Transmission-matrix-based image correction of optically levitated particles in hollow-core fibers

Light scattering analysis in hollow channels serves as a powerful tool for the precise, in-situ characterization of micro- and nano-particles. However, its accuracy is compromised by capillary-induced optical aberrations in the scattered light. Here we demonstrate a transmission-matrix-based scheme to correct such aberrations, which occur in optically levitated particles within anti-resonant hollow-core fibers. By leveraging the axial uniformity of the fiber, a simplified model describing the propagation of light fields through the fiber cladding structure is derived. Polystyrene particles of varying diameters were levitated both at the fiber endface and inside the hollow core. Their lateral-scattering images were employed, respectively, as the distortion-free and the distorted image, enabling the acquisition of the fiber cladding's transmission matrix. Experimental results confirm that, after image correction, the correlation coefficients between the corrected images and the distortion-free reference are, on average, 1.8 times higher for polystyrene particles with diameters ranging from 0.5 to 6 μm. The technique offers a solution for high-fidelity optical imaging of optically manipulated particles in hollow channels, with potential applications in microfluidics, particle metrology, and biological sensing.