Fringe projection assisted dynamic interferometry for phase retrieval in high-gradient refractive fields

• A single-shot hybrid method combining Spatial Carrier Interferometry and Fringe Pattern Projection is introduced for phase retrieval in high-gradient refractive fields. • Fringe Pattern Projection provides wavefront slope and displacement information that enables robust guided unwrapping of the interferometric phase. • The measured displacement field is used to correct geometric mapping errors caused by refractive ray bending. • Fourier-domain separation of SCI and FPP carriers enables clean demultiplexing from a single camera exposure. • Experimental validation on a strongly refracting thermal flow demonstrates artifact-free phase retrieval where conventional interferometry fails. We present a single-shot hybrid method that combines Spatial Carrier Interferometry (SCI) with Fringe Pattern Projection (FPP) to extend interferometric phase retrieval into regions with strong refractive-index gradients. The approach preserves the high sensitivity of SCI while gaining robustness to large ray deflections that typically cause phase discontinuities and loss of mapping. From the same exposure, the projected fringe pattern provides both (i) local ray-deflection-induced displacements that enable geometric remapping of the interferometric phase, and (ii) wavefront-slope information that can be integrated into a smooth, jump-free phase map to guide unwrapping. Because the projected fringe must remain in focus, the imaging plane is positioned slightly in front of the refractive object, introducing a small but measurable mapping error that the method subsequently corrects using the recovered FPP displacement field. Experiments on steep refractive-index distributions demonstrate artifact-free unwrapping and improved quantitative accuracy compared with standard interferometry, while maintaining SCI sensitivity. The technique is particularly suited for dynamic environments with strong gradients, such as compressible flows and shock waves.