Nonlinear synthetic Schlieren methods for free-surface topography measurement using telecentric imaging
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910212062969856 |
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| author | Zhang, Shimin Moisy, Frédéric Herreman, Wietze Lin, Zhiliang |
| author_facet | Zhang, Shimin Moisy, Frédéric Herreman, Wietze Lin, Zhiliang |
| contents | 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 realise 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11969 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonlinear synthetic Schlieren methods for free-surface topography measurement using telecentric imaging Zhang, Shimin Moisy, Frédéric Herreman, Wietze Lin, Zhiliang Fluid Dynamics 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 realise 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. |
| title | Nonlinear synthetic Schlieren methods for free-surface topography measurement using telecentric imaging |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2605.11969 |