LANTERN: Advanced Photonic & AI Systems

• LANTERN is a multifaceted term defining systems that integrate advanced photonics, computational imaging, and machine learning for diverse scientific applications.
• The technology employs adiabatic tapering, robust wavefront sensing, and neural network surrogates to enhance performance in astronomical instrumentation and optical calibration.
• These methods improve data throughput, calibration accuracy, and real-time processing across fields from cryogenic detector calibration to cosmological lightcone construction.

LANTERN

A range of advanced methods, devices, platforms, and frameworks across domains—including astrophotonics, cosmology, robotics, cryogenic calibration, computational imaging, LLMs, and multimodal machine intelligence—have independently adopted the term "LANTERN" (or variants thereof) as an acronym or product name. The most dominant technical usage pertains to photonic lanterns and their derivatives in astronomical and optical contexts, but several other high-impact applications exist. This article provides a rigorous survey of such LANTERN-based systems, focusing on their operating principles, mathematical formalisms, demonstrations, and scientific significance.

1. Photonic Lanterns: Principles, Structure, and Modal Theory

The photonic lantern is a passive, low-loss waveguide device that adiabatically couples a multimode (MM) input, supporting $M$ guided modes, to $M$ single-mode (SM) outputs without significant mode-mixing or excess loss. The canonical design consists of an array of SM cores bundled inside a low-index capillary, which is then heated and tapered to merge the SM cores into a single MM core. The process preserves the full modal content across the transition, as required by adiabaticity: $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$ where $\beta_n(z)$ are local propagation constants and the taper proceeds slowly enough (long length, small angle) so coupling out of the guided manifold is negligible (Birks et al., 2015, Leon-Saval et al., 2015).

The core mathematical structure leverages coupled-mode theory, with local mode amplitudes evolving as

$$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$

where $\kappa_{jk}(z)$ is the coupling matrix determined by refractive-index contrasts and modal field overlaps. For mode-number matched ($N_{\mathrm{SM}}=N_{\mathrm{MM}}$) configurations, the transformation is close to unitary, and total input power is preserved (aside from practical insertion losses on order $0.2$–$0.5$ dB per lantern) (Leon-Saval et al., 2015). Typical variants include fiber-bundle tapers, multicore-fiber tapers, direct-laser-written integrated chips, and mode-selective lanterns.

Modal throughput of a photonic lantern is dominated by:

• Adiabatic taper loss: Suppressed for long tapers and small angles as higher-order mode spacing ($\Delta\beta$) decreases.
• Mode-number mismatch: If $M$0, loss is at least $M$1 dB.
• Nonadiabatic and symmetry-induced losses: Mitigable by core geometry optimization, asymmetric layouts, and tailored pitch (Birks et al., 2015, Leon-Saval et al., 2015).

Photonic lanterns fundamentally allow the use of robust single-mode photonic technologies (Bragg gratings, diffraction-limited spectrographs, astronomical interferometry) in MM systems that receive aberrated or highly multimodal input light (Leon-Saval et al., 2015, 1311.0578).

2. LANTERNs in Astronomical Wavefront Sensing and Spectroscopy

In high-contrast exoplanet imaging and precision radial velocity astronomy, photonic lanterns serve as both focal-plane wavefront sensors (PLWFS, also termed "LANTERN") and high-throughput MM-SMF interfacing devices.

2.1. Photonic Lantern Wavefront Sensors (PLWFS / LANTERN)

PLWFS architectures leverage the mode-resolving property of lantern cores to reconstruct wavefront phase aberrations at the science focal plane, thus addressing non-common-path aberrations (NCPA) and petaling (segment piston/tilt) errors in large telescopes (Lin et al., 2023). For small phase perturbations $M$2, the intensity coupled into SM core $M$3 is: $M$4 with $M$5 the unaberrated PSF, and $M$6 the mode field of core $M$7. Wavefront sensing is performed by linearizing around the reference phase, with pre-determined response matrices

$M$8

and solving for modal coefficients $M$9 via Tikhonov-regularized inversion.

Demonstrated systems include:

• 19-port hexagonal lanterns: $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$0, SM pitch $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$1m, 1 kHz frame rate at Subaru/SCExAO (Lin et al., 2023).
• Performance metrics: Correction bandwidth $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$2–$$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$3 Hz, static WFE correction $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$4, dynamic rejection factor $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$5 4–12 at 1 Hz.
• Modal coverage: Up to 12 controlled modes (low-order Zernikes and petal modes).

PLWFS architectures achieve sub-nanometric control, outperform classical Shack-Hartmann or pyramid WFSs in eliminating NCPAs, and suppress segment-mode crosstalk that limits classical high-contrast imaging systems (Lin et al., 2023, Lin et al., 1 May 2025).

2.2. Spectroscopic and Nulling Applications

• High-throughput visible and IR spectroscopy: 19-port PLs on Subaru/SCExAO demonstrated $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$6 lab mean coupling (max $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$7), on-sky efficiency $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$8 at 680 nm under 1” seeing (Vievard et al., 2024). PLs offer improved aberration resilience versus SMF—especially for low-order residuals (tip/tilt), with effective Field of View (FoV) $$\left|\frac{d\beta_n(z)}{dz}\right|\ll |\beta_n(z)-\beta_m(z)| \quad \forall\, m\neq n,$$9 wider than SMF at equal f/# (Lin et al., 2021).
• Nulling interferometry: Mode-selective PLs enable spatial nulling by exploiting modal symmetry, achieving raw contrasts $\beta_n(z)$0 in lab for exoplanet starlight suppression, limited at present by residual wavefront errors and modal crosstalk (Xin et al., 2024).

PLs also underpin integral-field spectroastrometry and dark speckle interferometric imaging, with demonstrated H$\beta_n(z)$1 photocenter precision $\beta_n(z)$2 in Be star disks, resolutions below the classical $\beta_n(z)$3 limit (Kim et al., 22 Oct 2025, Kim et al., 2023).

3. LANTERNs in Computational Optical Imaging and Data-Driven Techniques

3.1. Computational Optical Imaging using Lanterns (COIL)

In microendoscopy, multicore-fiber photonic lanterns enable single-pixel compressive imaging by sequentially exciting single-mode inputs and projecting stable, spatially structured patterns onto the sample. The bucket detector records back-emitted intensity, and image reconstruction proceeds via inverse problems with sparsity or data-driven priors: $\beta_n(z)$4 using Morozov regularization and wavelet frame sparsity (SARA-COIL) or plug-and-play denoisers within primal–dual frameworks (Garcia et al., 2023, Choudhury et al., 2019).

Data-driven approaches leverage learned neural denoisers constrained for firm nonexpansivity/Lipschitz continuity to ensure provable convergence to monotone-inclusion solutions and superior PSNR/SSIM versus variational methods (gains $\beta_n(z)$55–8dB PSNR on real data) (Garcia et al., 2023).

3.2. Neural Network Surrogates for Photonic Lanterns

Deep MLPs trained on simulated or laboratory data model the mapping from Zernike phase coefficients and wavelength to N-port output intensities, achieving $\beta_n(z)$6 speed-up vs. physical beam propagation solvers. Surrogate models support rapid wavefront optimization (funneling, nulling), real-time propagation through seeing, and online calibration—even under broadband and manufacturing variations (Sweeney et al., 2021).

4. LANTERNs in Cryogenic Detector Calibration

"LANTERN" is also an acronym for an optical calibration system for sub-keV cryogenic calorimeters in dark matter and neutrino experiments (Castello, 23 Feb 2026). It consists of a fast (100 ns), 64-channel UV-Vis LED matrix permitting Poissonian photon pulse injection to each detector pixel. The absorbed signal variance $\beta_n(z)$7 is modeled as: $\beta_n(z)$8 where $\beta_n(z)$9 is detector responsivity, $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$0 is photon energy, and $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$1 is mean detected energy. The method spans gains from $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$2 to $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$3, achieves sub-2% calibration accuracy, and circumvents radioactive-source nonlinearities and radiopurity limitations (Castello, 23 Feb 2026).

Key features:

• Up to 64 independently triggered channels.
• Burst durations/energies fast relative to calorimeter response; all photon arrivals summed as one event.
• Cross-validation across multiple cryogenic platforms (BULLKID-DM, CALDER).
• Modular, in-vacuum LED electronics at 300 K prevent wavelength drift at cryogenic stages.

5. LANTERNs in Cosmological Lightcone Construction

The "LANTERN" code module (Lightcone generAtion via sNapshoT intERpolatioN) enables high-fidelity, observer-centric lightcone construction in cosmological N-body simulations (HACC) (Hollowed, 2019). Central mathematical formulation:

• The observer's past lightcone at time $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$4 consists of all events ($$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$5) satisfying

$$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$6

where $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$7 is conformal time. For object positions only known at snapshot times $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$8, interpolation is performed: $$\frac{dA_j}{dz} = -i \sum_{k=1}^M \kappa_{jk}(z)A_k(z),$$9 with quadratic (or higher-order) solution for exact lightcone-crossing $\kappa_{jk}(z)$0 between snapshots, and possible Newton-Raphson refinement.

The method incorporates:

• Linear or second-order (acceleration) interpolation.
• Corrections for redshift-space distortions and gravitational lensing.
• Full simulation-volume replication via integer-indexed shifts $\kappa_{jk}(z)$1 for full-sky or deep lightcones.
• Efficient parallel and incremental reading of simulation outputs.

6. LANTERNs in Machine Learning and Multimodal Reasoning

6.1. LANTERN for Scalable LLM Distillation

In natural language processing, "LANTERN" refers to a modular knowledge distillation framework for job–person fit/explanation tasks at LinkedIn (Fu et al., 7 Oct 2025). The architecture comprises:

• LM$\kappa_{jk}(z)$2: Lightweight encoder classifier distilled on teacher-generated labels for fit prediction.
• LM$\kappa_{jk}(z)$3: Decoder explainer trained via logit-level (token-distribution) distillation, mimicking teacher model distributions (forward KL, JS, TVD).

Training objectives combine supervised cross-entropy and soft alignment: $\kappa_{jk}(z)$4 with ablations showing two-stage distillation (7B → 1.5B → 0.5B) provides the highest ROUGE scores. Prompt engineering leverages decomposed subtasks and chain-of-thought instruction for teacher model consistency. Production serving exploits input compression and model parallelism for low latency (0.3s P95 for classification on a 0.4B encoder).

6.2. LanteRn: Latent Visual Structured Reasoning

"LanteRn" refers to a framework for latent visual reasoning in multimodal transformers, augmenting a vision–LLM (Qwen2.5-VL-3B) with the ability to interleave continuous visual latent embeddings (tokens) between text segments during inference (Viveiros et al., 26 Mar 2026). Formalized, for each inference segment:

• Latent blocks $\kappa_{jk}(z)$5 (dimension $\kappa_{jk}(z)$6) are generated upon emitting a control token, then attended over in downstream layers: $\kappa_{jk}(z)$7
• Combined supervised (cross-entropy for text, MSE for latent states) and RL objectives (Group Relative PPO with latent-state replay) align emissions with fine-grained visual reasoning and task rewards.

Benchmarks on VisCoT, V*, and Blink show improved visual grounding and spatial reasoning versus non-latent baselines, demonstrating the efficacy of compact, recurrent visual "thoughts" as an alternative to explicit image or pixel-level intermediate reasoning.

7. Future Directions and Cross-Disciplinary Significance

LANTERN-based methods, spanning physical optics, computational pipelines, and AI, address critical bottlenecks in science and engineering:

• Sub-nanometer, focal-plane wavefront control for ELT-class astronomical instrumentation.
• Broadband, robust MM–SM coupling enhancing both sensitivity and spectral purity.
• Compression and stabilization of high-dimensional optical and simulation data for real-time or large-scale analysis.
• Increasing model interpretability and capacity in neural language/vision architectures via explicit intermediate representations.

Key limitations include fabrication tolerances, finite mode number, core geometry drift, modal crosstalk, and scaling of calibration/reconstruction in computational pipelines. Ongoing research pushes towards larger port counts, fully integrated photonic chips, unified lantern–spectrograph instruments, and more expressive or efficient neural representations (Lin et al., 2023, Castello, 23 Feb 2026, Fu et al., 7 Oct 2025, Viveiros et al., 26 Mar 2026).

The diverse instantiations of LANTERN exemplify modularity, domain-specific optimization, and the embedding of physically and mathematically informed design principles in both hardware and software, with impact expected to accelerate in next-generation telescope arrays, microimaging, cryogenic physics, and scalable AI.