3D shape measurement of complex transparent liquid surfaces using monoscopic deformed fringe transmissometry

The measurement of transparent liquid surface topography is of great importance in many fields such as hydrodynamics of water-walking insects, liquid sloshing and flotation, etc. However, techniques for measuring these specular and rheological surfaces, especially for surfaces with floating objects, have been lacking. Here we report a monoscopic deformed fringe transmissometry for measuring complex transparent liquid surfaces with theoretical sensitivity up to 0.40 μm. The basic principle is to reconstruct the 3D liquid surfaces by the mathematical relations between the in-plane fringe phase-shift and the out-of-plane shape of the liquid surface. It only needs to project a single fringe pattern from the bottom of the liquid and capture a single deformed image from above. A sub-pixel sampling moiré method is proposed to process the captured fringe pattern to obtain the precise phase component and the displacement field, which is then used to reconstruct the 3D shape of the liquid surface. The discontinuous fringes in the pattern also settled by covering an extracted mask to the displacement filed. The verification test of floating 3D printed characters indicates that this new technique is robust in measuring the 3D shape of complex liquid surface. The developed technique provides a versatile tool to explore interfacial phenomena such as wetting, floating, surface wave, etc.