Theoretical analysis and experimental verification on optical rotational   Doppler effect
  We present a theoretical model to sufficiently investigate the optical rotational Doppler effect based on modal expansion method. We find that the frequency shift content is only determined by the surface of spinning object and the reduced Doppler shift is linear to the difference of mode index between input and output orbital angular momentum (OAM) light, and linear to the rotating speed of spinning object as well. An experiment is carried out to verify the theoretical model. We explicitly suggest that the spatial spiral phase distribution of spinning object determines the frequency content. The theoretical model makes us better understand the physical processes of rotational Doppler effect, and thus has many related application fields, such as detection of rotating bodies, imaging of surface and measurement of OAM light. 
Hailong Zhou, Dongzhi Fu, Jianji Dong, Pei Zhang, and Xinliang Zhang
physics.optics