Multidimensional position and displacement estimation using periodic coded optical apertures in a single-camera imaging system

Abstract

Accurately estimating multidimensional positions and displacements in fluid dynamic experiments is essential for understanding complex flow phenomena. This paper presents a novel optical measurement setup capable of determining velocity fields using periodic coded optical apertures in a single-camera imaging system. Our method involves placing a periodic transmission grating in front of the optical system and aligning a laser beam along the system’s optical axis. When particles intersect the laser beam, they scatter light, producing out-of-focus images on the imaging sensor resembling the periodic grating. The size and position of these images vary with the distance to the imaging system and the offset from the optical axis, allowing for accurate determination of particle positions. We derive mathematical formulas describing the imaging system and the relationship between image properties and particle positions and verify them through simulations. Additionally, we develop a calibration method enabling arbitrary optical imaging systems to be used with this technique. Finally, we demonstrate the effectiveness of our approach by measuring velocity fields near a ducted ship propeller, a practical application that underscores the real-world impact of our research in fluid dynamics.