Real-time holographic lensless micro-endoscopy through flexible fibers via fiber bundle distal holography

The study targets the long-standing challenge of performing minimally invasive, label-free, three-dimensional imaging through flexible, dynamically bent optical fibers without bulky distal optics. Conventional micro-endoscopes either require distal lenses and scanners (increasing diameter and tissue damage) or suffer from pixelation, limited resolution, fixed working distance, and poor axial sectioning when using imaging fiber bundles. Transmission-matrix-based lensless methods can compensate for multimode propagation but are highly sensitive to bending and typically lack video-rate operation. Prior approaches adding distal elements or separate illumination fibers face limitations in axial sectioning, field of view, twin-image artefacts, or require fluorescence labeling and raster scanning. The hypothesis is that by introducing a partially reflecting mirror at the distal tip of a standard multi-core fiber and using low-coherence phase-shifting holography with both illumination and reference traversing the same core, one can achieve bend-insensitive, calibration-free, video-rate, diffraction-limited, 3D imaging with axial sectioning and inherent phase contrast.

- Single-mode fiber micro-endoscopes are bend-insensitive but require distal scanners/lenses or spectral dispersers, increasing probe size and limiting minimally invasive use. - Imaging fiber bundles (multi-core fibers, MCFs) operate as pixelated image guides; conventional use yields limited resolution tied to core pitch, pixelation artefacts, fixed working distance, and limited axial sectioning even with confocal/structured illumination or OCT-like gating; strong tip reflections hinder label-free imaging. - Transmission-matrix (TM) and wavefront-shaping methods enable lensless endoscopy but are highly sensitive to fiber bending; single-TM solutions fail for flexible fibers; multi-measurement TM estimation is slow and incompatible with video-rate and dynamic bending. - Bend-insensitive MCFs with special inter-core phase relations exist but use few single-mode cores with low collection efficiency and fill-factor. - Related work (Czarske et al.) added a distal partial mirror to measure and correct fiber phase via SLM; imaging by raster scanning remains challenged by dynamics and often requires fluorescence. - Prior holographic endoscopy using MCFs as intensity-only guides needed extra illumination fibers and suffered poor axial sectioning, limited FoV, or coherent background from twin images. These gaps motivate a new approach combining coherence-gated holography with a distal mirror and single-core illumination/reference within commercial MCFs.

Approach (FiDHo): Add a partially reflecting mirror at the distal tip of a commercial multi-core fiber (MCF). Use a low-coherence laser split into two delayed replicas (illumination and reference) that co-propagate through the same single core and mode. The object-reflected illumination interferes with the mirror-reflected reference at the distal facet; the resulting intensity hologram is relayed back through the MCF cores and imaged proximally. Low-coherence phase-shifting holography (N≥3 frames) retrieves the complex field. Optical setup: - Illumination: diode laser λ = 640 nm, coherence length l_c ≈ 400 µm (iBeam-smart-640s), ~1 mW at proximal facet. - Interferometer: Mach–Zehnder with PBS and 50/50 BS for power splitting; half-wave plates for polarization control; two 4-f telescopes align both arms to couple into the same core’s fundamental mode. - Coupling to MCF: telescope (f=75 mm and f=200 mm lenses) + long working distance objective (Mitutoyo M Plan Apo 10×, NA 0.28). A 50/50 BS directs returning light to the camera path. - Detection: Proximal facet imaged onto sCMOS camera (Andor Zyla 4.2 Plus) via another 10× objective and relay optics with variable magnification. Cross-polarized detection (two orthogonal linear polarizers) suppresses proximal facet reflections. - Phase shifting and time gating: Reference arm controlled by a piezo-mounted mirror for phase steps and a motorized delay line to set delay τ. Coherence gating set to τ ≈ 2 z_o / c to match object–mirror distance. - Distal components: Partially reflecting mirror placed at z_m ≈ 2 mm from distal facet; fabricated by depositing ~10 nm Ti on glass; glass spacer and immersion oil (n≈1.52) reduce spurious reflections. Optional distal microscope/camera used only for ground-truth validation. - Fibers: Commercial MCFs used (e.g., Schott 153385 ordered cores; also tested Fujikura FIGH-06-300S with imperfect ordering). Signal model and reconstruction: - Acquire N≥3 intensity frames I_n with controlled phase φ_n on the reference. Reconstruct the distal complex object field E_o(x,y) via phase-shifting interferometry and normalization by the known spherical/ Gaussian reference field E_r(x,y) (approximated as the fundamental mode field from the single core). - Coherence gating suppresses undesired interference terms (reference reflected from object; illumination reflected from mirror) by choosing τ so only object–mirror interference falls within the source coherence window; undesired terms occur at distinct delays and are rejected. - Digital refocusing/back-propagation: Propagate E_o to desired axial distance z_prop to focus the object. Normalize by the expected illumination field E_illum(x,y,z_prop) to obtain amplitude and phase images at focus. Object distance can be estimated by scanning τ and maximizing total reconstructed field energy. Handling pixelation and aliasing: - The MCF samples the hologram at its core grid causing aliasing in k-space and ghost replicas after back-propagation. Apply a low-pass Fourier filter with cutoff f_cutoff = 1/(2p), where p is core pitch, to suppress aliasing and effectively interpolate between cores. This sets an effective detection NA and thus lateral resolution. Aliasing is naturally reduced by the minimal working distance set by the mirror geometry. Bending and modal considerations: - Bend insensitivity arises because both illumination and reference traverse the same core and mode (common-path-like), and detection is intensity-only. Higher-order core modes are temporally separated by modal GVD; short time gating selects the fundamental mode contribution. Low inter-core crosstalk and single-mode-like behavior per core improve robustness. Optimization guidelines: - MCF diameter D sets FoV and maximum depth for diffraction-limited performance; choose as large as application permits. - Core NA dictates lateral resolution; digital filtering may further limit effective NA. - Distal mirror distance z_m should be large enough that the reference phase is nearly constant within a core: z_m ≈ d^2/λ (d = core diameter). - Mirror reflectivity optimized to target reflectivity; ~2–14% mirror reflectivity is suitable for target reflected power fraction of ~0.1–4%. Acquisition speed: - One reconstructed frame requires three camera frames. With a 50 FPS camera, reconstructions can be formed at 50 FPS using overlapping triplets, yielding 16.6 unique frames per second. Higher speeds possible with faster cameras and faster phase modulators (e.g., AOM).

- Diffraction-limited, unpixelated imaging through commercial MCFs using FiDHo; digital refocusing across working distances without distal lenses. - Resolution: Resolved USAF group 7 element 4, indicating lateral resolution better than ~2.7 µm. Knife-edge measurements confirm diffraction-limited performance set by effective NA and filtering. - Field of view: Approximately half the fiber diameter; with D_fiber = 600 µm and z_m = 2 mm, measured FoV ≈ 250 µm (FWHM) and effective NA_eff ≈ 0.15; space-bandwidth product ≈ 5300. - Distance invariance: Resolution and FoV remain essentially constant over object distances Z_obj < n D_fiber/(2 NA) − Z_m (n≈1.51, NA≈0.15), yielding constant resolution up to ~1 mm in the reported system. - Axial sectioning: Achieved via low-coherence gating; demonstrated separation of two stacked USAF targets with ~300 µm axial spacing and 3D reconstruction of a tilted target by stitching sub-FoVs and retrieving depth via τ-scan. - Phase contrast: Human cheek cells were invisible in amplitude but clearly visible in phase reconstructions, validated by reference transmission microscopy. - Video-rate and bending robustness: Real-time operation at 50 FPS (3-frame phase-shifting), with insensitivity to fiber orientation and low sensitivity to dynamic bending; motion within the three-frame sequence can reduce quality but reconstructions remain feasible. - Calibration-free operation: No TM calibration or distal scanning required; simple non-iterative reconstruction. - Practical parameters: Demonstrated with λ=640 nm, coherence length ~400 µm, z_m ≈ 2 mm, NA_eff ≈ 0.15; digital filtering cutoff f_cutoff = 1/(2p) constrained by core pitch.

The findings demonstrate a practical route to lensless micro-endoscopy that simultaneously achieves video-rate imaging, diffraction-limited lateral resolution, axial sectioning via coherence gating, phase contrast, and robustness to fiber bending. By ensuring both illumination and reference share the same core and fundamental mode, the method is effectively self-referenced and avoids bend-induced TM recalibration. The partially reflecting distal mirror enables full-field, low-coherence holography with minimal distal footprint and no distal scanning. This advances beyond conventional MCF imaging (pixelation, fixed WD) and TM-based multimode approaches (bend sensitivity, slow updates). Performance is governed by MCF geometry (diameter, core NA, crosstalk), mirror placement and reflectivity, and source coherence length. Digital Fourier filtering suppresses MCF sampling artefacts at the cost of limiting effective NA. Coherence gating separates desired and spurious interference terms and provides axial sectioning akin to wide-field OCT. The method inherently exhibits coherent speckle (subjective and objective), which can be mitigated via incoherent compounding (scanning different cores), coherent compounding to enhance resolution, or computational denoising (compressed sensing). Disordered-core MCFs can further reduce aliasing and enable compressed-sensing reconstructions. Future engineering directions include single-shot off-axis holography (with SBP/FoV trade-offs), leveraging higher-order modal intensity information for improved resolution, adding a GRIN lens for higher NA if acceptable, using shorter coherence-length sources and higher well-depth, faster cameras and modulators for speed, and advanced reconstruction algorithms (computational aberration correction, compressed sensing). Biomedical translation may exploit OCT-like endogenous reflection contrast for diagnostic imaging (e.g., GI dysplasia detection).

FiDHo enables real-time, calibration-free, lensless holographic micro-endoscopy through flexible, dynamically bent commercial multi-core fibers. By adding a distal partial mirror and using low-coherence phase-shifting holography with single-core illumination/reference, it delivers diffraction-limited, unpixelated imaging with digital refocusing, axial sectioning, phase contrast, and robustness to bending at video rates. Demonstrations include sub-3 µm lateral resolution, ~250 µm FoV, phase imaging of weakly reflective cells, 3D imaging with ~300 µm axial separation, and 50 FPS operation. Future work should optimize mirror reflectivity and distance, employ shorter coherence-length sources and higher well-depth, faster cameras, and explore single-shot off-axis configurations and compressed-sensing reconstructions. Translation to in vivo label-free diagnostics leveraging OCT-like contrast, along with speckle reduction strategies and disordered-core MCFs, may further improve image quality and clinical utility.

- Coherent reflection contrast yields speckle noise (subjective and objective), which degrades image quality; mitigation requires compounding or computational denoising. - Axial resolution and minimal working distance are constrained by source coherence length; shorter coherence sources improve sectioning but must satisfy interference across cores. - Effective NA and resolution are limited by necessary digital low-pass filtering to suppress MCF sampling aliasing, especially with ordered core grids; residual aliasing may persist. - Motion during the three phase-shifting frames can reduce reconstruction quality; unique frame rate is lower than camera FPS due to frame sharing. - Performance degrades with inter-core crosstalk or multimode propagation; method assumes dominance of the fundamental mode selected via time-gating. - Distal partial mirror introduces design constraints (z_m, reflectivity) and adds a minimal object distance; strong spurious reflections require careful suppression (polarization filtering, time gating, immersion media). - FoV limited to roughly half the fiber diameter unless scanning or stitching is employed.