Nonlinear synthetic Schlieren methods for free-surface topography measurement using telecentric imaging

Abstract

Free-surface synthetic Schlieren (FS-SS) is a high-resolution, refraction-based optical technique for measuring the instantaneous elevation of a liquid interface. Under the assumptions of small amplitude, small slope, and small paraxial angle, the method yields a linear relationship between the gradient of the surface elevation and the apparent displacement field of a refracted pattern imaged through the surface. Here, we propose three new, nonlinear extensions of the FS-SS method that are specifically dedicated to telecentric imaging. Paraxial distortions are eliminated with a telecentric lens, thereby simplifying the optical model. This allows us to derive nonlinear surface reconstruction models that reach beyond the usual limits of small slope and small wave magnitudes. We implement these nonlinear surface reconstruction algorithms and compare them to the original, linear reconstruction algorithm in three different experiments, using a solid glass lens, spreading oil drops, and nonlinear Faraday waves. At the price of a few iterations, we can realize nonlinear surface reconstructions that are more precise, in particular when we reach high slopes or high-amplitude regimes. We share a library that encodes these nonlinear surface reconstruction algorithms.