Shock-wave distortion cancellation using numerical recalculated intensity propagation phase holography

Abstract

Digital holography is a three-dimensional (3D) measurement technique that can be used to quantitatively determine the size and 3D location of the objects inside a field-of-view. However, in systems where refractive index gradients are present, variations in optical phase due to high-speed shock-waves or low-speed thermal gradients can cause distortions that obscure objects. While techniques like phase-conjugate digital in-line holography and iterative phase measurement techniques have been developed in the past for phase removal or phase measurement, they require either nonlinear four-wave-mixing or iterative algorithms to operate. In this paper, we demonstrate a novel recalculated intensity propagation phase holography (RIPPH) method that captures distorted holograms using low-power continuous lasers, refocuses the hologram to the plane of the distortion, and cancels the phase distortion numerically in a single post-processing step. The resulting hologram can be numerically refocused to provide distortion-free 3D information describing objects that absorb or scatter light. In RIPPH, only the approximate z-locations of the phase distortions are needed, making this method significantly faster to compute than phase retrieval methods. Theoretical simulations are first used to describe and assess the distortion removal process. Experiments are then conducted to demonstrate at least 3× lower edge distortion for RIPPH compared to traditional digital in-line holography. We demonstrate, for the first time, how phase distortions from supersonic air jets, particle-laden spherically expanding shock-waves, and convectively-driven thermal gradients are numerically cancelled and show how objects of interest are accurately recovered.