This study aims to develop compact and lightweight imaging optical structures, transcending the challenges posed by intricate architectures, specialized materials, and unique surface configurations prevalent in traditional optical design paradigms. In response to these challenges, we introduce computational imaging techniques, seamlessly integrating the realms of optical design and image restoration. This integration alleviates the intricacies associated with front-end optical system design while concurrently streamlining the process through the application of image restoration algorithms. By transposing the complexities of optical design into the algorithmic realm, we endeavor to reduce optical system complexity while preserving image quality.

We propose an end-to-end (E2E) framework to facilitate the creation of the diffractive optical element (DOE) capable of extending the depth of field (DOF). This framework integrates point spread function (PSF) design, imaging models, and deep image restoration networks through the utilization of modern deep learning tools. As a significant departure from traditional practices, this framework eradicates the traditional segregation between front-end optical design and back-end image processing stages. This method uses image quality as the final evaluation criterion to find the optimal balance between the consistency of a given DOF range and PSF. Moreover, the holistic E2E approach introduced by this method encompasses the intricate task of designing lenses (or lens groups) to accomplish the focus function. This strategic integration effectively simplifies the design complexities intrinsic to DOE, steering the design focus exclusively toward extending the DOF. Specifically, we employ the phase coefficients of cubic phase plates and the one-dimensional height map of rotationally symmetric DOEs to facilitate the dimension reduction of optical design parameters. Network constraints encompass the L1 constraint as the loss function for the image, alongside the inclusion of PSF consistency at varying depths as a specialized constraint for large DOF design. The amalgamation of these constraints gives rise to the loss function for the E2E network, propelling the designed network toward optimization updates. To enhance the network's generalization capabilities, the proposed method undergoes alternating training on two datasets: the FlyingThings 3D dataset, containing 21818 training images and 4248 test images, and the DualPixel dataset, featuring 2506 training images and 684 test images. This dual dataset training regimen yields designs for optical components and culminates in the final imaging outcomes.

The efficacy of the proposed large DOF optical model is robustly validated through comparative analysis with Zemax results, visually depicted in Fig. 4. Subsequently, the E2E approach is efficaciously applied to the design of large DOF imaging systems, encompassing the design of both rotationally symmetric DOEs and cubic phase plate, depicted through their respective height maps in Fig. 5. To provide a comprehensive portrayal of the DOF extension effects within varying scenes, Fig. 6 presents the imaging quality of diverse DOF extension methods across different defocus levels, incorporating images from both the FlyingThings 3D and DualPixel datasets. Additionally, Fig. 7 effectively captures the graphs detailing variations in PSNR and SSIM concerning distinct DOF extension methods over the test dataset, showcasing the relative stability of imaging quality changes within a smaller defocus range for cubic phase plates. However, they experience performance degradation under more pronounced defocus levels, particularly evident in the real-image context of the DualPixel dataset, where rotationally symmetric DOEs outperform cubic phase plates. In contrast, the rotationally symmetric DOEs consistently maintain high image quality both at the focal point and under larger defocus levels. Furthermore, we underscore the robustness of the design method by meticulously validating its performance using non-design values within defocus ranges, as exhaustively detailed in Table 1. Empirical evidence derived from these experiments unequivocally demonstrates that E2E-optimized rotationally symmetric DOEs and cubic phase plates effectively elevate image quality within the defocus range of [-30, 30].

In summary, we introduce an E2E optical design method based on computational imaging. The overall design workflow and performance of DOE are successfully enhanced by constructing a comprehensive model that integrates two different domains, optical design, and image restoration and applying the idea of global optimization with image quality as the final evaluation criterion. The method reduces the requirement for imaging quality of the front-end optical system and eliminates residual aberrations using image restoration algorithms, thus realizing a compromise between optical design and image algorithms. The method covers key aspects of optical field propagation, detector noise, and image post-processing. By building the corresponding models and jointly optimizing the optical models and image algorithms with the modern deep learning models, we successfully design lightweight and thin DOEs suitable for extended DOF and achieve high-quality imaging in a simple optical system with significant DOEs. In conclusion, this research advances an E2E optical design method rooted in computational imaging, enhancing the design of DOEs for extended DOF. The implications of this work extend to the broader field of computational optical imaging, holding both theoretical and practical significance.