Learned Split-Spectrum Metalens

• The paper demonstrates that a learned split-spectrum metalens achieves a 32.29% PSNR gain over hyperbolic designs by rejecting near-depth occluders via spectral splitting.
• It employs a differentiable optimization framework that integrates PSF and image simulators to fine-tune meta-atom phase designs for diffraction-limited performance.
• Neural network postprocessing further enhances imaging quality, improving detection mAP and segmentation IoU, making it ideal for compact, mobile applications.

A learned split-spectrum metalens is a meta-optical system that enables broadband, obstruction-free imaging in the visible spectrum by employing a learned meta-atom phase pattern combined with spectral filtering and post-capture neural-network enhancement. This approach physically rejects signals from near-depth occlusions—such as raindrops, fences, or dust—that would otherwise degrade image quality, all within a compact, single-element design optimized for space-constrained applications.

1. Optical Principles: Depth–Wavelength Symmetry and Spectrum Splitting

A fundamental limitation in diffractive metalenses is the “depth–wavelength symmetry,” wherein a change in either the object depth ($\Delta z$) or the wavelength ($\Delta \lambda$) produces equivalent point-spread function (PSF) shifts. Mathematically, the symmetry is given by $$P_{\lambda+\Delta\lambda, z} \simeq P_{\lambda, z+\Delta z}$$, with the wavelength–depth relation under the paraxial approximation:

$z = \frac{\lambda_d f}{\lambda-\lambda_d}$

where $z$ is object distance, $f$ is focal length, and $\lambda_d$ is the design wavelength. A corresponding change in wavelength that mimics a depth shift is:

$$\Delta\lambda = \lambda_d f\Bigl(\frac{1}{z} − \frac{1}{z−\Delta z}\Bigr)$$

This symmetry complicates the simultaneous realization of broadband and obstruction-free imaging: near-depth occluders remain in focus across the spectrum. The split-spectrum approach addresses this by dividing each RGB channel $c\in\{R,G,B\}$ into “pass” ($\Lambda_{\mathrm{pass}}^c$) and “stop” ($\Lambda_{\mathrm{stop}}^c$) spectral bands via a multi-band filter. The metalens is optimized such that for scene depths beyond $z_{\mathrm{far}}\gtrsim0.5\,\mathrm{m}$ and $\lambda\in\Lambda_{\mathrm{pass}}^c$, the PSF is diffraction-limited. For near-occluders at $z_{\mathrm{near}}\approx0.045\,\mathrm{m}$, the symmetry ensures focused wavelengths shift into $\Lambda_{\mathrm{stop}}^c$, which are blocked. The overall transfer function for channel $c$, at each spatial location $(x, y)$, is thus

$$I_c(x, y) = \int P^c_z(\lambda; x, y)S_c(\lambda)A(\lambda, c)\,d\lambda \otimes \mathrm{Object}(x, y)$$

where $A(\lambda, c)$ is the amplitude mask (1 in pass band, 0 in stop band), and $S_c(\lambda)$ is the camera’s spectral sensitivity.

2. Meta-Atom Design and Fabrication

The meta-atom building block is fabricated from silicon-nitride (SiNₓ) with a thickness $h=700\,\mathrm{nm}$ and a unit-cell period $p=395\,\mathrm{nm}$. Each unit cell comprises an in-plane bar with width $w=305\,\mathrm{nm}$ and length $l=125\,\mathrm{nm}$. The cell functions as a Pancharatnam–Berry meta-atom: the in-plane orientation angle $\theta(x, y)$ encodes a local geometric phase $\varphi=2\theta$. This design enables “geometric phase” control with high efficiency, documented at 78.4%, 72.9%, 66.9% for the center wavelengths of the blue, green, and red pass bands ($457\,\mathrm{nm}$, $530\,\mathrm{nm}$, $628\,\mathrm{nm}$), respectively, with an average conversion efficiency of $\sim67.3\%$ over $\Lambda_{\mathrm{pass}}$.

Lens fabrication uses high-speed electron-beam lithography (EBL), followed by chromium evaporation as an etch mask, dry etching into SiNₓ, and mask lift-off. The completed metalens features a focal length $f = 4\,\mathrm{mm}$ and aperture $\varphi=2.516\,\mathrm{mm}$. Three lenses were produced for comparison: the learned split-spectrum metalens, a learned broadband metalens (without spectrum split), and a conventional hyperbolic metalens ($\lambda_d=532\,\mathrm{nm}$).

3. Differentiable Optimization and End-to-End Learning

The metalens design leverages a differentiable, end-to-end learning framework to optimize the local orientation map $\theta(x, y)$. Two modules are constructed:

• A PSF simulator generating $P^c_z = f_\mathrm{psf}(\theta, z, c)$.
• An image simulator generating $$I_\mathrm{captured} = f_\mathrm{img}(\theta; I_\mathrm{clean}, I_\mathrm{obs})$$, where $I_\mathrm{clean}$ is a clean far-scene DIV2K patch and $I_\mathrm{obs}$ is a simulated occlusion.

The loss function is:

$$\min_\theta \ L_\mathrm{img}(I_\mathrm{captured},I_\mathrm{clean}) + L_\mathrm{psf}(P_{z_{\mathrm{far}}})$$

with $L_\mathrm{img}$ quantifying the $\ell_2$ error to the ground-truth image and $L_\mathrm{psf}$ enforcing high-Strehl PSFs at $z_{\mathrm{far}}$ over $\Lambda_{\mathrm{pass}}$. Importance sampling over $\lambda$ proportional to $S_c(\lambda)$ speeds spectral integration during training. Optimization uses Adam on batches of clean/obstruction pairs.

4. Neural Network Postprocessing

Imaging fidelity is further improved through neural network postprocessing with the “LocalNet” (Kim et al., CVPR 2024) architecture: a U-Net–style encoder–decoder with skip connections, positional encoding, and per-channel spectral weighting. LocalNet is trained using metalens-captured, obstruction-obscured DIV2K image patches as input, paired with clean ground-truth images captured through an $f=8\,\mathrm{mm}$ compound lens. Loss consists of $\ell_1$ or $\ell_2$ error, supplemented with perceptual loss (VGG) terms. The positional encoding of $(x,y)$ enables correction of spatially varying aberrations. Neural enhancement is performed post-hoc without joint optimization with $\theta(x, y)$.

5. Experimental Validation and Quantitative Performance

Performance is assessed through PSF imaging (430–645 nm in 5 nm steps) at $z_{\mathrm{near}} \approx 45\,\mathrm{mm}$ and $z_{\mathrm{far}} \approx \infty$, and through imaging of printed 2D targets using a color CMOS sensor with standard Bayer RGB filter and the custom multi-band dichroic filter. Raw RGB images are processed through the pretrained LocalNet.

Quantitative results include:

Metric	Hyperbolic Metalens	Broadband Learned	Learned Split-Spectrum
PSNR (dB)	15.84	18.79	20.94
UAV Detection mAP	0.0350	0.0292	0.1704
Kvasir-SEG IoU	0.3472	0.5950	0.8317
Cityscapes mIoU	0.4666	0.4601	0.6701

The split-spectrum design achieves a PSNR gain of 32.29% over the hyperbolic baseline and 11.45% over broadband learned. For vision tasks under obstruction: detection mAP is improved by 13.54% (absolute) over hyperbolic design, IoU for polyp segmentation by 48.45%, and mIoU for semantic segmentation by 20.35%.

6. Advantages, Limitations, and Future Perspectives

The learned split-spectrum metalens provides a single-shot, zero-moving-parts optical solution to near-depth obstruction, within a fully flat, wafer-scale meta-optical form factor ($4\,\mathrm{mm} \times 2.5\,\mathrm{mm}$), suitable for mobile robots, drones, and endoscopes. Unobstructed imaging quality also surpasses conventional hyperbolic devices, with a PSNR gain of 23.9 %.

Limitations include reliance on an external multi-band filter; tighter integration of filtering and meta-atom amplitude engineering could improve throughput and size. The design is static for a fixed $z_{\mathrm{near}}$; extension to variable-depth or dynamic occluders may require dynamic filtering or event-based approaches. Expanding to other spectral bands (NIR, SWIR) or hyperspectral splitting may further enhance depth discrimination and obstruction removal.

By analytically exploiting and then breaking the depth–wavelength symmetry through learned spectral filtering and meta-atom phase design, the learned split-spectrum metalens demonstrates obstruction rejection and broadband imaging in a single, compact optical element, with observed gains in PSNR and performance on real-world vision tasks (Yoon et al., 27 Jan 2026).