Broadband thermal imaging using meta-optics

Long-wavelength infrared (LWIR) imaging is important for non-contact thermography, long-range imaging, and remote sensing, but traditional high-NA refractive LWIR systems are bulky and heavy. Diffractive alternatives such as multilevel diffractive lenses and subwavelength meta-optics can greatly reduce size and weight. However, strong axial chromatic aberration inherent to diffractive optics limits image quality in broadband conditions. Dispersion engineering can partially mitigate this but faces fundamental limits dictated by achievable group delay and group delay dispersion in large apertures. Computational imaging with forward-designed extended-depth-of-focus (EDOF) meta-optics has been used in the visible, but relies on designer intuition and provides limited guidance for further improvements, particularly when translating to LWIR where training data are scarce. Inverse design offers a principled approach by optimizing a figure of merit (FoM) and has succeeded in creating functional and non-intuitive meta-optics, including EDOF elements and end-to-end co-optimized optical-computational systems. Yet end-to-end methods can obscure how and why an optic works, complicating transfer across domains. This work proposes a new, interpretable design paradigm for broadband LWIR meta-optical imaging: maximizing the wavelength- and angle-averaged volume under a multichromatic MTF surface via a differentiable, multi-scale inverse-design framework that unifies meta-atom (local) and phase-mask (global) engineering.

The paper situates its contribution within prior work on LWIR imaging and meta-optics: (1) Conventional refractive LWIR systems provide high resolution but are bulky and heavy; diffractive and metasurface approaches enable thinner, lighter optics. (2) Prior LWIR metasurfaces and metalenses have demonstrated imaging under ambient conditions but with degraded image quality due to chromatic aberrations. (3) Dispersion engineering with dielectric metasurfaces can control chromatic dispersion but is fundamentally limited by group delay and group delay dispersion for large apertures. (4) Computational imaging with forward-designed EDOF meta-optics has shown broadband performance in the visible, but relies on heuristic design and offers limited scalability. (5) Inverse design has produced non-intuitive, effective meta-optics and EDOF lenses, and end-to-end approaches co-optimize optics and computation but reduce interpretability and are hard to transfer to domains with limited training data (e.g., thermal). The present work advances the field by introducing an MTF-based, fully differentiable inverse-design framework that jointly optimizes meta-atom structures and global phase-mask characteristics for broadband LWIR imaging.

Design framework: The authors develop a fully differentiable inverse-design pipeline to optimize broadband LWIR meta-optics that focus multiple wavelengths at a common image plane. The pipeline is multi-scale, combining local meta-atom modeling with global field propagation and MTF computation. - Meta-atom parameterizations: Two families are considered. Simple scatterers are defined by a single width parameter. Complex scatterers use three geometric parameters (p0, p1, p2) defining a binary silicon pillar profile with enforced fourfold symmetry for polarization insensitivity. The pillar height h is fixed at 10 µm. In design illustrations, a square lattice with periodicity Λ=4 µm is used; fabricated devices are all-silicon (silicon pillars on silicon substrate). - Surrogate modeling: For each archetype, a meta-atom library is generated by rigorous coupled-wave analysis (RCWA), simulating complex transmission coefficients E(p, λ) across sampled geometries and wavelengths. A deep neural network (DNN) surrogate is trained to map geometry parameters p to complex transmission Ê(p, λ), enabling differentiable scatterer-to-field mapping. - Forward model and FoM: The spatial modulation Ê(x,y,λ) from the meta-atom lattice is multiplied by an incident plane wave (incidence angle θ) and propagated to the sensor plane using the shifted angular spectrum method, producing the point spread function I(x,y; λ,θ). The modulation transfer function (MTF) M(kx,ky; λ,θ) is obtained via Fourier transform and normalized by the diffraction-limited MTF D(kx,ky; λ) to yield M. A modified Strehl ratio S(λ,θ) is defined as the integral of M over spatial frequencies normalized to the on-axis diffraction-limited case. The figure of merit F = log(∏λ,θ S(λ,θ)) corresponds to the wavelength- and angle-averaged volume under the MTF surface and is maximized when individual S(λ,θ) values are uniform, promoting even performance across wavelengths and angles. - Optimization: Automatic differentiation yields ∂F/∂p through the differentiable pipeline. Stochastic gradient descent optimizes geometry parameters p. Halting criteria: (1) parameter convergence ||p−p_{t−1}||2 < T or (2) max iterations N. Final designs are exported to GDSII for fabrication. - Training and sampling details: Complex scatterers use 40 samples per feature dimension (40^3 parameter samples) and 101 wavelengths (total 40^3×101 RCWA simulations) to train the surrogate. Simple scatterers use 1000 geometry samples and 101 wavelengths (1000×101 simulations). The DNN surrogate has four fully connected layers with 256 units each and a “hyperboloid tangent” activation; all operations are differentiable. During global optimization, 13 wavelengths uniformly spanning 8–12 µm and two incidence angles (0° and 10°) are used. Simulations for performance comparison use RCWA for meta-atoms, the DNN mapping for optimization, and include normally distributed perturbations to meta-atom parameters to emulate fabrication errors. - Device specifications: Target nominal focal length 1 cm and NA=0.45 (f/1). The meta-optics are polarization-insensitive. An all-silicon platform is chosen; despite silicon absorption in LWIR, ≈80% transmission is expected. A forward-designed hyperboloid metalens of comparable height and periodicity serves as baseline. Fabrication: Devices are made on a 500 µm thick double-side polished, lightly boron-doped silicon wafer (1–10 Ω-cm). Steps: (1) Direct-write lithography defines circular apertures in photoresist. (2) 220 nm Al is deposited and lifted off to form a metal mask around apertures. (3) A second direct-write pattern defines meta-atom scatterers aligned within apertures. (4) Deep reactive ion etching (DRIE) transfers the pattern 10 µm into silicon with high aspect ratio, vertical sidewalls. (5) Photoresist is stripped; devices are ready for characterization. Characterization and imaging: PSFs are measured with a confocal LWIR setup using a tunable QCL (8.23–10.93 µm, 500 ns pulses, 100 kHz), Ge aspheres (f1=20 mm, NA 0.63; f2=15 mm, NA 0.83), a ZnSe lens (f3=50.8 mm, 3–12 µm coating), and a FLIR A6751 SLS FPA (15 µm pitch, 640×512) cooled to 76 K. In-lab imaging uses a hotplate (150 °C) with high-emissivity tape as broadband thermal source and laser-cut aluminum targets coated matte black; a FLIR Boson 640 captures images for post-processing (background subtraction, contrast stretch, block-matching denoising). Narrowband performance is tested with 10±0.25 µm and 12±0.25 µm band-pass filters. In-the-wild imaging captures single frames under ambient indoor/outdoor conditions with a FLIR A65 sensor. Computational backend: A semi-blind deconvolution is solved per image using an implicit neural representation (INR) prior (WIRE architecture). The inverse problem jointly estimates the scene, the PSF K (initialized from simulations), and low-rank fixed-pattern noise F: - Base objective: minimize ||I_obs − K*N||^2 + λ_TV TV(N) - Extended objective with FPN: minimize ||I_obs − F·(K*N)||^2 + λ_TV TV(N), subject to rank(F)=r. This data-free prior promotes natural image structure and mitigates microbolometer fixed-pattern noise, enabling high-quality reconstructions despite limited thermal image datasets.

- Demonstrated a broadband, polarization-insensitive LWIR meta-optic (≈1 cm diameter, NA 0.45, f/1) designed via MTF engineering that unifies meta-atom and phase-mask optimization. - Simulations with fabrication-like perturbations show wavelength-averaged modified Strehl ratios: 0.045 (complex scatterers), 0.018 (simple scatterers), versus 0.0075 for a forward-designed hyperboloid metalens, yielding approximately a six-fold average improvement over the baseline. - Despite optimizing at discrete wavelengths (13 during optimization; 8 shown with RCWA evaluation), non-sampled wavelengths still outperform the hyperboloid lens, enabling effective broadband imaging across 8–12 µm. - Experimental imaging (lab targets) shows the complex-scatterer MTF-engineered optic produces the sharpest images; the simple-scatterer design also outperforms the hyperboloid lens. Narrowband tests with 10 µm and 12 µm filters confirm superior resolution and higher PSNR (values in Supplementary Materials). - In-the-wild ambient imaging demonstrates clear recovery of scene details (vehicles, person, background structures) with the MTF-engineered optic and computational backend, while the hyperboloid metalens exhibits central glow artifacts and poor sharpness. - Fabrication of all-silicon meta-optics using standard lithography and DRIE validates practicality; meta-optics offer significant thickness reduction versus refractive LWIR lenses.

The results directly address the core challenge of chromatic aberration in broadband LWIR meta-optical imaging. By maximizing the multichromatic MTF volume, the inverse-design framework enforces uniform performance across wavelengths and angles, improving effective Strehl and perceived image quality without relying on narrowband or EDOF-only heuristics. The combination of local meta-atom design (increased structural degrees of freedom) with global phase-mask optimization expands the solution space and provides dispersion-like flexibility, which explains the improved performance of complex parameterizations. The computational backend further mitigates residual aberrations and sensor artifacts, enabling practical ambient imaging. Importantly, the FoM implicitly penalizes poorly focused or highly scattered energy (via the MTF’s DC component), aligning the design with high effective focusing performance without explicitly optimizing a potentially ambiguous focusing efficiency metric. Overall, the approach yields interpretable design insights, robustness to fabrication imperfections, and substantial empirical gains over forward-designed hyperboloid metalenses, highlighting a clear path to compact, high-performance LWIR imagers.

This work introduces a universal, interpretable MTF-engineering framework for designing large-area, broadband LWIR meta-optics. By unifying local meta-atom and global phase-mask optimization in a differentiable pipeline, and coupling the optics with a simple yet effective deconvolution backend, the authors demonstrate a polarization-insensitive, NA 0.45, 1 cm-aperture, all-silicon meta-optic that achieves about a six-fold improvement in wavelength-averaged Strehl ratio over a forward-designed hyperboloid metalens, validated in lab and in-the-wild imaging. The study shows that increasing meta-atom structural degrees of freedom can substantially boost performance and offers a roadmap for future designs that leverage richer parameterizations and large-scale optimization. Future directions include voxel-level meta-atom engineering using advanced ML surrogates that go beyond local phase approximations, co-optimization strategies, and deployment of pretrained networks or fine-tuned models for real-time reconstruction in the thermal domain.

- Design and optimization rely on a DNN surrogate trained on RCWA data and the local phase approximation, which can understate inter-element coupling and reduce efficiency; while alternatives exist (physics-inspired neural networks without this approximation), they were not used here. - Optimization sampled a discrete set of wavelengths (13 in optimization; 8 in certain simulations) across 8–12 µm due to memory constraints, leading to lower Strehl between sampled wavelengths, though still superior to the baseline. - Performance gains depend on increased meta-atom parameterization, which raises sampling complexity exponentially and tightens fabrication resolution requirements; fabrication imperfections can degrade performance. - The approach emphasizes modified Strehl/MTF rather than explicit focusing efficiency; although the FoM indirectly accounts for focusing efficiency, absolute transmission/focusing efficiency metrics were not directly optimized. - All-silicon platform exhibits some LWIR absorption (≈80% transmission expected), which may limit throughput compared to ideal low-loss materials. - Computational backend is currently iterative and data-free, not real-time; paucity of high-quality thermal image datasets limits supervised, feed-forward reconstruction approaches.