Single-fiber hyperspectral imaging via nanophotonic disordered dispersion

Abstract

Optical fibers are widely used to transmit optical signals for communications and sensing. Extending this capability to hyperspectral imaging is attractive for compact imaging systems, but is fundamentally constrained by limited channel capacity and transmission distortion of fibers. Here, we demonstrate single-fiber hyperspectral imaging via nanophotonic disordered dispersion. A disordered-dispersion encoder at the distal fiber end can map high-dimensional spectral-angular information into a one-dimensional spectral measurement, which is then computationally decoded using sparsity-constrained reconstruction. Our disordered dispersion is achieved using nonlocal nanophotonic structures that support high mode density and multimode coupling, thereby enabling low-correlation compressive encoding. The system features angular reconstruction over a field of view of ±60°, spectral detection from 400 to 700 nm, and robustness against fiber distortion. This work circumvents the need for real-space pixelated encoders or detectors used in traditional hyperspectral cameras, offering a route toward ultra-compact high-dimensional imagers compatible with flexible single-fiber probes.

Researchers show that a single optical fiber can transmit hyperspectral images using a tiny nanophotonic encoder, opening a path toward compact, flexible probes for imaging and sensing.

Introduction

Nanophotonic technologies are revolutionizing optical systems, enabling light manipulation with ultra-compact devices^1–4. A compelling example is the evolution of hyperspectral imaging systems, where the replacement of bulky free-space optics with planar components like metasurfaces has shrunk system form factors from the benchtop^5–7 to the chip scale^8–13. The quest for further miniaturization, particularly for minimally invasive probes, drives the focus toward optical fibers as the ultimate platform for information transport through micrometer-scale apertures^14,15. While significant progress has been made in fiber-based intensity, depth, and holographic imaging^16–22, realizing hyperspectral imaging through a single fiber remains an unsolved challenge, despite the importance for revealing chemical and structural fingerprints^11,23,24.

The challenge of fiber-based computational hyperspectral imaging is twofold. First, the fiber tip has a limited aperture that results in a fundamental bottleneck in the encoding. Conventional hyperspectral cameras rely on real-space, pixelated encoders whose throughput (i.e., space-bandwidth product) is coupled to their physical footprint^5–12. This aperture constraint makes it difficult for a micron-scale fiber probe to collect high-throughput spatial-spectral information. Second, the fiber itself imposes a severe transmission bottleneck. Fiber bundles are constrained by core-density-limited information capacity^{19–22,25,26}. Multimode fibers (MMFs) offer higher spatial modal density, but the highly sensitive configuration-dependent transmission also makes spectral imaging challenging^{17,18,27–36}. Spectrally encoded endoscopy approaches correlate spatial positions with spectral signatures^37–41, where different wavelengths serve as deterministic spatial tags. However, this bijective wavelength-to-position mapping makes a single spectral measurement encode only spatial intensity rather than the local spectrum at each position, thereby limiting simultaneous spatial and spectral acquisition, i.e., hyperspectral imaging.

To overcome the dual constraints, we introduce a nanophotonic disordered-dispersion encoder (DDE) that redefines the imaging strategy, as shown in Fig. 1a. First, by shifting the encoding scheme from real space to the wavevector domain, the DDE circumvents the aperture-bandwidth trade-off inherent to conventional imagers. Second, the DDE enables the compressive mapping of high-dimensional hyperspectral data onto a low-dimensional spectral signal. This encoded spectrum can be robustly transmitted through the fiber with minimal distortion. As a result, this framework provides a compact strategy for single-fiber hyperspectral imaging.

Fig. 1. Single-fiber hyperspectral imaging.

a Light from the object, represented as a spectral-angular distribution at the fiber tip, is encoded into distortion-robust spectral transmission in the fiber. The hyperspectral image cube is reconstructed with a sparsity-driven algorithm based on spectral measurements. b The required disordered spectral-angular transmission is physically realized by the DDE, a nanophotonic device that generates rapidly varying angle- and wavelength-dependent responses through deliberately designed nanostructures at the fiber end. c The disordered spectral-angular transmission enables effective encoding of high-dimensional information in accordance with compressive sensing theory. d In contrast to conventional imaging schemes that trade off detection dimensionality against detector compactness, our approach enables high-dimensional detection with an ultra-compact single-fiber probe.

Exploiting engineered nonlocal nanophotonics^2,3,42–47, the DDE in front of a single fiber generates disorder in the spatio-temporal dispersion space. The DDE integrates a long-range periodic metagrating with a highly dispersive multilayer thin film, enabling multiple diffraction modes and inducing multimode coupling, as shown in Fig. 1b. The resulting spectral-angular encoding functions map the incident distribution into a compressed one-dimensional spectral signal, which is then fed into a sparsity-constrained reconstruction algorithm to recover the spectral-angular information over a large field of view at the fiber tip (Fig. 1c). Owing to the spatial-mode-invariant spectral transmission, the prototype remains intrinsically robust to fiber deformation. Consequently, our method combines high-dimensional detection with the compactness of a single-fiber probe (Fig. 1d and Supplementary Information section 1). This work establishes a framework for multidimensional information transmission through a single optical fiber, with potential extensions to compact microscopy, quantum information science, and other fields.

Results

Concept of hyperspectral imaging with a single fiber

We begin by outlining the fundamental architecture of the nanophotonics-assisted hyperspectral fiber imaging system based on spectral-angular encoding and decoding. While spatial modes in a single fiber suffer from limited information capacity and perturbation-induced modal distortion, the spatially averaged spectral power exhibits superior resolution and robustness. This observation motivates us to use the spectrum as the information carrier, as spectral power can be transmitted through a single fiber with relatively high stability and can be readily measured at the proximal end. Therefore, the key challenge is to encode spatial or angular information into this spectral signal.

Specifically, the fiber distal end serves as an ultra-compact aperture for the incident light carrying distinct spectral-angular components from the object, as characterized by $o\left(\lambda ,\theta \right)$. After modulation by the encoder, the fiber collects an angle-integrated spectral signal whose spectral profile is preserved during fiber transmission, as shown in Fig. 1b. The encoding process is formulated by

$$m\left(\lambda \right)=\int T\left(\lambda ,\theta \right)o\left(\lambda ,\theta \right)d\theta$$ 1

where $m\left(\lambda \right)$ is the spectral measurement, $T\left(\lambda ,\theta \right)$ is the transmission map created by the encoder, under the assumption that nonlinear optical effects are negligible. To emphasize the linearity of the encoding process, $o\left(\lambda ,\theta \right)$ and $m\left(\lambda \right)$ can be represented in $N_{\theta }{N}_{\lambda }$- and $N_{\lambda }$-dimensional discrete vector spaces, respectively, denoted as $\mathit{o}\in {\mathbb{R}}^{N_{\theta }{N}_{\lambda }}$ and $\mathit{m}\in {\mathbb{R}}^{N_{\lambda }}$. Thus, Eq. 1 can be rewritten as $\mathit{m}=\mathit{So}$, where $\mathit{S}\in {\mathbb{R}}^{\left(N_{\lambda }\right)\times \left(N_{\theta }{N}_{\lambda }\right)}$ is the compressive sampling matrix determined by the transmission map. This dimensionality reduction by a factor of $N_{\theta }$ renders the decoding process a severely ill-posed inverse problem as described by

$$\widehat{\mathit{o}}={\mathrm{argmin}}_{\mathit{o}}\mid \mathit{So}-\mathit{m}\mid$$ 2

Fortunately, the redundancy in the spectral-angular distributions of objects makes such compressive encoding and decoding feasible, provided that the encoding essentially satisfies the incoherence conditions^48,49. In optics, this can be done by introducing randomness into the sampling matrix, as mainly realized using real-space disordered structures, such as diffusers or metasurfaces^{10,11,35,50–53}. In contrast, our strategy in the hyperspectral fiber imaging system demands distinct, varied transmission across spectral-angular dimensions (that is, randomness in the dispersion, or frequency-wavevector, domain, rather than in real space), and this dispersion-space disorder has not yet been implemented.

Nanophotonic disordered-dispersion-assisted encoder

To design the DDE for compatibility with the compact fiber aperture, we note that most simple periodic optical nanostructures are insufficient. This insufficiency arises from their limited mode density and diversity, which leads to a strong correlation between the transfer function’s dependence on frequency (temporal dispersion) and on the wavevector (spatial dispersion, or nonlocality). We therefore stack a one-dimensional (1D) nanophotonic metagrating with a long-range periodicity and a multilayer thin film with alternating high and low refractive indices (silicon nitride/silicon dioxide), as shown in Fig. 2a. Specifically, each long-period metagrating supercell contains five disordered nanostructures, thus providing diverse diffraction modes over a broad spectral range. These modes further interfere and couple with the highly dispersive thin film, which increases the mode density and diversity while reducing correlations in the spectral-angular response (Supplementary Information section 2).

Fig. 2. Design and characterization of the DDE.

a Left: Incident light is diffracted and redistributed by the DDE, where a portion of the exiting light is collected for subsequent spectral detection. Right: scanning electron microscopic images of the fabricated DDE, consisting of a metagrating stacked with a multilayer thin film. b k-resolved DOS of the DDE across the $\left(f,k_x\right)$ plane. c Electric field distribution of four adjacent modes excited by incident light. Top left: $f$= 566.8 THz, $k_x$= 0.675 $\pi /U$; Top right: $f$= 567.1 THz, $k_x$= 0.686 $\pi /U$; Bottom left: $f$= 566.3 THz, $k_x$= 0.675 $\pi /U$; Bottom right: $f$= 561.1 THz, $k_x$= 0.686 $\pi /U$. d Measured transmission map. The inset shows a magnified view with the wavelength range of 500 nm to 540 nm and incident angle range of 15°–25°. e Correlation coefficient between $T$ slices along the angular (left) and spectral directions (right), where three different encoders are compared. f Mutual coherence between the sparsity basis $\mathit{\Psi }$ and the sampling matrix S generated by different structures under different compression ratios.

We numerically validate the high mode density and diversity of the nanophotonic DDE by calculating k-resolved density of states (DOS) and the electric field distributions of adjacent modes (Supplementary Information section 3). The k-resolved DOS map in Fig. 2b shows that the modes span a wide range of the frequency-wavevector space, which underpins the DDE’s superior modulation capability over a broad range of wavelengths and incident angles. Moreover, Fig. 2c shows the electric field maps of four adjacent eigenmodes selected with closely spaced frequencies and wavevectors. Although these modes correspond to very similar wavelengths and incident angles, they exhibit distinct electric field distributions, demonstrating that slight perturbations in incident parameters can excite different coupled modes and thereby give rise to the disordered response. The dense and unstructured mode distribution across the frequency-wavevector space explains the disordered spectral-angular response of the DDE, which is essential for high-fidelity encoding.

To characterize the nanophotonic DDE experimentally, we measure the transmission map over $\lambda$ ranging from 400 nm to 700 nm and ${\theta }_x$ from −60° to 60° under s-polarized conditions (Methods and Supplementary Information section 4). As shown in Fig. 2d, the transmission map maintains appreciable efficiency over a broad range of wavelengths and angles, while also showing localized, rapidly varying features. The broad response supports large-field-of-view and broadband measurements, whereas the local variations help distinguish different spectral-angular components.

From the measured transmission map, we quantitatively evaluate the randomness in the spectral-angular response by analyzing the correlation coefficient (CC), as shown in Fig. 2e (Supplementary Information section 5). Specifically, both inter-$\theta$ and inter-$\lambda$ CCs are computed, defined as the Pearson correlation coefficient calculated between different $\theta$ slices and $\lambda$ slices. Our results indicate that, compared with simpler structures such as a periodic grating (PG) and a periodic thin film (TF), the DDE exhibits significantly lower CC values. This validates our strategy of harnessing disordered dispersion to induce random modulation, which is essential for encoding.

Furthermore, we conduct a quantitative analysis within the framework of compressive sensing theory. The mutual coherence $\mu \left(\mathit{S},\mathit{\Psi }\right)$ between the sampling matrix $\mathit{S}$ and the sparse basis $\mathit{\Psi }$ is closely related to the number of observations required for successful reconstruction, thereby reflecting the compressive encoding efficiency (see definition in Supplementary Information section 5). As illustrated in Fig. 2f, mutual coherence increases with the compression ratio $N_{\theta }$, which is the compression ratio between underdetermined variables and measurements. Notably, the DDE exhibits lower mutual coherence than the PG or TF, indicating that the DDE design generates a better-conditioned sampling matrix for compressive sensing, requiring fewer measurements for successful reconstruction.

Compressive single-fiber hyperspectral imaging

We now validate the compressive imaging approach using our proposed DDE. The current design primarily resolves the ${\theta }_x$ dimension. Therefore, 2D imaging of $o\left(\lambda ,{\theta }_x,{\theta }_y\right)$ is achieved by introducing diversity along the y direction via scanning or rotating the probe. Despite this, by extending the disordered structure from 1D to 2D, hyperspectral 2D imaging can be realized through single-shot spectral measurement (Supplementary Information section 6).

We first perform compressive imaging with artificial 1D objects exhibiting different spectral-angular distributions along the ${\theta }_x$ dimension. In our experimental setup shown in Fig. 3a, the DDE and a polarizer are mounted at the distal end face of a single MMF with a core diameter of 400 μm. The objects constructed using slits and different color filters are positioned at different x locations, resulting in 1D objects with varying $\left(\lambda ,{\theta }_x\right)$ distributions.

Fig. 3. Hyperspectral image decoding.

a The experimental setup for spectral-angular imaging. b Spectral measurements (Mea.) and corresponding reconstructions (Rec.) of the three objects with diverse spectral-angular distributions. c Schematic illustration of the reconstruction algorithm. The spectral-angular output is retrieved from spectral-only input by iteratively updating the two sub-problems. d Slices of the reconstruction and ground truth (G.T.) along the spectral (left) and the angular (right) direction. e Hyperspectral image information $o\left(\lambda ,{\theta }_x,{\theta }_y\right)$ is recorded by multi-shot measurements with different rotation angles δ. f The artificial object (left) and the synthesized RGB image of reconstruction (right). g Reconstruction slices at different wavelengths. h Comparisons between the reconstructed spectra and ground truth. (a–d) are spectral-angular reconstructions from single-shot measurements, whereas (e–h) are hyperspectral imaging based on multi-shot measurements.

The compressive-sensing-based optimization algorithm is developed as shown in Fig. 3c using the measured encoded spectra as inputs to retrieve the spectral-angular signals (Fig. 3b). Leveraging the prior knowledge that the hyperspectral image distribution exhibits sparsity through a transformation $\mathit{v}={\mathit{\Psi }}^{-1}\mathit{o}$, the object is reconstructed by iteratively updating the fidelity term and the prior term (Methods). The reconstruction results, along with slices in both the spectral and incident angle directions, are presented in Fig. 3b, d, respectively. The results yield angular mean absolute errors (MAEs) of 7.86%, 11.26%, and 9.43%, while the spectral slices show MAEs of 11.94%, 19.43%, and 18.14%. Furthermore, our method accurately reconstructs the incident angle across a range of $\left[-{60}^{\circ },{60}^{\circ }\right]$, with an angular-averaged MAE of 6.44% and a spectral-averaged MAE of 6.27%, demonstrating large-field-of-view imaging capability (Supplementary Information section 7 and Supplementary Movie 1). This high-fidelity reconstruction is directly enabled by the efficient compressive encoding from the DDE’s disordered dispersion.

A key advantage of our nanophotonic front-end encoding strategy is the inherent immunity to modal distortions within the fiber. Benefiting from the spatial-mode-invariant spectral transmission, the spectral measurement and reconstruction exhibit robustness to external distortions of the fiber, such as bending or twisting, highlighting practicality in dynamic environments (Supplementary Information section 8 and Supplementary Movie 2). In addition, we compare imaging results using encoders based on DDE, PG, and TF. Only the DDE enables accurate reconstruction of full spectral-angular information, further validating the nontrivial role of disordered dispersion in the encoding process to preserve the spectral-angular distribution of the incident light (Supplementary Information section 5).

Next, we conduct hyperspectral imaging through multiple measurements. As a demonstration, we rotate the object about the z-axis, performing multiple measurements at different rotation angles $\delta$ to introduce diversity in the $y$-direction, as shown in Fig. 3e. By extending the reconstruction algorithm with a degree of freedom in the ${\theta }_y$ direction, a hyperspectral image cube is reconstructed. Here, we examine artificial targets in the shape of a windmill that exhibit four spatially distinct spectral characteristics, as shown in Fig. 3f, where the reconstruction is synthesized as an RGB image according to the CIE 1931 standard observer functions. Reconstruction slices at four wavelengths are shown in Fig. 3g and are further validated against measurements obtained with a commercial hyperspectral camera, as presented in Supplementary Information section 9, Figure S25. The reconstructed spectra of the four colored regions shown in Fig. 3h exhibit MAEs of 6.01%, 2.56%, 5.50%, and 8.30%, respectively, demonstrating hyperspectral imaging capability. The remaining artifacts mainly arise from residual ambiguity in the underdetermined reconstruction, where imperfectly encoded spectral-angular components can leak into each other. These artifacts are further enhanced by model mismatch, such as imperfect transmission-map calibration and small rotation-alignment errors. More details of the imaging experiments can be found in Methods and Supplementary Information section 9.

Last, we show single-fiber hyperspectral histological imaging of a stained, ex vivo mouse gastric tumor tissue slice. The imaging configuration and tissue sample are illustrated in Fig. 4a. The tissue sample is illuminated with converging broadband light and rotated to generate 36 measurements, as shown in Fig. 4b. We perform three independent measurements of the same sample, and the synthesized RGB image of the averaged reconstruction is shown in Fig. 4c. The corresponding reconstructed spectra and hyperspectral-camera ground-truth spectra from representative tissue regions are shown in Fig. 4e. Despite variations caused by alignment errors and spectrometer dark-current noise, the reconstructed spectral responses remain consistent across three repeated measurements.

Fig. 4. Proof-of-concept single-fiber hyperspectral histological imaging.

a Schematic of the single-fiber hyperspectral histological imaging experiment and photograph of the stained mouse gastric tumor tissue slice. b Spectral measurements acquired at different sample rotation angles. c Synthesized RGB image of the averaged reconstruction from three independent measurements. d Spectral segmentation of the reconstructed hyperspectral data using the k-means algorithm. e Comparison between reconstructed spectra and ground-truth spectra from representative necrotic and tumor tissue regions. The solid curves represent the mean reconstructed spectra, the semi-transparent regions indicate the standard deviation range, and the dashed curves represent the ground-truth spectra. The inset images show magnified microscopic views of the corresponding tissue regions.

The reconstructed hyperspectral data capture wavelength-dependent responses from different stained tissue regions. Based on the spectral curves at different pixel locations, the sample is segmented into three regions using the k-means algorithm, as shown in Fig. 4d. The red and blue regions exhibit distinct spectral responses, which correlate with different tissue regions due to their differences in staining and morphology, as shown in Fig. 4e. This proof-of-concept demonstration indicates the potential of single-fiber probes for hyperspectral histological imaging.

Discussion

To summarize, we demonstrate the nanophotonic DDE with low-correlation responses across spectral-angular dimensions for efficient compression of hyperspectral image signals. By loading the DDE onto the single fiber’s end face, hyperspectral image data cubes can be encoded compressively, transmitted robustly, and reconstructed computationally, thereby establishing a single-fiber hyperspectral imaging paradigm.

Our nanophotonic approach provides several advantages. By shifting the encoding process from real space to the wavevector domain, the DDE relaxes the aperture-related constraint on the number of encoding channels in conventional real-space encoders. Importantly, because the reconstruction relies on spectral-only measurements rather than fiber spatial modes, the framework remains in principle compatible with smaller-core and single-mode fibers (see Supplementary Information section 10). Nevertheless, the physical aperture affects photon collection and fiber-coupling efficiency, thereby affecting measurement SNR and reconstruction fidelity (see Supplementary Information section 11). This photon-budget consideration is the main reason why a 400 μm-core multimode fiber is used in the current proof-of-concept demonstration.

The current prototype’s image quality is constrained by several bottlenecks, which could nonetheless be addressed in future work. On the hardware side, the present DDE is designed using heuristic objectives and therefore may contain residual correlations in the sampling matrix. Future work could focus on inverse-design of nanophotonic structures to directly tailor the transmission matrix, with optimization objectives defined by information capacity, optical throughput, or end-to-end imaging performance. Reconfigurable devices could further reduce the ill-posedness of the inverse problem through diversely encoded measurements^12,54,55. The signal-to-noise ratio may become a limiting factor when the fiber-core diameter is further reduced to a few micrometers (see details in Supplementary Information section 11). Integrating illumination within the fiber-format probe and using high-sensitivity spectrometers^56–58 could improve photon collection.

On the algorithm side, the present sparsity-constrained iterative reconstruction uses explicitly designed priors for hyperspectral images, and reconstruction currently takes minutes. Future algorithmic improvements may include data-driven implicit regularization and deep-neural-network-based reconstruction models, which can exploit spatial–spectral priors and shift much of the computational burden from inference to offline training. Together, these improvements are expected to advance single-fiber hyperspectral imaging toward practical applications.

The principle of projecting a high-dimensional data cube onto a single measurement channel is exceptionally suited for applications where the physical interface is severely limited. Beyond the fiber platform, this paradigm holds potential for creating highly compact and advanced imaging modalities and could inspire novel architectures for optical computing and other information processing applications.

Methods

Numerical calculations

$T\left(\lambda ,{\theta }_x\right)$ is calculated as the sum of diffraction efficiencies within the fiber’s acceptance angle, each weighted by its coupling efficiency:

$$T\left(\lambda ,{\theta }_x\right)={\sum }_{i=1}^{N_d}{E}_i\left(\lambda ,{\theta }_x\right)C\left({\varphi }_{x,i}\right)$$ 3

where $N_d$ is the number of diffraction orders, and for each diffraction order $i$, $E_i$ and ${\varphi }_{x,i}$ denote the diffraction efficiency and exit angle, respectively. The diffraction properties of the DDE are simulated with the rigorous coupled wave analysis method⁵⁹. The coupling efficiency $C\left({\varphi }_x\right)$ is measured experimentally. The eigenmodes shown in Fig. 2b, c are calculated with COMSOL Multiphysics software. More details of the numerical calculation can be found in Supplementary Information section 4.

DDE fabrication

The SiO₂/Si₃N₄ multilayer films are deposited on a 500 μm-thick quartz substrate via magnetron sputtering physical vapor deposition, with the topmost layer being a 500-nm-thick Si₃N₄ layer designed for fabricating the grating pattern. Positive photoresist is applied, and the grating pattern is written using electron beam lithography. Next, a 40 nm Cr layer is deposited using electron beam evaporation coating (EBEC), followed by a lift-off process to create a patterned Cr mask. The pattern is then transferred to the Si₃N₄ layer via inductively coupled plasma reactive-ion etching. Subsequently, the Cr mask is removed using a chromium etchant, resulting in the fabrication of a DDE structure.

Finally, a 150 μm × 150 μm aperture is fabricated to ensure that only the DDE region allows light transmission. Positive photoresist is employed, and ultraviolet lithography is used to remove the photoresist from regions outside the grating. A 100 nm Cr layer is deposited using EBEC, followed by a lift-off process to remove Cr from the grating region, completing the fabrication process. A schematic illustration can be found in Supplementary Information section 12.

Experimental setup

To characterize the transmission map, we direct collimated broadband light with controllable incident angles $\left({\theta }_x,{\theta }_y\right)$ into the system. Light from a halogen lamp (OSL2IR, Thorlabs) is collimated and the light source is mounted on a rotation stage for precise angular control in both $x$ and $y$ directions. The DDE is placed adjacent to the fiber end face (400 μm diameter, FCM1-SMA-400L, JCOPTIX). A polarizer is placed between the source and the DDE to align the electric field with the grating orientation. The spectra in the fiber are detected with a spectrometer (HR6, Ocean Optics). By scanning the incident angles $\left({\theta }_x,{\theta }_y\right)$ and normalizing the measured spectra against the light source profile, we obtain the transmission map $T\left(\lambda ,{\theta }_x,{\theta }_y\right)$. More details of the characterization setup can be found in Supplementary Information section 4.

For imaging experiments, the imaging module that comprises a polarizer, DDE, fiber, and spectrometer is configured the same as in the characterization setup. The 1D samples with $\left(\lambda ,{\theta }_x\right)$ distributions are generated by passing collimated broadband light (OSL2COL, Thorlabs) through a diffuser (DG10-120-MD, Thorlabs), a slit aperture, and a color filter in sequence. The 1D sample is mounted on a rotation stage for precise x-direction angular control. The diffuser ensures uniform angular illumination, while the slit and rotation stage define the angle spread, and the filters control the spectral profile. The three 1D samples, O1, O2, and O3, use a single slit with a 550 nm longpass filter (Edmund), a single slit with a blue filter, and a double slit with no filter, respectively.

For the $\left(\lambda ,{\theta }_x,{\theta }_y\right)$ reconstructions shown in Fig. 3e–h and Fig. 4, both the artificial sample and the tissue slice are illuminated with converging broadband light. The object rotates about the fiber axis (z-axis) in 10^° increments, yielding 36 measurements, simulating rotation of the fiber’s distal tip. The integration time at each rotation angle is 30 ms for the artificial sample and 10 ms for the tissue slice, respectively. The stained mouse gastric tumor tissue section is produced by Wuhan Servicebio Technology Co., Ltd. The sample is a 4 μm-thick section stained with hematoxylin and eosin. More details of the imaging setup can be found in Supplementary Information sections 7 and 9.

Reconstruction algorithm

The unknown object $\mathit{o}$ is reconstructed from the following minimization problem according to compressive sensing theory,

$$\mathit{o}={\mathrm{argmin}}_{\mathit{o}}{\underbrace{\frac{1}{2}{\left.∣\right)\left.∣\right)\mathit{m}-\mathit{S}\mathit{o}\left.∣\right)\left.∣\right)}_2^2}}_{\mathrm{Fidelity}\mathrm{term}F\left(\mathit{o}\right)}+{\underbrace{\left.∣\right)\left.∣\right){\mathit{\Psi }}^{-1}\mathit{o}\left.∣\right)\left.∣\right)}}_{\mathrm{Prior}\mathrm{term}R\left(\mathit{o}\right)}$$ 4

where ${\mathit{\Psi }}^{-1}$ is the sparsity basis. Specifically, considering the differing statistical distributions of the hyperspectral cube along the spatial and spectral axes, the prior term is given by $\parallel {\mathit{\Psi }}^{-1}\mathit{o}\parallel =\alpha {\parallel {{\mathit{\Psi }}_{xy}}^{-1}\mathit{o}\parallel }_1+\beta {\parallel {{\mathit{\Psi }}_{\lambda }}^{-1}\mathit{o}\parallel }_2$. Here, $l_1$ and $l_2$ norms are applied to the spatial dimensions x, y and spectral dimension $\lambda$, respectively, with $\alpha$ and $\beta$ as hyperparameters. Following the fast iterative shrinkage-thresholding algorithm^60,61, the minimization problem can be solved by iteratively updating $\mathit{o}$ according to the fidelity term $F\left(\mathit{o}\right)$ and the prior term $R\left(\mathit{o}\right)$. More details of the reconstruction algorithm can be found in Supplementary Information sections 7 and 9.

Author contributions

G.H., L.C. and Y.M. conceived the project. Y.M., C.J. and G.H. performed the numerical calculations and design. Y.M., J.W., L.C. and G.H. performed the experiments. Y.M., J.W. and L.C. developed the reconstruction algorithm. All authors discussed and analyzed the results. All authors wrote and revised the manuscript. G.H. and L.C. supervised the project.

Peer review

Peer review information

Nature Communications thanks Jaime Viegas, Junjun Xiao, Cuifeng Ying and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

G. Hu is supported by the Nanyang Assistant Professorship Start-up Grant Optica Foundation, Ministry of Education (Singapore) under AcRF TIER1 (RG61/23), National Research Foundation of Singapore under award no. NRF-CRP29-0003 and NRF-CRP31-0001, A*STAR under its AME YIRG Grant (Project No. M23M7c0119), AME IRG Grant (Project No. M24N7c0081) and NSTIC White Space Fund (M25W2NS001). L. Cao is supported by the National Natural Science Foundation of China (62235009).

Data availability

The data supporting the findings of this study are available in the article and the Supplementary Information.

Code availability

The demo code of this work is available from the public repository at GitHub (https://github.com/THUHoloLab/Disordered-dispersion)⁶².

Competing interests

G.H. and Y.M. are named inventors on a pending patent application (Application No. 10202602600Y) filed by Nanyang Technological University, which covers the concept and implementation of single-fiber hyperspectral imaging via nanophotonic disordered dispersion. The other authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77550-9.