Traditional infrared optical systems are typically bulky and comprise numerous lenses. To achieve miniaturization, planar imaging elements with microstructured surfaces are often employed. However, these complex surfaces can pose processing challenges and increase costs. This study introduces a planar diffractive element that integrates Fresnel and diffractive surfaces to address the aforementioned issues. Diffractive optical elements possess unique dispersion and temperature characteristics. By combining a diffractive surface with a Fresnel surface, the optical system’s structure can be simplified, reducing its weight and achieving performance indices that are difficult for traditional systems to match. This approach is characterized by ease of processing and low cost. Increasing the field of view exacerbates off-axis aberrations, leading to diminished image quality. Analysis of these aberrations indicates that coma and field curvature are the primary monochromatic aberrations affecting Fresnel and diffractive surfaces. To address this, we propose a design method incorporating computational imaging to correct off-axis aberrations in planar diffractive elements, even as the field of view expands.

The formulas for monochromatic aberration in Fresnel and diffractive surfaces have been derived. Coma and field curvature become the primary monochromatic aberrations as the field of view increases. Therefore, correcting off-axis aberrations in optical design focuses on astigmatism, while coma and field curvature are addressed in the computational imaging phase. The imaging process in the optical system is essentially one of image degradation. The final image is obtained by passing a clear image through the optical system, convolving it with the point spread function (PSF), and adding noise. Thus, the PSF can be used as a restoration function to deconvolve the imaged image and obtain a clear image. A wavefront aberration model of the optical system is established using Zernike polynomial fitting. A PSF model is constructed using the Fourier transform. The blurred image is restored using a deconvolution algorithm. Differences in the PSF model at object distances of infinity and 4 m are discussed, and the data sizes of evaluation functions at different object distances are compared. The diffraction efficiency of the planar diffractive element at long-wave infrared wavelengths is calculated, addressing the need to determine its efficiency.

A planar computational diffractive optical system with a component thickness of 1 mm is designed to achieve miniaturization (Table 1). A PSF model, constructed using computational imaging methods, is employed for restoring blurred images. The restored image is evaluated based on power signal-to-noise ratio (PSNR) and structural similarity (SSIM) (Table 5), with evaluations conducted for images before and after restoration at object distances of infinity and 4 m. The PSNR increased from 21.475 to 39.7932 and the SSIM increased from 0.8135 to 0.9763 when the object distance is at infinity. The PSNR increased to 38.8915 and the SSIM increased to 0.9257 when the object distance is 4 m. These evaluation results demonstrate the effectiveness of this method. The diffraction efficiency of the diffractive element within the wavelength range is calculated, with all values exceeding 87.00%.

The proposed design method effectively achieves the miniaturization of optical systems. Images are restored by constructing a PSF model using the wave aberration model and applying a deconvolution algorithm. The restored image exhibits sharper contours and higher stripe contrast than processed and blurred images. Using PSNR and SSIM, the increments before and after recovery are 18.3182 and 0.1628 when the object distance is at infinity, and 17.4165 and 0.1122 when the object distance is at 4 m, respectively. The results show that the proposed method substantially improves image quality within a 4° field of view. The diffraction efficiency is greater than 87.00%, sufficient to maintain image quality. This study describes an easy-to-process, high-quality planar imaging system that utilizes computational imaging to eliminate the effects of off-axis aberrations on image quality and provides new insights into the integration and miniaturization of optical systems.