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The vortex beam with helical phase has great potential in detecting rotating targets. Offset, inclination and even the optical axis not in the same plane with the rotational axis often exist between the beam and the rotational axis when the non-cooperative rotating target is measured by vortex beam. To effectively measure rotational speed and eccentric distance (the distance of facula center and the center of rotation on the object being detected) of non-cooperative object, according to the scattering point model and rotational Doppler effect principle, this paper proposes a geometric projection method to study the detection problem about the incidence of the beam at arbitrary position relative to the object’s rotational axis, and analyzes the change of rotational Doppler frequency shift in the state of existing both offset and inclination, and obtains the rule of the extremum of the rotational Doppler frequency shift changing with the relative space position parameters. On this basis, the rotational speed and the eccentric distance are obtained when both eccentricity and inclination exist and the optical axis of vortex has no deflection. And a method for detecting the rotational speed and the eccentric distance of non-cooperative target is proposed. The conclusions obtained in this paper have some guiding significance for further application of rotational speed detection technology based on vortex beam.
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