Detection, Reconstruction, and Overheating Warning of Three-Dimensional Dynamic Temperature Fields Inside Conductive Polymer Gels.

Conductive polymer gel materials are inherently susceptible to localized overheating during electrical heating owing to spatially nonuniform conductivity distributions, while their internal three-dimensional temperature fields remain challenging to monitor in real time through noncontact means. Traditional inversion methods, such as Tikhonov-LSQR and TV-ADMM, perform frame-by-frame spatial regularization. The former enforces global smoothness, while the latter preserves sharp edges-but neither exploits the temporal evolution of the temperature field governed by the heat conduction equation, leading to unstable reconstructions in deep regions. To address this limitation, we propose a comprehensive methodology for the calibration, reconstruction, and overheating warning of three-dimensional dynamic temperature fields based on the focused light-field infrared camera. A forward electro-thermal coupled heat conduction model is established to characterize the transient temperature evolution within the gel throughout the heating process. Concurrently, a forward imaging model and its corresponding linear system matrix are constructed for focused light-field infrared imaging, enabling the acquisition of infrared light-field images and subsequent reconstruction of the three-dimensional dynamic temperature field. Furthermore, we develop an ETP-Causal LSQR online inversion algorithm tailored for real-time overheating warning during gel heating. Unlike conventional spatial regularization methods, we incorporate a temporal physical prior: the previous reconstruction is propagated through the heat conduction equation to predict the current temperature field, and this prediction is introduced as a soft constraint into the LSQR solver. The algorithm strictly respects causality, using only current measurements and historical reconstructions. Comparative results demonstrate that the proposed method consistently outperforms conventional Tikhonov-LSQR and TV-ADMM algorithms across multiple aspects, including reconstruction accuracy, noise robustness, physical consistency, cross-operating condition generalization, and computational efficiency, thereby validating the effectiveness and broad applicability of the physically constrained causal inversion framework.