# Acoustic Scattering Models from Rough Surfaces: A Brief Review and Recent Advances
## 5 Summary, Discussion and Perspectives
Nevertheless, this perspective has to be tested and validated, since such a model will generate head waves as if they have been created on successive local non-finite tangential plane. PT and KA are usually seen as complementary, PT being valid for small roughness scales and Kirchhoff for large scales. Several other approximations have been developed in the view of handling the inconveniences of the classical methods (PT and KA) and enlarge the simulation validity. Some of them (phase perturbation theory, two-scales models) found some applications in electromagnetism. A recent study [131] has just began in order to try to improve the two-scale models. We are not convinced that improving these models is the best perspective because they inherently own a certain complexity and there are probably better candidates (evoked in the following) in simulation methods. The small slope approximation (SSA) is a model based on an integral field equation; it is more efficient than Kirchhoff for grazing angles but is only valid for small surface slopes. Indeed, the SSA is of great importance in ocean applications for modeling scattering from ocean surfaces on which the incidence is generally near from grazing: in such a configuration the SSA accuracy is well established. One main future challenge is to extend this approximation to layered fluid seafloors. In a study published this year [116], different approximations are proposed but they give different results in the case of strong internal reflections and also differ from Kirchhoff in specular direction. Numerical validationsare clearly needed to try to find the best approximation among them; another problem is that only one extended from electromagnetism [118] can deal with multiple layers. The parabolic equation describes all physical effects including shadowing, but this method needs a complex and heavy numerical technique to solve the parabolic equation. The parabolic equation method has recently been extended to forward scattering, but numerous efforts should be necessary in the future to build a more robust model applicable for both forward and backward 3D scattering. Such a strategy can be seen complex when compared to other methods as fully numerical ones which are generic for all scattering directions. There is also recent progress in methods based on the integral equation; for instance the new development described in [132] leads to impressive results, notably for grazing angles; but the calculation time is still for the moment a limitation by comparison with simpler methods, if we are rather interested in near normal incidence. Numerical methods are obviously the main rivals of the existing analytical models. For numerical techniques, obtaining 3D simulations with a reasonable computation time remains a challenge. In a very recent study, the boundary element method has been adapted [133] to reduce the 3D calculation time; the proposed adaptation is validated by using approximated models (KA and PT) showing that the classical approximations are also useful for validation purposes. In the field of NDE, one major future challenge is to model scattering from roughness in components fabricated by additive manufacturing (AM). The fatigue life of AM specimens is very influenced by their surface topography [134]. AM processes for metallic parts are notably the selective laser melting (SLM), selective electron beam melting (SEBM), laser metal deposition (LMD) and also wire arc additive manufacturing (WAAM [135]). The corresponding roughness value of each process is discussed in [136; 137]: it is 4-11 \(\upmu\)m Ra for SLM, 15-35 \(\upmu\)m Ra for SEBM, 10 \(\upmu\)m Ra and 200 \(\upmu\)m Ra for LMD, and can be very important for WAAM. Note that models are searched for the prediction of surface roughness (see a list of studies in the introduction of [138]), the optimization of process parameters as well as the roughness minimization (as in [138]) for manufacturing using WAAM and milling.