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arXiv · 2603.16418

Looking down the rabbit hole: Towards quantum optimal estimation of surface roughness

Quentin Muller·Tommaso Tufarelli·Madalin Guta·Katherine Inzani·Samanta Piano·Gerardo Adesso
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Abstract

Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optics. By adopting quantum parameter estimation methods, we determine the ultimate precision limits for estimating spatial moments of a general three-dimensional distribution of incoherent point sources in the sub-diffraction regime. Specializing this result to the axial profile, we show that the information on the first moment (mean height) and standard deviation (roughness) is bounded by a constant. While classical imaging techniques fail to achieve this bound, a quantum inspired imaging technique based on spatial mode demultiplexing is proven to be optimal for estimating the axial standard deviation. This provides a powerful and experimentally accessible route to measuring roughness of nearly smooth surface patches beyond the diffraction limit.

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Quentin Muller, Tommaso Tufarelli, Madalin Guta, Katherine Inzani, Samanta Piano, Gerardo Adesso. 2026-03-17. Looking down the rabbit hole: Towards quantum optimal estimation of surface roughness. https://doi.org/10.1088/2058-9565%2Fae97ff

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