Dynamic Interferometry With Retrace Error Correction Using Fringe Projection For High-Gradient Fields

Abstract

This paper introduces an innovative approach aimed at advancing the characterization of high-gradient flow fields through the integration of dynamic interferometry and fringe projection techniques. Traditional interferometry offers a precise tool sensitive to optical path changes, typically used to measure refractive index variations induced by factors such as density changes in fluid flow. Rays are usually considered as straight lines, and refraction can be neglected. However, in scenarios involving high-gradient fields, such as supersonic flow with shock waves, optical path changes due to ray bending become significant. In these high-gradient fields, the trajectory of the ray is altered, leading to longer optical paths (resulting in incorrect values) and geometric distortions of the image (resulting in inaccuracies in position). Although retrace error corrections using numerical models of refractive index distribution can mitigate some effects, complete compensation is often challenging. To address this, our proposed technique integrates fringe projection, which is highly sensitive to ray deflections caused by variations in the index of refraction within a transparent medium. The method involves projecting a precisely defined multiplexed cosine fringe pattern across the measured area. Modifications in the pattern indicate ray bending, providing data for interferometric corrections. Real-time interferometry is seamlessly combined with the fringe projection technique to compensate for optical path length changes and mitigate mapping errors induced by ray deflections. The dynamic nature of this combined approach enables the instantaneous capture of both interferometric and fringe-projection data, making it a suitable tool for real-time measurements. Experimental verification of the technique demonstrates its efficacy, with a comparative study against traditional interferometry showcasing a significant reduction in mapping errors.