Component simplified design of the freeform reflective imaging systems based on optical-digital integration

Freeform surfaces are typically employed in off-axis reflective imaging systems to correct off-axis aberrations and achieve high-quality imaging over a wide field of view. However, the introduction of freeform surfaces leads to increased difficulty and cost in fabrication, testing and alignment. While a reduction in the number of reflective elements can lower system complexity, the resulting uncorrected off-axis aberrations severely degrade image quality. In this paper, a simplified design method for off-axis reflective systems is proposed based on optical-digital integration. Based on wavefront aberration theory, a wavefront aberration model is constructed using Zernike polynomials, from which a point spread function (PSF) model is established through Fourier transform. Subsequently, the Aberration-Correlated Homogenized PSF (ACH-PSF) model is obtained by evaluating the PSFs based on the dual judgment criteria of spatial distribution and intensity similarity. A Richardson-Lucy deconvolution algorithm, regularized by a Total Variation (TV) term, is employed to process the degraded image, thereby eliminating the impact of off-axis aberrations. An off-axis reflective system is designed for the 8∼12 µm waveband with a focal length of 97.2 mm, a F-number of 1.5 and a field of view of 8°×6°. Utilizing the proposed method, a three-mirror system with high-order freeform surfaces is simplified to a two-mirror system. Through a comparison of the degraded and restored images, the peak signal-to-noise ratio (PSNR) is increased from 29.21 dB to 34.48 dB, and the structural similarity index (SSIM) is improved from 0.8530 to 0.9410. The results validate the performance and effectiveness of the proposed method, providing a new approach for the simplified design of off-axis optical systems.