Optical ranging through underwater scattering using z-dependent angular rotation of a spatially structured beam

We experimentally demonstrate optical ranging through underwater scattering using a range(z)-dependent angular rotation of a spatially structured beam. This beam is generated by combining two Bessel modes, and each Bessel mode carries a unique pair of orbital angular momentum (OAM) order (l(i), i = 1 or 2) and longitudinal wavenumber (k(z)(li) , i = 1 or 2). With two OAM orders l, a transverse petal-like intensity pattern is formed. With two different k(z) values, the relative phase between the two Bessel modes linearly changes along the longitudinal position, and thus, the angular rotation of the petal-like intensity pattern changes with the propagation distance. By measuring the angular rotation of the reflected beam profile, the distance information is retrieved. In our experiment, the scattering extinction coefficient (gamma) is varied from 0 to 9.4 m(-1) with ranging distance up to 0.4 m. The experimental results show that (a) the measurement error (delta(z)) for our scenario is < 10 mm in clean water and (b) the petal-like intensity profile maintains its shape and delta(z) <20 mm is achieved under scattering conditions.