Objective Light is the most fundamental medium through which humans perceive the objective world, encompassing multiple physical dimensions such as amplitude, phase, and polarization, and these dimensions carry abundant information after light interacts with matter, making their rapid and accurate sensing of great scientific significance and application value. For highly transparent materials such as living cells, variations in the transmitted light field are mainly manifested in the phase dimension, and therefore the development of highly sensitive quantitative phase imaging techniques is crucial for fast and accurate biological tissue analysis and pathological diagnosis. When light interacts with a medium, its polarization state often changes due to the dielectric properties, microstructure, and morphological characteristics of the material, and measuring the polarization state of transmitted or reflected light not only enables the perception of material properties but also enhances optical sensing capabilities in special environments such as nighttime, fog, or haze. Consequently, improving the ability to simultaneously sense multiple physical dimensions of the light field, including amplitude, phase, and polarization, has long been one of the core research directions in optical imaging. While the amplitude of a light field can be directly obtained using photoelectric detectors due to its quadratic relationship with intensity, phase and polarization information are inherently difficult to measure directly. Existing approaches for quantitative phase sensing mainly include interferometric methods, such as digital holographic interferometry, and non-interferometric phase retrieval techniques based on Hartmann wavefront sensing and the transport of intensity equation (TIE). Polarization measurement is typically realized with waveplates, polarizers, and other bulk optical components through time-division, amplitude-division, or polarization-channel-division acquisition of multiple sets of orthogonally polarized images. However, such systems are usually constrained by complex optical layouts and the size of conventional components, which hinders efficient integration and miniaturization, and in particular, time-division imaging severely limits sensing speed and temporal resolution. The emergence of optical metasurfaces provides a promising solution to these challenges, as their ability to manipulate multiple wavefront parameters of light at subwavelength scales enables substantial reduction of imaging system volume while maintaining high imaging quality. Although significant progress has been achieved in metasurface-based imaging and extensive efforts have been devoted to realizing multidimensional light-field imaging using metasurfaces, it remains challenging to develop a compact, easily integrable multidimensional imaging system that is robust and adaptable to complex imaging scenarios.

Methods To address these issues, this work proposes a 4f optical architecture for multidimensional imaging based on a single-layer metasurface and single-shot acquisition. By employing a space- and polarization-multiplexed multi-channel metasurface, three-dimensional spatial decoupling of the orthogonal circular polarization components of the incident light field is achieved, enabling four-channel imaging with jointly controllable defocus and off-axis distances. Four intensity images are simultaneously recorded at the image plane in a single exposure, and through accurate cropping, calibration, and matching of these images, the complex amplitudes of the orthogonal circular polarization components are precisely reconstructed using the transport of intensity equation. Without the need for interferometric reference beams, the proposed architecture enables the simultaneous acquisition of intensity, phase, and polarization ellipticity information of the light field in a single exposure, significantly improving imaging efficiency and system robustness. The non-interferometric multidimensional imaging architecture is further integrated into a commercial microscope platform, demonstrating its compatibility with existing optical systems.

Results and Discussions Quantitative phase imaging of a microlens array is performed to verify phase reconstruction accuracy, and polarization imaging of murine tendon tissue is conducted to demonstrate its capability for revealing birefringent and anisotropic structures in biological samples. Experimental results confirm that the proposed system enables label-free, fast, and multidimensional imaging of biological tissues and cells, effectively overcoming limitations of conventional imaging approaches for highly transparent samples and biological specimens, such as limited imaging dimensionality, high system complexity, and restricted applicability to in vivo measurements. Moreover, the proposed architecture introduces a system design concept that balances miniaturization, functional integration, and imaging performance, providing a practical pathway toward compact multidimensional optical imaging systems.

Conclusions In principle, the proposed framework can achieve full Stokes parameter sensing based on TIE-derived phase and intensity information of orthogonal polarization components. However, in practical experiments, noise, model mismatch, and uncertainties in boundary conditions make it difficult for existing algorithms to accurately reconstruct the phase of complex tissues, especially in regions with large intensity gradients, where distortions and blurring are prone to occur, thereby hindering the reliable determination of the Stokes parameters s1 and s2. Future work will therefore focus on improving TIE-based phase retrieval algorithms to enhance reconstruction accuracy and robustness, as well as optimizing the matching and registration of intensity images acquired from different off-axis directions to mitigate off-axis effects, with the aim of further extending the applicability of the proposed metasurface-based multidimensional imaging architecture to complex biological, medical, and environmental sensing scenarios.