Efficient end-to-end optimization of extended depth of field imaging systems and Wiener filter based deconvolution with weighted transfer functions

Extended depth of field (EDOF) is a critical requirement for modern compact imaging systems, often necessitating a holistic design of optical elements and digital reconstruction algorithms. This paper presents an efficient end-to-end, damped least square based optimization framework that combines a higher-order free-form phase plate and a Wiener deconvolution filter into a single computational imaging pipeline. The proposed forward model comprehensively incorporates the image sensor transfer function, sampling effects, and noise characteristics alongside the optical propagation. A key contribution of this work is the joint optimization of the optical surface and the reconstruction parameters within a unified differentiable framework. Specifically, the Wiener deconvolution filter is optimized simultaneously with the phase plate, adapting its variably weighted system transfer function and Wiener SNR parameter to the specific optical aberrations introduced during the optimization process. We design the loss function based on the Structural Similarity Index (SSIM) to ensure perceptual image quality and employ standard optical system analysis metrics to validate the approach. Comparative results demonstrate that this co-design strategy yields significantly higher system performance than standalone optimization of the optical components. The proposed method offers a robust pathway for designing EDOF systems where optical coding and digital decoding are perfectly matched. 44 design (Modelle & Methoden) Henning Rehn