Rotational Doppler shift of the light transmitted behind a rotating object with rotational symmetries: rotational Doppler shift of the transmitted light

We investigate both theoretically and experimentally the decomposition of a fundamental Gaussian beam transmitted behind an absorbing propeller-like object. We use a Laguerre Gaussian basis which modes carry orbital angular momentum. The main contributing components correspond to modes having the same rotational symmetry as the object, thus enabling pattern recognition. When the object is rotated, the frequency of the modes of the basis experiences a rotational Doppler shift characterizing the movement, that can be easily detected. Potential applications in target recognition and rotation identification are then considered, including rotational Doppler shifts using microwaves.