Monocular complex amplitude imaging via a polarization-multiplexed liquid-crystal-lens-informed Fourier neural network

The success of data-driven deep learning in computational imaging is often constrained by the need for extensive labeled datasets. Recent progress in physics-informed neural networks has mitigated this issue by integrating analytical physical models, allowing data-free training. However, for challenging imaging tasks, such as to simultaneously acquire complex amplitude light-field information, the weak physical constraints of conventional imaging hardware largely limit the spatiotemporal imaging resolution. Here, we propose an extremely simple yet powerful monocular camera for complex amplitude imaging based on a liquid-crystal (LC)-lens-informed Fourier neural network. Combining a polarization-multiplexed bifocal LC lens with a polarization image sensor, the camera acts as a polarization phase-shifting radial shearing interferometer. Without any labeled data, the LC-lens-informed Fourier neural network can reconstruct the complex amplitude of a variety of scenes from captured polarization images in a single shot with high fidelity. We experimentally demonstrate the reconstruction of wavefront aberrations involving 136 Zernike modes with a phase accuracy of <i>λ</i>/35 as well as static hologram retrieval and dynamic monitoring of air flow and flame fields. This complementary hardware-algorithm framework offers a promising pathway for developing compact, versatile and high-performance complex amplitude imaging systems for adaptive optics, hologram reconstruction and material diagnosis applications.