Coherent detection of the rotational Doppler effect measurement based on triple Fourier transform.

In recent years, the rotational Doppler effect (RDE) has been widely used in rotational motion measurement. However, the performance of existing detection systems based on the RDE are generally limited by the drastic reduction of signal-to-noise ratio (SNR) due to the influence of atmospheric turbulence, partial obscuration of the vortex beam (VB) during propagation, and misalignment between the optical axis of VB and the rotational axis of the object, which poses a challenge for practical applications. In this paper, we proposed a coherent detection method of the RDE measurement based on triple Fourier transform. First, the weak RDE signal in backscattered light is amplified by using the balanced homodyne detection method, and the amplified signal still retains the same characteristic of severe broadening in the frequency domain as the original signal. Furthermore, we proposed the triple Fourier transform to extract the broadened RDE frequency shift signal after the coherent amplification. The proposed method significantly improves the SNR of RDE measurement and facilitates the accurate extraction of rotational speed, which helps to further improve the RDE detection range and promote its practical application.