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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
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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.

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