Novel optical method for reconstruction of axisymmetric capillary wave surface topography: theory, simulation, and experimentation*

Mathematical modeling of waves is integral for gaining insight into real-world phenomena. Despite their omnipresence, water waves were considered unsuitable for elementary courses by Feynman due to their inherent complexities and non-linear behavior. However, capillary waves on liquid-gas interface are described quite accurately by the linear wave theory. Resulting equations relate the fundamental liquid properties like surface tension and viscosity to the wave properties like wavelength and attenuation.

A novel optical method is presented to reconstruct wave surface topography of parametrically excited finite-amplitude axisymmetric capillary waves. Leveraging refraction of light to magnify amplitude, the method solves the inverse (geometric) optics problem while exploiting the underlying symmetric nature to recreate the entire wave surface uniquely and accurately. Its novelty lies in the simplicity and affordability (laser pointer and smartphone) making it ideal for classroom demonstrations. A MATLAB script is developed to serve as a proof-of-concept for the proposed method. Additionally, multiphase flow simulations are conducted to assess the agreement between the theoretical predictions and the real-world behavior observed in the experiments. This analysis yields valuable insights for determining the optimum tuning parameter values. Subsequently, an experimental investigation is performed to rigorously assess the accuracy and feasibility of the proposed method.