As the low diffraction efficiency of the single-layer diffractive element in the visible broadband results in blurred images and poor contrast, an optical-digital joint design method is proposed to solve this problem. Diffractive optical elements have special dispersion characteristics and temperature characteristics. When they are applied to the traditional refraction imaging system, the structure of the system can be simplified, and the weight of the system can be reduced. The performance index that is difficult to achieve in the traditional system can be achieved. The single-layer diffractive optical element features a simple structure, easy processing, and low costs. However, when the incident wavelength is far away from the central wavelength, the diffraction efficiency of the single-layer diffraction optical element will be significantly reduced, and the imaging quality will be severely affected by the low diffraction efficiency. Therefore, the single-layer diffractive optical element can only be applied to an optical system with a narrow wavelength range. As a result, multi-layer diffractive optical technology has emerged to improve the diffraction efficiency in the broadband. Despite the high diffraction efficiency of the multi-layer diffractive element in the broadband, its structure is complex, and the diffraction efficiency is easily affected by factors such as processing errors and ambient temperature compared with the single-layer diffractive element. Therefore, we hope to propose a design method combined with computational imaging to improve the visible broadband imaging quality of the single-layer diffractive element and expand the applicable band of the single-layer diffractive element.

The imaging process of the optical system is the process of image degradation. After a clear image passes through the optical system, convolves with the point spread function (PSF) of the optical system, and is added with noise, a new image is obtained. Therefore, the PSF can be used as a restoration function to perform a deconvolution operation on the obtained image to produce a clear image. Since the PSF obtained in the optical design software does not consider diffraction efficiency, the diffraction efficiency of each order is assumed to be 100%, and hence, it is necessary to reconstruct a PSF affected by diffraction efficiency. In this paper, the PSF model of the visible broadband affected by diffraction efficiency is constructed in three steps. Firstly, the energy distribution of a certain characteristic wavelength in a certain analysis level needs to be constructed. Secondly, the energy distribution of the wavelength in all analysis levels needs to be calculated and superimposed. Thirdly, the energy distribution of all characteristic wavelengths is obtained according to the method of the first two steps. The obtained energy distribution is superimposed with the quantum efficiency of the detector by weight and then normalized, and thus, the PSFs of the R, G, and B channels are obtained. After the PSF model is deconvolved with the grayscale images of the three channels of the blurred image, the three grayscale images obtained are recombined to obtain a clear color image free from the influence of diffraction efficiency.

Firstly, the existing patent optical system (Table 2) is optimized and adjusted, and a single-layer diffractive element is introduced. Without considering the diffraction efficiency, the image quality remains unchanged (Fig. 5 and Fig. 7), while the band range is expanded from 486.1-656.3 nm to 400.0-800.0 nm, and the number of lenses is reduced from six to four (Fig. 6). Then, the R, G, and B three-channel PSF model of the optimized system affected by diffraction efficiency is constructed according to the previous method (Figs. 8-10). The Richardson-Lucy algorithm and the constructed PSF model are used to deconvolute the three-channel grayscale images of the simulated image. After that, the restored grayscale images (Fig. 12) are combined to obtain a restored color image (Fig. 11). The grayscale mean gradient (GMG) function and the blind image quality index (BIQI) function are employed to evaluate the images before and after restoration (Table 3). The BIQI value of the R-channel grayscale image decreases by 5.00%, and the GMG value increases by 51.61% after restoration. The BIQI value of the G-channel grayscale image decreases by 5.44%, and the GMG value increases by 24.28% after restoration. The BIQI value of the B-channel grayscale image decreases by 1.23%, and the GMG value increases by 48.79% after restoration. The effectiveness of this method is proven by the evaluation results.

The design method in this paper can effectively improve the visible broadband imaging quality of the optical system with a single-layer diffractive optical element. The image obtained by restoration with the PSF model and the unrestored image are evaluated, and the evaluation results are as follows. Subjectively, the image quality after restoration is significantly improved as the image is clearer and has higher contrast. Objectively, the GMG function and the BIQI function are used for evaluation. The GMG evaluation value of the restored image increases by 40.33%, and the BIQI evaluation value decreases by 4.30%, which all indicate that the image quality after restoration is better. The simulations show that this method can be used in the design of a system with a single-layer diffractive element in the visible broadband.