We demonstrate optical ranging through turbid underwater medium using a structured beam. This beam consists of two Bessel modes, each carrying a pair of orbital angular momentum order and longitudinal wavenumber. As a result, the beam has a “petal-like” intensity profile with different rotation angles at different distances. The object’s distance (z) is retrieved by measuring the rotation angle of the petal-like profile of the back-reflected beam. We demonstrate ⪅ 20-mm ranging errors through scattering with extinction coefficient γ up to 9.4 m-1 from z = 0 to 0.4 m. We further experimentally demonstrate the enhancement of ranging accuracy using multiple (⪆2) Bessel modes. With the number of modes increasing from two to eight, the average error decreases from approximately 16 mm to approximately 3 mm for a Υ of 5 m-1. Moreover, we simulate both coarse- and fine-ranging by using two different structured beams. One beam has a slower rotating petal-like profile, leading to a 4X larger dynamic range for coarse ranging. A second beam has a faster rotating profile, resulting in higher accuracy for fine ranging. In our simulation, ⪅ 7-mm errors over a 2-m dynamic range are achieved under 𝛾 = 4 m-1 .
We recover the shape and orientation of an object by analyzing the spatial phase and amplitude of a transmitted optical beam using a single pixel. We experimentally demonstrate using the complex spatial spectrum of multiple sequential measurements of a varying probe beam. Specifically, we transmit a structured beam that is tailored to have one mode of the Laguerre-Gaussian (LG) modal basis set, and the beam is varied to sequentially have a unique azimuthal (l) and radial (p) value. When each uniquely structured beam probes an object, there will be coupling of power from the pure mode to other LG modes. The complex phase and amplitude coefficients of this modal power coupling will provide a “signature” of the probed object’s 2D structure, and this signature can be detected using a single pixel. We identify a “fan-shaped” object with an opening angle of 120˚ and different angular orientations by analyzing the corresponding complex spatial spectrum of multiple sequential measurements, such that each subsequent tailored mode has l and p indices in the range -15 - +15 and 0-30, respectively. Results show that the amplitude spectrum is insensitive to the object’s angular orientation, whereas the phase spectrum predictably shifts with orientation. Additionally, we demonstrate that an irregular image with a ‘SC’ logo can be reconstructed using the complex modal spectrum. The structural similarity (SSIM) of the reconstructed image increases as the number of modes increases. Specifically, the SSIM increases by 83.5% when the number of modes increases from 36 (6 by 6) to 961 (31 by 31).
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