Compressed sensing for surface characterization and metrology

Surface metrology is the science of measuring small-scale features on surfaces. In this paper, a novel compressed sensing (CS) theory is introduced for the surface metrology to reduce data acquisition. We first describe that the CS is naturally fit to surface measurement and analysis. Then, a geometric-wavelet-based recovery algorithm is proposed for scratched and textural surfaces by solving a convex optimal problem with sparse constrained by curvelet transform and wave atom transform. In the framework of compressed measurement, one can stably recover compressible surfaces from incomplete and inaccurate random measurements by using the recovery algorithm. The necessary number of measurements is far fewer than those required by traditional methods that have to obey the Shannon sampling theorem. The compressed metrology essentially shifts online measurement cost to computational cost of offline nonlinear recovery. By combining the idea of sampling, sparsity, and compression, the proposed method indicates a new acquisition protocol and leads to building new measurement instruments. It is very significant for measurements limited by physical constraints, or is extremely expensive. Experiments on engineering and bioengineering surfaces demonstrate good performances of the proposed method.