Fig. 1. Framework of proposed physics-informed design paradigm for manufacturing-robust imaging system with computational optics. First, a physics-informed tolerance analysis for computational optics is employed to determine the manufacturing error boundaries. Subsequently, the learned Wiener-based FOV_KPN neural network is introduced to effectively reconstruct images degraded by manufacturing errors.

Fig. 2. Details of the physics-informed tolerance analysis for computational optics. (a) Flowchart. (b) Assembly tolerance analysis process, including setup of assembly tolerances, performing Monte Carlo raytracing, and identifying the worst-performing case. (c) Manufacturing error generation process, including building the manufacturing error model, determining parameter boundaries, and generating manufacturing errors. (d) Image rendering process, including generating a degraded image through the convolution of the target image with the system PSF, derived from the system wavefront via ray-tracing. (e) Image reconstruction and evaluation process, including applying the Wiener filter to restore degraded images, followed by performance evaluation using MTF calculation.

Fig. 3. Architecture of learned Wiener-based FOV_KPN neural network. We integrate learned Wiener deconvolution and FOV_KPN neural network to address spatially varying severe degradation, enabling effective recovery of high-frequency details across all fields and significant suppression of noise and artifacts specific to different fields.

Fig. 4. Optical layout and performance of the off-axis three-mirror freeform system. We present the optical layout of the freeform system (a), along with performance evaluation including MTFs (b) and spot diagrams (c) in various fields.

Fig. 5. Tolerance analysis results. (a) The relationship between the minimum MTF@72 lp/mm and the manufacturing errors of each mirror individually. (b) The relationship between the minimum MTF@72 lp/mm and the scale factor Ra under incorporating manufacturing errors of all mirrors. We set the system MTF@72 lp/mm to be larger than 0.3.

Fig. 6. Validation results of the proposed tolerance analysis method. (a) Target images from 100 randomly selected FOVs displayed on the right panel, along with detailed blocks from three FOVs showing recovery results from the Wiener filter and the proposed learned Wiener-based FOV_KPN neural network. (b) Comparison of recovered MTF values between the Wiener filter algorithm and the proposed learned Wiener-based FOV_KPN neural network, with the red isoline representing the fitting line.

Fig. 7. Assessment in simulation. Reconstruction performance, including PSNR (dB), SSIM, and MTF, is evaluated for four methods: U-Net, FOV_KPN, Wiener filter, and our proposed learned Wiener-based FOV_KPN. The reconstruction result of our proposed method is presented on the left side, whereas magnified results from different methods are displayed on the right side, with corresponding positions highlighted on the left side. (a) Image from DIV2K⁴⁵ dataset. (b) MTF test image.

Fig. 8. All-aluminum freeform mirror performance and the system assembly. First, we employed the SPDT technology to fabricate the freeform mirrors and their manufacturing errors are depicted in (a). We then assembled the system (b) with system wavefronts (d) and conducted a comprehensive PSF test across the entire FOVs (c).

Fig. 9. Experimental assessment. We evaluated the proposed method in both indoor (a) and outdoor (b) environments. In the indoor setting, we acquired and reconstructed five-bar Nyquist frequency target images from nine different fields, with MTF values displayed on each detail block, as shown on the left of (a). In the outdoor setting, we included images with detail blocks in different fields of a sensor capture from a Canon lens [on the left of (b)], a degraded measurement, and a recovery result from our proposed prototype [on the middle and right of (b), respectively].