The orbital angular momentum (OAM) of beams provides a new dimension, and have already found lots of applications in various domains. Among such applications, the precisely and quantitatively diagnostic of intensity distributions among different OAM modes, namely the OAM spectrum of a beam, is of great significance. In this paper we propose and experimentally validate a simple interferential method to achieve this goal. By analyzing the interference pattern formed by the beam and a reference field, the OAM spectrum can be obtained instantaneously. Furthermore, the proposed method is also available for more complex light fields, for instance, the multi-ring optical vortices. In the proof-ofconcept experiment, the OAM spectra of both single-mode and N-fold multiplexed OAM modes with various intensity distributions are well detected. Our work offers a new way to precisely measure the OAM spectra of beams and will advance the development of many applications ranging from classical to quantum physics as the OAM based large-capacity data transmissions, rotation detection, quantum manipulation and so on.

Bessel-Gauss beams carrying orbital angular momentum are widely known for their non-diffractive or self-reconstructing performance, and have been applied in lots of domains. Here we demonstrate that, by illuminating a rotating object with high-order Bessel-Gauss beams, a frequency shift proportional to the rotating speed and the topological charge is observed. Moreover, the frequency shift is still present once an obstacle exists in the path, in spite of the decreasing of received signals. Our work indicates the feasibility of detecting rotating objects free of obstructions, and has potential as obstruction-immune rotation sensors in engine monitoring, aerological sounding, and so on.

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