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.