Edge detection is one of the common data processing methods and can resolve core problems in the field of machine vision, which has a wide range of applications in object detection, image segmentation, data compression, microscopic imaging, and object suggestion generation. Edges can be extracted by the spatial differentiator (SD) and reflect the key information in the image more efficiently. In the biomedical field, intensity changes of phase objects such as biological tissues and cells are usually weak. To more clearly and directly reflect the morphological boundary and structural characteristics of phase objects, it is of great significance to develop edge detection technologies for phase objects.

Optical analog computing is a powerful tool to replace digital signal processing for large-scale data processing at the speed of light and has the characteristics of high-speed parallelism, large data throughput and low energy consumption. For the imaging of pure phase objects, phase contrast microscopy based on Fourier optical spin splitting and quantitative phase gradient can only image one-dimensional edges, which cannot avoid anisotropy and artifacts. In order to complete isotropic 2D edge detection, it is necessary to design subwavelength structure meta-surface and place it on the Fourier plane of 4f system, which makes it difficult to integrate and miniaturize the imaging system.

Differential Interference Contrast (DIC) technology, as a common phase imaging method, can produce relief effect on the observed phase objects, even if it is not dyed. However, the beam splitting prism can only be set in one direction of the image, and the emboss effect can only enhance a one-dimensional edge.

To solve the above problems, researchers from the University of Shanghai for Science and Technology (USST) have designed an all-optical edge detection system based on the principle of differential interferometric contrast. The all-optical signal processor can be directly integrated with the differential interferometric contrast microscope to extract edges with adjustable resolution for colorless and transparent phase targets. Academician Gu Min, Professor Qiming Zhang and Professor Hui Yang were the corresponding authors, and Dr. Yiming Li was the first author. The research results are published in Chinese Optics Letters, Vol. 22, Issue 1, 2024: Yiming Li, Ran Li, Quan Chen, Haitao Luan, Haijun Lu, Hui Yang, Min Gu, Qiming Zhang. Differential interference contrast phase edging net: an all-optical learning system for edge detection of phase objects[J]. Chinese Optics Letters, 2024, 22(1): 0111021.

In this study, a diffractive neural network (Differential Interference Contrast Phase Edging Net, DPENet) based on the principle of differential interference contrast was proposed to detect the edges of phase objects in an all-optical manner. During simulation, the phase object was divided into incident and reference light by dual Wollaston prisms (DWPs). Differential interference was achieved through polarized light aligned in the same direction by polarizers. The original differential signal was processed by the diffractive neural network to obtain the edge image of the corresponding phase object. The scale of the edge could be adjusted by varying the air gap of the DWPs during detection. The performance and generalization capability of the system were assessed with the MNIST and NIST datasets. F-scores of 0.9308 and 0.9352 were respectively achieved on the MNIST and NIST datasets, with the highest imaging resolution reaching 420 nm. Furthermore, the application of DPENet in the field of biological imaging was validated, demonstrating its ability to detect the edges of biological cells and achieve a maximum F-score of 0.7462.

The green laser with a wavelength (λ) of 532 nm is used as the input light source for DPENet. The pixel size is configured to be 420 nm, and the inter-layer propagation distance is set at 40λ. The output from the spatial light modulator (SLM) is discretized by the Diffractive Deep Neural Network (D²NN) processor to a resolution of 200 × 200 pixels to match the model. Simulation results depicting edge detection for resolution test charts are presented in Figure 1. Within the region delineated by the red box, the edges produced under the split beams at distances of 1, 2, 4, and 6 pixels are depicted. To achieve adjustable-scale edge detection, the spacing of the split beams can be altered by adjusting the air gap of the dual Wollaston prisms (DWPs). This feature proves particularly valuable when the size of the observed object is uncertain. A wide edge is unsuitable for small objects as it fails to capture details, whereas a narrow edge is not conducive to observing large objects due to diminished contrast. Consequently, the scale of edge detection can be freely adjusted based on the characteristics of the target object. Importantly, the scale of edges can be regulated directly by adjusting the gap without necessitating retraining of DPENet.

Passive diffractive layers serve as the optical processing device to ensure high speed and transmission efficiency in edge detection. The entire system successfully reduces device complexity by eliminating the need for lenses and imaging systems. Unlike artificial neural networks, the proposed edge detection system does not require prior collection of intensity distribution data, it directly modulates the complex light field to achieve real-time online edge detection of phase objects. In the future, with advancements in high-performance diffractive neural network models and research on nonlinear activation, we anticipate the development of end-to-end real-time edge detection for phase targets, offering significant support for high-resolution biomedical imaging.

Figure. 1 Schematic diagram of an all-optical edge detection system based on differential interference contrast (DIC) principle.