Full-Field 3D Deformation Measurement of Flexible Structures with Multistable Configurations using ETL-Enhanced Single-Camera Stereo DIC

Abstract Full-field three-dimensional (3D) deformation measurement of flexible structures undergoing large reconfigurable deformation remains a significant challenge in experimental solid mechanics, particularly when pronounced surface curvature and large out-of-plane displacements exceed the depth-of-field limitations. Local defocusing leads to incomplete displacement fields and deteriorated measurement accuracy in stereo digital image correlation (stereo DIC). To address the challenge, this paper presents a single-camera stereo DIC system integrated with an electrically tunable lens (ETL) to enable large-depth-of-field 3D deformation measurement. High-quality speckle pattern imaging is achieved by dynamically adjusting the focal state. To address the intrinsic inconsistency of geometric parameters induced by ETL-driven focal variation, a cross-current calibration and coordinate unification framework is developed, allowing 3D reconstructions obtained under different focal states to be accurately mapped into a unified physical coordinate system. A periodic calibration target and a defocus-robust frequency-domain feature extraction strategy are employed to ensure reliable reference point localization under defocused conditions. The performance of the proposed system is validated through experiments, including repeatability assessment under repeated focal switching, large-range axial translation measurement over 200 mm and full-field deformation measurement of a flexible multistable thin-shell structure undergoing configuration transitions. The results demonstrate that the proposed approach achieves continuous and physically consistent 3D displacement fields across an extended depth range, with high repeatability and low measurement error. The developed method provides an effective experimental tool for investigating large deformation and reconfiguration behaviors of flexible structures.