In contrast to conventional imaging systems that map an object point by point, measurements with random sensing functions in combination with computational reconstruction may afford novel imaging architectures. Here we demonstrate imaging of axial reflectivity profiles using random temporal-spatial encoding created by modal interference in a multimode fiber (MMF). Light from a broadband source (∆λ = 60nm) centered at 1310nm is split into a sample and a reference arm. In the sample arm, light in a single spatial mode is reflected by the axial reflectivity profile of the sample and coupled back into the same spatial mode. The reference light propagates through a MMF and interferes with the sample light in an off-axis geometry on a camera for holographic recording. Since the MMF supports various guided modes with distinct propagation constants, the short-coherence sample light only interferes with the spatial modes of the reference light that have matching path length. During an initial calibration procedure, interference patterns of a mirror reflection in the sample arm are recorded for varying axial mirror positions. Once this random sensing matrix (RSM) is established, the axial reflectivity profile of an object in the sample arm can be reconstructed from a single interference pattern by the multiplication with the inverse of RSM. By using a 2m long 0.22 NA MMF and tailoring the coupling regime within the MMF, we achieved axial ranging more than a centimeter. Flexible integration of polarization sensing or multi-focus imaging in a single snapshot could be envisioned in this random imaging architecture.
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