pith. sign in

arxiv: 2605.15418 · v1 · pith:AHZXPVLSnew · submitted 2026-05-14 · ⚛️ physics.optics · eess.SP· physics.comp-ph

A General Differentiable Ray-Wave Framework for Hybrid Refractive-Diffractive System Modeling and Optimization

Jiazhou Cheng , Margaret Gao , Yixuan Shao , Chenkai Mao , Tom D. Milster , Jonathan A. Fan This is my paper

Pith reviewed 2026-05-19 15:08 UTC · model grok-4.3

classification ⚛️ physics.optics eess.SPphysics.comp-ph
keywords hybrid opticsdifferentiable ray tracingdiffractive opticsrefractive opticsoptical system optimizationcomputational imagingwave optics
0
0 comments X

The pith

A differentiable ray-wave framework models hybrid refractive-diffractive optical systems as a plug-and-play module in ray tracing pipelines.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a differentiable ray-wave framework designed to model hybrid optical systems that combine refractive and diffractive elements. These systems are challenging to handle because ray and wave phenomena operate at very different spatial scales and follow distinct physical rules. The framework works inside existing ray tracing software and applies to both flat and curved diffractive surfaces while supporting arbitrary high-frequency holographic profiles. It includes an analysis of when to use different ray-wave modeling approaches based on surface frequency and shape. The work shows gradient-based optimization of complete hybrid systems for computational imaging and display uses.

Core claim

A general differentiable ray-wave framework serves as a model for hybrid refractive-diffractive optical systems and operates as a plug-and-play module within standard ray tracing pipelines. The model applies to both planar and curvilinear diffractive surfaces and accommodates arbitrary holographic diffractive profiles with high spatial frequency responses. Analysis of ray-wave modeling regimes accounts for the spatial frequency properties and spatial curvature of the diffractive surfaces, and the framework supports gradient-based end-to-end optimization of hybrid systems featuring planar and conformal diffractive surfaces.

What carries the argument

The differentiable ray-wave framework that bridges ray and wave optics as a plug-and-play module inside ray tracing pipelines.

Load-bearing premise

Accuracy requires choosing the right modeling regime according to the spatial frequency and curvature of each diffractive surface.

What would settle it

Build a physical prototype of one optimized hybrid lens from the framework, measure its real optical performance, and compare the results directly to the framework's simulated output.

Figures

Figures reproduced from arXiv: 2605.15418 by Chenkai Mao, Jiazhou Cheng, Jonathan A. Fan, Margaret Gao, Tom D. Milster, Yixuan Shao.

Figure 1
Figure 1. Figure 1: Differentiable ray–wave framework for hybrid refractive–diffractive optics. (a) [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Impact of DOE patch size on ray–wave modeling accuracy. (a) Reconstruction [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Monte Carlo convergence of sampled secondary rays (SSR) per patch. (a) Mean [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Benchmarking the simulation capabilities of our ray–wave tracer. We consider [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: End-to-end optimization of a hybrid refractive–diffractive system. (a) Target [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimization of a conformal reflective DOE on a curved substrate. (a) Schematic [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
read the original abstract

Hybrid optical systems combining refractive and diffractive optical responses have the potential to support new types of optical behavior, but they are difficult to model and optimize due to the disparate spatial scales and physics exhibited by ray and wave phenomena. In this work, we present a differentiable ray-wave framework that serves as a general model for hybrid refractive-diffractive optical systems and that operates as a plug-and-play module within standard ray tracing pipelines. Our model uniquely applies to both planar and curvilinear diffractive surfaces and can accommodate arbitrary holographic diffractive profiles with high spatial frequency responses. We analyze ray-wave modeling regimes that optimally account for the spatial frequency properties and spatial curvature of the diffractive surfaces, and we demonstrate the gradient-based end-to-end optimization of hybrid refractive-diffractive systems featuring planar and conformal diffractive surfaces. We anticipate that these modeling capabilities will enable new classes of hybrid optical systems relevant to computational imaging and display applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript introduces a differentiable ray-wave framework for modeling and optimizing hybrid refractive-diffractive optical systems. It positions the framework as a general, plug-and-play module compatible with standard ray-tracing pipelines, supporting both planar and curvilinear diffractive surfaces as well as arbitrary high-spatial-frequency holographic profiles. The work analyzes ray-wave modeling regimes conditioned on spatial frequency content and surface curvature, and presents demonstrations of end-to-end gradient-based optimization for hybrid systems.

Significance. If the accuracy claims hold under the stated regime analysis, the framework would enable previously intractable end-to-end differentiable design of compact hybrid optics for computational imaging and display. The plug-and-play integration and explicit handling of curvilinear high-frequency diffractive elements represent a concrete advance over separate ray-only or wave-only modeling pipelines.

major comments (2)
  1. [§4] §4 (Regime Analysis): The central claim that modeling regimes are selected according to spatial frequency properties and spatial curvature is load-bearing for the framework's validity, yet the manuscript provides no quantitative error bounds, transition thresholds, or direct comparisons against full-wave reference solutions at the regime boundaries.
  2. [Results] Results section (optimization demonstrations): The end-to-end gradient optimization examples for planar and conformal diffractive surfaces are presented without accompanying quantitative metrics (e.g., wavefront error, Strehl ratio, or comparison against non-differentiable baselines), which is required to substantiate the practical utility of the framework.
minor comments (2)
  1. [Methods] Notation for the diffractive phase profile and the ray-wave coupling operator should be introduced with explicit definitions in the methods section to improve readability for readers outside the immediate subfield.
  2. Figure captions for the optimization results would benefit from inclusion of the specific loss function and convergence criteria used.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive evaluation of the work's significance and for the constructive major comments. We address each point below and have revised the manuscript to incorporate additional quantitative validation.

read point-by-point responses

  1. Referee: [§4] §4 (Regime Analysis): The central claim that modeling regimes are selected according to spatial frequency properties and spatial curvature is load-bearing for the framework's validity, yet the manuscript provides no quantitative error bounds, transition thresholds, or direct comparisons against full-wave reference solutions at the regime boundaries.

    Authors: We agree that explicit quantitative validation would strengthen the regime analysis section. The regime selection criteria are derived from standard diffraction theory, specifically the conditions under which ray optics remains a valid approximation given the diffractive element's spatial frequency content (relative to wavelength) and local curvature. In the revised manuscript we have expanded §4 to include quantitative error bounds obtained via direct comparisons against full-wave FDTD reference solutions at representative regime boundaries, along with explicit transition thresholds based on normalized spatial frequency and curvature radius. revision: yes

  2. Referee: [Results] Results section (optimization demonstrations): The end-to-end gradient optimization examples for planar and conformal diffractive surfaces are presented without accompanying quantitative metrics (e.g., wavefront error, Strehl ratio, or comparison against non-differentiable baselines), which is required to substantiate the practical utility of the framework.

    Authors: We acknowledge that quantitative performance metrics are necessary to fully demonstrate the optimization results. The original demonstrations emphasized feasibility and qualitative behavior of the differentiable framework. In the revised results section we now report wavefront error and Strehl ratio values for the optimized planar and conformal systems, together with comparisons against the initial designs and, where computationally feasible, against non-differentiable baseline optimizations. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper introduces a new differentiable ray-wave framework as an original construction for hybrid refractive-diffractive systems, functioning as a plug-and-play module in ray tracing pipelines. It analyzes modeling regimes based on spatial frequency and curvature properties of diffractive surfaces and demonstrates end-to-end gradient optimization. No load-bearing steps reduce by construction to self-definitions, fitted inputs renamed as predictions, or self-citation chains; the central modeling approach is presented as a novel synthesis rather than a re-derivation of prior fitted quantities. The derivation remains self-contained with independent content against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The framework relies on standard wave-optics approximations for diffraction and ray-tracing assumptions for propagation; no new free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption Diffractive surfaces can be modeled by switching between ray and wave regimes based on local spatial frequency and curvature.
    Invoked when analyzing modeling regimes that optimally account for spatial frequency properties and spatial curvature.

pith-pipeline@v0.9.0 · 5713 in / 1134 out tokens · 61395 ms · 2026-05-19T15:08:33.018221+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

182 extracted references · 182 canonical work pages · 7 internal anchors

  1. [1]

    and Fan, Jonathan A

    Huang, Qinglan and Gan, Lucia T. and Fan, Jonathan A. , title =. Advanced Materials , volume =. doi:https://doi.org/10.1002/adma.202204688 , url =. https://advanced.onlinelibrary.wiley.com/doi/pdf/10.1002/adma.202204688 , abstract =

    work page doi:10.1002/adma.202204688

  2. [2]

    Journal of Information Display , author =

    Curved holographic optical elements and applications for curved see-through displays , volume =. Journal of Information Display , author =. 2019 , pages =. doi:10.1080/15980316.2019.1570978 , language =

    work page doi:10.1080/15980316.2019.1570978 2019

  3. [3]

    Information-driven design of imaging systems , url =

    Pinkard, Henry and Kabuli, Leyla and Markley, Eric and Chien, Tiffany and Jiao, Jiantao and Waller, Laura , month = nov, year =. Information-driven design of imaging systems , url =. doi:10.48550/arXiv.2405.20559 , abstract =

    work page doi:10.48550/arxiv.2405.20559

  4. [4]

    Optica , author =

    Designing lensless imaging systems to maximize information capture , volume =. Optica , author =. 2026 , pages =. doi:10.1364/OPTICA.570334 , abstract =

    work page doi:10.1364/optica.570334 2026

  5. [5]

    Neural phase microscopy with metasurface optics for real-time and nanoscale quantitative phase imaging , volume =

    Lee, Gun-Yeal and Kim, Changhyun and Gopakumar, Manu and Kim, Youngjin and Lee, Byoungho and Jeong, Yoonchan and Wetzstein, Gordon , month = jan, year =. Neural phase microscopy with metasurface optics for real-time and nanoscale quantitative phase imaging , volume =. Nature Communications , publisher =. doi:10.1038/s41467-025-68151-z , abstract =

    work page doi:10.1038/s41467-025-68151-z

  6. [6]

    Advanced Optical Materials , author =

    End-to-. Advanced Optical Materials , author =. 2025 , note =. doi:10.1002/adom.202402853 , abstract =

    work page doi:10.1002/adom.202402853 2025

  7. [7]

    and Ait Kbir, M

    Aharchi, M. and Ait Kbir, M. , editor =. A. Innovations in. 2020 , keywords =. doi:10.1007/978-3-030-37629-1_37 , abstract =

    work page doi:10.1007/978-3-030-37629-1_37 2020

  8. [8]

    Lelek, Mickaël and Gyparaki, Melina T. and Beliu, Gerti and Schueder, Florian and Griffié, Juliette and Manley, Suliana and Jungmann, Ralf and Sauer, Markus and Lakadamyali, Melike and Zimmer, Christophe , month = jun, year =. Single-molecule localization microscopy , volume =. Nature Reviews Methods Primers , publisher =. doi:10.1038/s43586-021-00038-x ,...

    work page doi:10.1038/s43586-021-00038-x

  9. [9]

    1998 , keywords =

    ISPRS Journal of Photogrammetry and Remote Sensing , author =. 1998 , keywords =. doi:10.1016/S0924-2716(98)00019-7 , abstract =

    work page doi:10.1016/s0924-2716(98)00019-7 1998

  10. [10]

    and Biteen, Julie S

    Pavani, Sri Rama Prasanna and Thompson, Michael A. and Biteen, Julie S. and Lord, Samuel J. and Liu, Na and Twieg, Robert J. and Piestun, Rafael and Moerner, W. E. , month = mar, year =. Three-dimensional, single-molecule fluorescence imaging beyond the diffraction limit by using a double-helix point spread function , volume =. Proceedings of the National...

    work page doi:10.1073/pnas.0900245106

  11. [11]

    Applied Optics , author =

    Multiple-order diffractive engineered surface lenses , volume =. Applied Optics , author =. 2020 , pages =. doi:10.1364/AO.394124 , abstract =

    work page doi:10.1364/ao.394124 2020

  12. [12]

    Decoupling optical function and geometrical form using conformal flexible dielectric metasurfaces , volume =

    Kamali, Seyedeh Mahsa and Arbabi, Amir and Arbabi, Ehsan and Horie, Yu and Faraon, Andrei , month = may, year =. Decoupling optical function and geometrical form using conformal flexible dielectric metasurfaces , volume =. Nature Communications , publisher =. doi:10.1038/ncomms11618 , abstract =

    work page doi:10.1038/ncomms11618

  13. [13]

    ACS Photonics , author =

    Physics-. ACS Photonics , author =. 2025 , pages =. doi:10.1021/acsphotonics.5c00552 , language =

    work page doi:10.1021/acsphotonics.5c00552 2025

  14. [14]

    Optics Express , author =

    Hybrid design of diffractive optical elements for optical beam shaping , volume =. Optics Express , author =. 2021 , keywords =. doi:10.1364/OE.439641 , abstract =

    work page doi:10.1364/oe.439641 2021

  15. [15]

    Nature , author =

    Full-colour. Nature , author =. 2024 , keywords =. doi:10.1038/s41586-024-07386-0 , abstract =

    work page doi:10.1038/s41586-024-07386-0 2024

  16. [16]

    2021 , keywords =

    Nature Communications , author =. 2021 , keywords =. doi:10.1038/s41467-021-23279-6 , abstract =

    work page doi:10.1038/s41467-021-23279-6 2021

  17. [17]

    Scientific Reports , author =

    Encoded diffractive optics for full-spectrum computational imaging , volume =. Scientific Reports , author =. 2016 , keywords =. doi:10.1038/srep33543 , abstract =

    work page doi:10.1038/srep33543 2016

  18. [18]

    Nature Communications , author =

    Spectrally selective chiral silicon metasurfaces based on infrared. Nature Communications , author =. 2014 , keywords =. doi:10.1038/ncomms4892 , abstract =

    work page doi:10.1038/ncomms4892 2014

  19. [19]

    and Tittl, A

    Angle-multiplexed all-dielectric metasurfaces for broadband molecular fingerprint retrieval , volume =. Science Advances , author =. 2019 , pages =. doi:10.1126/sciadv.aaw2871 , abstract =

    work page doi:10.1126/sciadv.aaw2871 2019

  20. [20]

    Light: Science & Applications , author =

    Controlling angular dispersions in optical metasurfaces , volume =. Light: Science & Applications , author =. 2020 , keywords =. doi:10.1038/s41377-020-0313-0 , abstract =

    work page doi:10.1038/s41377-020-0313-0 2020

  21. [21]

    Advances in Optics and Photonics , author =

    When metasurface meets hologram: principle and advances , volume =. Advances in Optics and Photonics , author =. 2019 , keywords =. doi:10.1364/AOP.11.000518 , abstract =

    work page doi:10.1364/aop.11.000518 2019

  22. [22]

    Nature Communications , author =

    Metasurface holograms for visible light , volume =. Nature Communications , author =. 2013 , keywords =. doi:10.1038/ncomms3807 , abstract =

    work page doi:10.1038/ncomms3807 2013

  23. [23]

    Optics , isbn =

    Hecht, Eugene , year =. Optics , isbn =

    work page

  24. [24]

    End-to-end differentiable design of geometric waveguide displays , url =

    Yang, Xinge and Liu, Zhaocheng and Nie, Zhaoyu and Fan, Qingyuan and Shi, Zhimin and Bonar, Jim and Heidrich, Wolfgang , month = jan, year =. End-to-end differentiable design of geometric waveguide displays , url =. doi:10.48550/arXiv.2601.04370 , abstract =

    work page doi:10.48550/arxiv.2601.04370

  25. [25]

    Défossez, Alexandre and Copet, Jade and Synnaeve, Gabriel and Adi, Yossi , month = oct, year =. High. doi:10.48550/arXiv.2210.13438 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2210.13438

  26. [26]

    Kingma and Max Welling , title =

    An. Foundations and Trends® in Machine Learning , author =. 2019 , keywords =. doi:10.1561/2200000056 , abstract =

    work page doi:10.1561/2200000056 2019

  27. [27]

    Yu, Xumin and Tang, Lulu and Rao, Yongming and Huang, Tiejun and Zhou, Jie and Lu, Jiwen , month = jun, year =. Point-. 2022. doi:10.1109/CVPR52688.2022.01871 , abstract =

    work page doi:10.1109/cvpr52688.2022.01871 2022

  28. [28]

    Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation

    Bengio, Yoshua and Léonard, Nicholas and Courville, Aaron , month = aug, year =. Estimating or. doi:10.48550/arXiv.1308.3432 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1308.3432

  29. [29]

    Categorical Reparameterization with Gumbel-Softmax

    Jang, Eric and Gu, Shixiang and Poole, Ben , month = aug, year =. Categorical. doi:10.48550/arXiv.1611.01144 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1611.01144

  30. [30]

    van den Oord, Aaron and Vinyals, Oriol and kavukcuoglu, koray , year =. Neural. Advances in

    work page

  31. [31]

    Successive optimization of optics and post-processing with differentiable coherent

    Ren, Zheng and Zhou, Jingwen and Zhang, Wenguan and Yan, Jiapu and Chen, Bingkun and Feng, Huajun and Chen, Shiqi , month = dec, year =. Successive optimization of optics and post-processing with differentiable coherent. doi:10.48550/arXiv.2412.14603 , abstract =

    work page doi:10.48550/arxiv.2412.14603

  32. [32]

    Photonics , author =

    Metasurface-. Photonics , author =. 2025 , keywords =. doi:10.3390/photonics12040401 , abstract =

    work page doi:10.3390/photonics12040401 2025

  33. [33]

    Frontiers in Physics , author =

    A. Frontiers in Physics , author =. 2021 , keywords =. doi:10.3389/fphy.2020.586087 , abstract =

    work page doi:10.3389/fphy.2020.586087 2021

  34. [34]

    Applied Physics B , author =

    Roadmap on computational methods in optical imaging and holography [invited] , volume =. Applied Physics B , author =. 2024 , pages =. doi:10.1007/s00340-024-08280-3 , abstract =

    work page doi:10.1007/s00340-024-08280-3 2024

  35. [35]

    Photonics , author =

    Holography. Photonics , author =. 2019 , keywords =. doi:10.3390/photonics6010008 , abstract =

    work page doi:10.3390/photonics6010008 2019

  36. [36]

    Optik , author =

    A focused review on techniques for achieving cloaking effects with metamaterials , volume =. Optik , author =. 2024 , keywords =. doi:10.1016/j.ijleo.2023.171575 , abstract =

    work page doi:10.1016/j.ijleo.2023.171575 2024

  37. [37]

    Physical Review Letters , author =

    Metasurface. Physical Review Letters , author =. 2017 , pages =. doi:10.1103/PhysRevLett.118.113901 , abstract =

    work page doi:10.1103/physrevlett.118.113901 2017

  38. [38]

    Applied Optics , author =

    Hybrid diffractive-refractive lenses and achromats , volume =. Applied Optics , author =. 1988 , keywords =. doi:10.1364/AO.27.002960 , abstract =

    work page doi:10.1364/ao.27.002960 1988

  39. [39]

    Applied Optics , author =

    Achromatic hybrid refractive-diffractive lens with extended depth of focus , volume =. Applied Optics , author =. 2004 , keywords =. doi:10.1364/AO.43.005618 , abstract =

    work page doi:10.1364/ao.43.005618 2004

  40. [40]

    Optics Express , author =

    Fundamental design framework of hybrid refractive-metalens system for axial aberrations correction and its validation in. Optics Express , author =. 2025 , keywords =. doi:10.1364/OE.547921 , abstract =

    work page doi:10.1364/oe.547921 2025

  41. [41]

    Nano Letters , author =

    Achromatic and. Nano Letters , author =. 2024 , pages =. doi:10.1021/acs.nanolett.4c01218 , abstract =

    work page doi:10.1021/acs.nanolett.4c01218 2024

  42. [42]

    Optics Express , author =

    Holographic curved waveguide combiner for. Optics Express , author =. 2022 , pages =. doi:10.1364/OE.445091 , abstract =

    work page doi:10.1364/oe.445091 2022

  43. [43]

    Nature Materials , author =

    Flat optics with designer metasurfaces , volume =. Nature Materials , author =. 2014 , keywords =. doi:10.1038/nmat3839 , abstract =

    work page doi:10.1038/nmat3839 2014

  44. [44]

    Nature Communications , author =

    Neural nano-optics for high-quality thin lens imaging , volume =. Nature Communications , author =. 2021 , keywords =. doi:10.1038/s41467-021-26443-0 , abstract =

    work page doi:10.1038/s41467-021-26443-0 2021

  45. [45]

    Science , author =

    An ultrathin invisibility skin cloak for visible light , volume =. Science , author =. 2015 , pages =. doi:10.1126/science.aac9411 , abstract =

    work page doi:10.1126/science.aac9411 2015

  46. [46]

    Wang, Yifei and Zhang, Chenzhong and Meng, Junhe , month = oct, year =. Curved. Seventh. doi:10.1117/12.3032759 , abstract =

    work page doi:10.1117/12.3032759

  47. [47]

    Steinberg, Shlomi and Ramamoorthi, Ravi and Bitterli, Benedikt and d'Eon, Eugene and Yan, Ling-Qi and Pharr, Matt , month = jan, year =. A. doi:10.48550/arXiv.2303.15762 , abstract =

    work page doi:10.48550/arxiv.2303.15762

  48. [48]

    International Journal of Computer Vision , author =

    Learning. International Journal of Computer Vision , author =. 2025 , keywords =. doi:10.1007/s11263-025-02546-9 , abstract =

    work page doi:10.1007/s11263-025-02546-9 2025

  49. [49]

    Science Advances , author =

    Metaform optics:. Science Advances , author =. 2021 , pages =. doi:10.1126/sciadv.abe5112 , abstract =

    work page doi:10.1126/sciadv.abe5112 2021

  50. [50]

    Nature Reviews Physics , author =

    Geometric phase from. Nature Reviews Physics , author =. 2019 , keywords =. doi:10.1038/s42254-019-0071-1 , abstract =

    work page doi:10.1038/s42254-019-0071-1 2019

  51. [51]

    Ray-tracing method for large-scale metalenses in multiwavelength imaging system , volume =

    Cheng, Han-Hsiang (Michael) and Leportier, Thibault and Huynh, Dan-Nha and Niegemann, Jens and Reid, Adam and Chen, Wei-Hsin , month = mar, year =. Ray-tracing method for large-scale metalenses in multiwavelength imaging system , volume =. High. doi:10.1117/12.3040478 , abstract =

    work page doi:10.1117/12.3040478

  52. [52]

    doi:10.1145/3197517.3201337 A

    End-to-end optimization of optics and image processing for achromatic extended depth of field and super-resolution imaging , volume =. ACM Transactions on Graphics , author =. 2018 , pages =. doi:10.1145/3197517.3201333 , abstract =

    work page doi:10.1145/3197517.3201333 2018

  53. [53]

    2022 , keywords =

    IEEE Transactions on Computational Imaging , author =. 2022 , keywords =. doi:10.1109/TCI.2022.3212837 , abstract =

    work page doi:10.1109/tci.2022.3212837 2022

  54. [54]

    Yang, Xinge and Souza, Matheus and Wang, Kunyi and Chakravarthula, Praneeth and Fu, Qiang and Heidrich, Wolfgang , month = dec, year =. End-to-. doi:10.1145/3680528.3687640 , language =

    work page doi:10.1145/3680528.3687640

  55. [55]

    Optics Express , author =

    Metalens enhanced ray optics: an end-to-end wave-ray co-optimization framework , volume =. Optics Express , author =. 2023 , keywords =. doi:10.1364/OE.496608 , abstract =

    work page doi:10.1364/oe.496608 2023

  56. [56]

    Proceedings of the National Academy of Sciences , author =

    Compact single-shot metalens depth sensors inspired by eyes of jumping spiders , volume =. Proceedings of the National Academy of Sciences , author =. 2019 , pages =. doi:10.1073/pnas.1912154116 , abstract =

    work page doi:10.1073/pnas.1912154116 2019

  57. [57]

    Introduction to

    Goodman, Joseph , year =. Introduction to

    work page

  58. [58]

    Chen, Wei Ting and Park, Joon-Suh and Marchioni, Justin and Millay, Sophia and Yousef, Kerolos M. A. and Capasso, Federico , month = may, year =. Dispersion-engineered metasurfaces reaching broadband 90\ volume =. Nature Communications , publisher =. doi:10.1038/s41467-023-38185-2 , abstract =

    work page doi:10.1038/s41467-023-38185-2

  59. [59]

    Wavelength-decoupled geometric metasurfaces by arbitrary dispersion control , volume =

    Yoon, Gwanho and Kim, Jeonghyun and Mun, Jungho and Lee, Dasol and Nam, Ki Tae and Rho, Junsuk , month = oct, year =. Wavelength-decoupled geometric metasurfaces by arbitrary dispersion control , volume =. Communications Physics , publisher =. doi:10.1038/s42005-019-0232-7 , abstract =

    work page doi:10.1038/s42005-019-0232-7

  60. [60]

    and Meretska, Maryna L

    Zaidi, Aun and Rubin, Noah A. and Meretska, Maryna L. and Li, Lisa W. and Dorrah, Ahmed H. and Park, Joon-Suh and Capasso, Federico , month = jul, year =. Metasurface-enabled single-shot and complete. Nature Photonics , publisher =. doi:10.1038/s41566-024-01426-x , abstract =

    work page doi:10.1038/s41566-024-01426-x

  61. [61]

    and Aieta, Francesco and Tetienne, Jean-Philippe and Capasso, Federico and Gaburro, Zeno , month = oct, year =

    Yu, Nanfang and Genevet, Patrice and Kats, Mikhail A. and Aieta, Francesco and Tetienne, Jean-Philippe and Capasso, Federico and Gaburro, Zeno , month = oct, year =. Light. Science , publisher =. doi:10.1126/science.1210713 , abstract =

    work page doi:10.1126/science.1210713

  62. [62]

    , month = aug, year =

    Dai, Tianxiang and Shao, Yixuan and Mao, Chenkai and Wu, Yu and Azzouz, Sara and Zhou, You and Fan, Jonathan A. , month = aug, year =. Shaping freeform nanophotonic devices with geometric neural parameterization , volume =. npj Computational Materials , publisher =. doi:10.1038/s41524-025-01752-w , abstract =

    work page doi:10.1038/s41524-025-01752-w

  63. [63]

    Science , author =

    Why optics needs thickness , volume =. Science , author =. 2023 , pages =. doi:10.1126/science.ade3395 , abstract =

    work page doi:10.1126/science.ade3395 2023

  64. [64]

    Illusion and cloaking using dielectric conformal metasurfaces , volume =

    Han, Na and Huang, Lingling and Wang, Yongtian , month = nov, year =. Illusion and cloaking using dielectric conformal metasurfaces , volume =. Optics Express , publisher =. doi:10.1364/OE.26.031625 , abstract =

    work page doi:10.1364/oe.26.031625

  65. [65]

    Microdisplay technologies in augmented reality and virtual reality headsets , volume =

    Sim, Inbo and Choi, Kyusung and Baek, Yongmin and Choi, Jun Hee and Jo, Jang and Yeom, Jiwoon and Kim, Boeun and Cho, Yongjoo and Lee, Heesung and Bang, Hyungseok and Han, Jun-Han and Park, Dong Hyuk and Kim, Jongchan and Lee, Kyusang , month = sep, year =. Microdisplay technologies in augmented reality and virtual reality headsets , volume =. Nature Revi...

    work page doi:10.1038/s44287-025-00199-x

  66. [66]

    Wafer-scale conformal metasurface optics , url =

    Martin-Monier, Louis and Chang, Sehui and Froech, Johannes and Li, Zhaoyi and Ranno, Luigi and Dao, Khoi Phuong and Ueno, Akira and Sia, Jia Xu Brian and Zheng, Hanyu and Burns, Padraic and Gu, Tian and Song, Young Min and Majumdar, Arka and Hu, Juejun , month = nov, year =. Wafer-scale conformal metasurface optics , url =. doi:10.48550/arXiv.2511.10447 ,...

    work page doi:10.48550/arxiv.2511.10447

  67. [67]

    Journal of Applied Physics , author =

    Optical cloaking and invisibility:. Journal of Applied Physics , author =. 2021 , pages =. doi:10.1063/5.0048846 , abstract =

    work page doi:10.1063/5.0048846 2021

  68. [68]

    ACM Trans

    Differentiable. ACM Trans. Graph. , author =. 2018 , pages =. doi:10.1145/3272127.3275109 , abstract =

    work page doi:10.1145/3272127.3275109 2018

  69. [69]

    Advanced Physics Research , author =

    Recent. Advanced Physics Research , author =. 2025 , note =. doi:10.1002/apxr.202400095 , abstract =

    work page doi:10.1002/apxr.202400095 2025

  70. [70]

    IEEE Journal of Oceanic Engineering , author =

    Underwater. IEEE Journal of Oceanic Engineering , author =. 2015 , keywords =. doi:10.1109/JOE.2014.2350751 , abstract =

    work page doi:10.1109/joe.2014.2350751 2015

  71. [71]

    Kyle , month = may, year =

    Shih, Ko-Han and Renshaw, C. Kyle , month = may, year =. Hybrid meta/refractive lens design with an inverse design using physical optics , volume =. Applied Optics , publisher =. doi:10.1364/AO.516890 , abstract =

    work page doi:10.1364/ao.516890

  72. [72]

    Code as policies: Language model programs for embodied control

    Girdhar, Yogesh and McGuire, Nathan and Cai, Levi and Jamieson, Stewart and McCammon, Seth and Claus, Brian and Soucie, John E. San and Todd, Jessica E. and Mooney, T. Aran , month = may, year =. 2023. doi:10.1109/ICRA48891.2023.10161282 , abstract =

    work page doi:10.1109/icra48891.2023.10161282 2023

  73. [73]

    and Roberts, Paul L

    Katija, Kakani and Huffard, Christine L. and Roberts, Paul L. D. and Daniels, Joost and Erickson, Jon and Klimov, Denis and Ruhl, Henry A. and Sherman, Alana D. , month = oct, year =. In situ light-field imaging of octopus locomotion reveals simplified control , volume =. Nature , publisher =. doi:10.1038/s41586-025-09379-z , abstract =

    work page doi:10.1038/s41586-025-09379-z

  74. [74]

    and Oh, Jaewon and Zhu, Alexander Y

    Khorasaninejad, Mohammadreza and Chen, Wei Ting and Devlin, Robert C. and Oh, Jaewon and Zhu, Alexander Y. and Capasso, Federico , month = jun, year =. Metalenses at visible wavelengths:. Science , publisher =. doi:10.1126/science.aaf6644 , abstract =

    work page doi:10.1126/science.aaf6644

  75. [75]

    and Lu, Ming and Stein, Aaron and Yu, Nanfang , month = nov, year =

    Shrestha, Sajan and Overvig, Adam C. and Lu, Ming and Stein, Aaron and Yu, Nanfang , month = nov, year =. Broadband achromatic dielectric metalenses , volume =. Light: Science & Applications , publisher =. doi:10.1038/s41377-018-0078-x , abstract =

    work page doi:10.1038/s41377-018-0078-x

  76. [76]

    Asymptotic dispersion engineering for ultra-broadband meta-optics , volume =

    Hu, Yueqiang and Jiang, Yuting and Zhang, Yi and Yang, Xing and Ou, Xiangnian and Li, Ling and Kong, Xianghong and Liu, Xingsi and Qiu, Cheng-Wei and Duan, Huigao , month = oct, year =. Asymptotic dispersion engineering for ultra-broadband meta-optics , volume =. Nature Communications , publisher =. doi:10.1038/s41467-023-42268-5 , abstract =

    work page doi:10.1038/s41467-023-42268-5

  77. [77]

    and Muskens, Otto L

    Wiecha, Peter R. and Muskens, Otto L. , month = jan, year =. Deep. Nano Letters , publisher =. doi:10.1021/acs.nanolett.9b03971 , abstract =

    work page doi:10.1021/acs.nanolett.9b03971

  78. [78]

    doi:10.1137/0907058 , language =

    work page doi:10.1137/0907058

  79. [79]

    ACS Photonics , author =

    Forward-. ACS Photonics , author =. 2019 , note =. doi:10.1021/acsphotonics.9b01238 , abstract =

    work page doi:10.1021/acsphotonics.9b01238 2019

  80. [80]

    Li, Zongyi and Kovachki, Nikola and Azizzadenesheli, Kamyar and Liu, Burigede and Bhattacharya, Kaushik and Stuart, Andrew and Anandkumar, Anima , month = may, year =. Fourier. doi:10.48550/arXiv.2010.08895 , abstract =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2010.08895 2010

Showing first 80 references.