Quantitative phase imaging through an ultra-thin lensless fiber endoscope

Quantitative phase imaging (QPI) is an effective and label-free method for cell and tissue imaging in biomedicine. 3D images of transparent samples can be reconstructed with QPI in a non-invasive manner, enabling nanoscale sensitivity to morphology and dynamics. Meanwhile, quantitative biophysical parameters such as refractive index, dry mass, matter density, and skewness can be extracted from the quantitative phase shift, providing both morphological and quantitative biophysical information for digital pathology. Recent research combining QPI with deep learning has been used for virtual staining and dynamic blood examination, which was reported as a high throughput approach to detecting the SARS-CoV-2 virus. On the other hand, current QPI methods are mostly based on bulky and expensive microscope platforms with limited working distance and penetration depth, requiring invasive sampling or sectioning of diseased tissues or organs for pathological diagnosis. Such invasive approaches limit the in vivo application of QPI in clinical diagnosis, especially in the early diagnosis of cancer and tumors. In clinical diagnosis, endoscopes with diameters of a few millimeters are commonly used for in vivo imaging. Multi-core fiber bundles (MCFs) are ultra-thin fiber bundles consisting of thousands of single-mode fiber cores, and recent advances in MCF-based computational imaging demonstrate great potential for minimally invasive microendoscopy. However, in conventional MCF imaging the phase information is lost due to incoherent illumination; despite computational methods proposed to recover 3D information, precise QPI via MCF with nanoscale sensitivity remains challenging. Coherent imaging via multimode fibers using transmission matrices or wavefront shaping, and similar MCF-based coherent approaches, require bulky, expensive optics (e.g., spatial light modulators), complicated calibration, and often slow scanning, limiting clinical translation. Furthermore, microendoscopes with nanoscale optical path length (OPL) sensitivity have not been reported, motivating a simple, cost-effective 3D microendoscope with nanoscale sensitivity.

The authors propose a computational lensless quantitative phase microendoscope (QPE) that uses a bare multi-core fiber bundle (MCF) as a phase encoder and introduces a far-field amplitude-only speckle transfer (FAST) algorithm to reconstruct the incident complex field at the measurement side from intensity-only speckles captured at the detection side. Principle: - Due to core-to-core variations, the MCF imposes intrinsic optical path length (OPL) differences across cores, yielding a stable, random phase at the detection side for a given illumination when the fiber is static. This encodes the incident complex field into a far-field speckle pattern. - The system first performs a reference measurement to calibrate the intrinsic phase map of the MCF. A collimated laser beam or point source illuminates the measurement facet; two far-field speckle patterns at axial positions z0 and z1 on the detection side are magnified and recorded by a camera. Using the FAST algorithm, the intrinsic phase distribution φ0(x,y) at the detection facet (fiber core array) is reconstructed from the reference speckles. Sample measurement and complex field recovery: - A sample placed at an axial distance zs from the measurement facet (e.g., a USAF target 1.6 mm away) is illuminated coherently. The resulting far-field speckle pattern at distance z1 is captured on the detection camera. - From this single intensity-only speckle, FAST reconstructs the complex field on the fiber facet, yielding amplitude A1(x,y) and phase φ1(x,y). - The sample-induced phase at the measurement side is recovered by subtracting the intrinsic MCF phase: φ′(x,y) = φ1(x,y) − φ0(x,y). - The complex field at the detection side is E(x,y) = A1(x,y)·exp[iφ1(x,y)]. The incident field at the measurement side is then numerically propagated to arbitrary axial planes using the angular spectrum method to refocus digitally onto the sample plane(s). Digital refocusing and 3D imaging: - Because the full complex field is recovered, the method enables computational refocusing without mechanical scanning. Slices at different axial distances are obtained by propagating the reconstructed field to the desired z-planes. This allows 3D reconstruction of multi-layer samples from a single captured speckle image. Experimental setup: - The microendoscope consists of a bare MCF (example shown: 10,000 cores, ~350 µm diameter facet), coherent illumination delivered via a single-mode fiber, relay optics (microscope objective, achromatic lens), and a detection camera at the far-field plane; a linear polarizer is included as needed. The speckle patterns are magnified and imaged onto the camera. Samples (e.g., resolution targets, microchannels with beads, phase calibration targets) are positioned millimeters from the fiber facet on the measurement side. Validation procedures: - Resolution target imaging: USAF negative and positive resolution targets were placed at millimeter-scale distances. Reference speckles were recorded, intrinsic phase reconstructed, and complex fields recovered to refocus onto target planes. Recovery quality was assessed by resolving group elements and comparing amplitude/phase reconstructions. - Multi-layer sample: Two stacked positive targets with 1.4 mm axial separation (top layer at 1.26 mm, bottom at 2.66 mm from the facet) were reconstructed from a single speckle, and compared to images acquired with a conventional reflective microscope (which required mechanical focus change). - Dynamic sample: Glass bead flow in a microchannel located ~1 mm from the facet was recorded at 10 fps, with frames processed offline to reconstruct motion. - Quantitative phase calibration: A known phase target was projected on the MCF, speckle captured, and the quantitative phase reconstructed. Background phase tilt was numerically corrected by subtracting a simulated phase mask. Optical path difference (OPD) profiles extracted from the reconstruction were compared to the ground-truth target, and a 3D OPD map generated. Lateral resolution dependence on phase amplitude was characterized (details in Supplementary Materials).

- The MCF can function directly as a phase encoder, enabling recovery of the incident complex field from a single intensity-only far-field speckle using the FAST algorithm. - Quantitative phase imaging (QPI) is achieved through an ultra-thin lensless fiber microendoscope with microscale lateral resolution (up to ~1 µm in the ideal case) and nanoscale axial sensitivity to optical path length (OPL). - Digital refocusing: 3D image stacks are computationally reconstructed without mechanical motion. In a two-layer target separated by 1.4 mm (top at 1.26 mm, bottom at 2.66 mm from the facet), both layers were refocused from one speckle image, recovering amplitude and phase. - Top layer reconstructed line width: ~22.1 µm. - Bottom layer reconstructed line widths: ~11.05, 9.84, and 8.77 µm. - USAF resolution target: Groups 6 and 7 were resolved in both amplitude and phase after numerical back-propagation; the method extended the effective field of view beyond the physical facet diameter. - Dynamic imaging: Glass bead flow in a microchannel 1 mm from the facet was captured at 10 fps and reconstructed offline, demonstrating capability for dynamic samples. - Quantitative phase accuracy: Reconstructed phase of a calibration target matched the ground-truth optical path difference (OPD) profiles with high fidelity; a 3D OPD map was generated. Lateral resolution as a function of phase amplitude was measured (details in Supplementary Materials).

The study demonstrates that a bare multi-core fiber bundle, combined with the FAST computational reconstruction, enables label-free quantitative phase imaging through an ultra-thin lensless microendoscope. By calibrating the intrinsic phase of the static MCF and decoding the complex field from far-field speckles, the system overcomes classical MCF limitations (pixelated amplitude-only imaging tied to core spacing) and recovers both amplitude and quantitative phase with high fidelity. This approach directly addresses the challenge of bringing QPI into minimally invasive, in vivo contexts: it eliminates bulky interferometric modules or spatial light modulators, requires no distal optics, and enables digital refocusing to reconstruct 3D information from a single acquisition. The nanoscale OPL sensitivity and microscale lateral resolution are sufficient for biomedical applications such as cell morphology quantification and tissue assessment. The accurate OPD reconstruction from a known phase target validates the quantitative nature of the method, while successful reconstructions of multi-layer targets and flowing beads highlight robustness for volumetric and dynamic scenes. The authors note potential applicability to three-dimensional imaging of human cancer cells, underscoring relevance for clinical diagnostics and digital pathology.

The authors introduce a lensless quantitative phase microendoscope that leverages a bare multi-core fiber bundle as a phase encoder and a new FAST reconstruction algorithm to recover the incident complex field from intensity-only far-field speckles. The method achieves microscale lateral resolution and nanoscale OPL sensitivity, enables digital refocusing for 3D imaging without mechanical scanning, and accurately reconstructs quantitative phase, as verified with resolution and phase calibration targets as well as dynamic bead flows. The approach substantially simplifies coherent endoscopic imaging by removing distal optics and complex wavefront-shaping hardware, paving the way for minimally invasive, in vivo QPI and broader clinical applications. The technique also shows potential for nanoscale metrology, such as measuring the height of semiconductor structures. Future work may further optimize reconstruction speed and robustness, extend calibration and stability for in vivo operation, and translate the method to clinical settings.