Fig. 6. Utilizing the OAM spectrum of probe beams for complex object assessment.

a The distinct OAM spectrum provides an additional degree of freedom and conserved quantities, facilitating high-precision measurements at micro- and nano-scale levels. Vortex light serves as an exceptionally sensitive probe. b Leveraging the OAM spectrum allows for rapid and accurate identification of geometric structures by correlating the positions of intensity minima to the object’s aperture angle and the gradient of the OAM phase spectrum to the object’s angular orientation. c Asymmetry in the OAM spectrum, induced by a moving obstructing object, directly reveals the object’s rotational and lateral motions, with phase differences in the OAM spectrum providing the determination of its rotational dynamics. References given in the insets