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.
The fringe model can directly explain the principle of dual beam differential Doppler effect. Superimposed state vortex light is a petal-like interference fringe superposed by positive and negative topological charge vortex beams. Based on this, the idea of fringe model is applied to the principle of rotational speed measurement based on the rotation Doppler. The rotation Doppler frequency shift based on the model was derived by means of spatial geometric transformation. According to the relative location between the optical axis of vortex and the object rotation axis, three typical incident conditions which are coincident, offset and tilt are considered. The results show that the frequency shift based on the fringe model is consistent with that of the traditional rotation Doppler model, which proves that the model is suitable for the interpretation of the principle of rotation Doppler velocity measurement. This study provides a more intuitive and concise theoretical explanation for the rotational Doppler effect, which has certain guiding significance.
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