Phase-retrieval of thermal lenses from an intensity-only reconstruction IA algorithm

Abstract The measurement of the optical wavefront phase remains a fundamental challenge in classical optics, particularly in systems where light–matter interactions induce complex thermal and refractive effects. Among these, thermal lensing represents a key manifestation of laser-induced heating, in which localized temperature gradients modify the refractive index of the medium, thereby altering light propagation. Notably, thermal lensing has been employed to characterize materials in the liquid state, as it produces a diffraction pattern that can be regarded as an optical fingerprint of the liquid. Precise phase retrieval is, therefore, essential for extracting the physicochemical properties of materials. In this work, we introduce and experimentally validate a robust phase retrieval method specifically designed for the accurate characterization of thermal lenses. The proposed approach is based on a novel intensity-only reconstruction framework using an artificial intelligence algorithm, specifically, a genetic algorithm, that requires only a single measurement of the photothermal-induced diffraction pattern, acquired through a simple, non-interferometric setup. The algorithm is optimized to efficiently handle the smooth phase gradients characteristic of thermal lenses, thereby overcoming convergence issues associated with wide search spaces. We demonstrate the efficacy of the method by quantitatively reconstructing the phase profile of thermal lenses induced in binary mixtures of water and methanol at different power levels, achieving excellent agreement between experimental observations and reconstructed results. These findings demonstrate that incorporating artificial intelligence–based phase reconstruction methods enables high-precision characterization of thermal lenses, revealing subtle features of light–matter interactions. Importantly, this approach opens new avenues for the study and characterization of materials, allowing simultaneous evaluation of their optical, thermal, and dynamic properties.