Methods and systems for monitoring structural health using diffractive optical processors / networks

Abstract

A system for monitoring the structural health of structures uses diffractive layer(s) along with one or more light sources that input light onto the diffractive layers(s). The diffractive layer(s) are affixed to the structure and include a diffractive surface that includes different physical features or regions on the surface(s) thereof having different diffractive properties. One or more optical sensors are configured to capture optical signal(s) resulting from the reflection and diffraction of input light off the one or more diffractive layers, wherein the optical signal(s) comprises time-series information on oscillation of the structure containing the diffractive layer(s). A decoder or digital neural network can be employed to receive outputs from the optical sensor(s) to identify quantitative and / or qualitative information on the frequencies or harmonics associated with the movements of the one or more diffractive layers.

Description

PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2METHODS AND SYSTEMS FOR MONITORING STRUCTURAL HEALTH USING DIFFRACTIVE OPTICAL PROCESSORS / NETWORKSRelated Application

[0001] This Application claims priority to U. S. Provisional Patent Application No.63 / 755,950 filed on February 7, 2025, which is hereby incorporated by reference in its entirety. Priority is claimed pursuant to 35 U. S. C. § 119 and any other applicable statute.Technical Field

[0002] The technical field generally relates to methods and devices for monitoring the health of structures and structural components using diffractive optical processors or diffractive neural networks. The diffractive optical processors / neural networks use diffractive layers optimized using deep learning to perform statistical inference through light propagation and diffraction, thereby manifesting a novel, all-optical computing framework for low-power, ultra-fast, scalable, and highly accurate structural health assessments of a variety of types of civil infrastructure, such as, bridges, tunnels, dams, and buildings.Background

[0003] In the face of escalating challenges posed by natural disasters and the aging of civil infrastructure, the need for a paradigm shift in Structural Health Monitoring (SHM) has never been more critical. A resilient community is expected to withstand extreme events with minimal damage and functionality disruptions. The capability to rapidly restore the functionality of damaged civil structural and infrastructural systems (e.g., buildings, bridges, tunnels, dams, etc.) is a vital element of hazard resilience. Continuous monitoring and inspections of these systems to obtain quantitative estimates of their damage levels is a prerequisite to direct recovery efforts, allocate resources optimally, minimize unnecessary downtime, and avoid secondary catastrophic failures and their consequent losses and fatalities. Traditional SHM methodologies, while foundational, are increasingly recognized for their limitations — subjectivity, labor-intensiveness, and scalability issues. Specifically, Non-Destructive Testing / Evaluation (NDT / NDE) and vibration-based methods, despite their methodological and technological advancements, face constraints in universal applicability and cost-effectiveness. Addressing these complexities calls for an innovative leap beyond conventional frameworks.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2

[0004] Traditionally, structural investigations have relied on visual inspections, which suffer several shortcomings, including: (1) subjectivity leading to potentially differing results between inspectors, (2) labor intensiveness and high costs, which limit regional scalability, (3) inability to provide quantitative diagnoses of damage location and severity, and prognoses of residual capacity, (4) lack of uncertainty quantification associated with human-based assessment efforts. To address these challenges, sensor-based SHM has gained prominence in the past few decades. These methods generally fall into two categories: (i) Non-Destructive Testing / Evaluation (NDT / NDE) and (ii) vibration-based SHM methods. Examples of NDT / NDE methods include infrared thermography, ground-penetrating radar, and acoustic, electromagnetic, chemical, radiological, and physical (impact) tests, which are utilized to identify various hidden damages within structures. While these techniques are widely used, they are primarily useful for detecting localized damage only and require prior knowledge of the damaged area and accessibility. More importantly, they do not directly offer quantitative measures of the damage severity (e.g., residual strength, percent loss of stiffness, etc.).Moreover, they require specialized and expensive equipment as well as service closures of the inspected structure.

[0005] Vibration-based SHM methods utilize data collected through a network of sensors (accelerometers, displacement transducers, strain gauges, etc.) distributed along the structure. In these systems, the sensing system records the vibration response of the structure under various types of excitations at multiple locations and then transmits this data to a processing module for analysis. SHM systems can be categorized based on their processing module, which typically involves a system identification technique. System identification techniques fall into two families of techniques: data-driven and data-model fusion methods. Data-driven techniques have a rich history due to their extensive applications across diverse fields such as aerospace, electrical, mechanical, and civil engineering. This category encompasses a wide range of methods, from simple peak-picking to parametric / modal identification methods, each of which is suitable for specific problems based on the statistical properties of the signals (deterministic, stochastic, stationary, non-stationary), the domain of interest (time, frequency, time-frequency), and access to the input excitation.

[0006] In the data-model fusion methods, sometimes referred to as model-based methods, a parametric model, such as a Finite Element (FE) model, is updated using data. Unlike data-driven methods, where modal parameters (or parameters of a general state-space model) are estimated solely from data, a numerical model constrains the results because its parametersPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2have direct physical meanings. FE model updating is not new, but its classical version is applicable to only linear elastic structures, limiting its applications. During the last 15 years, due to continuous advances in computational resources, a new branch of model updating methods has emerged. These methods employ Bayesian estimation techniques to update the posterior Probability Density Function (PDF) of uncertain parameters of a finite element model. The structural engineering team involved in this proposal has expanded these techniques to address real-life problems. These new techniques are computationally expensive, and thus, they developed a parallel-processing SHM toolbox to make them feasible in practical applications.

[0007] These advances in time-domain model updating have paved the way for developing Digital Twins (DTs) of civil structures. A DT serves as the virtual counterpart of a real asset, continuously updated through real or near-real-time data obtained from the sensing system deployed on the physical structure. DTs enable predictions of structural performance in future events (e.g., earthquakes), continuous health assessments and maintenance, and evaluation of performance under operational conditions. DTs can also be utilized for post-event SHM.

[0008] All of the aforementioned SHM methods, ranging from the very basic to the highly complex, are rendered ineffective without sufficient and reliable data. Traditionally, structural vibrations are recorded by wired / wireless accelerometers, which are single-node sensors measuring the absolute accelerations at their locations. Accelerometers have a rich history and have found extensive applications in structural engineering. Since structural damage typically correlates better with displacements, it has been crucial for engineers to extract displacement responses (e.g., inter-story drifts for buildings). However, obtaining displacements through numerical integration of accelerations is hindered by low-frequency errors in the acceleration data. Strain gauges and displacement transducers could offer a solution, but these sensors are two-node sensors capable only of measuring the relative displacement between two points (e.g., the ceiling and floor of a story). There are a few other options to measure absolute displacements, which are relative to a distant reference location. The Laser Doppler Vibrometer (LDV) is an example of such sensors operating based on the Doppler effect on laser beam lights. Ultrasound displacement sensors are also available, functioning either through the Doppler effect or air coupling. While there are efforts to utilize these sensors, particularly laser-based sensors, they have not been widely adopted due to their limitations and cost. Recently, a new optical sensor concept for measuring displacements,PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2namely Discrete Diode Position Sensors (DDPS), has been developed by McCallen et al. In this sensor, a laser beam, diffracted by an optic to create a laser line source, is propagated across a building story onto a staggered grid of light-sensitive diodes that serve as on / off switches. Each photodiode generates a voltage when contacted by incident laser light. By identifying which diodes are actively being contacted by the incident light at any instant of time, the location of the laser line source can be determined as it moves across the sensor face during story drift. This measurement of displacements, while extremely useful for post-event damage assessment, still requires signal processing (digitization, denoising, etc.). This means that every unit has to be in communication with a dedicated digitizer / processor unit. As the sensor unit itself also has many electronic components and requires wiring and local power that both bear costs and need to remain functional (e.g., for 30 years) to capture relatively rare events, there are yet no practical applications and deployments of these systems. Videobased displacement monitoring techniques have also been investigated. While successful results have been obtained in lab experiments, they have not found their way into practice due to the sensitivity of measurements to environmental effects.

[0009] There is a clear need for low-power, fast, scalable, and highly accurate systems that can perform structural assessments.Summary

[0010] The devices and systems employing the same described herein may be used to monitor and analyze the health of various structures in response to exposure to a stress event like an earthquake, hurricane, or the like. The systems may also be used to monitor the health of structures or other infrastructure over time outside of particular stress events (although these may be captured as well). In one embodiment, a system for monitoring the structural health of a structure includes one or more light sources that generate light or electromagnetic radiation that is input to one or more diffractive layers that are disposed on the structure. The light may be spatially coherent, partially coherent, or spatially incoherent. The one or more light sources may include, by way of example, a laser, laser diode, or light-emitting diodes (LEDs), solid state lasers, gas lasers, liquid lasers, or tunable lasers. One or more diffractive layers are affixed to the structure to be monitored. The one or more diffractive layers may be mounted on an exterior or interior surface of the structure. The structure to which one or more diffractive layers are affixed experiences oscillations at specific amplitudes and frequencies. The one or more diffractive layers may be exposed to the external environment.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2Alternatively, the one or more diffractive layers may be covered or enclosed by an optically transparent window or the like. In one embodiment, the one or more diffractive layers include a diffractive surface or layer that includes different physical features or regions on the surface(s) or layer(s) thereof having different diffractive properties as a function of lateral coordinates across the diffractive layer. The diffractive properties of the diffractive layer / surface may include reflective properties in some embodiments (i.e., light reflecting off the diffractive surface) while in other embodiments diffractive properties include transmissive properties through the diffractive layer / surface (i.e., light passing through the diffractive layer / surface). These different physical features or regions on the diffractive layer act as different “neurons” of the one or more diffractive layers, which function as diffractive optical processors. The particular configuration and arrangement of these physical features or regions on the diffractive layer are designed during a training phase where the system is modelled electronically prior to forming the physical embodiment that is actually used in the field. The system further includes one or more optical sensors configured to capture the one or more diffracted / reflected optical signal(s) resulting from the diffraction / reflection of input light off the one or more diffractive layers.

[0011] In one embodiment, when a plurality of different optical sensors are used, each optical sensor may be configured to capture a particular oscillation frequency or frequency band or range that is diffracted / reflected by the diffractive layer and illustrative of the oscillation frequency of the structure being monitored. In another embodiment, a “hybrid” system is used in which the one or more diffractive layers are integrated with an electronic decoder or digital neural network “back-end”. The decoder or digital neural network can extract and identify key oscillation frequencies and their amplitudes, which can be used for health diagnosis of the structure on which the one or more diffractive layers are mounted.

[0012] For example, in one embodiment, a monochrome-based system for monitoring the structural health of a structure includes one or more diffractive layers integrated with a trained digital neural network back-end. An optimized reflective diffractive layer will be attached to the monitored structure, which oscillates at a specific amplitude and frequency. Input light reflected from the smart diffractive layer is captured by a plurality of detectors (e.g., in an array in some embodiments), which will record the time series signals generated by the oscillation. The signals are processed by a jointly trained digital neural network to decode the oscillation's amplitude and frequency for two or more orthogonal directions (e.g.,PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-22D or 3D) to assess the structural health of the structure with the diffractive layer(s) disposed thereon.

[0013] In another embodiment, a multi-wavelength diffractive optical network or system is designed for multiplexed and high-throughput structural health monitoring with electronic neural network-based decoding. Each diffractive layer is optimized using deep learning during training for a specific wavelength (e.g., NIR, THz bands) and will be attached at various locations on the structure of interest, exhibiting unique oscillation amplitudes and frequencies. Here, different optical sensors or groups of such optical sensors capture the reflected and diffracted light from the different diffractive networks / processors with a specific wavelength assigned to that smart diffractive layer. The collected time series signals of these input wavelengths are processed by a trained digital neural network to simultaneously measure the 3D and / or 2D oscillation amplitudes and frequencies at each location, aiding the diagnosis of structural health using cost-effective, low-power, and deep learning powered diffractive processors.

[0014] In another embodiment, the diffractive layer(s) includes one or more transmissive diffractive layers that includes different physical features or regions on the surface(s) or layer(s) thereof having different transmissive properties as a function of lateral coordinates (e.g., length, width, radial coordinates, etc.) across the diffractive layer. These different physical features or regions on the diffractive layer act as different “neurons” of the optical network or processor although light transmits through the layers. A mirror or reflective surface is provided after the last of the one or more transmissive diffractive layers to redirect the light back through the one or more diffractive transmissive layers. This is a double-pass configuration in which light passes through the one or more diffractive transmissive layers in two directions (forward and reverse). The diffracted / reflected light from this diffractive transmissive layer is then captured by one or more optical sensors configured to capture the one or more diffracted / reflected optical signal(s) resulting from the diffraction / reflection off the transmissive diffractive layer. The information or data captured by the one or more optical sensors can then be fed to a trained digital neural network that outputs quantitative and / or qualitative information on the frequencies or harmonics associated with the movements of the one or more diffractive layers and structure in one or more directions.

[0015] This system provides a universally deployable, cost-effective, and highly accurate tool for the comprehensive monitoring of structural health, capable of delivering rapid assessments with unprecedented precision and objectivity while also achieving cost-PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2effectiveness and ultra-low power consumption through passive light-matter interactions and analog optical computing. The diffractive sensor system revolutionizes the SHM field by eliminating the need for expensive networked conventional sensors, their data acquisition systems, and the application of complex damage identification algorithms, which require significant digital computations that limit their ability to be useful at regional scales. The diffractive SHM sensors enable real-time or instant processing that can be used to rapidly classify and quantify the damage levels in structures. This will significantly reduce costs that have been a substantial barrier to the deployment of SHM systems at a broad scale.

[0016] In one embodiment, a system for monitoring the structural health of a structure includes: one or more light sources generating input light; one or more diffractive layers affixed to the structure, the one or more diffractive layers each comprising a diffractive surface or layer that includes different physical features or regions on the surface or layer thereof having different reflective properties across the diffractive layer; and one or more optical sensors configured to capture one or more diffracted optical signal(s) resulting from reflection and the diffraction of the input light off the one or more diffractive layers in response to illumination with the input light, wherein the optical signal(s) comprise timeseries information on oscillation of the structure.

[0017] In one embodiment, the one or more optical sensors or detectors may specifically target a particular amplitude and / or frequency range. That is to say, when a particular optical sensor or detector (or group of multiple such sensors or detectors) receives illumination, this corresponds to a particular amplitude and / or oscillation frequency experienced by the one or more diffractive layers.

[0018] In another embodiment, an electronic decoder or digital neural network that is connected or coupled to the one or more optical sensors and configured to output quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more diffractive layers in one or more directions. This information can then be, optionally, fed to a damage identification module that takes this information and outputs inferred or suspected damage to the user. The damage identification module may output inferred or suspect damage based on the amplitude and / or frequency information extracted directly, as noted above, or using one or more electronic decoders / digital neural networks.

[0019] In another embodiment, a system for monitoring the structural health of a structure includes one or more light sources generating an input light; one or more transmissive diffractive layers affixed to the structure, the one or more transmissive diffractive layersPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2comprising one or more diffractive surfaces or layers that are optically transmissive to the input light, the one or more transmissive diffractive layers having different physical features or regions on the surface(s) or layer(s) thereof having different diffractive properties across the respective transmissive diffractive layer; a mirror disposed along an optical path of the one or more transmissive diffractive layers and configured to reflect light back through the one or more diffractive layers; and one or more optical sensors configured to capture one or more diffracted optical signal(s) resulting from the diffraction of the reflected input light off the one or more transmissive diffractive layers and the mirror in response to illumination with the input light, wherein the optical signal(s) comprise time-series information on oscillation of the structure.

[0020] As in the prior embodiment, the one or more optical sensors or detectors may specifically target a particular amplitude and / or frequency range. Alternatively, an electronic decoder or digital neural network that is connected or coupled to the one or more optical sensors and configured to output quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more diffractive layers in one or more directions. This information can then be, optionally, fed to a damage identification module that takes this information and outputs inferred or suspected damage to the user. The damage identification module may output inferred or suspect damage based on the amplitude and / or frequency information extracted directly, as noted above, or using one or more electronic decoders / digital neural networks.

[0021] In another embodiment, a method of monitoring the structural health of a structure includes: providing one or more light sources generating input light; one or more diffractive layers affixed to the structure, the one or more diffractive layers comprising a diffractive surface that has different physical features or regions on the surface(s) thereof having different diffractive, transmissive, and / or reflective properties as a function of lateral coordinates across the diffractive layer; and one or more optical sensors configured to capture the one or more diffracted optical signal(s) resulting from reflection and diffraction of input light off the one or more diffractive layers, wherein the optical signal(s) comprise time-series information on oscillation of the structure. The one or more diffractive layers affixed to the structure are illuminated with the input light and capture one or more reflected and diffracted optical signal(s) resulting from the diffraction off the one or more diffractive layers.Quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more diffractive layers in one or more directions is outputted usingPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2the time-series information on oscillation of the structure acquired by one or more optical sensors configured to capture one or more diffracted optical signal(s).

[0022] The one or more optical sensors or detectors may specifically target a particular amplitude and / or frequency range. Alternatively, an electronic decoder or digital neural network that is connected or coupled to the one or more optical sensors and configured to output quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more diffractive layers in one or more directions. This information may also be fed to a damage identification module that takes this information and outputs inferred or suspected damage to the user.Brief Description of the Drawings

[0023] FIG. 1 illustrates a schematic of a system for monitoring the structural health of a structure according to one embodiment.

[0024] FIG. 2A illustrates a diffractive layer that forms a diffractive optical processor / neural network according to one embodiment. In this embodiment, the diffractive layer is reflective.

[0025] FIG. 2B illustrates diffractive layers that form a diffractive optical processor / neural network according to one embodiment. In this embodiment, two separate diffractive layers that are transmissive to electromagnetic radiation are aligned along an optical path with a mirror so that the transmitted light is reflected back through the two separate diffractive layers in a double-pass arrangement. While two layers are illustrated in FIG. 2B, it should be understood that a single layer may be used (or more than two layers).

[0026] FIG. 3 illustrates a schematic of a system for monitoring the structural health of a structure according to one embodiment that uses a monochrome coherent light source (in one embodiment) onto a plurality of different diffractive layers. The output is collected by a detector array that is fed to an electronic decoder or one or more trained digital neural networks.

[0027] FIG. 4 illustrates a schematic of a system for monitoring the structural health of a structure according to one embodiment that uses a multi-wavelength coherent light source (λ1, λ2, λ3) (in one embodiment) onto a plurality of different structure surfaces (reflective / diffractive layers). The output is collected by a detector array with detectorsPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2specific to different wavelengths that is fed to an electric decoder or one or more trained digital neural networks.

[0028] FIG. 5 illustrates a schematic of a system designed for high-throughput structural vibration monitoring with a shallow electronic neural network-based decoding. The diffractive layer, optimized using deep learning, is attached at various locations on a target structure, where it encodes local oscillatory motion into wavelength-dependent, structurally optimized diffraction patterns. A few optical sensors or detectors capture the reflected light, which varies in signal strength based on the displacement amplitudes and frequencies at each point that is being monitored. The resulting time series signals are rapidly decoded by a shallow neural network backend, which in this embodiment includes two trained neural networks that function, respectively, as a displacement decoder and a frequency processor to simultaneously extract 3D oscillation features of the structure under test. This integrated system can enable cost-effective, low-power structural health diagnostics powered by deep learning-designed diffractive processors.

[0029] FIG. 6A illustrates one embodiment of a sensing module that includes one or more optical sensors along with a power source (e.g., a battery or AC power source) and a microcontroller or other circuitry that interfaces with the one or more optical sensors and one or more processors that, in this embodiment, are used to execute the one or more trained digital neural networks.

[0030] FIG. 6B illustrates another embodiment of a sensing module. In this embodiment, a separate computing device is provided that communicates with the sensing module.

[0031] FIG. 7 A provides an illustrative system configuration for vibration monitoring. An input wave (incident at θinc) reflects off of an optimized diffractive layer, which is attached to an oscillating structure. The resulting optical signal (in reflection) is captured by a detector array and rapidly processed by a displacement decoder and a frequency processor (e.g., respective trained neural networks), which measure the displacement and the 3D oscillation spectrum of the structure under test. NDL. NDand NFare the number of trainable parameters in the optimized diffractive layer, displacement decoder network and frequency processor network, respectively.

[0032] FIG. 7B illustrates the optimized phase modulation pattern of the trained surface of the diffractive layer used in the vibration monitoring system. The diffractive processor phase profile was jointly trained with a displacement decoder that has ND= 6.39k trainable parameters.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2

[0033] FIG. 7C illustrates the optical sensor / detector array layout with four single-pixel detectors.

[0034] FIGS. 8A-8B illustrate a comparison of 3D oscillation spectra inference performance across different optical configurations; ND= 2.98k. FIG. 8A shows phase modulation patterns of a jointly trained diffractive layer, a separately trained diffractive layer, a Fresnel lens array and a random phase diffuser, displayed from top to bottom, respectively. FIG. 8B shows ground truth 3D oscillation spectra (two examples in each direction) and the diffractive inference results for each configuration. The shaded region in the middle highlights the frequency band of interest (9-11 Hz), i.e., the training range of the spatial oscillations. The spectral MSE values corresponding to the phase modulation patterns reported in the first column of Table 1 are 1.109 × 10-2(jointly optimized DL),1.419 x 10-1(separately optimized DL), 3.576 x 10-1(Fresnel lens array), 6.243 x 10-1(random diffuser). The jointly optimized diffractive layer consistently achieved the lowest spectral MSE, with more than an order of magnitude improvement over other configurations - all of which used ND= 2.98k at the digital backend.

[0035] FIGS. 9A-9B illustrate an analysis of 3D oscillation spectra inference performance. FIG. 9A shows confusion matrices for single frequency inference across various system configurations and displacement decoder sizes (1VD). The horizontal axis represents input frequencies (ground truth), and the vertical axis represents the inference spectra (9-11Hz) for structural oscillations in x, y, and z. The bar shows the inference intensity. FIG. 9B shows the trade-off between the decoder network complexity and the spectral MSE. Increased model capacity with a larger NDleads to improved spectral accuracy at the cost of an increase in the number of FLOPs needed.

[0036] FIGS. 10A-10C illustrate wavelength-multiplexed diffractive system for simultaneous multi-point vibration monitoring. FIG. 10A is a schematic diagram of the multiplexed sensing configuration. Three coherent input waves with distinct wavelengths (λ1, λ2, λ3) simultaneously illuminate the input aperture at specific incidence angles(θ1, θ2, θ3). These waves propagate over an axial distance to interact with three spatially distinct diffractive layers (DL1, DL2, DL3), each attached to a different desired monitoring point on the structure. The reflected optical fields, modulated by the local 2D displacements (xi, yi) of each point (including all the cross-talk terms), are collected by a shared detector array. A digital backend, comprising a displacement decoder and a frequency processor, processes the multiplexed signals to simultaneously extract the oscillation spectra at multiplePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2observation points. FIG. 10B shows the optimized phase modulation patterns of the three diffractive layers, trained to encode structural vibrations at their respective wavelengths and spatial locations. FIG. 10C shows the comparison of the ground truth (solid lines) and the diffractive inference results (dashed lines) for the 2D oscillation spectra (% and y) across the three monitored points, demonstrating accurate multi-point spectral reconstruction in the target frequency range.

[0037] FIGS. 11A-11B illustrate the experimental validation of the 1D diffractive vibration monitoring system using a millimeter-wave (λ = 3 mm) source. FIG. 11A is a photograph of the experimental setup and the pipeline for 1D spectrum inference. FIG. 11B is a schematic of the types of perturbations and structures tested in these experiments.

[0038] FIG. 12 illustrates experimental results of the 1D diffractive vibration monitoring system using a millimeter-wave source. Spectral inference results of different configurations with various types of perturbations and structures are compared against the ground truth. WN: white noise. The non-zero energy at zero frequency was caused by the displacement of the base level (0thlevel) due to the manual perturbation.

[0039] FIGS. 13A-13C illustrate temporal averaging improves spectral inference fidelity in diffractive vibration monitoring. FIG. 13A shows a schematic of the temporal averaging method: raw sensor signals are processed using a sliding window to generate multiple timeseries segments. Each segment's spectrum, extracted by the nonlinear digital backend, is then averaged to produce the final spectral output. FIG. 13B shows the trade-off between the spectral inference accuracy and the computational cost. FIG. 13C is a comparison of the extracted spectra (amplitude vs. frequency) for different temporal averaging times (Δt) under three different experimental conditions. WN: white noise. The non-zero energy at zero frequency was caused by the displacement of the base level (0thlevel) due to manual perturbation.

[0040] FIGS. 14A-14D illustrate experimental validation of the 2D vibration monitoring system using a millimeter- wave source. FIG. 14A is a photograph of the experimental setup for 2D vibration spectrum inference. FIG. 14B is a top-down schematic view showing the placements of the laser rangefinders (used for ground truth measurements) and the diffractive layer. The experimental performance comparison of the 2D diffractive vibration monitoring system between FIG. 14C (the optimized diffractive layer) and FIG. 14D (a reflective flat mirror) that are both 3D printed are illustrated in FIGS. 14C-14D. The non-zero energy atPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2zero frequency was caused by the displacement of the base level (0thlevel) due to the manual perturbation.

[0041] FIGS. 15A-15B illustrate a comparison of 2D oscillation spectra inference performance across different optical configurations. FIG. 15 A illustrates the phase modulation patterns of a jointly trained diffractive layer, a separately trained diffractive layer, a Fresnel lens array and a random phase diffuser, displayed from top to bottom, respectively. FIG. 15B illustrates the Ground truth 2D oscillation spectra (two examples in each direction) and the diffractive inference results for each configuration. The shaded region highlights the frequency band of interest (9 -11 Hz), i.e., the training range of the spatial oscillations. The spectral MSE values corresponding to the phase modulation patterns reported in the first column of Table 1 are 7.656 × 10-3(jointly optimized DL), 6.507 x 10-2(separately optimized DL), 2.826 x 10-2(Fresnel lens array), 7.134 x 10-1(random diffuser); ND= 2.96k. The jointly optimized diffractive layer consistently achieved the lowest spectral MSE, with at least an order of magnitude improvement over other configurations - all of which used ND= 2.96k at the digital backend.

[0042] FIG. 16 shows an analysis of 2D spectral inference performance. Confusion matrices for single frequency inference across various system configurations and displacement decoder sizes (ND). The horizontal axis represents input frequencies, and the vertical axis represents the inference spectra (9-11 Hz) for structural oscillations in x and y. The color bar shows the inference intensity.

[0043] FIG. 17 illustrates the evaluation of the diffractive vibration monitoring system under randomly introduced imperfections. The spectral MSE is reported for varying levels of random height error (6htest) independently applied at each pixel of the diffractive surface during its blind testing to simulate 3D fabrication inaccuracies or other random perturbations. The performance of the standard "unvaccinated" diffractive model is compared against the "vaccinated" models, which were trained by explicitly incorporating random height noise (δhtrain) into the diffractive layer during the joint optimization process to enhance its robustness. The error bars represent the standard deviation of the spectral reconstruction performance. Also see Table 3 for the statistical significance of the observed differences. Asterisks denote statistical significance levels: * p < 0.05, ** p < 0.01, *** p < 0.001; ns: not significant.

[0044] FIGS. 18A-18B illustrate the performance analysis of the diffractive vibration monitoring system as a function of the angular misalignment of the illumination source. FIG.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-218A shows the spectral MSE plotted on a logarithmic scale as a function of the incidence angle of the input wave (θinc,test). The diffractive layer was optimized for an incidence angle of θinc,train= 15° (dashed line). FIG. 18B shows the comparison of the ground truth (solid lines) and the reconstructed (dashed lines) 3D oscillation spectra for various test incidence angles. The results demonstrate the system's angular tolerance, showing high-fidelity reconstruction near the design angle and a gradual degradation in performance as the misalignment increases.

[0045] FIG. 19A-19C illustrate the performance comparison of simultaneous multi-point vibration monitoring with varying numbers of detectors (Adt). The detector array layouts (left column) and the corresponding spectral inference results (right columns) are shown for configurations using (FIG. 19A) Ndt= 4 detectors, (FIG. 19B) Ndt= 6 detectors, and (FIG.19C) Ndt= 9 detectors. The spectral plots compare the ground truth (solid lines) and the diffractive inference (dashed lines) for three monitored points along both the x and y axes. The under-determined system in FIG. 19A exhibits significantly larger inference errors (1.446 x 10-1+ 4.646 x 10-2), while the determined (inference error 5.301 x 10-4+ 7.244 x 10-4) and over-determined systems (inference error 3.555 x 10-4± 2.772 x 10-4) in FIGS. 19B and 19C, respectively, yield higher fidelity reconstructions. Also see Table 4 for the statistical significance of the observed differences.

[0046] FIGS. 20A-20C illustrate the performance comparison between monochrome and wavelength-multiplexed configurations for simultaneous multi-pomt vibration monitoring. FIG. 20A is a schematic overview of the monochrome diffractive system for simultaneous multi-point vibration monitoring. FIG. 20B shows spectral inference results for the monochrome configuration (Spectral MSE 7.175 x 10-4+ 4.368 x 10-4), where all three monitoring points are simultaneously illuminated by the same wavelength (2) and measured / monitored by a9-pixel detector array, (i.e., Ndt= 9). FIG. 20C shows spectral inference results for the wavelength-multiplexed configuration (as described with regards to discussion of FIGS. 10A-10C). Utilizing the same detector array geometry (Ndt= 9), the wavelength-multiplexed system demonstrates superior spectral reconstruction fidelity (spectral MSE 3.555 x 10-4± 2.772 x 10-4with a p value of 2.196 × 10-10) compared to the monochrome approach.

[0047] FIG. 21 illustrates additional experimental results of the 1D diffractive vibration monitoring system using a millimeter-wave source. Spectral inference results of differentPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2configurations with various types of perturbations and structures are compared against the ground truth.

[0048] FIG. 22 illustrates experimental performance comparison of the 1D diffractive vibration monitoring system between the optimized diffractive layer and a reflective flat mirror that are both 3D printed. The non-zero energy at zero frequency was caused by the displacement of the base level (Oth level) due to the manual perturbation. WN: white noise.

[0049] FIG. 23 schematically illustrates details regarding the displacement decoder network and a frequency processor network that make up the electronic decoder or digital neural network according to one embodiment.Detailed Description of Illustrated Embodiments

[0050] FIG. 1 schematically illustrates an embodiment of a system 2 for monitoring the structural health of a structure 100 or multiple structures 100. The structure(s) 100 may include any type of civil infrastructure, like a building, bridge, tower, dam, tunnel, etc. The structure 100 that is monitored may include a single structure 100 but this is an illustrative example and two or more separate structures 100 are contemplated, such as that illustrated in FIGS. 1 and 4. The system 2 includes a one or more light sources 10 that generate input light or electromagnetic radiation 12 onto one or more diffractive layers 20 affixed to the structure(s) 100. The input light 12 may be light is spatially coherent, partially coherent, or spatially incoherent. The light source(s) 10 may include monochromatic or quasi-monochromatic light sources in some embodiments. The light emitted from the light source 10 may include visible light or it may include light or electromagnetic radiation outside of the visible spectrum. In some embodiments, the light sources 10 emit light at a single wavelength or a plurality of different wavelengths or wavelength ranges such as that illustrated in FIG. 4. The diffractive layers 20 described herein effectively operate as diffractive optical processors. The one or more light sources 10 may include, by way of example, laser(s), laser diode(s), or light emitting diode(s), solid state lasers, gas lasers, liquid lasers, or tunable lasers. In some embodiments, a single light source 10 may be used to illuminate a plurality of diffractive layers 20 (e.g., FIGS. 1 and 3). This may be done using conventional optical techniques used in conjunction with the light source(s) 10 such as beam steering and the like. For example, the light source(s) 10 may rapidly scan different diffractive layers 20. Alternatively, each diffractive layer 20 may be associated with its own light source 10. The light source(s) 10 may be contained within a housing or module is suitable for handling a variety of weather orPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2environmental conditions. The light source(s) 10 may be mounted to another fixed structure such as, for example, another structure 100 that is within the line of sight of the structure(s) 100 to be monitored. The light source 10 is preferably located in a fixed location and operates continuously or semi-continuously over a period of time to illuminate the one or more diffractive layers 20. In one embodiment, the light source(s) 10 may be triggered to operate for a period of time after a triggering event. For example, an earthquake warning system or earthquake alarm system, which is a system of accelerometers, seismometers, communication, computers, and alarms that is devised for rapidly notifying adjoining regions of a substantial earthquake once one begins may trigger the light source(s) 10. Such a warning or alarm system may be connected to the system 2 to turn on the light source(s) 10 when an early warning alert is triggered.

[0051] These diffractive layers 20 may be located on different parts of the same structure 100 (e.g., FIG. 3) and / or different structures 100 (e.g., FIG. 1). For example, the diffractive layers 20 may be located on areas of structure(s) 100 prone to damage, weakness, or fatigue. The diffractive layers 20 may be located in a holder or mount (not shown) that is attached to the structure 100 using fasteners, adhesives, or the like. The diffractive layers 20 may be mounted on the exterior or interior of the structure 100. The one or more diffractive layers 20 include a diffractive surface or layer that includes different physical features or regions on the surface or layer thereof having different diffractive properties as a function of lateral coordinates across the diffractive layer 20. The different diffractive properties may include different reflective properties in certain embodiments (e.g., FIGS. 1, 2A, 3-5). In other embodiments, the different diffractive properties include different transmission properties (e.g., FIG. 2B). FIG. 1 illustrates an example of a diffractive layer 20 that diffracts / reflects incident electromagnetic radiation. As explained herein, the particular locations of the physical features that make of the one or more diffractive layers 20 are created by digitally training a model that uses physical models / laws governing the light propagation and diffraction which capture oscillation frequency and amplitudes of the structure(s) 100 having the one or more diffractive layers 20 mounted thereto. The oscillations of the structure(s) 100 may include oscillations in different planes, e.g., x, y, and z directions as one example. FIGS.3 and 4 illustrate movement of the diffractive layers 20 in two orthogonal directions (2D) (arrows) but it should be appreciated that the system 2 disclosed herein may be used to measure and monitor oscillatory movement in three dimensions (3D) as illustrated in FIG. 5.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2

[0052] The forward model of a diffractive optical processor, such as the diffractive layers 20 contemplated herein can be mathematically formulated as a complex-valued matrix operator that multiplies an input field to create an output field at a detector plane. This operator is designed / trained using, e.g., deep learning to transform a set of complex fields at the input of the optical network into another set of corresponding fields at the output plane created through the interaction of the input light 12 with the designed diffractive surfaces as well as free-space propagation within the optical network or processor. The training stage of the diffractive optical processor or diffractive layer 20 is performed using a computer, and relies on deep learning and error back-propagation methods to tailor the light-matter interaction across the diffractive layer 20 that collectively perform a given machine learning task which here is generating diffracted optical signal(s) 22 that capture time-series information on oscillation of the structure(s) 100 that contain the diffractive layer(s) 20 as well as obtaining amplitude information for temporal frequencies associated with movement of the one or more diffractive layers 20 on the structure(s) 100 in one or more directions (e.g., x, y, or z direction).

[0053] The one or more diffractive layers 20 that reflect / diffract light are optimized for a particular wavelength of the light source(s) 10. The wavelength of the light source(s) 10 may vary depending on the application. Experiments described herein are conducted in the THz range of the electromagnetic spectrum but the invention is not so limited. The near-infrared range (NIR) of the electromagnetic spectrum is another band or range of the electromagnetic spectrum that has particular applicability. This may include light in the range of around 800 nm to around 900 nm. The size of the diffractive layer(s) 20 may vary depending on the wavelength of the light used. Longer wavelengths require larger diffractive layers 20. It is envisioned that the one or more diffractive layers 20 will have a cross-sectional size that is typically within the range of around 0.1 mm2and 1000 cm2. While the diffractive layers 20 illustrated herein are generally rectangular in shape, the invention is not so limited as the diffractive layers 20 may have different cross-sectional shapes.

[0054] The diffractive layers 20 may be formed from a substrate that includes or is coated with a reflective surface. This may include, for example, a metal such as aluminum or gold. The various layer / surface features that form the “neurons” of the diffractive layer that alter the reflective parameters / coefficients across the surface of the diffractive layers 20 may be fabricated in the one or more diffractive layers 20 using known additive manufacturing techniques (e.g., 3D printing) or photolithographic techniques used in the semiconductorPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2fields. For diffractive layers 20 that transmit electromagnetic radiation therethrough (FIG. 2B), the various features that alter the transmission parameters / coefficients across the diffractive layers 20 may be formed by adjusting the thickness of the substrate layer(s) that form the diffractive layers 20. These different thicknesses may define peaks and valleys in the substrate layer that act as the artificial “neurons.” The surface features may also be fabricated in the layer(s) of the diffractive layers 20, formed by altering the material composition or material properties of the layer(s) of the diffractive layer(s) 20 at different lateral locations across the layer(s). This may be accomplished by doping the diffractive layer(s) 20 with a dopant or incorporating other optical materials therein. Metamaterials or plasmonic structures may also be incorporated into the diffractive layer 20. The diffractive layer(s) 20 may also be reconfigurable in some embodiments, where the optical properties of the various artificial neurons may be changed, for example, by application of a stimulus (e.g., electrical current or field). An example includes spatial light modulators (SLMs), which can change their optical properties. In this embodiment, the neuronal structure is not fixed and can be dynamically changed or tuned as appropriate.

[0055] Referring to FIGS. 1-5, the system 2 includes one or more optical sensors 30 or detectors configured to capture one or more diffracted optical signal(s) 22 resulting from the reflection and diffraction off the one or more diffractive layers 20 in response to illumination with the light source(s) 10, wherein the optical signal(s) 22 include time-series information on oscillation of the structure 100. The one or more optical sensors 30 may include a plurality of optical sensors 30 as illustrated in FIGS. 1, 2A, 2B, 3-5. In some embodiments, this may include an array of optical sensors 30. As explained herein, for experimental results, a THz continuous wave scanning system is used, but the invention is not so limited. Optical sensors 30 may be used, for example, for NIR implementations.

[0056] In one embodiment, particular optical sensors 30 or detectors of the plurality may be associated with a particular frequency or frequency band of collected optical signals 22 that correspond to oscillation frequencies of the one or more diffractive layers 20. In this embodiment, there is no need for a further electronic decoder or digital neural network 40 as explained herein as the oscillation frequencies and / or amplitudes are directly captured by the optical sensors 30 (this is seen in the direct path output branch in FIG. 1). This information can then be, optionally, fed to a damage identification module 50 that takes this information and outputs inferred or suspected damage to the user. The damage identification module 50 may output inferred or suspect damage based on the amplitude and / or frequency informationPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2extracted directly, as noted above or using one or more electronic decoders / digital neural networks 40, discussed in more detail below. Empirical data stored or accessed by the damage identification module 50 may be compared with actual spectral data obtained with the system 2 that can be used to output inferred or suspect damage. This may include particular frequencies of interest or amplitudes at certain frequencies that exceed thresholds. The output from the damage identification module 50 may be in the form of a report or the like that can readily be used by field engineers to asses structure health.

[0057] In another embodiment, the signal outputs of the one or more optical sensors 30 is then fed to one or more trained digital neural networks 40 which measures the frequencies and amplitudes at each location. The one or more trained digital neural networks 40 is / are jointly trained with the training of the diffractive layers 20 during training. The trained one or more digital neural networks 40 may be used to output quantitative and / or qualitative information on the frequencies or harmonics associated with the movements of the one or more diffractive layers 20 (secured to structure 100) in one or more directions. The one or more trained digital neural networks 40 may be executed using a separate computing device 200 or one or more processors 202 as illustrated in FIG. 6B or through one or more processors 66 that are associated with the one or more optical sensors 30 as seen in FIG. 6A. As in the prior embodiment, this information can optionally then be fed to a damage identification module 50 that takes this information and outputs inferred or suspected damage to the user. The one or more trained digital neural networks 40 can also be integrated with the one or more optical sensors 30 as a sensing module 60.

[0058] FIG. 6A illustrates one example of a sensing module 60 that includes one or more optical sensors 30 (a plurality is illustrated) along with a power source 62 (e.g., a battery or AC power source) and microcontroller 64 or other circuitry that interfaces with the one or more optical sensors 30 and one or more processors 66 that, in this embodiment, are used to execute the one or more trained digital neural networks 40. On-board memory 68 may be provided in the sensing module 60 for executable code or other instructions for the one or more trained digital neural networks 40. The memory 68 may also be used for storing data regarding the quantitative and / or qualitative information on the frequencies or harmonics associated with the movements of the one or more diffractive layers 20. A communication chip or module 70 may be provided that provides for the transfer of data to and from the sensing module 60. For example, spectra data or a damage report acquired by the sensing module 60 may be communicated to a user via a wired or wireless connection. The damagePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2identification module 50 may be incorporated into the sensing module 60 in some embodiments. Alternatively, the damage identification module 50 may be executed by the separate computing device 200 as discussed below.

[0059] FIG. 6B illustrates another of a sensing module 60. In this embodiment, a separate computing device 200 is provided that communicates with the sensing module 60. In this embodiment, the one or more trained digital neural networks 40 (e.g., 40a, 40b) are executed by one or more processors 202 in the separate computing device 200. This separate computing device 200 may be co-located with the sensing module 60 or it may be remotely located from the sensing module 60 (e.g., a remote server or the like). Data obtained from the one or more optical sensors 30 are transferred off the sensing module 60 using a wired or wireless connection where they are processed by the one or more trained digital neural networks 40 in the separate computing device 200.

[0060] In some embodiments, a multi-wavelength system 2 is used (FIG. 4). In this embodiment, the light source(s) 10 is / are designed for multiplexed and high-throughput structural health monitoring with electronic neural network-based decoding. Each diffractive layer 20 is optimized using deep learning for a specific wavelength or wavelength range (e.g., NIR, THz bands), and can be attached at various locations on the structure(s) 100, exhibiting unique oscillation amplitudes and frequencies. A plurality of optical sensors 30 capture the reflected and diffracting light (i.e., optical signals 22) from the one or more diffractive layers 20 with a specific wavelength assigned to a particular diffractive layer 20. Different optical sensors 30 or detectors are used for the various wavelengths as seen in FIG. 4. The collected or captured optical signals 22 which capture the time series signals of these input wavelengths will be processed by a trained digital neural network 40 to measure the 3D oscillation amplitudes and frequencies experienced by the different diffractive layers 20, aiding the diagnosis of structural health of the structure(s) 100 using cost-effective, low-power and deep learning powered diffractive processors.

[0061] In one embodiment, the one or more trained digital neural network 40 includes two networks, namely, displacement decoder network 40a and a frequency processor network 40b. The displacement decoder network 40a extracts the measured signals into the structural displacements in different directions, while the frequency processor network 40b extracts the oscillation spectra in the target range from the extracted displacement in different directions. In one preferred embodiment, the displacement decoder network 40a is composed of three fully connected layers with ReLU (rectified linear unit) activation. For the frequencyPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2processor network 40b an initial FFT layer 42 converts the time-domain signal to the frequency domain, after which a single-layer perceptron (without activation) extracts the desired spectral band in different directions (x, y and z). For simultaneous multi-point vibration monitoring tasks, the architecture of the displacement decoder network 40a is expanded with additional layers to accommodate the increased dimensionality of the inverse problem. As explained herein, for example, for a system that has three diffractive layers 20 at three different layers, the displacement decoder network 40a used five fully connected hidden layers with dimensions of Nh= [256, 128, 64, 32, 16] with ND= 46.42k. The final output layer dimension was set to No= 6, allowing for the simultaneous prediction of the x and y displacements as a function of time for all three monitored locations on the structure 100.

[0062] FIG. 2B illustrates the structure of an embodiment that uses one or more diffractive layers 20 that are optically transmissive to the light. The one or more diffractive layers 20 have different physical features or regions thereon with different diffractive (transmissive) properties as a function of lateral coordinates across the diffractive layers 20. In this embodiment, electromagnetic radiation or light passes through the one or more diffractive layers 20 (multiple layers are illustrated in this embodiment). A minor 26 is disposed along an optical path of the one or more diffractive layers 20 and is configured to reflect electromagnetic radiation or light back through the one or more diffractive layers 20. This embodiment uses a double-pass configuration where light is reflected by mirror 26 through a transmissive diffractive layer 20 that still reflects electromagnetic radiation to the one or more optical sensors 30.

[0063] To use the system 2 to monitor the structural health of a structure 100 one or more light sources 10 are provided that generate input light 12 that is directed onto one or more diffractive layers 20 affixed to the structure(s) 100 to be monitored. The system 2 includes one or more optical sensors 30 configured to capture the one or more diffracted optical signal(s) 22 resulting from the reflection and diffraction of input light off (or through) the one or more diffractive layers 20, wherein the optical signal(s) 22 include time-series information on oscillation of the structure 100. The one or more diffractive layers 20 affixed to the structure 100 are illuminated with the input light 12 generated from the light source(s) 10 and one or more diffracted optical signal(s) 22 resulting from the reflection and diffraction of the input light 12 off the one or more diffractive layers 20 are captured with the one or more optical sensors 30. The captured optical signal(s) 22 include time-series information on the oscillation of the structure 100 with the one or more diffractive layers 20.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2

[0064] In one embodiment, the one or more optical sensors 30 are able to directly identify the oscillation frequences or the amplitudes in one or more dimensions without the need to a trained digital neural network 40. FIG. 1 illustrates this pathway (left after optical sensors 30). In this embodiment, a particular optical sensor 30 (or sub-group of optical sensors 30) within a plurality of optical sensors 30 may correspond to a particular oscillation frequency, range of frequencies, amplitudes, and / or amplitude ranges. In this regard, the optical sensors 30 may directly reveal oscillation amplitudes and frequencies of a structure 100.

[0065] In one embodiment, the intensity variations of the optical signal(s) captured by the one or more optical sensors 30 are then run through one or more trained digital neural networks 40. Specifically, the output of the one or more optical sensors 30 may include a digital signal or analog signal (e.g., varying voltage or current) that corresponds to the captured intensity at the particular optical sensor 30. In one embodiment, the one or more trained digital neural networks 40 are integrated with the one or more optical sensors 30 as a sensing module 60. Alternatively, the one or more trained digital neural networks 40 may be executed using a separate or remote computing device 200 or one or more processors 202. The output of the one or more optical sensors 30 may be communicated electrically or wirelessly to the trained digital neural networks 40. As explained herein, in one preferred embodiment, the one or more trained digital neural network 40 includes a displacement decoder network 40a and a frequency processor network 40b. The output of the one or more trained digital neural networks 40 includes quantitative and / or qualitative information on the frequencies or harmonics associated with the movements of the one or more diffractive layers 20 in one or more directions (e.g., x, y, z). In one embodiment, the one or more trained digital neural networks 40 outputs spectra corresponding to movement or displacement of the one or more diffractive layers 20 over a range of frequencies. For example, this may include x, y, and / or z axis displacement as a function of frequency (Hz). In some preferred embodiments, a target band of interest may be a frequency range that encompasses a key or fundamental mode of a structure 100.

[0066] In some embodiments, the system 2 may include a damage identification module 50, which is a system identification tool tailored to the type of data collected through the sensing module 60. The sensing module 60 can be customized to focus on a specific oscillation frequency, a range of frequencies, or multiple frequency bands tailored to the characteristics of a particular structure 100. The damage identification module 50 outputs inferred or suspected damage to the user. For example, a report may be generated thatPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2identifies or flags potential structural issues with the structure 100 that is being monitored. This may include highlighting various regions of the structure 100 that may warrant further inspection or analysis. These potential structural issues may be flagged when measured amplitudes of the measured oscillations exceed a pre-determined threshold or setpoint. Structural issues may also be flagged or identified based on measured frequencies. For instance, an extended period of oscillations within a particular frequence range or band may warrant further investigation of the structure 100 for issues such as fatigue or the like. These reports maybe generated electronically and forwarded to the appropriate recipients.

[0067] Experimental

[0068] Results

[0069] Diffractive systems for monitoring 3D structural vibrations

[0070] A diffractive system 2 capable of measuring and extracting 3D structural oscillations of a structure 100 was developed using an optimized reflective layer as the diffractive layer 20. The system 2 was configuration as depicted in FIG. 5. The input light 12 was incident at an oblique angle relative to the normal and propagates through free space onto the reflective diffractive layer 20 (shown in FIG. 7B). This reflective diffractive layer 20, affixed to the target structure 100 under test, consists of a 200x200 array of trainable, phase-only diffractive features, each approximately ~λ / 2 in lateral size, where λ is the illumination wavelength. Mechanically attached to the structure 100, this passive diffractive layer 20 follows the structure's displacements, modeled as a linear combination of various harmonics in x, y and z directions with randomly generated amplitudes and phases (see Methods for details). The diffractive optical signal 22 or reflected wave is spatio-temporally modulated by the optimized diffractive layer 20 and propagates to the output plane and is sampled by four optical sensors or detectors 30 which operated at 50 Hz. The detected diffractive optical signals 22 serve as an encoded input to a shallow displacement decoder network 40a that rapidly estimates the 3D structural displacement time series (see the Methods sub-section 'Network Structure for the Digital Backend' for architectural details). The detector array contains four single-pixel optical sensors or detectors 30 arranged uniformly, with a center-to-center spacing of 16Z (Fig. 2C). The detected time signals serve as an encoded input to a shallow displacement decoder network 40a that estimates the 3D structural displacement time series, i.e., x(t), y(t), and z(t) A subsequent frequency processor network 40b then analyzes the displacement data to extract the 3D oscillation spectra, covering a pre-determined range of 9 to 11 Hz (selected, without loss of generality, as thePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2target band of interest) in x, y and z directions (FIG. 7A). This selected spectral range aligns with the fundamental frequencies of the experimental structure 100. This selection is further justified by its applicability to civil infrastructure; specifically, for low-rise buildings, the fundamental mode (ty pically associated with the highest modal participation) often falls within this range, although the exact frequency may vary depending on the structure type. The ease of re-designing the diffractive layer 20 allows for practical adjustments to accommodate different configurations.

[0071] The diffractive layer's phase profile with a lateral pitch of ~λ / 2 and the digital parameters of the backend neural networks 40a, 40b were co-optimized through a joint training procedure (detailed in Methods) to maximize the accuracy of the 3D spectral reconstructions. A sequential, three-stage optimization strategy was employed: the diffractive layer 20 was first optimized to maximize signal energy and variation (Loss 1); then, the diffractive layer 20 and the displacement decoder 40a were jointly optimized (Loss 2); and finally, the entire system 2, including the frequency processor 40b, was trained end-to-end, to maximize spectral reconstruction accuracy (Loss 3). For quantitative comparison, additional optical elements were used as baseline designs to compare with the jointly optimized diffractive system 2. Specifically, an optimized diffractive layer 20, a Fresnel lens array and a random phase diffuser were evaluated separately (see Methods for details). In this comparison, the separately trained diffractive layer 20 had the same number of optimizable diffractive features, and its surface profile was optimized to efficiently communicate with and focus light onto the output detector array; see FIG. 8A. Importantly, the backend neural network 40 architecture, including the displacement decoder network 40a and the frequency processor network 40b, remained the same across all the configurations used in this comparison; in these cases, the backend networks 40a, 40b were trained separately for accurate reconstruction of the vibration spectra of the structure after the corresponding optical components were fixed.

[0072] The performance comparison of these different designs is shown in FIG. 8B, where the input spectra and the reconstructed spectra for each configuration are compared to each other. Performance was quantified using the Mean Squared Error (MSE) of the spectrum within the target frequency range, i.e., 9 Hz to 11 Hz. The performance of the 3D spectral inference for these four configurations is also reported in Table 1 as a function of the number of trainable parameters (AD) within the displacement decoder network 40a. The jointly optimized diffractive layer 20 consistently achieved the lowest MSE, with more than an orderPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2of magnitude improvement (spectral MSE values are reported in Table 1) over the other configurations across different model capacities. While some of the alternative configurations showed some predictive capability, they exhibit significantly higher spectral reconstruction errors, as reported in FIGS. 8B and 8C and Table 1, even with a larger number of trainable parameters in the digital backend 40. On the other hand, the diffractive vibration monitoring system, with the jointly optimized diffractive layer 20 and electronic decoders or digital neural networks 40, revealed a significantly better 3D spectral inference performance.Table 1Spectral MSE ND= 2.98k ND= 1.75k Nn= 0.85k Diffractive layer 1.109 x 10’21.400 x 10’21.654 x 10-2(jointly optimized)Diffractive layer 1.419 x 10’11.675 x 10’12.016 x 10-1(separately optimized)Fresnel lens array 3.576 x 10’13.834 x 10’14.264 x 10-1Random diffuser 6.243 x 10’16.545 x 10’16.760 x 10-1

[0073] The superior performance of the jointly trained SHM system 2 is further demonstrated through its blind testing performance in single-frequency extraction (in 3D), as detailed in the confusion matrices reported in FIG. 9A. In this analysis, various singlefrequency oscillations were applied to the structure 100 under test along one of the directions within the target spectral range. The diffractive system’s inference results, denoted as x. y and z, corresponding to these single frequency inputs are shown as columns in the confusion matrix (FIG. 9A). The presence of a clear diagonal in all the configurations of the jointly optimized diffractive layer 20 represents the accurate prediction of these single harmonic oscillations in all three directions (x, y, z) with minimal crosstalk between neighboring frequencies; on the other hand, significant spectral crosstalk or even complete failures (especially for oscillations in depth, i.e., the z direction) are observed in the alternative configurations as shown in the corresponding confusion matrices reported in FIG. 9A. Apart from these 3D analyses, similar results were obtained for 2D vibration analysis using diffractive layers 20 as reported in FIGS. 15A-15B and 16 and Table 2.Table 2Spectral MSE ND= 2.96k ND= 1.74k ND= 0.84k Diffractive layer 7.656 x 10-31.143 1.269(jointly optimized) x IO’2x IO’2Diffractive layer 6.507 x IO’27.702 9.195(separately optimized) x IO’2x IO’2PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2Fresnel lens array 2.826 x 10-24.179 4.864X IO’2x IO’2Random diffuser 7.134 x 10-17.218 7.507x 10’1x 10’1

[0074] Table 2: 2D spectral MSE results of different optical configurations, evaluated as a function of the number of trainable parameters (ND) of the displacement decoder network 40a.

[0075] While the joint optimization of the diffractive layer 20 and electronic decoders or digital neural networks 40 demonstrated significant performance advantages, as reported above, a common objective is to develop more compact models that require less computational resources, thereby enhancing deployment. This practical consideration motivates a deeper investigation into the relationship between the inference model complexity and performance. To better understand this relationship, the trade-off between the displacement decoding network 40a complexity (AD) and 3D spectral reconstruction performance was analyzed. For this analysis, the network's hidden layer dimensions were varied and examined the correlation between the total floating-point operations (FLOPs) and the resulting 3D spectral MSE. As shown in FIG. 9B, an increased model capacity with a larger NDgenerally leads to improved spectral inference accuracy, quantifying the performance trade-off between the spectral MSE and the computational cost; these observations are also in agreement with the results reported in Table 1.

[0076] To assess the resilience of the diffractive vibration monitoring system against imperfections, the impact of surface profile variations on the spectral reconstruction fidelity was numerically analyzed. These variations were modeled at the pixel level by introducing random height noise to the optimized design of the diffractive layer 20, simulating structural discrepancies that may arise from fabrication imperfections / errors or environmental factors. The height noise (δhtest) at each pixel of the diffractive layer 20 was independently applied following a uniform distribution with a maximum deviation of ±5 / zm, ±10gm and ±15 / zm. To mitigate the potential performance degradation caused by such deviations, a "vaccination" strategy was implemented during the joint optimization process, where a random height noise (δhtrain) ateach pixel of the diffractive layer 20 was dynamically injected into the diffractive layer model during the training phase to condition the system against physical surface irregularities. As illustrated in FIG. 17, the "vaccinated" models demonstrated statistically significantly better robustness compared to the standard models that were not vaccinatedPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2(with a p value <0.05 under the Welch’s t-test, reported in Table 3). While the spectral MSE of the standard design increased with the amplitude of 8htest, the diffractive system 2 that was vaccinated with δhtrain~[−10μm, 10μm] maintained ahigh accuracy, achieving a spectral MSE of 1.556 x 10“2even under a noise level of < Stest~[-15pm, 15pm], These results indicate that incorporating statistical imperfections into the co-design process might be used to safeguard the output performance against e.g., manufacturing constraints or potential environmental effects.Table 3P value δhtest~[−5μm, 5μm] δhtest~[−10μm, 10μm] δhtest~[−15μm, 15μm] δhtrain~[−5μm, 5μm] 4.584 x 10-113.901 x 10-151.565 x IO’5δhtrain~[−10μm, 10μm] 1.693 x 10’111.411 x 10-144.332 x IO’9δhtrain~[−15μm, 15μm] 5.286 x 10’89.583 x 10-131.045 x IO’2

[0077] Table 3: Statistical significance of the performance improvements achieved by the vaccination strategy. P-values calculated between the spectral MSE distributions of the baseline (unvaccinated) models and the models vaccinated with varying amplitudes of uniformly distributed training noise (8htrain). These statistical comparisons were conducted using 100 independent tests across different testing noise conditions (6htest). confirming that the performance differences observed between the unvaccinated baseline models and each of the vaccinated models are statistically significant, in favor of the vaccinated diffractive designs.

[0078] Beyond structural surface imperfections or height deviations, the sensitivity of the diffractive system 2 was investigated with respect to optical alignment errors, specifically variations in the incidence angle of the illumination beam. To quantify this effect, the spectral reconstruction performance was evaluated of a diffractive layer 20 optimized for a nominal incidence angle of θinc,train= 15° across a range of test angles (θinc,test). As shown in FIG.18A, the spectral MSE exhibits a minimum at the design angle (i.e., θinc,test= θinc,train) and increases as the misalignment grows with \θinc,test- 9inc train\ > 0. However, the system 2 demonstrates a functional degree of angular tolerance; as visualized in FIG. 18B, small misalignments (e.g., ±1° shift in illumination angle) result in negligible performance degradation with the reconstructed spectra closely matching the ground truth. While larger deviations (e.g., more than ±3°) lead to increased spectral distortions, this analysis indicates that the system retains its monitoring capability under minor alignment drifts.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2

[0079] The presented diffractive SHM system 2 comprises four primary components: the illumination or light source 10, the diffractive layer 20, the signal optical sensors or detectors 30, and the digital backend which includes the one or more electronic decoders / digital neural networks 40 (e.g., 40a and 40b). The illumination or light source 10, operating in either the terahertz or millimeter- wave band, utilizes an output power of -40-400 mW. For a standard measurement duration of 5 seconds, this results in a total energy consumption of 200 mJ to 2 J. The surface of the diffractive layer 20 functions as a completely passive encoder and consumes no energy during its operation on its own. The voltage-based optical sensor / detector 30 operates as a passive device converting optical signals into voltage; an associated readout circuitry would typically require 7.5 mJ-0.5 J per measurement cycle. The digital backend which includes the one or more electronic decoders / digital neural networks 40, capable of real-time spectrum reconstruction, requires approximately 72.5 MFLOPs per spectrum reconstruction. Assuming a hardware energy efficiency of 0.5-5.5 pJ / FLOP, the digital inference consumes -0.036-0.40 mJ per measurement. Consequently, the total energy consumption of the system 2 is dominated by the illumination or light source(s) 10, which can be improved with the use of more efficient sources. Furthermore, the computational latency for spectral reconstruction is -30 ms on an NVIDIA RTX4090 GPU processor 202, which is negligible compared to the signal acquisition time, indicating the system's capability for real-time monitoring.

[0080] Wavelength multiplexed diffractive systems for multi-point monitoring

[0081] To demonstrate the scalability of the system 2 for high-throughput assessment, a wavelength-multiplexed diffractive system 2 was developed that was designed to monitor structural vibrations at multiple points simultaneously. As illustrated in FIG. 10A, this multipoint configuration employs three coherent light sources 10 with distinct wavelengths= 0.70 mm, λ2= 0.75 mm, and λ3= 0.80 mm) incident through a common input aperture 14 at incidence angles (θinc) of 30°, 45° and 60° respectively. The incident waves co-propagate to illuminate three independent diffractive layers 20, each spatially positioned according to the corresponding incidence angle. These spatially distributed diffractive layers 20 modulate the incident wavefronts, including all the wavelengths and cross-talk terms, to encode the local 2D (x and y) structural displacements at their corresponding locations under test and reflect the optical signals toward a shared detector array with the optical sensors / detectors 30, positioned along the reflection path of the illumination waves. The optical sensors / detectors 30, characterized by a uniform spectral response across the illumination wavelengths, capturePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2the total aggregated energy from the three wavelength channels, generating multiplexed timeseries signals. These signals are subsequently processed by the one or more electronic decoders / digital neural networks 40, where the displacement decoder 40a and frequency processor 40b disentangle the mixed optical information to simultaneously reconstruct the independent vibration spectra for the three monitored points. The phase profiles of the three optimized diffractive layers 20 are depicted in FIG. 10B. The system's efficacy is further evidenced in FIG. 10C, which presents a comparison between the ground truth and the predicted spectra for the three distinct points that are under test; the close agreement observed in both x and y oscillation spectra confirms the capability of the jointly optimized system 2 to perform accurate, spectrally multiplexed monitoring of distributed locations on the structure 100.

[0082] To further characterize the information decoding capacity of this wavelength-multiplexed system 2, the relationship between the number of detectors (Ndt) and the spectral reconstruction fidelity was investigated. To effectively solve this inverse problem, the dimensionality of the measurements must meet or exceed the total degrees of freedom being monitored; specifically, the product of the number of monitored spatial points and the number of vibration axes per point. In the experimental setup, simultaneously monitoring 2D vibrations (x and y) across three distinct locations establishes 6 degrees of freedom.Therefore, the system's performance was evaluated using optical sensor / detector arrays with the number of optical sensors or detectors 30 set at Ndt= 4, 6 and 9 (illustrated in Table 4), while maintaining identical training strategies and digital backend architectures (model capacity) to ensure a controlled and fair comparison.Table 4Ndt= 4 Ndt= 6 Ndt= 9 Spectral MSE 1.446 X 10’15.301 x 10’43.555 x 10’4(g ± <r) ±4.646 x 10’2±7.244 x 10-4±2.772 x 10’4

[0083] Table 4: Spectral MSE results and the statistical significance of wavelength multiplexed multi-point monitoring performance improvement with increasing number of detectors (Ndt). The spectral MSE is calculated by 100 samples and reported with mean (ji) and standard deviation (<±).

[0084] As shown in FIG. 19A, the configuration with Ndt= 4 represents an underdetermined system; consequently, it failed to accurately disentangle the multiplexed spectral features, resulting in a relatively high spectral MSE of 1.446 X 10-1± 4.646 X 10-2(meanPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2± standard deviation). In contrast, when the number of optical sensors or detectors 30 was increased to meet or exceed the required degrees of freedom, i.e., Ndt> 6, the system 2 successfully recovered the vibration spectra. As demonstrated in FIGS. 19B-19C, the architectures with Ndt= 6 and Ndt= 9 achieved accurate spectral inference with significantly reduced MSE values of 5.276 X 10-4± 7.224 X 10-4and 3.555 x 10-4± 2.772 x 10-4, respectively. The statistical significance of this performance improvement as a function of Ndtis also reported in Table 4. These results confirm that accurate, simultaneous multi-point monitoring is achievable provided that the detector count is scaled to accommodate the dimensionality of the target structural dynamics.

[0085] To better quantify the advantages of spectral diversity in high-throughput multipoint monitoring, the performance of the wavelength-multiplexed system 2 was compared against a baseline monochrome configuration (shown in FIG. 20 A) where all three diffractive layers 20 were illuminated by the same wavelength, also through a common input aperture 14 at incidence angles (0inc) of 30°, 45° and 60° - same as before. Stated differently, in this baseline comparison, illumination angle diversity for multi-point monitoring was kept while the wavelength multiplexing was dropped out to better quantify its impact on the output performance. As illustrated in FIGS. 20A-20C, despite using an identical detector array geometry (Ndt= 9), the monochrome system (FIG. 20B) exhibited increased deviations (spectral MSE 7.175 x 10“4± 4.368 x 10-4) from the ground truth multi-point spectra. Conversely, the wavelength-multiplexed system (FIG. 20C) achieved a statistically significantly better reconstruction fidelity' (spectral MSE 3.555 x 10-4± 2.772 x 10-4, with a p value of 2.196 × 10-10) compared to the monochrome setup. This quantitative comparison highlights that spectral diversity serves as a powerful encoding dimension, allowing the digital backend which includes the one or more electronic decoders / digital neural networks 40 to effectively disentangle mixed vibration signals from shared optical sensors or detectors 30 and enabling accurate parallel monitoring of multiple target points on a structure 100, significantly outperforming monochrome spatial multiplexing.

[0086] Experimental demonstration of diffractive vibration monitoring

[0087] The system 2 was used to monitor vibrations in a model structure 100 using 3D-printed diffractive layers 20 and millimeter wave illumination as the light source 10. An initial experimental setup, depicted in FIG. 11 A, was designed to monitor the 1D (x-axis) oscillations of a test structure 100, which was a four-level building model with its base floor mounted on a programmable shake table for controlled perturbations. This experimentalPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2validation is not only a performance check but also a demonstration of how physical encoding combined with minimal-data processing can operate in noisy, non-ideal conditions, a key benchmark for deployment in uncontrolled environments. To suppress displacements in the z-direction and concentrate motion primarily along the x-axis, metal wires were used to constrain the model 100 along the z-axis, effectively increasing its stiffness in that direction. Ground truth displacement data for the test structure were simultaneously acquired using laser rangefinders. The core of the diffractive vibration monitoring system involved an optimized, 3D-printed diffractive layer 20, which was affixed to the first level of the building model 100 (FIG. 11 A). A coherent light source 10 at λ = 3 mm illuminated the structure 100, and the reflected waves or diffracted optical signals 22 were spatio-temporally modulated by the displacements of the passive diffractive layer 20 on the structure 100; these reflected signals 22 were captured by two (single-pixel) optical sensors or detectors 30 (see Methods section). During these measurements, various excitation methods were used to induce different structural vibrations (shown in FIG. 11B), including applying a white noise signal to the shake table, programmed shaking profiles of the base floor, and manual perturbations to the base, first and upper levels. Furthermore, to simulate variations in the building structure, a mass block was systematically placed and fixed at different levels, altering both the mass distribution and the dynamic response of the system, thereby changing its natural frequency.

[0088] The temporal signals captured by the two detectors 30 were decoded by a trained digital backend 40a, 40b, which predicted the frequency spectra of the structure's vibrations within a predefined spectral range of interest. FIG. 12 and FIG. 21 compare the ground truth spectra (measured by a laser rangefinder) and the spectra extracted by the diffractive system 2 for various structures with different mass placements and perturbations. The accurate predictions of both the vibration frequencies and their corresponding amplitudes in these experimental results confirm the feasibility and effectiveness of the diffractive system 2 for monitoring structural dynamics. The inference performance of the optimized diffractive layer 20 was compared to that of a reflective flat mirror, as depicted in FIG. 22. In this comparison, both sets of the digital backend neural networks 40a, 40b were trained / optimized using an identical number of measurements with the same network architecture (i.e., with the same number of trainable parameters) to provide a fair comparison. The configuration with the optimized diffractive layer 20 yielded a significant improvement in its spectral MSE results over the results achieved with a flat mirror, which stems from the optimized diffractivePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2layer's ability to interact more effectively with the output detectors 30. Compared to a flat mirror or another reflective optical element, an optimized diffractive layer 20 enhances the standard deviation of the detected signals under various structural vibrations. This results in an enhanced 3D oscillation encoding capability through the diffractive layer 20 since a higher standard deviation in the detected signals means that different oscillation spectra produce more distinguishable intensity distributions across the output detectors 30. making it easier for the jointly optimized digital decoder 40 to learn the mapping required for accurate spectral reconstructions.

[0089] To further improve the spectral inference accuracy of this approach, a postprocessing method was developed based on temporal averaging, outlined in FIG. 13 A. This strategy employs a sliding window of constant duration across each detector's temporal signal stream to generate multiple (potentially overlapping) time-series segments. The range of the sliding windows is defined by the temporal averaging time At, representing the total temporal span across which the centers of the sliding windows are distributed for the averaging calculation. Each segment serves as an individual input to the trained electronic decoder / digital neural network 40, which extracts the oscillation spectrum associated with that time window. The final spectral output is then computed by averaging the ensemble of vibration spectra extracted from all of the time segments. The inherent trade-off between spectral MSE and the cumulative FLOPs is depicted in FIG. 13B; averaging over a greater number of temporal windows improved the spectral inference accuracy (lowering the spectral MSE) while also increasing the required computational time. FIG. 13C provides a comparison of the extracted spectra for different Atvalues, illustrating the impact of this approach on the quality of the spectral reconstructions.

[0090] The diffractive processor-based vibration monitoring system 2 was further investigated by measuring 2D (x and z) oscillations of the same building model 100 (see FIG.14A). For these experiments, the restraining wires that were previously used to prevent motion along the z-axis were loosened to allow for 2D displacements of the test structure 100. Laser rangefinders were installed on adjacent sides of the first level (shown in FIG. 14B) to provide reference (ground truth) measurements of 2D displacements. Another optimized diffractive layer 20 (shown in FIG. 14A), mounted on the same level of the structure 100, was used to spatio-temporally modulate the incident wave in accordance with the structure's 2D vibrations. The test structure 100 was subjected to 2D oscillations using a programmable shake table that reproduced seismic waveforms in the x-direction from the NGA-West2PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2earthquake dataset, applied at both full scale and O.lx scale while the perturbations of the z-axis were introduced by pushing manually (details in Methods). To rigorously evaluate the system's generalization capabilities, data was collected from twenty independent earthquake records and partitioned the dataset into non-overlapping training (80%) and testing (20%) subsets. Consequently, the results presented here are derived exclusively from the testing subset, representing out-of-distribution (OOD) performance on unique seismic signals corresponding to new earthquakes that were not seen during the training of the digital backend. The diffractive processor-based system 2 simultaneously extracted the spectra of the building's displacements in both x and z directions from the two detector 30 signals.Examples of spectral inference results for x- and z-directions are visualized in FIG. 14C, along with the corresponding ground truth measurements. The performance advantages of the optimized diffractive layer 20 compared to the 2D inference results obtained with a flat mirror are also illustrated in FIG. 14D, supporting the same conclusions as in the earlier experiments reported in FIG. 22.

[0091] The performance advantages observed through the joint optimization of the diffractive layer 20 and the electronic decoder(s) / digital neural networks 40 (e.g., 40a and 40b) extends beyond mere accuracy improvements; it represents a new approach to how sensing systems can be designed. By co-designing the passive optical encoder material with the subsequent shallow neural network decoder 40, the system implicitly learns to transform complex, multi-dimensional structural oscillation information into highly distilled, yet robustly decodable, optical signals that can be captured by a minimal number of detectors 30. This optical pre-processing effectively offloads significant computational burden from the digital domain to the physical diffractive layer 20, enabling the use of shallow and low-power neural networks 40a, 40b for rapid and accurate spectral reconstruction, a capability unattainable with traditional sensing architectures that would require far more detectors and extensive post-processing for comparable performance. This fundamental principle of learned physical-digital compression holds transformative potential for numerous sensing applications where data efficiency, low power, and remote operation are critical constraints, such as in autonomous navigation and distributed environmental sensing. The synergy between the optimized physical-layer encoding and the efficient neural network decoding signifies a move towards “intelligent sensing at the source,” where essential information is extracted and compacted through light-matter interactions before traditional digital processing takes over. This minimizes data and computational overhead, addressing a criticalPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2bottleneck in ubiquitous, high-density sensor deployments and laying the groundwork for truly distributed, low-latency monitoring networks.

[0092] A hybrid system 2 for monitoring vibrations of a structure 100 is disclosed that integrates, a jointly optimized diffractive layer 20 with a shallow, trained digital neural network 40 backend for rapidly extracting structural vibration frequency spectra. The effectiveness of this hybrid system 2 was demonstrated through both numerical simulations and experiments using millimeter- wave illumination as the light source 10. Major performance improvements were observed through the joint optimization of the diffractive layer 20 and the backend neural networks 40a, 40b; this jointly-optimized system 2 not only significantly outperformed other optical configurations with non-trainable optical elements such as flat mirrors, Fresnel lens arrays, or random diffusers, but also showed major performance improvements compared to separately optimized diffractive layers 20. These observations can be attributed to the jointly optimized diffractive layer's ability to effectively encode 3D structural vibrations into the optical wavefront, enhancing signal variations at the output optical sensors or detectors 30 and creating more distinguishable spatio-temporal patterns in response to various structural perturbations, helping the decoder backend to reveal the 3D oscillation spectra accurately.

[0093] The use of trainable diffractive optics (i.e., diffractive layer(s) 20) as a front-end signal encoder, paired with a jointly trained neural network decoder 40, introduces a new strategy for compact, low-data-rate sensors that can operate without dense sampling or extensive storage. SHM methods are commonly categorized based on their measurement approach, including vibration-based, static or quasi-static, acoustic or ultrasonic, and optical or imaging-based techniques. The system 2 falls under the optical sensing category but introduces a fundamentally different mechanism for vibration acquisition and interpretation. Traditional optical systems, such as laser vibrometry, offer high accuracy but are limited by alignment requirements, line-of-sight access, and power consumption. Vibration-based and static networks provide reliable local data but require dense deployment and wiring, increasing installation and maintenance costs. Vision-based systems can capture distributed motion fields, but are sensitive to lighting and computationally intensive. In contrast, the diffractive system 2 disclosed herein uses a spatially optimized passive layer 20 that encodes 3D vibrations into modulated light, rapidly and efficiently decoded in real time by a shallow and low-power neural network 40. While substantially improving scalability,, energy efficiency, robustness and multiplexing capabilities, it maintains comparable accuracy andPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2frequency resolution. Consequently, the system 2 unifies the strengths of high-performance optical sensing and scalable vibration-based monitoring, advancing SHM toward a more energy-efficient and data-efficient paradigm. The significance of this system 2 extends beyond potential performance gains in SHM. Its hybrid design paradigm may inspire new classes of passive sensors in disciplines such as aerospace engineering and robotics, where power and size constraints preclude conventional sensing architectures.

[0094] While diffractive neural networks have shown promise in computational imaging and classification of static objects, their application to sensing dynamic physical systems remains nascent. This work moves beyond static inference tasks by demonstrating a system that leverages a passive diffractive encoder, co-optimized with a temporal decoder, to extract complex, time-varying 3D spectral information from a moving object. Unlike standard end-to-end optimization approaches, this is achieved through a hierarchical training scheme that first maximizes physical signal contrast before jointly optimizing for temporal displacement decoding. Therefore, another conceptual advancement is the joint physical-digital optimization strategy that simultaneously encodes multi-point 3D structural dynamics, a problem space with unique challenges, such as continuous-time signals from multi-axis and multi-point displacements, into a low-data-rate optical stream.

[0095] Another critical advantage of the system 2 is its inherent generalizability, which eliminates the need for structure-specific retraining or hardware re-fabrication. This scalability arises from the system's hierarchical architecture, which decouples motion sensing from structural diagnostics; the diffractive layer 20 and the electronic decoder / digital neural network 40 are jointly optimized to map optical signals directly into quantitative 3D displacement time series; a physical mapping independent of structural identity. By utilizing a training curriculum based on randomized harmonic oscillations rather than specific building dynamics, the system 2 functions as a general-purpose motion sensor capable of extracting vibration spectra from diverse structures 100 without modifications of its architecture.

[0096] Beyond demonstrating the core functionality of diffractive vibration monitoring systems 2, practical trade-offs influencing the system's performance and computational demands were examined. The relationship between the complexity of the digital backend network 40 and spectral reconstruction accuracy was examined by varying the hidden layer dimensions of the displacement decoding network 40. As illustrated in FIG. 9B, employing decoder networks 40 with more trainable parameters, corresponding to higher numbers of FLOPs, generally leads to reduced 3D spectral MSE. Additionally, a temporal averaging-PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2based post-processing strategy was experimentally validated, which leverages multiple time segments from the sensor stream to enhance the final spectral reconstruction fidelity significantly. These findings provide valuable insights for tailoring the diffractive system's configuration to specific application requirements, balancing accuracy, latency, and available computational power. A key aspect of the temporal averaging-based post-processing method is its departure from traditional linear operations, such as those employed in standard periodograms. This technique utilizes a non-linear neural network-based displacement decoder 40a, which interacts differently with the diverse features present in individual segments of the time-sequence detector data. This processing through the network's architecture underpins a complex N-to-N non-linear mapping from the raw temporal segments to their respective spectral estimates. Such temporally shifted successive non-linear mappings offer distinct advantages, particularly in the capacity to more effectively mitigate noise and handle unexpected or out-of-distribution data points that may be present in the measured time signals.

[0097] While experimental validation at millimeter-wave frequencies on a laboratoryscale model of a structure 100 demonstrates the foundational principles and remarkable efficacy of this diffractive vibration monitoring system 2, the path toward widespread real-world deployment also presents unique challenges and opportunities that warrant careful consideration. Translating the millimeter-wave results to optical or infrared wavelengths for civil infrastructure applications will necessitate the development of large-area, robust diffractive layers 20 with feature sizes on the order of hundreds of nanometers, resilient to environmental factors such as temperature fluctuations, humidity, and structural deformation over long periods. Furthermore, ensuring the long-term stability and calibration of both the diffractive layer 20 and the remote illumination / detection system in dynamic outdoor environments will be crucial for maintaining the high accuracy demonstrated in controlled settings. The development of self-calibrating mechanisms or adaptive learning algorithms to compensate for environmental drift and material degradation will be important steps toward robust field implementations.

[0098] A significant future direction in diffractive SHM systems involves scaling this technology for higher throughput assessment of structures by monitoring numerous locations simultaneously. Extending the current approach for this goal could involve spatial multiplexing, where multiple co-designed monochrome diffractive vibration diffractive layers 20 monitor different points on a structure 100, potentially feeding data into a unified backendPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2neural network 40. An even more advanced concept involves spectral-spatial multiplexing, assigning distinct wavelengths to different monitored locations of a structure 100, each potentially utilizing a specifically tuned diffractive layer 20 and detector array, allowing for potentially higher density of structures to be monitored in parallel and processed by a common backend decoder 40.

[0099] The exploration of shorter operational wavelengths, particularly within the visible and IR spectra, presents a compelling avenue for enhancing the accuracy and resolution of diffractive SHM systems due to the scalability of diffractive optical processors with respect to the wavelength of illumination. While the presented work experimentally validated the diffractive SHM systems using millimeter waves, the underlying principles of diffractive layer design allow for scalability across different parts of the electromagnetic spectrum by adjusting the dimensions of the diffractive features proportional to the illumination wavelength. Transitioning the illumination wavelengths to the visible or infrared spectrum would require the fabrication of diffractive elements with significantly smaller lateral feature sizes. This refinement in feature resolution, achievable with advanced 3D manufacturing techniques such as two-photon polymerization and optical lithography that provide submicron fabrication precision, offers the potential for more precise wavefront modulation. Furthermore, to ensure robustness against inevitable fabrication tolerances at these reduced feature sizes, a 'vaccination' strategy (detailed in the Results section) can be employed. By explicitly incorporating various forms of noise, distortions or imperfections into the training schedule, the diffractive layers can be optimized to remain resilient to manufacturing imperfections. The capability to produce such fine structures is critical for operating effectively at shorter wavelengths and could lead to substantial improvements in the sensitivity and overall accuracy of diffractive SHM systems. These advances could pave the way for a new generation of high-accuracy, compact, multiplexed and more cost-effective SHM solutions.

[0100] Given its foundation in diffractive optics and neural computation, the disclosed system 2 is inherently adaptable to other spectral bands, functional targets, and time-varying environments. The potential to extend this approach into the visible or near-infrared regime, enabled by nano-scale fabrication, would enable ultra-compact sensors for environmental monitoring or industrial robotics. The physical encoding strategies described here will find broader applications across science and engineering, enabling systems where sensing andPCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2computation are not considered separately, but co-optimized within the same physical substrate.

[0101] Methods

[0102] Numerical Forward Model

[0103] In the design of a diffractive vibration monitoring system 2, the optical forward model can be depicted by two successive operations: (i) shifted free-space propagation of the optical field, and (ii) wave modulation by the reflective diffractive layer. The shifted free space propagation for an axial distance d and lateral shifting distance x0, y0of the complex field u(x, y), was calculated using the shifted angular spectrum approach, and can be written as:Px0.y0.d<x,y) = ^-1{^{u(%,y)J H'(fx, fy; x0,y0, d)} (1)

[0104] where PX(),y(),d represents the free-space propagation operator for a lateral shift of (%0, y0) and an axial distance of d. T and T-1are the two-dimensional Fourier transform and the inverse Fourier transform operators, respectively. H'(jx, fy; x0, y0, d is the transfer function of free space, defined as:Jfy - fy.o H'{fx,fy; x0ly0, d) = H(fx, fy; x0,y0, direct M - — re ct I — j (2)\ J x, width \ J y, width(exp {j’27r(d I A2- fx2- f2+ xofx+ yQfy}, H(fx,fy; x0,y0, d) =I

[0105] where k = — and A is the wavelength of the light. fxand fyare the spatialfrequencies along the x and y directions, respectively, rect(-) is the unit rectangular function that is used as a bandpass filter to avoid aliasing errors. The central frequency / |X.yj,0and bandpass width f{x,y},wi thcanbe calculated by:I ) [x,y], limit J [x,y], limit (2A / {x,y})1< {x,y}Q( limit limit -(2A / {x,y})1< {x,y}0< (2Z\ / {x,y})1(4) I 2 ’ I f(+)limit +Jf ((x-,y)), limit {x, y}0< — (2A / ,x y!)1v 2PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2(A+) _f(-) I ’ (x,y\, limit’ < {%, y}o f{x,y], width—{x,y), limit ' J {x,y}, limit’ -(Wfcy})’1< {x,y}0< (2A / fcy})“1(5) / ■(“) _ r(+) Mo < -(2A / '{x,y}, limit J {x,y}, limit’{xy})-1

[0106] where A / (XJ / j is the sampling frequency in the {x, y} axis, and the limit spatial frequency values are calculated by:f(±) ■'{x.y}, limit (6)

[0107] The optimizable diffractive layer is modeled as a reflective diffractive optical element that modulates the phase of the incident wavefront. The reflectance coefficient r(x,y) of the diffractive layer can be written as:r(x,y) = exp(j< / >(%, y)} (7)

[0108] where <^(x, y) is the phase modulation function of the trainable diffractive layer. The reflectance coefficient of the shifted diffractive layer can be calculated as:rshifted{x,y,xd:0,yd:0) = exp (j4>(x - xdfi,y - yd Q]) = T-1^{e%p(j< / >(%,y))} x exp (-]2n{fxxdfi+ / yyd,0))}(8)

[0109] where xd 0,yd Qrepresent the lateral displacement of the diffractive layer.

[0110] The forward model for multi-point vibration monitoring (see FIGS. 10A-10C and FIGS. 19A-19C and 20A-20C) was extended to simulate the simultaneous illumination of the spatially distributed diffractive layers 20 by multiple incident wavefronts. In both the wavelength-multiplexed and monochrome illumination-based multi-point monitoring, the model explicitly accounted for optical crosstalk by calculating the interaction of each incident wave with the complete array of diffractive layers 20, rather than treating each diffractive layer 20 in isolation. For the wavelength-multiplexed configuration, coherence was maintained within each wavelength channel; the complex optical fields reflected from all the diffractive layers 20 under a single illumination wavelength ( were first coherently added to determine the field distribution for that channel; the total intensity at the detector plane was then computed as the linear sum of the intensities resulting from the distinct wavelength channels. For the single-wavelength (monochrome) configuration, where all the incident waves share the same wavelength, the system 2 was modeled as a fully coherent architecture.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2In this case, the complex fields resulting from all the illumination angles and diffractive layer 20 interactions were summed prior to the final intensity calculation, thereby incorporating the interference effects arising among all the reflected and propagating wavefronts.

[0111] The Fresnel lens array was generated by stitching four Fresnel lens phase patterns, each aligned such that the center of the corresponding sensor coincided with the focus point. The Fresnel lens phase pattern was calculated by:27T 0 Fresnel = “ y (7 / 2+ *2+ T2“ / ) (9)

[0112] where f is the focal length of the Fresnel lens.

[0113] Network Structure for the Digital Backend

[0114] The digital backend electronic decoder / digital neural network 40 used in spectral reconstructions is composed of a displacement decoder network 40a and a frequency processor network 40b. The displacement decoder network 40a extracts the measured signals into the structural displacements in different directions, while the frequency processor network 40b extracts the oscillation spectra in the target range from the extracted displacement in different directions. The displacement decoder network 40a was composed of three fully connected layers with ReLU (rectified linear unit) activation. The parameter NDdenotes the number of trainable parameters of the displacement decoder network 40a, e.g. ND= 2.98k for the network used for 3D spectral reconstructions with the input dimension JVdt= 4, the hidden layer dimension Nh- [64, 32, 16] and the output dimension No- 3. For the frequency processor network 40b, NFdenotes the number of trainable parameters, and an initial FFT layer converts the time-domain signal to the frequency domain, after which a single-layer perceptron (without activation) extracts the desired spectral band in different directions (x, y and z). FIG. 23 illustrates both the displacement decoder network 40a and a frequency processor network 40b. The input to the displacement decoder network 40a is the measured signals from the optical sensors or detectors 30 which may include a voltage signal. This voltage signal may be resampled as explained herein or it may be raw voltage signal. The three fully connected (FC) layers with ReLU (rectified linear unit) activation are illustrated that output structural displacement. Multiple structural displacement records over time (in the time domain) are then input to the frequency processor network 40b. The FFT layer converts the time-domain signal to the frequency domain followed by the single-layer perception extracts the desired spectral band in the different directions, namely, the x, y, and z directions.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2

[0115] For the simultaneous multi-point vibration monitoring tasks, the architecture of the displacement decoder network 40a was expanded to accommodate the increased dimensionality of the inverse problem. This multi-point network comprised five fully connected hidden layers with dimensions of Nh= [256, 128, 64, 32, 16] with ND= 46.42k. To investigate the relationship between the measurement sparsity and the decoding performance, the input dimension of the network was varied based on the number of detectors used in the array, specifically evaluating configurations with NdtE {4, 6, 9}. The final output layer dimension was set to No= 6, allowing for the simultaneous prediction of the x and y displacements as a function of time for all three monitored locations on the structure of interest.

[0116] Training Data Preparation

[0117] The displacements along the axes were synthesized by a linear combination of harmonic oscillations in the target frequency window. The amplitudes of the harmonic oscillations were randomly generated with an amplitude upper bound of Amax] (10)

[0118] where Amaxwas set as -1.5A while the phase values of the harmonic oscillations(l){x,y,z},jwererandomly generated between 0 and 2TT. The displacement of the diffractive layer at time stamp t was calculated using:MA{x, y, z}t — A^x y zjj S\n(j2nfjt + (t>{x,y,z],j') (11)7=1

[0119] where M represents the total number of discrete frequencies considered, fj denotes the j-th frequency component, selected from the discrete set {8.0, 8.2,..., 11.8, 12.0} Hz.

[0120] Training Scheme and Loss Function

[0121] The whole model, including the diffractive layer 20, displacement decoder network 40a and frequency processor network 40b, was trained for 200 epochs. In the first 10 epochs, only the diffractive layer 20 was optimized with the following loss function:

[0122] where K is the number of time sampling points, D is the number of detectors 30, S E RDXKwhere the element in the i-th row and t-th column is denoted as si t, representing the ithdetector reading value at the sampling time t, normalized by the total energy of thePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2input wave. Ip is a 1 xD matrix (a row vector) with all entries equal to 1. stri(-) is the standard deviation function, which is used to maximize the intensity variations on the detectors 30 when the structure 100 under test is oscillating in the target range of frequencies. a4and a2are hyperparameters, which are both empirically set as 1.

[0123] Between the 11thepoch and the 100thepoch, the diffractive layer 20 and displacement decoder network 40a were jointly optimized using the following loss function:loss2— loss4+ a3MSE (DispNet S), {Axt, Ayt, Azt}) (13)

[0124] where DispNet ) is the displacement decoder network 40a predicting the displacement at different directions (x, y and z), MSE ) is the mean square error function, Ext, ytand Aztare the ground truth displacement vectors for x, y and z, respectively. cr3is a hyperparameter empirically set as 0.1.

[0125] During the 101stepoch to the 200thepoch, the diffractive layer 20, displacement decoder network 40a and the frequency processor network 40b were jointly trained using the following loss function:loss3— loss2+ a4MSE(FreqNet(j)ispNet(jty, riy,riz]) (14)

[0126] where Freq Net (■) is the frequency processor network 40b that transforms the extracted temporal displacement into the frequency domain within the pre-determined spectral range of interest, and Ax, Ayand Azare the ground truth oscillation amplitudes in the frequency domain along the x, y and z directions, respectively. a4is a hyperparameter that is empirically set as 1.

[0127] In comparative analyses, the separately optimized diffractive layer 20 was first trained over 10 epochs with the same strategy as the training of the jointly trained diffractive system 2, using the same loss function as described in Eq. 12. Starting from the 11thepoch, the digital backends 40a, 40b for the separately optimized diffractive layers were trained for 190 epochs (i.e., for the same number of epochs used in the training of the digital backends of the jointly trained configuration). Until the 100thepoch, the displacement decoder network 40a was trained using the following loss function:loss4— a3MSE(DispNet(S'), {A%t, Ayt, Azt}) (15)

[0128] while for the remaining epochs, the displacement decoder network 40a and frequency processor network 40b were jointly optimized with the following loss function:loss5= loss4+ a4M SE (FreqN et( )ispN t(S ), [Ax, Ay, riz]) (16)PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2

[0129] A similar strategy was also applied for the optimization of the digital backends for the Fresnel lens array and random diffusors used for comparison to the jointly optimized diffractive vibration monitoring system.

[0130] Experimental Design and Testing

[0131] The feasibility of the diffractive vibration monitoring system 2 was experimentally validated by deploying 3D-printed diffractive layers 20 (Stratasys, Objet30 Pro) at the first level of a four-level structure 100 mounted on a programmable shake table. Millimeter wave illumination was used as the light source 10 at λ = 3 mm, generated by a tunable wave source 10 (MI-WAVE, 840WF-10) with an antenna (MI-WAVE, 261W-15) was incident to the reflective diffractive layer at 30° to the normal direction of the diffractive layer 20. The axial distance between the emitting antenna and the reflective diffractive layer 20 was -0.18 m. The reflected wave or diffractive optical signal 22 was captured by two nun-wave sensors 30 (MI-WAVE, 950W) and measured by an oscilloscope that recorded the voltage response. The center of the detectors 30 was separated by a distance of 34 mm. Laser rangefinders (Banner Engineering, LE550DQ, sampling rate 256 Hz) were positioned at the height of each floor of the structure 100 and directed toward the corresponding level of the structure to measure its dynamic displacement. These measurements were used as ground truth displacements for each level. For the ID vibration experiments, the structure 100 was excited by various types of perturbations, including white noise, manual push and pull on the base level as well as the 1stand the upper levels. For the 2D experiments, the shake table was programmed to deliver seismic excitation, simulating the structural displacements induced by, e.g., earthquakes. These programmed displacements input to the shake table included white noise, synthetic chirp signals and earthquake data from NGA-West2 with the original intensity and 0.1X scaled down versions.

[0132] The measured voltage signal and displacement were resampled to 50 Hz and synchronized to eliminate the difference in the measurement starting point. The measured voltage signal was first processed by an optimized ID U-Net, which served as the displacement decoder network 40a, DispNet, in the experiments. The down-sampling path of the ID U-Net used a series of convolution layers and max pooling to reduce temporal dimensions while increasing depth with feature channels of 16, 32 and 64. After the bottleneck layer of the ID U-Net structure, the up-sampling path employed transposed convolutions, skip connections from the encoder to recover temporal details, and applied convolutional layers to refine the temporal features. The final 1x1 convolution maps thePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2resulting features to the desired output channels (ID and 2D displacement predictions).FreqNet 40b remained the same as before.

[0133] Experimental data for the ID spectral measurements were generated by systematically applying six distinct perturbation types across three structural configurations (shown in FIG. 11B). Five independent measurements were acquired for each of these eighteen resulting experimental conditions. For the digital backend optimization, the acquired data were partitioned into non-overlapping training and testing subsets. The training set consisted of 80% of the measurements, while the remaining 20% was reserved for blind testing. The digital backend networks, DispNet 40a and FreqNet 40b, were trained jointly by minimizing an experimental loss function, Lossexp. defined as:lossexp= a5MSE(jN'eqNet( )ispNet(j, {Ax, Az})+ a6MSE log ^Freq et(DispN et(S)^, log({ / lx, Az})+a7MSE(DispNet(S), (17)

[0134] which included the linear and log-scale MSE of the vibration spectral inference of FreqNet as well as the MSE of the displacement inference of DispNet. a5, a6and a7are hyperparameters, which were empirically set as 1, 2 and 1, respectively.

[0135] Similarly, for the 2D spectral measurements, a push on the 4thlevel was first applied before the programmable shake table started to follow the seismic data. The whole dataset was 80%-20% separated into two sets (training and testing datasets) for the training of DispNet 40a and FreqNet 40b, which followed the same procedures and hyperparameters as the ID case reported above.

[0136] While embodiments of the present invention have been shown and described, various modifications may be made without departing from the scope of the present invention. The invention, therefore, should not be limited, except to the following claims, and their equivalents.

Claims

PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2What is claimed is:

1. A system for monitoring the structural health of a structure comprising: one or more light sources generating input light;one or more diffractive layers affixed to the structure, the one or more diffractive layers each comprising a diffractive surface or layer that includes different physical features or regions on the surface or layer thereof having different reflective properties across the diffractive layer; andone or more optical sensors configured to capture one or more diffracted optical signal(s) resulting from reflection and the diffraction of the input light off the one or more diffractive layers in response to illumination with the input light, wherein the optical signal(s) comprise time-series information on oscillation of the structure.

2. The system of claim 1, wherein the one or more diffractive layers comprise a plurality of diffractive layers affixed to different parts of the structure and wherein the input light is configured to illuminate the plurality of diffractive layers.

3. The system of claim 1, wherein the one or more light sources generate the input light at a wavelength, a plurality of wavelengths or wavelength ranges and wherein the one or more optical sensors comprise a plurality of optical sensors configured to detect the input light diffracted by the one or more diffractive layers at the input wavelength, plurality of wavelengths or wavelength ranges.

4. The system of claim 1, wherein the one or more light sources comprise monochromatic or quasi-monochromatic light sources and wherein the one or more optical sensors comprise a plurality of optical sensors configured to detect the input light diffracted by the one or more diffractive layers.

5. The system of claim 1, wherein the one or more light sources comprise one or more of: laser diodes, light emitting diodes (LEDs), solid state lasers, gas lasers, liquid lasers, or tunable lasers.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-26. The system of claim 1, wherein the input light is spatially coherent, partially coherent, or spatially incoherent.

7. The system of claim 1, wherein the different physical features or regions on the surface or layer of the one or more diffractive layers are fabricated in accordance with a trained digital model.

8. The system of claim 1, further comprising an electronic decoder or digital neural network that is connected or coupled to the one or more optical sensors and configured to output quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more diffractive layers in one or more directions.

9. The system of claim 1, wherein the one or more diffractive layers have respective surface areas that are between 0.1 mm2and 1000 cm2.

10. The system of claim 8, further comprising a damage identification module configured to generate an output that reflects inferred damage or suspected damage of the structure.

11. A system for monitoring the structural health of a structure comprising: one or more light sources generating an input light;one or more transmissive diffractive layers affixed to the structure, the one or more transmissive diffractive layers comprising one or more diffractive surfaces or layers that are optically transmissive to the input light, the one or more transmissive diffractive layers having different physical features or regions on the surface(s) or layer(s) thereof having different diffractive properties across the respective transmissive diffractive layer;a mirror disposed along an optical path of the one or more transmissive diffractive layers and configured to reflect light back through the one or more diffractive layers; and one or more optical sensors configured to capture one or more diffracted optical signal(s) resulting from the diffraction of the reflected input light off the one or more transmissive diffractive layers and the mirror in response to illumination with the input light, wherein the optical signal(s) comprise time-series information on oscillation of the structure.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-212. The system of claim 11, wherein the one or more transmissive diffractive layers comprise a plurality of diffractive layers affixed to different parts of the structure and wherein the input light is configured to illuminate the plurality of transmissive diffractive layers.

13. The system of claim 11, wherein the one or more light sources generate the input light at a wavelength, a plurality of wavelengths or wavelength ranges and wherein the one or more optical sensors comprise a plurality of optical sensors configured to detect reflected input light diffracted by the one or more transmissive diffractive layers and the mirror at the input wavelength, plurality of wavelengths or wavelength ranges.

14. The system of claim 11, wherein the one or more light sources comprise monochromatic or quasi-monochromatic light sources and wherein the one or more optical sensors comprise a plurality of optical sensors configured to detect reflected input light diffracted by the one or more transmissive diffractive layers and the mirror.

15. The system of claim 11, wherein the one or more light sources comprise one or more of: laser diodes, light emitting diodes (LEDs), solid state lasers, gas lasers, liquid lasers, or tunable lasers.

16. The system of claim 11, wherein the input light is spatially coherent, partially coherent, or spatially incoherent.

17. The system of claim 11, wherein the different physical features or regions on the surface or layer of the one or more diffractive layers are fabricated in accordance with a trained digital model.

18. The system of claim 11, further comprising an electronic decoder or digital neural network that is connected or coupled to the one or more optical sensors and configured to output quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more transmissive diffractive layers in one or more directions.PCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-219. The system of claim 11, wherein the one or more transmissive diffractive layers have respective surface areas that are between 0.1 mm2and 1000 cm2.

20. The system of claim 18, further comprising a damage identification module configured to generate an output that reflects inferred damage or suspected damage of the structure.

21. A method of monitoring the structural health of a structure comprising: providing:one or more light sources generating input light;one or more diffractive layers affixed to the structure, the one or more diffractive layers comprising a diffractive surface that has different physical features or regions on the surface(s) thereof having different diffractive, transmissive, and / or reflective properties as a function of lateral coordinates across the diffractive layer; andone or more optical sensors configured to capture the one or more diffracted optical signal(s) resulting from reflection and diffraction of input light off the one or more diffractive layers, wherein the optical signal(s) comprise time-series information on oscillation of the structure;illuminating the one or more diffractive layers affixed to the structure with the input light and capturing one or more reflected and diffracted optical signal(s) resulting from the diffraction off the one or more diffractive layers; andoutputting quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more diffractive layers in one or more directions using the time-series information on oscillation of the structure acquired by one or more optical sensors.

22. The method of claim 21, wherein the one or more diffractive layers comprise a plurality of diffractive layers affixed to different parts of one or more structures and wherein the input light is configured to illuminate the plurality of diffractive layers.

23. The method of claim 22, wherein the one or more light sources generate the input light at a wavelength, a plurality of wavelengths or wavelength ranges and wherein the one or more optical sensors comprise a plurality of optical sensors configured to detect thePCT / US26 / 12952 28 January 2026 (28.01.2026)2025-201-2input light diffracted by the one or more diffractive layers at the input wavelength, plurality of wavelengths or wavelength ranges.

24. The method of claim 21, wherein the one or more light sources comprise monochromatic or quasi-monochromatic light sources and wherein the one or more optical sensors comprise a plurality of optical sensors configured to detect the input light diffracted by the one or more diffractive layers.

25. The method of claim 21, wherein the different physical features or regions on the surface or the layer of the one or more diffractive layers are fabricated in accordance with a trained digital model.

26. The method of claim 21, further comprising providing an electronic decoder or digital neural network that is connected or coupled to the one or more optical sensors and configured to output quantitative and / or qualitative information on frequencies or harmonics associated with movements of the one or more transmissive diffractive layers in one or more directions.

27. The method of claim 26, further comprising generating an output that reflects inferred damage or suspected damage of the structure with a damage identification module interfacing with the electronic decoder or digital neural network.

28. The method of claim 26, wherein time-series information on oscillation of the structure acquired by one or more optical sensors is subject to time shifting prior to input to the electronic decoder or digital neural network.

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