Membrane diffraction imaging has become an important technology for high-quality imaging of large aperture space telescopes due to the advantages of Diffractive Optical Elements (DOE) such as light weight, loose surface tolerance, small size, foldable and unfoldable, and low cost. The main DOEs include Fresnel Zone Plate (FZP), Photon Sieve (PS), Composite Photon Sieve (CPS) and Stitched Zone Plate (SZP). Among them, the FZP has the advantages of ultra-lightness and foldability, and is widely used in optical microscopy, X-ray imaging, astronomical observation, optical communication, optical ranging and aerospace technology. However, due to the multi-level diffraction characteristics of FZP, its non-imaging diffraction order light becomes a strong background noise of the imaging order light, resulting in low contrast of the imaging image; on the other hand, the inevitable processing errors and structural defects in the FZP manufacturing process lead to low diffraction efficiency of FZP, and introduce wavefront distortion of the imaging beam, resulting in a sharp drop in the resolution of the imaging image. In addition, multi-order diffraction is coupled with the beam wavefront aberration, which leads to further degradation of FZP imaging quality. Many factors limit the performance of FZP diffraction imaging, resulting in the fact that its imaging contrast and resolution cannot meet the high requirements of space imaging applications. In this paper, FZP is used as the primary imaging mirror, and the FZP diffraction imaging system is built to study its image degradation process. Starting from the multi-order diffraction characteristics of FZP, the establishment, solution and optimization of its imaging model are carried out. In view of the problem of FZP multi-order diffraction imaging, the equivalent point spread function method is proposed, the numerical solution of the equivalent point spread function is obtained based on the imaging model, and the image restoration study is carried out. In view of the problem of slow algorithm convergence in the process of solving the FZP imaging model, a FZP diffraction efficiency initial value measurement system and measurement method are designed, a measurement experimental platform is built, the initial value of the FZP diffraction efficiency is obtained, and the algorithm convergence speed is accelerated. Specifically, the FZP diffraction efficiency measurement study is carried out. According to the measurement reciprocity principle, synchronous trigger imaging technology is adopted, and micron-level optical path adjustment is achieved by worm and stepper motor. The FZP diffraction efficiency measurement device is established, and the initial value of FZP diffraction efficiency is obtained by averaging multi-frame image data. The parameter solution and image restoration research based on the imaging model are carried out. The equivalent point spread function method is proposed to characterize the interference of many non-imaging diffraction lights of FZP, and the mathematical relationship between the point spread function, equivalent point spread function and diffraction efficiency of the primary and secondary light of FZP is analyzed, and the FZP imaging model is established; then, the equivalent point spread function is solved based on the FZP imaging model and SPGD algorithm by combining numerical simulation and experiment. To avoid the SPGD algorithm from falling into the local optimum during the iterative solution process, the SA algorithm is used for verification. The similar solution results of the two algorithms prove the feasibility of the method; finally, the experimental research of image restoration is carried out based on experimental data. The experimental results show that the restored diffraction image has improvements in contrast, gradient, etc., verifying the feasibility of the parameter solution method of the FZP imaging model proposed in this paper and the model-based diffraction image restoration research.
