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.
One appealing aspect that compressive sensing offers is the possibility of retrieving a signal’s spectral information using a bucket detector and a characterized measurement matrix. Demonstrations of CS applied to optical coherence tomography (OCT) were performed, however, in the final signal-processing instead of the acquisition end. Here we propose a novel OCT system with a broadband superluminescent excitation and a bucket photodetector where the interferogram is obtained by spectral reconstruction. In particular, this system assumes the same interferometric setup as typical swept-source OCT systems except the excitation is replaced by a broadband source. The interferogram then passes through an off-the-shelf, fast tunable Fabry-Perot filter (FPF) of modest finesse whose free spectral range is designed to be much less than the excitation bandwidth. The spectral response is characterized a priori, before the filtered output is integrated by the photodetector. The spectral sampling measurement is repeated by altering the FPF’s resonant conditions multiple times through the cavity length. Having acquired the integrated photodetector values and the corresponding spectral filter functions, we reconstruct the original interferogram whose Fourier transform generates the tomogram. The sensitivity of this OCT technique is evaluated and compared using simulations with synthetic data. Moreover, B-scan reconstruction of the interferogram due to a fingertip was simulated using our scheme and the resultant image shows excellent reconstruction fidelity compared to the original OCT B-scan. These illustrations point towards a promising future of a new class of tomographic system which combines the respective strengths of swept-source and spectral-domain OCT.
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