Using a complex optical orbital-angular-momentum spectrum to measure object parameters.

Light beams can be characterized by their complex spatial profiles in both intensity and phase. Analogous to time signals, which can be decomposed into multiple orthogonal frequency functions, a light beam can also be decomposed into a set of spatial modes that are taken from an orthogonal basis. Such decomposition can potentially provide a tool for spatial spectrum analysis, which may enable stable, accurate, and robust extraction of physical object information that may not be readily achievable using traditional approaches. As a proof-of-concept example, we measure an object's opening angle using orbital-angular-momentum (OAM) -based complex spectrum, achieving a >15  dB signal-to-noise ratio. Moreover, the dip (i.e., notch) positions of the OAM intensity spectrum are dependent on an object's opening angle but independent of the opening's angular orientation, whereas the slope of the OAM phase spectrum is dependent on the opening's orientation but independent of the opening angle.