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Synthetic aperture lidar is an optical remote sensing method that can theoretically achieve centimeter-level imaging resolution. It faces unprecedented research problems in physical optics, one of which is the single beam modulation mode, which greatly limits its large-scale application. A vortex beam carrying orbital angular momentum can theoretically generate an infinite variety of mutually orthogonal modulation modes. Applying it to imaging detection has the potential to bring richer information freedom while ensuring imaging resolution. In this paper, a vortex beam imaging model based on synthetic aperture method is proposed by combining vortex beam and synthetic aperture technology. Based on the basic principle of synthetic aperture and the theory of vortex beam orbital angular momentum, a synthetic aperture vortex beam imaging radar model is established. The data acquisition process of synthetic aperture vortex beam imaging is also deduced, and the phase angle position relationship in the echo data is analyzed. Finally, the range resolution and azimuth resolution of synthetic aperture vortex beam imaging under specific conditions are solved. Theoretical analysis shows that the rate of change of the topological charge of the vortex beam during the imaging process will have a great impact on the azimuthal resolution, which is consistent with the expected results. This paper lays a foundation for the follow-up research on vortex beam synthetic aperture imaging, and also provides a reference for the development of new radar technology.
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