Modeling light propagation for under-display sensing in a smartphone

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Synopsis of the paper

该论文提出了一个通用的光学模型，用于分析智能手机中的屏下传感（UDS）技术。作者提出，通过使用菲涅尔数，可以将不同的屏下传感器（包括环境光传感器ALS、屏下摄像头UDC和接近传感器）分别归类到几何光学、夫琅禾费衍射和菲涅尔衍射三种不同的光学传播机制中。该模型基于对商用智能手机的微观结构分析，并通过仿真与实验进行验证。结果表明，该模型能够准确预测ALS的角度响应衰减（Figure 6）、UDC的图像模糊和衍射伪影（Figure 8），以及接近传感器的背景噪声与传感器布局和间隙的关系（Figure 9, 10），为UDS系统的设计和优化提供了物理层面的指导。

Summary of Review

本文提出了一个清晰且具有物理洞察力的统一框架，用于建模和分析不同类型的屏下传感器所面临的光学挑战。论文最显著的优点在于其全面且严谨的实验验证，针对三种不同的传感器分别建立了模型，并展示了仿真结果与在商用设备上获得的实验数据之间的高度一致性（see Figures 6, 8, 9, 10）。然而，论文的核心概念——即基于菲涅尔数的“通用模型”——在其分类标准和计算细节上缺乏明确的阐述（No direct evidence found in the manuscript）。此外，研究仅基于单一商用设备，其结论对不同显示技术的普适性有待讨论（see Abstract）。

Strengths

• 新颖的统一物理框架 (Novel Unifying Physical Framework)

  • 该研究创造性地使用菲涅尔数作为核心物理量，将三种主流的屏下传感技术统一到一个连贯的光学分析框架中（Abstract）。这种分类方法（几何光学、夫琅禾费衍射、菲涅尔衍射）不仅简洁，而且为理解和解决各自面临的信号失真问题提供了根本性的物理见解。
  • 该框架成功解释了不同传感器对光学效应的敏感性差异，例如，为何简单的几何遮挡模型足以描述ALS（Figure 5），而UDC则必须考虑远场的衍射效应（Figure 7, 8）。这为传感器设计提供了清晰的指导原则。
  • 通过该框架，论文为接近传感器的优化设计（如发射器-接收器45度角的最优布局）提供了理论依据，并成功通过实验验证（Figure 9e），展示了该框架的实用价值。

• 全面且严谨的实验验证 (Comprehensive and Rigorous Experimental Validation)

  • 论文为模型中的每一种光学机制都提供了坚实的实验支持，涵盖了从ALS的角度响应到UDC的成像质量，再到接近传感器的噪声特性（Figures 6, 8, 9, 10）。这种全面性大大增强了所提模型的可信度。
  • 实验结果与仿真预测在定量上高度吻合。例如，ALS角度响应的半峰全宽（FWHM）误差小于10度（Figure 6c, 6f），UDC模拟图像与实拍照片的结构相似性（SSIM）指数很高（Figure 8e），接近传感器噪声随角度和间隙的变化趋势也与实验数据一致（Figure 9e, 10a）。
  • 实验直接在一款商用智能手机上进行，这使得研究结果非常贴近实际应用场景，增强了其对工业界设计师和工程师的参考价值（Abstract; Figure 9f）。

• 高质量的可视化与清晰的陈述 (High-Quality Visualization and Clear Presentation)

  • 论文的图示质量非常高，有效地结合了原理示意图、像素显微照片、仿真结果和实验装置照片（e.g., Figure 5, 8, 9）。这种多模态的可视化方法极大地帮助读者理解复杂的光学现象和实验设置。
  • 文章结构逻辑清晰，每个传感器作为一个独立的案例进行分析，遵循“问题提出-模型建立-仿真验证-实验对比”的流程，使得论文易于阅读和理解（Sections on ALS, UDC, Proximity Sensor）。
  • 通过并列展示参考图像、模拟图像和实拍图像（Figure 8c, 8d, 8e），论文直观地展示了其UDC模型的有效性，使读者能迅速把握衍射效应对成像质量的核心影响。

Weaknesses

• 模型普适性的讨论不足 (Insufficient Discussion on Model Generalizability)

  • 所有实验和分析均基于“一款商用智能手机”（Abstract），但论文并未提供该手机显示屏的关键参数，如技术类型（OLED/LCD）、子像素排列方式（RGB stripe/PenTile）、像素密度等。这使得评估模型对其他不同显示技术的适用性变得困难。
  • 论文未讨论模型对显示面板参数变化的敏感性。例如，不同的像素开口率、屏幕堆叠层厚度或材料折射率将如何影响ALS的角度响应或UDC的点扩散函数（PSF）。（No direct evidence found in the manuscript.）
  • 虽然模型被冠以“通用”之名，但其对未来可能出现的显示技术（如Micro-LED、可折叠/卷曲屏幕）的潜在适用性或局限性完全没有被提及，削弱了其前瞻性。（No direct evidence found in the manuscript.）

• 核心分类依据的细节缺失 (Lack of Detail on the Core Classification Criterion)

  • 论文的核心思想是使用菲涅尔数（Fresnel number）来区分光学机制（Abstract），但稿件中并未给出菲涅尔数的具体计算公式，也没有为三种传感器场景展示实际的计算过程和数值结果。这使得其分类的论证过程不够透明和可复现。
  • 光学机制的转变通常是渐进的，而非突变的。论文将三者严格划分为三个区域，但并未讨论当菲涅尔数处于临界值（例如 F ≈ 1）时可能出现的混合效应或模型的适用边界。（No direct evidence found in the manuscript.）
  • 在推导接近传感器的模型时，论文提到信号是“一个缩放的夫琅禾费衍射图样”（Abstract），这本质上是对菲涅尔衍射的一种近似。然而，从菲涅尔积分到此近似解的数学推导步骤和所依赖的假设条件没有在文中清晰展示，影响了模型的严谨性。

• 方法与实验设置的关键信息遗漏 (Omission of Key Methodological and Experimental Details)

  • 在UDC的仿真部分，论文没有说明所使用的相机镜头模型参数（例如焦距、F数），也未阐明是否考虑了镜头本身的像差（Figure 7）。镜头的点扩散函数（PSF）与屏幕衍射产生的PSF是卷积关系，缺少前者信息会影响结果的复现性。
  • 论文提及通过“显示面板的显微照片”来生成仿真用的二值化掩模（Abstract; Figure 6），但并未详细描述图像处理的具体步骤，例如使用的阈值分割方法、对不同颜色子像素透明度的假设等。
  • 在分析接近传感器的背景噪声时，论文将其归因于发射器-接收器之间的“串扰（crosstalk）”（Figure 9d），但没有在模型中明确区分是源于衍射、面板内反射还是其他物理机制，使得噪声模型的物理基础不够清晰。

Suggestions for Improvement

• 补充关于模型普适性的讨论 (Supplement Discussion on Model Generalizability)

  • 请在实验部分明确说明所用智能手机的显示面板类型（如AMOLED）、子像素布局（如PenTile-like）和大致的像素密度。如果出于匿名性考虑无法提供型号，也应提供这些关键的技术规格。
  • 建议增加一个段落或子章节，通过仿真分析讨论关键显示参数（如像素开口率、面板厚度）变化对模型预测结果的影响，以评估模型的鲁棒性和敏感性。
  • 在结论部分，建议简要讨论该模型框架在应用于其他（包括未来）显示技术时可能面临的挑战和需要进行的调整，以增强论文的广度和深度。

• 明确并详述菲涅尔数分类框架 (Clarify and Detail the Fresnel Number Classification Framework)

  • 请在论文方法部分的开头增加一个表格或段落，明确给出菲涅尔数的定义公式，并为ALS、UDC和接近传感器这三个场景，分别代入参数（如孔径大小a、波长λ、传播距离z）进行计算，展示其数值并解释为何它们分属不同区域。
  • 请在讨论中简要说明光学机制过渡区域（regime transition）的可能性，并论证为何在本文所分析的三个具体应用中，采用单一主导机制建模是合理且充分的。
  • 请在接近传感器部分，补充从菲涅尔衍射积分出发，推导出“缩放的夫琅禾费衍射图样”这一近似解的关键步骤和物理假设，以增强该部分建模的数学严谨性。

• 提供更多方法与实验细节 (Provide More Methodological and Experimental Details)

  • 请在UDC仿真方法部分，补充所用的镜头模型及其关键光学参数（如有效焦距、光圈值），并说明是否以及如何处理了镜头像差。
  • 请在描述如何从显微照片生成二值化掩模时，提供更多技术细节，例如图像处理软件、阈值选择方法（如Otsu's method）以及如何处理彩色子像素等。
  • 在接近传感器模型部分，请更清晰地定义“背景噪声/串扰”的物理来源，并说明您的仿真模型是如何将这些来源（衍射、反射等）考虑在内的。

References

None

Synopsis of the paper This paper proposes a unified physical model for under-display sensing (UDS) in smartphones, which is degraded by light distortion from the display panel. The authors use the Fresnel number as a criterion to classify the dominant light propagation mode for different sensors. The study identifies that under-display ambient light sensors (ALS), cameras (UDC), and proximity sensors operate in the geometric optics, Fraunhofer diffraction, and Fresnel diffraction regimes, respectively. Each of these models is implemented and simulated. To validate the framework, the authors conduct experiments on a commercial smartphone. The simulation results show strong agreement with measurements for ALS angular response, UDC image blurring, and proximity sensor background noise. Based on these validated models, the paper provides practical design insights, such as an optimal orientation for the proximity sensor to minimize crosstalk.

Summary of Review This paper presents a clear and valuable physics-based framework for modeling and optimizing under-display sensing systems, a topic of high industrial relevance. The primary strength is the elegant use of the Fresnel number to unify the analysis of three distinct sensor types within a single coherent methodology (Sec. 2). This framework is rigorously validated through comprehensive experiments on a commercial device, showing excellent correspondence between simulation and reality for all three sensor modalities (Fig. 6, 8, 9). However, the mathematical derivation for the Fresnel diffraction model of the proximity sensor lacks sufficient detail, making a key part of the method difficult to verify (Sec. 5.1). Additionally, the manuscript could better contextualize its contribution with respect to the broader optics and computational imaging literature (Sec. 1).

Strengths

• Unified and Intuitive Physical Framework

  • The use of the Fresnel number (F) as a single criterion to classify the optical regime for different UDS systems is a powerful and elegant contribution (Sec. 2, Eq. 1). This provides a systematic, physics-grounded approach to a complex engineering problem.
  • This classification successfully explains why different modeling approaches are necessary for ALS (F >> 1), UDC (F << 1), and proximity sensors (F ~ 1), providing clear physical intuition that is often missing in purely data-driven approaches (Fig. 1).
  • The framework is well-justified with explicit calculations of the Fresnel number for each sensor configuration, grounding the choice of model in physical parameters (stated in Sec. 3.1, 4.1, 5.1).

• Thorough and Convincing Experimental Validation

  • The paper's claims are substantiated with a comprehensive set of experiments performed on a commercial smartphone, which anchors the theoretical models to a real-world application.
  • For the ALS, the simulated angular response based on geometric optics shows strong quantitative agreement with measured data, with the full width at half maximum (FWHM) matching within 10 degrees (Fig. 6c, 6f).
  • For the UDC, the simulated point spread function (PSF) from the Fraunhofer model is used to generate a blurred image that is both visually and quantitatively very similar to an actual UDC photograph (Fig. 8d, 8e), as supported by the reported SSIM metric.
  • For the proximity sensor, the Fresnel model accurately predicts non-trivial behaviors, including the background noise's dependence on source-detector orientation (Fig. 9e) and the sensor-to-display gap (Fig. 10a), demonstrating the model's predictive power.

• Actionable and Practical Design Insights

  • The work extends beyond mere modeling to offer concrete guidance for designing better UDS systems, which significantly increases its practical impact.
  • A key finding is the identification of an optimal 45-degree orientation for the proximity sensor's transmitter-receiver pair, which minimizes crosstalk by avoiding alignment with the pixel grid's diffraction orders (Sec. 5.2, Fig. 9d, 9e).
  • The analysis of the gap between the sensor and the display demonstrates the necessity of the Fresnel model over simpler approximations and provides engineers with a tool to optimize this critical design parameter (Sec. 5.3, Fig. 10a).
  • The methodology for extracting and binarizing pixel layouts from micrographs (Fig. 6b, 9c) provides a clear and reproducible pipeline for applying this model to different display panels.

Weaknesses

• Clarity and Completeness of Mathematical Formulations

  • The mathematical derivation for the proximity sensor model in the Fresnel regime is opaque. The paper presents the general Fresnel-Kirchhoff integral but does not show the steps leading to the final equation used for simulation (Sec. 5.1). This makes it difficult to assess the correctness of the implementation.
  • The central claim that the signal on the detector is an "approximate solution" that can be modeled as a "scaled Fraunhofer diffraction pattern" (Abstract, Sec. 5.1) is stated without mathematical proof or justification. The conditions for this approximation's validity and its potential error are not discussed.
  • The notation for key physical parameters is inconsistent. For instance, the gap between the sensor and the display is denoted as H for the ALS (Fig. 5b) but as g for the proximity sensor (Fig. 9a). Similarly, some variables in the equations, such as k and j in Eq. (2), are not explicitly defined in the surrounding text, hindering readability.

• Insufficient Contextualization and Positioning of Novelty

  • The introduction establishes the industrial importance of UDS but does not sufficiently situate the work within the academic literature on diffraction modeling, computational optics, or light propagation through periodic microstructures.
  • The core physical principles (geometric optics, Fraunhofer/Fresnel diffraction) are well-established. The paper's primary conceptual contribution—whether it is the Fresnel number classification scheme itself, the specific approximate model for the proximity sensor, or the comprehensive validation for this specific application—is not clearly articulated against prior art.
  • A more detailed discussion of related work would help clarify the novelty. For example, it is unclear how this work improves upon or differs from other physical optics simulations used in display or semiconductor design. (No direct evidence found in the manuscript, as this weakness concerns the absence of a thorough literature review in Sec. 1).

• Limited Scope and Simplifications in the UDC Model

  • The UDC model focuses exclusively on the blurring effect (PSF) caused by diffraction from the pixel layout (Sec. 4). It omits other critical degradation factors in UDCs, such as significantly reduced quantum efficiency (light loss), color shifts due to wavelength-dependent diffraction, and noise from display light leakage.
  • The application of the model is limited to simulating the forward process of image degradation via convolution (Sec. 4.2). There is no discussion of how this physically-grounded PSF could be integrated into inverse-problem algorithms for UDC image restoration, which is the ultimate goal of such modeling.
  • The analysis is based on only two pixel layouts (Fig. 8a). While illustrative, this limits the generalizability of the conclusions. A parametric study showing how the PSF varies with key pixel geometry parameters (e.g., aperture shape, fill factor, sub-pixel arrangement) would be more impactful for display designers.

Suggestions for Improvement

• Enhance Mathematical Rigor and Transparency

  • Provide a more detailed derivation of the proximity sensor model, showing the steps from the Fresnel-Kirchhoff integral to the final simulated equation. This could be included in an appendix if space is a concern.
  • Provide a formal justification for the approximation that the Fresnel pattern is a scaled Fraunhofer pattern. This should include the assumptions made and a discussion of the approximation's domain of validity.
  • Standardize notation throughout the manuscript (e.g., use a single symbol for the sensor-display gap) and define all mathematical symbols immediately upon their first use to improve clarity and reproducibility. For example, explicitly define k as the wave number and j as the imaginary unit next to Eq. (2).

• Strengthen the Discussion of Novelty and Related Work

  • In the Introduction (Sec. 1), expand the literature review to compare the proposed framework with existing methods for modeling light propagation through micro-aperture arrays or in related fields (e.g., digital holography, computational microscopy).
  • Sharpen the statement of contributions to explicitly delineate the core novelty. For example, state clearly whether the main contribution is the application-specific framework, the simplified Fresnel model, or the extensive experimental validation in a novel context.
  • Add a dedicated paragraph in the conclusion to discuss the limitations of the proposed models (e.g., the assumptions made, the factors not modeled) and suggest concrete directions for future research.

• Broaden the UDC Analysis and its Implications

  • In the discussion (Sec. 4 or Sec. 6), acknowledge the other physical factors affecting UDC image quality (e.g., transmission loss, color crosstalk) and briefly discuss how the current diffraction model could be extended to account for them.
  • Add a short discussion on the practical application of the simulated PSF. For example, explain how it could serve as a valuable prior for non-blind deconvolution algorithms or be used to train UDC image restoration networks.
  • To improve generalizability, consider adding a supplementary analysis that shows how the simulated PSF (Fig. 8b) changes as a function of one or two key pixel layout parameters (e.g., aperture size or pitch). This would provide more direct design rules for engineers.

References None

Synopsis of the paper
本论文针对智能手机“屏下传感（Under-Display Sensing, UDS）”中的光传播问题，提出了一种基于菲涅耳数（Fresnel number）的通用建模框架，以区分不同传感器工作在几何光学、菲涅耳衍射或夫琅禾费衍射区域。作者通过商用智能手机平台验证模型的通用性，分别针对屏下环境光传感器（ALS）、屏下摄像头（UDC）及屏下接近传感器进行了仿真与实验比对，并展示了光线遮挡、衍射与成像模糊的可解释建模结果。

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Summary of Review
论文提出通过菲涅耳数统一描述屏下光传播模式的思路较具启发性（see Sec. 2; Eq. (5)）。实验部分覆盖了多种传感器类型（see Figs. 6–10），验证了该模型与实际测量结果的一致性。然而，数学推导的完整性略显不足（see Sec. 3.2, "approximate solution"），实验结果虽较丰富，但误差分析不足（No direct evidence found in the manuscript）。论文结构清晰，但部分变量定义和图表说明尚需细化（see Figs. 4 and 9 captions）。总体而言，论文在工程意义与理论结合方面具有潜力，但仍需进一步量化与形式化支撑。

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Strengths

· 概念框架统一性

• 证据：Sec. 2, Eq. (5) 引入以菲涅耳数区分光传播模式。
• 重要性：提供了一个从几何光学到衍射光学的连续模型框架，提高了跨设备建模的一致性。
• 补充：Figs. 1–3 展示了几何与衍射区域的直观联系，增加模型可解释性。

· 实验验证充分性

• 证据：Figs. 6–10 各模块展示了从ALS、UDC到接近传感器的实验与仿真对比。
• 重要性：覆盖多种传感器类型与波段，验证模型适用性。
• 补充：Fig. 10(a) 显示噪声强度实验值与模拟值一致趋势，说明模型预测物理现象的合理性。

· 数据一致性与合理误差范围

• 证据：Abstract 与 Fig. 6(c)(f) 中指出，实验与仿真全宽半高（FWHM）视角误差小于 10°。
• 重要性：展示了建模精度的定量指标。
• 补充：此一致性支持方法的实验再现实性。

· 图像质量与定性对比清晰

• 证据：Figs. 8(d)(e) 比较模拟模糊与真实图像的结构相似性（SSIM）。
• 重要性：体现模型可解释性与感知层面的有效性。
• 补充：通过多波长仿真（700/540/440 nm）说明其波长普适性。

· 工程实践相关性

• 证据：Sec. 4 探讨源探测器角度与背景噪声关系（Fig. 9(e)）。
• 重要性：提供直接指导智能手机UDS设计的实证规律。
• 补充：Fig. 10(b) 实拍装置展示技术可实现性。

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Weaknesses

· 数学公式与推导不完整

• 证据：Sec. 3.2 提出“approximate solution”但缺乏明确推导步骤。
• 重要性：影响模型普适性的理论严谨度。
• 补充：No explicit derivation for scaling factor related to Fresnel pattern magnification.

· 误差与不确定性分析不足

• 证据：Figs. 6(c)(f), 10(a)中虽展示数据一致性，但未标注误差条或统计显著性。
• 重要性：无法评估模型鲁棒性与实验重复性。
• 补充：No standard deviation or confidence interval information provided.

· 变量与参数定义不完全

• 证据：Fig. 4及Fig. 9中多处参数（如H、g、θ）未在正文首定义。
• 重要性：影响可重复性及阅读连续性。
• 补充：Eq. (5)中的常数项无物理单位说明。

· 模型泛化性说明不足

• 证据：研究仅使用单一商用手机样机（Sec. 4），无多样本验证。
• 重要性：限制论文声明的“universal model”适用范围。
• 补充：No direct evidence of cross-device validation.

· 图表标注与层次说明欠清晰

• 证据：Figs. 5、9 同时包含多子图，缺乏统一比例尺及部分(a)-(f)说明。
• 重要性：削弱结果可读性与比较的准确性。
• 补充：Fig. 9(e) 图例中符号定义缺失。

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Suggestions for Improvement

· 补充数学推导与符号定义

• 建议：在Sec. 3.2中增加菲涅耳衍射近似求解过程的完整推导，明确定义各符号（见Eq. (5)、Fig. 1）。
• 验证：可通过推导与数值模拟结果对比验证正确性。
• 再拓展：附录中展示关键方程的边界条件处理。

· 增强误差与不确定性分析

• 建议：在Figs. 6、10中添加误差条，报告样本数量与重复实验标准差。
• 验证：在统计表格中提供相关t-test或方差分析说明。
• 再拓展：分析不同测量条件下误差分布。

· 完善参数与符号说明

• 建议：在每节首引入变量表格，统一物理量单位与含义（见Fig. 4, 9）。
• 验证：检查文中符号一致性，特别是H、g、θ与Eq. (5)的符号匹配。
• 再拓展：建立符号索引附录方便读者对照。

· 展示模型跨设备验证

• 建议：在Sec. 4补充至少一种不同品牌或面板结构样机仿真与实验比对。
• 验证：通过FWHM误差与SSIM值比较支持“universal”主张。
• 再拓展：讨论模型扩展到微型显示或AR设备的潜力。

· 统一图表格式并补充说明

• 建议：在Figs. 5、9中完善子图标注、比例尺与图例说明。
• 验证：确保所有坐标轴单位和符号在正文一致。
• 再拓展：可将关键图形合并为摘要式图表以突出统一结论。

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References
None

Synopsis of the paper
The paper presents a unified optical modeling framework for under-display sensing (UDS) in smartphones. It identifies the operative light propagation modes—geometric optics, Fresnel diffraction, or Fraunhofer diffraction—through the Fresnel number criterion. The authors analyze three sensor types—under-display ambient light sensors (ALS), under-display cameras (UDC), and proximity sensors—each exhibiting distinct propagation regimes. Extensive simulations and experimental measurements on a commercial smartphone validate the proposed models. Specifically, the geometric-optics-based ALS simulation reproduces angular responses within 10° full width at half maximum (Fig. 6c–f); the diffraction-based UDC model predicts realistic image blur and color artifacts (Fig. 8b–e); and the Fresnel-diffraction model for proximity sensing accurately explains background noise behavior and optimal sensor orientation (Figs. 9–10). The work aims to provide both a physically grounded theoretical framework and design guidelines for UDS optimization.

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Summary of Review
The paper addresses an important and emerging problem in smartphone optical design with a physically motivated, unified model of under-display light propagation. The proposed Fresnel-number-based classification is conceptually clear (Sec. 2; Fig. 1) and effectively connects different sensing modalities. The experimental validation appears careful and quantitatively consistent with simulation (Table values not shown, but Fig. 6 and Fig. 8 show strong agreement). However, theoretical derivations of Fresnel and Fraunhofer regimes are condensed, with limited mathematical details (No direct evidence found in the manuscript). Additionally, while figures are rich, some parameters of the experimental setup (beam profile, polarization, measurement repeatability) are insufficiently documented (Fig. 9f). Overall, the study combines theoretical insight and practical relevance, though its generality and reproducibility could be substantiated further.

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Strengths

Comprehensive Unified Framework

• Provides a single physical model based on the Fresnel number to distinguish between geometric, Fresnel, and Fraunhofer regimes (Sec. 2; Fig. 1).
• Articulates how each regime corresponds to a specific UDS device type—ALS, UDC, and proximity sensors—enhancing conceptual clarity (Sec. 2.3–2.5).
• This framework fills a modeling gap for optical phenomena in multilayer smartphone displays, supporting generalizable analysis.

Strong Experimental–Simulation Agreement

• ALS angular attenuation simulation matches measured curves within <10° FWHM deviation, suggesting accurate geometric modeling (Fig. 6c–f).
• UDC image simulations based on Fraunhofer diffraction yield high SSIM similarity scores with actual photographs (Fig. 8e), highlighting empirical soundness.
• Fresnel diffraction prediction of signal-level variation for proximity sensing aligns closely with measured noise trends versus angle and spacing (Figs. 9e and 10a).

Practical Design Relevance

• Derivation of an optimal 45° source-detector orientation (Fig. 9e) provides explicit design guidance for minimizing background noise.
• The dependence of signal characteristics on display–sensor spacing (Fig. 10a–b) offers quantitative insight for device assembly tolerances.
• Each case study operates on a commercial smartphone, ensuring relevance to real-world integration challenges (Sec. 4).

Clarity of Visual Presentation

• Figures consolidate theoretical schematics, microscopic images, and experimental data cohesively (Figs. 1–10).
• Microscopic and binary-processed images (Fig. 6a–b, Fig. 9c) visually confirm the model’s assumptions about pixel aperture geometry, aiding reproducibility.
• Multi-panel design (e.g., Fig. 8) systematically contrasts theoretical PSFs, simulated images, and empirical photographs, improving interpretability.

Insightful Regime-Specific Analysis

• Clearly delineates optical effects governing each sensing mode: pixel obstruction (geometric optics), pixel-array diffraction (Fraunhofer), and near-field interference (Fresnel) (Sec. 3–5).
• Demonstrates how these effects dictate signal quality and device placement constraints, enriching cross-domain understanding.
• Establishes a link between optical theory and device-engineering optimization, seldom achieved in prior UDS studies (No direct claim verification possible due to lack of related-work detail).

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Weaknesses

Limited Mathematical Transparency

• Equations outlining Fresnel and Fraunhofer diffraction solutions are summarized without derivations or variable definitions (No direct equation labeling found in the manuscript).
• Parameter dependencies (wavelength, aperture size) appear only qualitatively described, limiting reproducibility.
• The transition criterion between regimes via Fresnel number lacks numerical demonstration or thresholds (Sec. 2 mentions the criterion but provides no examples).

Insufficient Experimental Documentation

• Several key system parameters—LED spectral width, display-layer refractive indices, and detector characteristics—are absent (No direct evidence found).
• Measurement uncertainty or error bars are missing in Figs. 6c, 8e, and 9e, obscuring statistical confidence.
• The calibration procedure for angle or spacing control (e.g., Fig. 9f experimental platform) is only schematically shown without quantitative description.

Generality and Scalability Not Demonstrated

• Validation relies on a single commercial smartphone architecture (Sec. 4.1); applicability to different OLED or microLED panels remains untested.
• The approach’s dependence on wavelength and pixel geometry is discussed but not empirically varied beyond red/green/blue cases (Fig. 8b).
• No results on computational efficiency or how the model scales to multi-sensor arrays.

Incomplete Discussion of Limitations

• The paper does not examine potential non-optical artifacts such as electromagnetically induced interference or display-driving noise (No direct evidence found).
• The assumption of uniform pixel periodicity may break for curved screens or embedded sensors; this is unacknowledged.
• The authors present strong matches but avoid discussing mismatch cases (e.g., residual errors around 45° in Fig. 6f).

Ambiguity in Notation and Physical Consistency

• Some figure variables (z, z′, H, g) lack cross-reference in text, reducing interpretability (Figs. 1, 4, 9).
• The optical path labeling between screen, lens, and detector (Figs. 3, 7) does not explicitly connect with Eq. forms, creating minor consistency gaps.
• Units and coefficients (e.g., scaling factor for Fraunhofer pattern magnification) are mentioned qualitatively, not quantitatively, impairing equation clarity.

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Suggestions for Improvement

Enhance Mathematical Transparency

• Provide explicit derivations or at least reference equation numbers for Fresnel and Fraunhofer approximations; clarify variable definitions (z, a, λ).
• Include numerical examples of Fresnel number values demarcating each propagation regime to ground the classification.
• Supply dimensional units and normalization constants in all equations and captions.

Add Complete Experimental Metadata

• Include a parameter table listing illumination source specs, display stack refractive indices, and detector model.
• Add error bars or confidence intervals to all comparison plots to express measurement precision.
• Briefly describe calibration for angular positioning and spacing (e.g., rotation stage accuracy, measurement repeat count).

Demonstrate Generality Across Devices

• Validate or simulate the model using at least one additional display type (e.g., LTPO OLED) to test generality.
• Investigate wavelength dependence systematically by varying pixel geometry and confirming predicted scaling across λ = 400–800 nm.
• Discuss extension to multi-sensor configurations or system-level simulation efficiency.

Explicitly Discuss Model Limitations

• Dedicate one subsection acknowledging unmodeled factors such as electric or thermal coupling, and how they might influence measurements.
• Include one example where the model diverges from observed data and interpret causes (e.g., alignment error, nonuniform aperture).
• Outline future improvement paths, e.g., integrating electromagnetic simulation or polarization effects.

Standardize Notation and Physical Consistency

• Maintain a variable-definition table keyed to figure labels (z, z′, H, g, d, l) for unambiguous interpretation.
• Check that optical path variables are consistent across Figures 1, 3, and 7, and reconcile any discrepancies in text.
• Provide explicit scale factors in equations linking Fresnel and Fraunhofer solutions to detector signal levels.

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References
None