Coherent diffraction imaging (CDI) is a high-resolution technique that does not require X-ray lenses. With advances in scientific technology, such as synchrotron radiation, X-ray free-electron lasers, and coherent electron sources, CDI has been applied to diverse fields, such as biology, medicine, and semiconductors, as a high-resolution, nondestructive measure. With the rapid increase in demand for these applications, enhancing the efficiency of processing high-volume data has become a significant challenge for promotion. In this study, we proposed an algorithm that combines Kramers–Kronig (KK) relations with oversampling smoothness (OSS). The results were evaluated by introducing an error coefficient. We found that the error of the KK-OSS algorithm is always reduced by approximately 50% compared with the error reduction (ER) algorithm and OSS in real space. In the diffraction space, the error in the KK-OSS decreased by 15%. With 100 iterations, KK-OSS spent 163.1 s on reconstructing most of the sample information, while ER took 258.1 s and the reconstruction was still a random value. In Fraunhofer diffraction, it cost KK-OSS 58.8 s to reconstruct, while OSS took 61.9 s. Therefore, this method can reduce the reconstruction error, shorten the reconstruction time, and improve the efficiency compared with the ER and OSS algorithm using a random phase as the initial value.
Electron beam propagation in the light standing wave for both high and low intensity has been calculated by Thermal Wave Model (TWM). The electrons are scattered in high light intensity, as described in the Kapitza-Dirac effect. Numerical results show the significance of the transverse beam emittance to the quality of the diffraction pattern. In low light intensity, the electrons cannot be scattered, but we demonstrate that only the phase of the electron beam is shifted. Theoretical results show that the transverse average beam momentum σp
varies while the effective beam σx
size remains. The TWM phase-space distributions of the electron beam are given and show the influence of the transverse emittance ε on the beam spreading in this situation. Our works show the possibility of using lasers to design electron beam phase plates and quantify the transverse coherence of electron beams.
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