Physics-constrained decoupling of multi-layer magneto-optical images for quantitative reconstruction of artificially machined rail-head cracks

During magneto-optical (MO) inspection of rail heads, surface curvature produces spatially varying lift-off between the MO film and rail surface. Coupling of this lift-off effect with crack leakage magnetic fields distorts crack responses and hinders quantitative characterisation. This study proposes a physics-constrained decoupling method based on multilayer MO imaging to reconstruct crack-related magnetic responses on curved rail surfaces. Treating MO images as coupled responses of lift-off and crack leakage fields, the method combines lift-off characteristics of magnetic flux leakage (MFL) predicted by a conventional magnetic dipole model with curvature-induced lift-off variations to decouple the surface lift-off field. Experiments on artificially machined inclined-surface cracks and rectangular-slot cracks validate the method. Over a lift-off range of 1–1.8 mm, the peak-to-peak width of crack-induced MFL responses increases monotonically with lift-off, exceeding 50% growth in representative regions, while peak amplitude changes by less than 2%, supporting the physical constraints. Reconstructed surface inclination has an error below 4%. For rail-head rectangular slots, the reconstructed lift-off field closely matches the actual curvature profile, representing an equivalent height variation of approximately 0.2 mm, and enables accurate crack reconstruction.