Non-contact anisotropic roughness estimation with physics-informed unrolled optimization of the Harvey–Shack model

Abstract

We present a physics-informed deep-learning method for non-contact estimation of an anisotropic-autocorrelation representation and calibrated directional-roughness labels from a single scattering pattern. The anisotropic generalized Harvey–Shack model is reduced via polar expansion to order-by-order Hankel transforms, giving a differentiable forward operator that supplies synthetic training pairs. A warm-started encoder with six weight-shared refinement steps replaces the previous Nelder–Mead inversion, cutting runtime from ten minutes to under one minute per specimen. In a reanalysis of 16 tool-steel cylinders (Rq 0.1–1.0 μm, 45°, 642 nm), an identity-prior affine calibration places 22/32 core-parameter predictions within ±20% of contact-stylus references on eight held-out, coverage-stratified specimens. Because the statistics constrain σx, σy only through their product, the directional roughnesses are calibrated labels rather than uniquely identifiable parameters, and the along-lay correlation length stays compressed. A fixed configuration passes for two of eight specimens; no leakage-free selection exceeds three, versus seven–eight for a test-aware oracle, indicating preliminary feasibility toward near-line inspection.