SPIRE spec-
trophotometric observations of various photodissociation regions, to
characterise this evolution. The aim of this paper is to trace the evolution of
dust grains in the Orion Bar photodissociation region. We use Herschel/PACS (70
and 160 mic) and SPIRE (250, 350 and 500 mic) together with Spitzer/IRAC
observations to map the spatial distribution of the dust populations across the
Bar. Brightness profiles are modelled using the DustEM model coupled with a
radiative transfer code. Thanks to Herschel, we are able to probe finely the
dust emission of the densest parts of the Orion Bar with a resolution from 5.6"
to 35.1". These new observations allow us to infer the temperature of the
biggest grains at different positions in the Bar, which reveals a gradient from
\sim 80 K to 40 K coupled with an increase of the spectral emissivity index
from the ionization front to the densest regions. Combining Spitzer/IRAC
observations, which are sensitive to the dust emission from the surface, with
Herschel maps, we have been able to measure the Orion Bar emission from 3.6 to
500 mic. We find a stratification in the different dust components which can be
re- produced quantitatively by a simple radiative transfer model without dust
evolution. However including dust evolution is needed to explain the brightness
in each band. PAH abundance variations, or a combination of PAH abundance
variations with an emissivity enhancement of the biggest grains due to
coagulation give good results.
