Cascaded optical convolutional neural network for quantitative phase imaging (<italic>invited</italic>)

ObjectiveQuantitative Phase Imaging (QPI) is a vital label-free technique in biomedical detection, capable of acquiring morphological and refractive index distribution information of samples. However, existing digital reconstruction methods face significant bottlenecks in computing power and power consumption. Furthermore, traditional All-optical Diffractive Neural Networks (DNNs) suffer from the lack of light field convergence capabilities, leading to bulky systems with multi-layer stacking, severe diffraction loss, and difficulties in optimization where training often falls into local optima. To address these challenges and meet the demand for high-throughput, low-latency online detection, this paper proposes a compact QPI method based on an Optical Convolutional Neural Network (OCNN). By introducing physical constraints into the optical path, the proposed method aims to achieve high-fidelity phase recovery with a minimized system footprint.MethodsAn OCNN architecture based on a cascaded single-lens 2f imaging path is constructed. Different from traditional pure diffractive networks, this design introduces an equivalent lens factor with a quadratic phase distribution into each diffraction layer. This configuration physically decouples the functions of the optical elements: the lens factor is responsible for refocusing the divergent light field and constraining the beam aperture, while the Diffractive Optical Element (DOE) focuses exclusively on feature filtering and phase contrast conversion in the frequency domain. Numerical simulations are performed using the PyTorch deep learning framework on the Tiny-ImageNet dataset, which is preprocessed to simulate phase objects The system parameters are configured with a working wavelength of 632.8 nm and a neuron size of 3.74 μm. The network is trained using the Mean Squared Error (MSE) loss function and the Adam optimizer to update the phase parameters of the DOEs.Results and DiscussionsThe simulation results demonstrate that the OCNN architecture achieves high-fidelity phase recovery using only two diffraction layers. Quantitatively, the Pearson Correlation Coefficient (PCC) between the output image and the ground truth reaches 0.8974, and the MSE is as low as 0.0972. Compared with the conventional 2-layer DNN, these metrics are improved by approximately 52.9% and reduced by 69.2%, respectively. In terms of convergence analysis, although the DNN shows a faster loss reduction in the initial training stage by prioritizing the learning of basic light focusing, it quickly hits a bottleneck. In contrast, the OCNN, relieved of the focusing burden by the lens factor, focuses on learning complex high-frequency features from the beginning. It exhibits a stronger continuous optimization capability and achieves a significantly better steady-state convergence limit Visual comparisons show that OCNN clearly reconstructs high-frequency texture details and edges that are lost in DNN results. Furthermore, the analysis of the phase modulation layer reveals that the DOE in OCNN presents a clear, structured texture across the full aperture, whereas the DNN exhibits a center-edge difference where edge neurons are wasted as virtual stops to prevent light leakage.ConclusionsA compact quantitative phase imaging architecture based on OCNN is designed. By integrating lens factors into the diffractive units to build a relay imaging path, the system physically decouples the functions of light field convergence and feature extraction. This design effectively solves the problems of beam divergence and optimization difficulty inherent in traditional DNNs. Numerical simulations verify that the system achieves high-performance phase recovery (PCC>0.89) with a compact 2-layer structure. The method not only significantly reduces the number of diffractive devices and compresses the axial size of the system but also improves energy utilization and physical interpretability. This study provides a new technical path and theoretical support for building low-power, high-integration on-chip all-optical computing imaging systems.