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Dressed-photon–phonon (DPP) etching is a disruptive technology in planarizing material surfaces because it completely eliminates mechanical contact processes. However, adequate metrics for evaluating the surface roughness and the underlying physical mechanisms are still not well understood. Here, we propose a two-dimensional hierarchical surface roughness measure, inspired by the Allan variance, that represents the effectiveness of DPP etching while conserving the original two-dimensional surface topology. Also, we build a simple physical model of DPP etching that agrees well with the experimental observations, which clearly shows the involvement of the intrinsic hierarchical properties of dressed photons, or optical near-fields, in the surface processing.