Optical mapping of fluid density interfaces: Concepts and implementations

Abstract

Several ideas of color encoding for surface slope measurements are systematically explored and reviewed to develop a new set of fundamental concepts. It is shown that different systems, such as shadowgraphs, Schlieren optics, and our water surface gradient detectors, can also be universally described through the concepts of sun glitter functions, incident light‐source encoding, and observer encoding. These concepts provide a more precise way of mathematically formulating and physically interpreting the flow visualization images, thereby providing quantitative results. It is this new system of concepts that uncover the quantitative potential of these optical methods. The measurement abilities of various existing optical systems are thus enhanced from qualitative observation or visualization to the well‐defined quantitative measurement. This is a critical step forward. The concepts can also be further extended to measure fluid flows with multiple density layers or flows with continuous density variations. As an example of implementation, the method of measuring a water‐surface gradient is extended into a reflective approach of detecting small changes of surface slope at an air–water interface. In this process, fluid surface slopes (surface gradients) are first optically mapped into color space. An array of lenses is used to transform the rays of an optical light source into a series of colored parallel light beams by passing the light through a group of two‐dimensional color palettes at the focal planes of the lens array. This system of parallel light beams is used to illuminate a free surface of water. The reflected rays from the free surface are captured by a charge‐coupled device color camera located above the surface. The slopes are derived from the color images after the calibration, and surface elevations are obtained by integrating the slopes. This technique is then applied to observe free‐surface deformations caused by near‐surface turbulence interacting with the free surface.