Rapid Three-Dimensional Flame Temperature Reconstruction Using Mid-Infrared Dual-Comb Spectroscopy

Rapid Three-Dimensional Flame Temperature Reconstruction Using Mid-Infrared Dual-Comb Spectroscopy | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Rapid Three-Dimensional Flame Temperature Reconstruction Using Mid-Infrared Dual-Comb Spectroscopy CHENGLIN GU, Menglin Zhang, Gehui Xie, Chenyu Liu, Xingyu Liu, and 7 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7722786/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Accurate, rapid, and multidimensional temperature diagnostics are essential for understanding and controlling combustion processes under extreme conditions. Unlike conventional techniques that often require complex multi-detector configurations, we present a single-detector method for three-dimensional (3D) flame temperature reconstruction based on mid-infrared dual-comb spectroscopy. By employing frequency-domain spectral encoding, the system simplifies implementation while enhancing stability and spatiotemporal resolution. This method integrates laser-spectrum optimization and time-division multiplexing, eliminating the need for detector arrays and synchronization. Simulations and experiments confirmed that an acquisition time of ~ 9 ms provides sufficient accuracy (SNR ≈ 20, error < 4%), whereas sub-ms acquisition reduces the SNR to ~ 6 and increases errors to ~ 10%. Guided by this finding, we achieved high-precision 3D temperature reconstruction of flames fields and determined the dynamic evolution of acoustically perturbed combustion with a temporal resolution of 9 ms, highlighting the potential of this high-resolution, multi-line absorption approach for rapid combustion-field diagnostics. This work demonstrates the ability of this technology to obtain full-field, high-spatiotemporal-resolution measurements, offering new opportunities for investigating transient phenomena and optimizing combustion systems. Physical sciences/Optics and photonics/Other photonics/Frequency combs Physical sciences/Optics and photonics/Optical techniques/Optical spectroscopy/Infrared spectroscopy Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Introduction Combustion is an essential process that supports human production and daily life and plays an indispensable role in industries such as energy, transportation, manufacturing, and aerospace 1 , 2 . Improving combustion efficiency, optimizing resource utilization, and mitigating the effect of combustion‑generated pollutants on air quality require comprehensive and systematic investigations of the underlying mechanisms 3 – 5 . Consequently, combustion diagnostic techniques are essential for combustion research and have attracted significant attention. These techniques provide both qualitative and quantitative assessments of fuels, intermediate species, and major products, as well as important physical parameters such as temperature, species concentration, and velocity distributions, enabling indirect evaluation of burner performance 6 , 7 . Laser-based spectroscopic diagnostics provide noninvasive, simultaneous multiparameter measurements with high accuracy, rendering them suitable for modern combustion operations at high temperature, pressure, and flow velocity 2 , 8 . These methods can be systematically classified based on their excitation and detection methods. Point-based techniques, such as coherent anti-Stokes Raman scattering (CARS), enable picosecond temporal resolution 9 , 10 . In multistream combustors, CARS has reported temperatures up to ~ 2450 K and validated fuel-flow effects 11 . However, this technique requires complex optical alignment and precise calibration, which limits its portability and ease of deployment 12 . Line-array excitation with point detection, represented by tunable diode laser absorption spectroscopy (TDLAS), enables real-time monitoring 13 – 15 . Dual-wavelength TDLAS with quantum cascade lasers has achieved 800–4000 K measurements in industrial furnaces 16 . Nevertheless, TDLAS requires a precisely synchronized multi-detector configuration, which makes the results susceptible to mechanical vibrations 17 , 18 . Planar methods, such as Rayleigh scattering (RS) and planar laser-induced fluorescence (PLIF), yield rapid two-dimensional mapping 19 – 24 . RS has detected kHz-rate temperature fields in turbulent jet flames 25 , whereas PLIF has visualized ignition/extinction in scramjets and produced flame-angle estimates that are consistent with simulations 26 . However, both RS and PLIF require careful calibration and are sensitive to quenching effects and background luminosity 27 . Despite their effectiveness, these methods are limited in their ability to collect full-field, real-time 3D temperature data 28 , 29 , highlighting the need for diagnostic approaches that combine high precision, robustness, and spatio-temporal resolution. Dual-comb spectroscopy (DCS) integrates the strengths of traditional broadband spectroscopy and tunable laser spectroscopy into a single platform 30 . Unlike conventional techniques, DCS performs Fourier transform interferometry without moving components, enabling the simultaneous acquisition of all spectral channels with a single detector 31 . This design decreases the effect of environmental vibrations on measurement accuracy. Owing to its ability to obtain rapid, broadband, high-resolution, and high-SNR measurements, DCS has attracted increasing attention in combustion diagnostics 32 – 34 . For example, Schroeder et al. monitored gas-turbine exhaust temperatures with a temporal resolution of 10 s 35 . In addition, near-infrared DCS achieved 704 µs resolution in tracking temperature variations in a fast compressor 36 . Long et al. reported 20 ns resolution for temperature measurements in supersonic pulse jets 37 , and Yun et al. obtained 2D temperature profiles in a dual-mode ramjet and ignition-induced temperature transients with subsecond resolution 6 . In our previous work, the change in temperature distribution was monitored at a 10 ms resolution 38 . Despite these advancements, most reported applications focus on point or path-integrated temperature measurements. The extension of DCS to full 2D or 3D temperature field reconstruction, which would fully exploit its broadband and high-resolution potential, remains challenging. In this paper, we present a rapid three-dimensional reconstruction technique for flame fields enabled by DCS, which, to the best of our knowledge, has not been applied to high-precision spatiotemporal temperature measurements. A single-detector flame temperature reconstruction method was developed based on mid-infrared (MIR) DCS frequency-domain spectral encoding, which incorporates laser-spectrum optimization and time-division multiplexing. This approach effectively overcomes the complexity of detector arrays and synchronization issues inherent in traditional measurement systems. Empirical analysis demonstrated that ~ 9 ms acquisition time ensures sufficient SNR (~ 20) and < 4% error, whereas sub-ms acquisition decreases the SNR and increases errors (~ 10%). Accordingly, we achieved 3D temperature reconstruction of the flame field, accurately resolving spatial temperature gradients. In addition, the dynamic temperature profile of a perturbed flame was constructed with a temporal resolution of 9 ms, enabling time-resolved analysis of transient combustion phenomena. These results demonstrate the accuracy and reliability of the technique for combustion diagnostics, providing a robust foundation for high-precision measurement of transient processes and for advancing research on combustion-field dynamics. Results Principle: Neural Network-based Discrete Flame Imaging The absorption spectrum obtained via the line-of-sight (LOS) sensing technique is the result of path integration along the laser propagation direction. To reconstruct the 3D distribution of flame field parameters from the absorption spectrum, the sensing area can be discretized into grids, enabling parameter retrieval at distinct spatial locations. As shown in Fig. 1(a), the entire profile is evenly divided into n×n grids, with the physical parameters assumed to be uniform within each grid cell. According to the Beer-Lambert law, the integral absorbance of the laser with a central wavelength n after it passes through the flame field can be expressed as follows: where P [atm], X, and L [cm] represent the pressure, concentration and optical path length, respectively, within the i-th grid. The line strength is determined by the temperature of the lower state energy associated with the specific transition. Unlike conventional techniques that rely solely on physical beam arrays or multiple detectors, our approach uses the multi-line characteristics of broadband spectra to construct an effective beam array for three-dimensional flame-field diagnostics. In this work, a laboratory-scale 16-beam DCS sensor was designed for flame temperature measurements, and each beam has distinct spectral components that serve as independent diagnostic channels. As shown in Fig. 1(b), tside length of the square sensing region is 80 mm. This region is uniformly divided into 64 subregions (n=8), each intersected by two laser beams. The system employs eight parallel beams in each direction, with every beam containing two wavelength components. The integrated absorbance for the j-th laser beam can be expressed as follows: With respect to the horizontally arranged beams: ; and with respect to the longitudinally arranged beams: . Because laser beams of different wavelengths traversing the same grid have distinct values, Eq. (2) constitutes an ill-posed inversion problem for retrieving spatially resolved parameters. Conventional flame field reconstruction techniques typically combine two-line temperature measurements with iterative tomography to obtain temperature distributions 17,29,39 . Despite their effectiveness, these methods require the precise synchronization of multiple lasers and detectors, resulting in complex system setups and challenging optical path alignment 40 . In contrast, our approach exploits the multi-line characteristics of broadband MIR DCS for spectral path encoding and uses a single-detector architecture with optimized reconstruction algorithms, eliminating the need for multiple transceivers and synchronization. This configuration not only simplifies the optical setup but also improves system stability, rendering it suitable for practical and dynamic combustion environments. Additionally, a modified fully convolutional neural network (D-FCNN) was developed and optimized based on the FCNN architecture to address the ill-posed problem of the reconstruction process. The network connects neurons across layers through fully connected mappings, enabling robust and accurate reconstruction of spatial temperature fields. As shown in Fig. 2, the D-FCNN model consists of one input layer, thirteen hidden layers, and two output layers. The integral absorption value vectors and represent the network input, whereas the reconstructed temperature distribution vector represents the output. A total of 300,000 samples were randomly generated based on a random mixture of Gaussian functions, representing various states within the flame region. Each sample was assigned distinct flame center positions and physical parameters, replicating the multimodal and asymmetric flame distributions typically observed in practical combustion devices. Specifically, the integrated absorbance of each laser beam was calculated with Eq. (2) based on the assumed temperature matrix and concentration matrix . Together, these components form the D-FCNN sample dataset . Of these, 70% of the samples were allocated for model training, whereas the remaining 30% were reserved for testing. In addition, the reconstruction error was defined as the ratio between the norm of the difference and the norm of the true flame parameter values and served as a quantitative measure of the reconstruction accuracy. The reconstruction results of the D-FCNN model for three representative flame field distributions—unimodal (a–c), bimodal (d–f), and flat-topped concave (g–i)—at an integrated absorbance signal-to-noise ratio (SNR) of 20 are presented in Fig. 3. In our experiments, achieving an integrated absorbance SNR of 20 required an acquisition time of ~9 ms. When the acquisition time was reduced to the sub-ms level, the corresponding SNR decreased to ~6, leading to reconstruction errors of about 10%. Therefore, 9 ms was selected as the optimal acquisition time. Even under low SNR conditions, the temperature distributions of different flame shapes are accurately reconstructed, with reconstruction errors within 4%. The simulation results indicate that the D-FCNN model achieves high-precision temperature reconstruction, strong noise robustness and excellent reconstruction accuracy. Future work will focus on increasing the number of measurement paths and extending the reconstruction model to enable simultaneous reconstruction of multiple flame parameters (i.e., , and ). Experimental Setup The flame field was generated with a commercial butane lighter. The lighter consists of a grinding wheel, a flint, a spark aperture, and a gas nozzle. Rapid friction between the spark pin and the grinding wheel produces sufficient heat, melting metal particles on the wheel surface and generating sparks. These sparks ignite the nearly pure butane gas emitted through the aperture, resulting in the formation of a flame with an irregular spatial distribution. The flame has three regions: the flame core near the nozzle, the inner flame, and the outer flame. Owing to oxygen deficiency, the core exhibits incomplete combustion and a relatively low temperature, whereas the outer flame is well oxygenated and reaches a higher temperature. In this experiment, the flame tip was selected as the target region, and a measurement volume of 8×8×21 mm³ was set up with it as the center. Afterward, the lighter was mounted on a precision z-axis displacement stage, enabling fine positional adjustments to scan various sections of the flame field. MIR DCS Frequency-domain Encoding System The flame field reconstruction system based on the MIR DCS is shown in Fig. 4. The system employs two MIR frequency comb sources with slightly different repetition rates. The output of the first MIR comb is divided into two beams by a pellicle beam splitter (BP145B4, Thorlabs). Each beam passes through a modular optical delay line before it is combined with the second comb, resulting in the formation of a DCS pair with an adjustable temporal delay. The DCS beams subsequently entered the frequency-domain encoding module for spectral filtering and beam alignment. This module consists of an MIR grating, a CaF₂ prism, a lens assembly, a square reflector, and an aperture. First, the dispersive elements spatially separate the beams according to their wavelength components, producing a beam footprint larger than the target detection area. Second, the long- and short-wavelength components were spatially filtered and aligned via reflector and aperture assembly. This configuration enables the precise selection of spectral components and allows the two beams to be parallel and symmetrically distributed. Stray-wavelength interference in gas absorption is effectively suppressed in this configuration, resulting in increased accuracy in gas-molecule detection. The MIR spectral region has strong CO₂ absorption features, where even small molecular variations induce obvious spectral changes, which is an advantage over near-infrared CO₂ absorption sensors. Consequently, a 4.2 μm MIR DCS system was selected for flame field temperature sensing 41,42 . The spectral resolution of the system is 160 MHz, which is sufficient to resolve CO₂ absorption lines with gigahertz-level linewidths. To avoid spectral aliasing and achieve a high refresh rate, the repetition rate difference was 20 kHz, yielding a temporal resolution of 50 μs, which is suitable for probing the kinetics of the combustion reaction. To increase sensitivity to low-temperature regions, the DCS beams were spatially arranged in alternating “long-wave/short-wave” and “short-wave/long-wave” sequences, where purple and red denote long-wavelength components and short-wavelength components, respectively. The grating and prism positions were optimized to produce an 8 mm beam diameter, covering the flame tip region. Last, all the signals were collected by a single detector and digitized with a 12‑bit acquisition card at 500 MS/s. The single-cycle time-domain signal recorded by the system is presented in Fig. 5(a). The first and third interference peaks originate from one group of symmetrically arranged, parallel DCS beams, whereas the second and fourth peaks belong to the orthogonal beam group. The delayed optical paths separate the four interference signals in time, enabling high temporal resolution and distinct isolation of identical spectral components. This optical‑path configuration enables the complete acquisition of all spectral information with a single detector. The spatial resolution of the system is characterized by an optical filtering module. By translating the displacement platform, the spectral components of the same beam at different spatial positions are sequentially filtered, as shown in the lower panel of Fig. 5(b). The spectral components of each beam group exhibit a symmetric distribution, allowing the entire measurement plane to be divided into an 8 × 8 grid and discrete flame‑field temperature measurements. Reconstruction of 3D Temperature Distribution in Flame Field We evaluated the ability of the MIR DCS system to reconstruct 3D flame field temperature distributions by sequentially obtaining two-dimensional slices at different flame heights. Each slice was recorded within 50 ms, and the flame was moved upward in 1 mm increments with a precision z-axis stage, yielding a total of 21 slices for 3D reconstruction. The reconstructed flame temperature reached values near 2100 K, which is consistent with the expected temperature of complete butane combustion. Figures 6(a) and 6(b) show one representative slice of the reconstructed temperature field, clearly indicating the flame structure and that the temperature decreased from the core to the periphery. To further confirm the reconstruction accuracy, a cold aluminum plate was positioned at a 45° angle relative to the laser beam on one side of the flame. The convective interaction between hot and cold air caused the flame tip to tilt toward the plate, which is clearly observed in the reconstructed temperature distributions at multiple heights, as shown in Fig. 6(c). The progressive leaning of the flame tip in the y=8 direction along each measurement plane is consistent with the effect of the cold aluminum plate. These results indicate that the reconstruction accurately reveals the characteristic structure of the flame and validates the reliability of the MIR DCS system for 3D flame‑field temperature mapping. Reconstruction of Temperature Distribution in Dynamic Flame Field Spatio-temporal measurement of flame temperature parameters is scientifically important for dynamic combustion, because it provides essential data for understanding and controlling complex physical and chemical phenomena during combustion. To determine the spatio-temporal resolution capability of the MIR DCS frequency-domain encoding system, an experimental setup for generating dynamic flames under acoustic excitation was designed and constructed. First, an acoustic excitation system consisting of a loudspeaker and a power amplifier was placed near the flame to modulate the flame using a fixed‑frequency acoustic signal, as shown in Fig. 7(a). The sinusoidal signal was increased by the power amplifier and then delivered to the loudspeaker, which generated acoustic waves that acted on the flame. Under acoustic excitation, the flame exhibited periodic oscillations at the harmonic frequency, revealing the phenomenon of flame disturbance induced by the acoustic field. To obtain high‑accuracy temperature measurements, the extracted absorption spectral lines were fitted with Voigt profiles. Numerical simulations indicate that a signal-to-noise ratio (SNR) of the integrated absorbance above 20 is sufficient to keep the reconstruction error below 4%. In our experiments, the raw spectral intensity data collected within a 9 ms time window achieved a single-point SNR of approximately 500. Considering the line depth and the number of independent resolution elements across the absorption feature, this corresponds to an integrated absorbance SNR exceeding 20, thus meeting the requirement. Therefore, a temporal resolution of 9 ms was used to analyze the dynamic evolution of the 2D flame temperature distribution. Within a 1 s time window, the temporal evolution of the flame cross‑sectional temperature is shown in Fig. 7(b), which clearly shows the dynamic response of the flame under acoustic excitation. The corresponding dynamic process is further described in the Supplementary Information. Furthermore, the temporal evolution of the temperature distribution across a representative cross-section is presented in Fig. 8(a). The figure displays the temperature variations over time across a 1 × 8 spatial grid. Under external perturbation, the flame clearly exhibits dynamic temperature fluctuations over time. A specific pixel within this cross-section was then selected for detailed analysis, as indicated by the black dashed line in Fig. 8(a). The temporal evolution of the temperature of this pixel is extracted and shown in Fig. 8(b), where obvious periodic oscillations directly reflect the dynamic response of the flame to the acoustic field. To quantitatively analyze this periodic variation, a Fourier transform was performed on the temperature variation over a 1-second period to extract the dominant frequency information representing the temperature variation, as shown in Fig. 8(c). The red curve represents the scenario where the loudspeaker output frequency is 10 Hz, with the reconstructed frequency exhibiting a slight offset of 0.09 Hz. To avoid randomness, the acoustic excitation frequency was increased to 15 Hz, and the reconstructed dominant frequency (blue curve) shows a 0.01 Hz offset. These results indicate that the frequency of the reconstructed temperature variation is consistent with the applied acoustic excitation, fully confirming the spatiotemporal resolution capability of the DCS frequency-domain encoding system for measuring dynamic flame-field temperature distributions. Discussion We propose a novel method for spatio-temporal flame temperature measurement based on MIR DCS. Integrating spatial frequency-domain coding with a single-detector configuration simplifies conventional multi-detector architectures and enables efficient acquisition of combustion data. We developed the D-FCNN model to reconstruct the flame field temperature distribution with an accuracy of less than 4%, enabling accurate 3D temperature reconstruction of flame fields. Additionally, the dynamic flame temperature variations under acoustic excitation were obtained with a temporal resolution of 9 ms, demonstrating the ability of the system for spatio-temporal resolution diagnostics. Overall, this technique provides a robust, scalable solution for high-precision, high-resolution measurements in combustion fields, and a powerful tool for advancing combustion modeling, optimizing energy systems, and improving emission control strategies. Declarations Code availability The code employed in this study for reconstructing flame temperature from integrated absorbance is available from the corresponding author. Acknowledgements This work was supported in part by the National Natural Science Foundation of China (12274141, 12134004, 62425503, 12574436, 62505086). Conflict of interest The authors declare no competing interests. References Janbozorgi, M., Far, K. E. & Metghalchi, H. Combustion Fundamentals. in Handbook of Combustion (Wiley, Online, 2010). Aldén, M. Spatially and temporally resolved laser/optical diagnostics of combustion processes: From fundamentals to practical applications. Proceedings of the Combustion Institute 39 , 1185-1228 (2023). Chen, H., He, J. & Zhong, X. Engine combustion and emission fuelled with natural gas: A review. J. Energy Inst. 92 , 1123-1136 (2019). Izah S C,Ogwu M C.Shahsavani A. The Handbook of Environmental Chemistry 134 , Germany, (2024). Liu, Q., Baccarella, D. & Lee, T. 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(a) Propagation path of a single laser beam through the discretized measurement area; (b) Experimental con􀏐iguration with 16 orthogonally arranged laser beams, each carrying distinct spectral components, encompassing an 80 mm × 80 mm square sensing region uniformly divided into 8 × 8 grids. With frequency-domain spectral encoding, all signals are collected by a single detector, which eliminates the need for multiple detectors and complex synchronization, simpli􀏐ies the setup and improves system stability.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/71fb41a85268db1045fac76b.png"},{"id":93026169,"identity":"0f657720-1eaf-4caa-8966-4bdb01920cda","added_by":"auto","created_at":"2025-10-08 09:28:56","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":191431,"visible":true,"origin":"","legend":"\u003cp\u003eArchitecture of the D-FCNN used for 􀏐lame 􀏐ield temperature reconstruction. The network comprises one input layer, thirteen hidden layers, and two output layers, connecting neurons across layers through fully connected mappings to extract spatial features and reconstruct temperature 􀏐ields. Input vectors (𝐴𝐴𝑎𝑎 and 𝐴𝐴𝑏𝑏) represent the integral absorbances of the orthogonal laser beams, and the output vector 𝑇𝑇 represents the reconstructed temperature distribution.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/3c6917cf3c1d2f7c19a3cbc8.png"},{"id":93027012,"identity":"dcd68711-88fa-4513-a22b-5f17293decc4","added_by":"auto","created_at":"2025-10-08 09:36:56","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":508412,"visible":true,"origin":"","legend":"\u003cp\u003eNumerical simulation results of the D-FCNN reconstruction model. Left: simulated temperature distributions; middle: temperature 􀏐ields reconstructed by the D-FCNN; and right: reconstruction errors. Panels (a–c) show unimodal 􀏐lame temperature 􀏐ields; (d–f) to bimodal 􀏐lame temperature 􀏐ields; and (g–i) to 􀏐lat-topped concave 􀏐lame temperature 􀏐ields. In all the scenarios, the reconstruction errors remain below 4%.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/967b72ded7891c5e211db62d.png"},{"id":93024985,"identity":"05794b18-dadc-4d5c-8d17-017942db1dfd","added_by":"auto","created_at":"2025-10-08 09:20:56","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":395514,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic of the 􀏐lame 􀏐ield temperature reconstruction system, employing two mid-infrared frequency combs, a pellicle beam splitter (BS), and two spectral encoding modules (SEM). All encoded beam signals are collected by a single balanced detector (BD), enabling the simultaneous acquisition of all optical paths without the need for detector arrays or synchronization. The recorded interferometric signals are processed through a D-FCNN algorithm to reconstruct the three-dimensional temperature distribution of the 􀏐lame.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/9ace716510ad2949d11c61c5.png"},{"id":93026170,"identity":"17d94cb7-f579-4466-b0df-83201fcf7866","added_by":"auto","created_at":"2025-10-08 09:28:56","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":191557,"visible":true,"origin":"","legend":"\u003cp\u003eSingle-cycle time- domain and frequency-domain signals of the MIR DCS system. (a) Four interference peaks in the time domain corresponding to two orthogonal groups of parallel beams separated by optical delays. (b) The spectral 􀏐iltering module resolves the spectral components of parallel beams at different spatial positions, yielding 16 beams with distinct spectral information, demonstrating the ability of the system to achieve an 8 × 8 grid spatial resolution on the measurement plane.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/873e5218bd8097cb1dacaf66.png"},{"id":93026177,"identity":"012226cc-16c1-4036-8993-a2af4d4a0f8c","added_by":"auto","created_at":"2025-10-08 09:28:56","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":426517,"visible":true,"origin":"","legend":"\u003cp\u003eReconstructed 3D temperature distribution of the 􀏐lame. (a–b) Representative slices of the reconstructed temperature 􀏐ield shown with different orientations, which reveal the internal 􀏐lame structure. These views clearly indicate the spatial gradients, with the temperature gradually decreasing from the high-temperature core to the cooler periphery. (c) The temperature maps at multiple heights reveal a tilt of the 􀏐lame tip in the y=8 direction, which is consistent with the de􀏐lection caused by a nearby cold aluminum plate.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/13b790b6a038c6400ef96617.png"},{"id":93026176,"identity":"b644b1b7-f170-4e47-8b90-0a1dbc5fe379","added_by":"auto","created_at":"2025-10-08 09:28:56","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":428280,"visible":true,"origin":"","legend":"\u003cp\u003eDynamic 􀏐lame experiment under acoustic excitation. (a) Experimental setup for generating acoustically excited 􀏐lames. (b) Temporal evolution of the 􀏐lame cross-sectional temperature within a 1 s window, clearly showing dynamic 􀏐lame oscillations induced by the acoustic 􀏐ield.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/5ec3d22100e541dbd65455a3.png"},{"id":93024989,"identity":"b81b97b2-b3e5-46b9-a0ef-13d0f68958ef","added_by":"auto","created_at":"2025-10-08 09:20:56","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":261700,"visible":true,"origin":"","legend":"\u003cp\u003eTemporal and frequency analysis of dynamic 􀏐lame temperature variations. (a) Temporal evolution of the reconstructed 􀏐lame temperature distribution across a representative cross-section within a 1 s window. (b) Temperature variation at a selected pixel indicated by the black dashed line in (a), clearly showing periodic oscillations over 1 s. (c) Spectral pro􀏐iles of the 􀏐lame temperature oscillations under acoustic excitation at 10 Hz (red) and 15 Hz (blue), with reconstructed frequencies closely matching the applied excitation.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/8478b7d624d73e3807283d8e.png"},{"id":95526710,"identity":"ec4f494d-e2b0-49a2-a9d3-bee68153fad1","added_by":"auto","created_at":"2025-11-10 10:07:39","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3427987,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7722786/v1/d6e0e216-53b6-4a8d-a091-453874c9b78b.pdf"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Rapid Three-Dimensional Flame Temperature Reconstruction Using Mid-Infrared Dual-Comb Spectroscopy","fulltext":[{"header":"Introduction","content":"\u003cp\u003e\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eCombustion is an essential process that supports human production and daily life and plays an indispensable role in industries such as energy, transportation, manufacturing, and aerospace\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e. Improving combustion efficiency, optimizing resource utilization, and mitigating the effect of combustion‑generated pollutants on air quality require comprehensive and systematic investigations of the underlying mechanisms\u003csup\u003e\u003cspan additionalcitationids=\"CR4\" citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Consequently, combustion diagnostic techniques are essential for combustion research and have attracted significant attention. These techniques provide both qualitative and quantitative assessments of fuels, intermediate species, and major products, as well as important physical parameters such as temperature, species concentration, and velocity distributions, enabling indirect evaluation of burner performance\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e,\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\u003cp\u003eLaser-based spectroscopic diagnostics provide noninvasive, simultaneous multiparameter measurements with high accuracy, rendering them suitable for modern combustion operations at high temperature, pressure, and flow velocity\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. These methods can be systematically classified based on their excitation and detection methods. Point-based techniques, such as coherent anti-Stokes Raman scattering (CARS), enable picosecond temporal resolution\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. In multistream combustors, CARS has reported temperatures up to ~\u0026thinsp;2450 K and validated fuel-flow effects\u003csup\u003e\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. However, this technique requires complex optical alignment and precise calibration, which limits its portability and ease of deployment\u003csup\u003e\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Line-array excitation with point detection, represented by tunable diode laser absorption spectroscopy (TDLAS), enables real-time monitoring\u003csup\u003e\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Dual-wavelength TDLAS with quantum cascade lasers has achieved 800\u0026ndash;4000 K measurements in industrial furnaces\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Nevertheless, TDLAS requires a precisely synchronized multi-detector configuration, which makes the results susceptible to mechanical vibrations\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Planar methods, such as Rayleigh scattering (RS) and planar laser-induced fluorescence (PLIF), yield rapid two-dimensional mapping\u003csup\u003e\u003cspan additionalcitationids=\"CR20 CR21 CR22 CR23\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. RS has detected kHz-rate temperature fields in turbulent jet flames\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e, whereas PLIF has visualized ignition/extinction in scramjets and produced flame-angle estimates that are consistent with simulations\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. However, both RS and PLIF require careful calibration and are sensitive to quenching effects and background luminosity\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e. Despite their effectiveness, these methods are limited in their ability to collect full-field, real-time 3D temperature data\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e, highlighting the need for diagnostic approaches that combine high precision, robustness, and spatio-temporal resolution.\u003c/p\u003e\u003cp\u003eDual-comb spectroscopy (DCS) integrates the strengths of traditional broadband spectroscopy and tunable laser spectroscopy into a single platform\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Unlike conventional techniques, DCS performs Fourier transform interferometry without moving components, enabling the simultaneous acquisition of all spectral channels with a single detector\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e. This design decreases the effect of environmental vibrations on measurement accuracy. Owing to its ability to obtain rapid, broadband, high-resolution, and high-SNR measurements, DCS has attracted increasing attention in combustion diagnostics\u003csup\u003e\u003cspan additionalcitationids=\"CR33\" citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. For example, Schroeder et al. monitored gas-turbine exhaust temperatures with a temporal resolution of 10 s\u003csup\u003e35\u003c/sup\u003e. In addition, near-infrared DCS achieved 704 \u0026micro;s resolution in tracking temperature variations in a fast compressor\u003csup\u003e\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. Long et al. reported 20 ns resolution for temperature measurements in supersonic pulse jets\u003csup\u003e\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e, and Yun et al. obtained 2D temperature profiles in a dual-mode ramjet and ignition-induced temperature transients with subsecond resolution\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. In our previous work, the change in temperature distribution was monitored at a 10 ms resolution\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. Despite these advancements, most reported applications focus on point or path-integrated temperature measurements. The extension of DCS to full 2D or 3D temperature field reconstruction, which would fully exploit its broadband and high-resolution potential, remains challenging.\u003c/p\u003e\u003cp\u003eIn this paper, we present a rapid three-dimensional reconstruction technique for flame fields enabled by DCS, which, to the best of our knowledge, has not been applied to high-precision spatiotemporal temperature measurements. A single-detector flame temperature reconstruction method was developed based on mid-infrared (MIR) DCS frequency-domain spectral encoding, which incorporates laser-spectrum optimization and time-division multiplexing. This approach effectively overcomes the complexity of detector arrays and synchronization issues inherent in traditional measurement systems. Empirical analysis demonstrated that ~\u0026thinsp;9 ms acquisition time ensures sufficient SNR (~\u0026thinsp;20) and \u0026lt;\u0026thinsp;4% error, whereas sub-ms acquisition decreases the SNR and increases errors (~\u0026thinsp;10%). Accordingly, we achieved 3D temperature reconstruction of the flame field, accurately resolving spatial temperature gradients. In addition, the dynamic temperature profile of a perturbed flame was constructed with a temporal resolution of 9 ms, enabling time-resolved analysis of transient combustion phenomena. These results demonstrate the accuracy and reliability of the technique for combustion diagnostics, providing a robust foundation for high-precision measurement of transient processes and for advancing research on combustion-field dynamics.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003ePrinciple: Neural Network-based Discrete Flame Imaging\u003c/p\u003e\n\u003cp\u003eThe absorption spectrum obtained via the line-of-sight (LOS) sensing technique is the result of path integration along the laser propagation direction. To reconstruct the 3D distribution of flame field parameters from the absorption spectrum, the sensing area can be discretized into grids, enabling parameter retrieval at distinct spatial locations. As shown in Fig. 1(a), the entire profile is evenly divided into n\u0026times;n grids, with the physical parameters assumed to be uniform within each grid cell. According to the Beer-Lambert law, the integral absorbance \u003cimg width=\"11\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAVCAMAAACXIvXeAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgBmOjqQOpDbZgAAZjpmZrbbZrb/kDoAkDo6kGY6kJA6kNv/tmYAtmY6tv//25A625Bm25CQ2////7Zm/9uQ//+2///bxLrTBQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAdUlEQVQoU7WNQRbCIAwFE1qtVEHbamoD3P+ahnQT2DsL4A0/+QB/psTxaCsIO5PvS2fegYaPnUq3ozXluQK51WTYA7A1eUbBGpIIMAY5SRvTVFvStRqlxEu9dvTy1NEXOvllXXTGLaxxy1Y7LCWGbzsmmx8APwSdBVFJiAvxAAAAAElFTkSuQmCC\" alt=\"image\"\u003e\u0026nbsp;of the laser with a central wavelength n after it passes through the flame field can be expressed as follows:\u003c/p\u003e\n\u003cp\u003e\u003cimg width=\"641\" height=\"25\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere P [atm], X, and L [cm] represent the pressure, concentration and optical path length, respectively, within the i-th grid. The line strength \u003cimg width=\"24\" height=\"14\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e\u0026nbsp;is determined by the temperature of the lower state energy \u003cimg width=\"15\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABYAAAAVCAMAAAB1/u6nAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOjqQOpDbZgAAZgBmZjqQZrb/kDoAkGYAkNv/tmYAtv//25A62////7Zm/9uQ/9u2//+2///bWurdEgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAgklEQVQoU7WP2xKCMAxEV1Ggilqgtfz/l7JJOoCVRzgz3V7SJBvgcJK7jVD5IdYdoAKEi8E/oep5FyHD9QNMrztPXCaya9h3DDFdRfA5jPRkLxWSXIvpnb+sDmLNfrnNxpeUjk1hlaVL95qizv6xodLDZlgIMsy3TInORm/3Kp3yNgNNSgThPY5icgAAAABJRU5ErkJggg==\" alt=\"image\"\u003e associated with the specific transition. Unlike conventional techniques that rely solely on physical beam arrays or multiple detectors, our approach uses the multi-line characteristics of broadband spectra to construct an effective beam array for three-dimensional flame-field diagnostics. In this work, a laboratory-scale 16-beam DCS sensor was designed for flame temperature measurements, and each beam has distinct spectral components that serve as independent diagnostic channels. As shown in Fig. 1(b), tside length of the square sensing region is 80 mm. This region is uniformly divided into 64 subregions (n=8), each intersected by two laser beams. The system employs eight parallel beams in each direction, with every beam containing two wavelength components. The integrated absorbance\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003cimg width=\"8\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAVCAMAAABFcv+GAAAAAXNSR0IArs4c6QAAAFFQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgBmOjqQOpDbZgAAZjpmZrb/kDoAkDo6kGY6kJA6kNv/tmY6tv//25A625Bm2////7Zm/9uQ//+2///bX/KnHAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAXUlEQVQoU62PSw6AIAxEW/wriGjld/+D2kYCaxObdPFmppMU4J/Jpve1ibBB2o4Gp6buKrE4+wp5d0DKvU5YeAukFXkKEBsQUEsoTtITR4FsBpFuFN+iYi3Uo6/vPb5CA33M+wh9AAAAAElFTkSuQmCC\" alt=\"image\"\u003e\u0026nbsp;for the j-th laser beam can be expressed as follows:\u003c/p\u003e\n\u003cp\u003e\u003cimg width=\"624\" height=\"39\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA6gAAAA7CAYAAAB2W6dYAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAB6CSURBVHhe7Z19UFTnvcd/55xleuHmTuZO5k4mrH9d2F1edDq5ExuWK7bNDagsviRK25g7qS8QyW0iL5rWaFxg1dz2qhAxqQhGyZ2JImCjCOJLJ70JsKRqGkmEFVia6bTpH525rXDLWmXPnvs7ZwEBRXeXZWHhe2aYETjneX7P53lk97u/N11xcTHhAgEQAAEQAAEQAAEQAAEQAAEQAIHpJqCbbgMwPwiAAAiAAAiAAAiAAAiAAAiAAAioBCBQcQ5AAARAAARAAARAAARAAARAAARmBAEI1BmxDTACBEAABMKbgNX6oly2yCjmtSZRSVcLmUpSyFLRSoq5lLpacskoCJLNZvOE9yphPQiAAAiAAAiAwFQTgECdasIYHwRAAATmAIHeAw1kOHaDStfHUe36TbSmqpnkrQcpxdRBToWoXZgDELBEEAABEAABEACBSROAQJ00QgwAAiAAAiDwQV+fZDU45TNtiph4tpz01wRJeKRjsM2cIMayODUyIhswgQAIgAAIgAAIgMBDCECg4oiAAAiAAAgEh0DTaapUsunsUoEGRKKmTRVkzuwiU50gFTsQ3hscyBgFBEAABEAABGY3AQjU2b2/WB0IgAAIhIyAs/s6UfYOspyqk5TMJwfLOkQxcWUsHespk507d9JfOQ/VgTzUkO0HJgIBEAABEACBcCQAgRqOuwabQQAEQGCGEfAWSSoWzWtiqVUL6HWScT5RXkYKKQ1VlMpeVAe8qDNs12AOCIAACIAACMw8AhCoM29PYBEIgAAIhB0Bm+0DidIKKa2/mr8439RGEkUXUlERL+XqCXKE3YpgMAiAAAiAAAiAwHQQgECdDuqYEwRAAARAAARAAARAAARAAARA4B4CEKg4FCAAAiAAAiAAAiAAAiAAAiAAAjOCAATqjNgGGAECIAACIAACIAACIAACIAACIACBijMAAiAAAiDgEwHrwq9lyVIpehTFp/t9uim5lLpacsnIFX5tqPDrEzLcBAIgAAIgAAKzmQAE6mzeXawNBEAABIJJYNmPqTS5kvJaiVSJmlzaTXb9Ne5x6vD4M43VulY+n2MS0ys82ji4QAAEQAAEQAAEQGCYAAQqzgIIgAAIgIBPBNRKvdaWRrlTsogVHoXs+euotLtF1pN/LWRstuOStbxBfrmSx/FpZtwEAiAAAiAAAiAwVwhAoM6VncY6QQAEQCAIBGy2K1J5Q7ZcyaG+imKnfOMmapQPy/GiVXL4EaKrjrMyS5ErrpMYBLMwBAiAAAiAAAiAwCwhAIE6SzYSywABEACBUBGwXdFL3aVm2ZBvZ5FaSZacVUSpA1TspwHLVr1MQofg51O4HQRAAARAAARAYDYTgECdzbuLtYEACIDAFBGIyf1vervWwPmoCimVFkpO6JYL4zM5H9Xmcz6qKnQL0/qoeteuKbISw4IACIAACIAACIQbAQjUcNsx2AsCIAACM4DAffNRuzgfNdO/UN8ZsBSYAAIgAAIgAAIgMIMIQKDOoM2AKSAAAiAQTgTuyUddf0BtGSNnWq1oGRNOGwlbQQAEQAAEQGAGEYBAnUGbAVNAAARAINwIjMlHteeTaZMxoHzUcFs37AUBEAABEAABEJgaAhCoU8MVo4IACIDAnCEwPh81e5Usx8eLksOPfNQ5AytMFmq1vug+X7ZX2l0TT9s/2UwDoqDjKs1yMM1f++gF93pHprRtSy65DMEfP5i2YiwQAAEQAIH7E+De5q6L75ZG7jlpoK2XXqW/fUMXxa8Xtx7Gi18DXNmO1ZEFeZsp+nFdVOPBu89AoD6MHn4PAiAAAiDwQALj81ErLSmUwPmo8chHDcuTo4rTshSjVLO6no42p1O7MDXi8XjfEl3zVsGdsj5Fit/2sftmvFU33xFcERyWGwCjQQAEQCBMCKji9N1nFkSezKim8o8y6AmdFHXQB3GqLo9fA6J+tVVyPZP9TGRMwSXXYxZrVFSjV6RCoIbJAYCZIAACs5MA/3H3lC0yCnlKiZq/SQZBEG02mxJuq52KfFTrwq9lifutepRxOJKTqXRHFekHDCHx0q596mt53fJK0e7hisWUTQ3yYUoXe+lgiomrGHtINc9c2kX5emNI7FHPhnXtU3LO+rfEilY7z+/lYzZn05tV5TTQLurYex2Qt/OuOHVQtL5dxxWWtXGGf57P62UME17ZDW666ZJ8Fpq243265mOZ7sVx35ae7/jYzUW2JuWp5TPj1mVUSvKQkf7aE27/72AvCIAACEwXgbvi9Aq5BvVRdW/tGfGaqr/rvXg+smRPAVW0DJJbre+ftIH2vldO8hMRUbeHvKX8GhD1UeVq1zMLUiPjr1xyDb5m1X4HgTpdu4p5QQAEQIAJOA/8kPLsLHzM4Y9DzUft4v6oJu6P6glCPurd8Ujcf6OZ9EZRyiTnYFmOSczLWEclN5pD4qU9flUvbc9S5OWVZrHkRjm5REHaZTvusb6RJeezcE0qOUvv5xr4wwUim23q99G69lE5xZQhevafpRufpJNRECTngeRBU74gKjE8P6cBU6B2NP0XFdiz6Mz/xJJLMhKHaQ0tqJscbfz+Yn8X6ee162r+5Y+3U4wFUkL9HfoLC9KaJw/cTomrlRJiBdKbiJ/znYMqUo/uV9xxGw9KHR/nurnIlo4/pAlIYPOZ0d0oMbvjCtqkb+1z+CWWfbcYd4IACIAACFDTXnq99SU60WiiO5ERY/7uN20y0KqjRP9e9yVteVUf9dMnP/3fVxesinwjkajOVe66Y7WOhAGrIrXip7JrwX+8G3nl0maXnn8HgYrzBQIgAALTRMBqXejJWfS1UFpKlF/D6mYWXLG571Np7ZBnkfujBicfdT4ZWfgMqLrLdlyyrmRhWFEpdjqJ9O2hgZb++tuUfKR2zGTnzlQQZTVQm94indjle//XyVp8bm8e2ZNKybHZK05ZzHmsa79PyXWkeuApUCTDXlIlq54yXjilK57vuCsSm05TZdZZktvatZ/3/vEC2SmJnmdVPm94QnMmpfP3gejjWMv3KHlLLTU5X6MvTNJkEfHzWbRjs4FFtn9iOQgTYwgQAAEQmPUEhr2n7peqaVXx6ajiKMe9OacbTtPRNgf/7he3bA6KyvvpU673Xq+KrL/4Dv3TnQiKGkVJfQ0wbztFF3t+RIN6HUJ8Z/0JwgJBAARmLIGml3eTsqOF0rtTKL+tk3rYUsOMtdY3wzQB2dIgd0oWsYLDLCstObRKPizHi/73R+UXQLkspVhUWPjE8vSBCB/frPbhrlgLZSYXUM05J+W2G2nto+fldRdLRdWDaRBD4zlVrRxhMs5k/gRaSk0lqt69y4fFTHBLbwPV2lnabVuqekXHKDvVM2mNvkoU7X22u5NvTCohC39wwDj4g4M+3aTmZ75rkrdQTZOTor8w0fzAV0E9bJtiXqOdGXbmBuxMnoQJeBQEQAAEZjcBZyOdapPph7lp9NidyHs+CbyiL47aMe7j0ljjfBKEy/fnwq8Bq83b6OTFHjVcGAJ1dp8erA4EQGCmEuAwTc+idd8Tjh0mElRlOouusfmolWTJWRVg65ke6uTwZ/P+dDKdEqTioarATacrtFzQVUvZq8riMBQKRBXea9c8LefXnhPf2L5fXlf7fTrG1W0NHO6rejBDtX2qHU8leGShMl/c15ROqRZVtgfp6u6ktlFeUccEw7Ln3/2KTpSUDUYy/aBurKc1QFN4XbqF8bK7zeGUPPYvaH6ACnW0bXHjvcAB2obHQAAEQAAExhHo6aRPPU9TeoxIsp7o9kQvGKMeU1+7Zc8GWpGm45DgsZqWXwOinjL8zXW5yxl5+x9vQ6DiwIEACIBAqAl4CyOtEzKPNWtFkZyKwqGU14VuDllNnwIX6sKvC2VLJYnjaw3du24uPtTdQvprwqSL/aj5ow3ZZp7XLpoTYjkcNAD/pxpWygV5NhpjKY/jezPZo3o+Z52YXskFgUq2kmWUaPV3D72eSM5lbUmiki5vfivnWz5QaMZaOIy2IJ+WW7LorBx8cTpiU+vTnF/L+zCBTemHGym7czlVLDfR9awGuerwzpFQX385BHR/bzdd533JXnmvpzWg8UY/1NFNNz7Oc5skYUweKrNxly2Ok/JbvkX7HM00zyTdv5iSs5s6eLwsto2LNSG+d9IbggFAAARAYPIE+EN5LoQUEflS3TvU1hARxQmo929Dw7k7X/4yw4Uc1MkzxwggAAIg4B8BLkRTk3mMWg2C2McVe60LuWqA9rZ6ai4OtZGKinwbu//ELur37dYH3qUW8llkahOVrEay69vZ+1ntt5fR2X2d51DDhCViTerNh0zOptKGY1oF3yUh7rPqbDxJ7NAlJXslZUxCHE8Wr812VSpv7pITctaLeRXLyXRdqwAtx3Nxocn0Ku1l3goH1xq50JLrQZ8n+Ohpnew6A3ne2VjDe5REz3F87zw/izUFMh+eAQEQAIG5SEB9fVaUBDKwB1Xzhj4Awki+6p7f0Oc3/ha14vbeh/ZIhUCdi6cKawYBEJg2AlphJLFIsCssufLIU8iWqF+svKbNpmBPrHkCF5lEO+codh1epnr3OEfRj7KuQwZ5cwlLqas5l4yjQmn7r56YtIhWQ2UptZCKOG+zv3r3Q8ezcqsZafkCsb5kAa0oqKf68nTZwnm1wQzv9ccm7d7oVOoulblqcoG4riyd5tnbAw6NVZHHqPlBdJ26e1ncPaDSkhZirWQ/XMgG8WCpIcD0rJUKnyX6v5N7Jnwz5D0zJZTOubHIPw3iBmAoEAABEBhFwJtPyrUzej1aiO9E17A4zY+ppsE/eQsm+QISAtUXSrgHBEAABIJEwHlgN13nnplKrkEsHup3al34B49oOSJ0TlGVpFCH+Krl5fPsyRymmkvtXGW2OoAcTRbyco4kiBzfy/mndeyBdfjtgQ3SlnHPUbWty0Vxv+MTSjdepOwtFnqrbAu59EHM/wzQ2NjcNym7gMN9+fCo7UkDTN30eXZvpd9iieN776306/MoD7gx0UhxLwSW16qGAR9cbJMoQR1jXBXiYNiGMUAABEAABPwioL4fKDCcpt+8k0H6CIkOPuzDak4JWlDYjjYzflHGzSAAAiAwCQJaYSTjfGG7HEvpPM6IT9GQqPlPp6rRTChDfNc+ekE2FZGY1cB5ne2cy1odYAGhoVzC7FVL6VmuhOQIRSWk++yt1foUC+XlYkL9oJYTust22bMiyyNXcrGkbzYb5Mwge1EfdLzUysHrqUrcHG28J0fYnGAgPXtQJ3UZE8hMR+hGj8LFkiYQu0OVfpOe5/lUN6sPhTF8sWm4uJF5byxFBxqby1UlazkGe+NPxuafWhd+7V58ZqX0978TI8zmy25f7ME9IAACIAACDyBgSKAk8Rh1sQf1MX4dGN0yZvgpfj/gWvDL/ZGfXbKo4jSKxekt/nvseqYnP7L/1uMc6ntwxJvKr7Wu16K+EbnQFku32CULDypOHwiAAAiEgIC3MJJRsGc3kIULIw17T9WpnY0dXESIcxu5SpLAVZIUTcjmC63mLGpsOUzpfD81vSyL/GCDXK59z6GlqsNsRl3DeadJJV1UOSBK8yaRI9rEvT5beYXx41Y4trhRFZlK1pOlonUoFNhEJd/OoIoWD5mZsz3VMlL5NxBQw3NVcF9QxSVK+iFPsDHBTFRZS+ecm7nFivdjhbEFjt7X7MqosJNHDXNuGbKr1UNJ3Dc1n+1yBMCmu7ON7JX7aNuNw7I108oVgJyD53NMYqWykerVnp95RsrsLXOnGPOk1qe5kFNLOblEUZfZtOm2LoOkM3cOcV9QceI81ZgMrZVOfv158vzFdd9w4d4GzvFkX+1GTlS9OSpRVStilMJFjFrVIkZVFFe6kdffyuvfTzda4qhU3Zeh9c+76dLNH91jVftPoBY3MtOa9FjSB5o7ylUl7Yp5TP4pn0n34rhiKe70u/R7Hb/luXxZ3avBg4vjdHlawSU+Q29vpBWHW0lWbW020dvfXUGHW2Teq7P06O91ELWB/OfBMyAAArObwFBbmPyGizT42B0qHqdQvUWRpMg9V35EjS5d1O2fsTi1rnVdfHVBpBz72r1snD3UoXyLnltq4D6o34BAnd2nB6sDARCYCQQ0cZqzTshj747SuoejI5d5rFarJjKHw3sVLrFrz19HpZYWj9NpoRaPkXLEPdTDlX1HmqMmc0GCmbCg+9jgDcm1aHmnN3INnHcaeG/QYS+sWnW40pJCCV3NcjwLMrXKrvNAIxmO3qDS9XFUu34vralqJnnrQVpsyqP1OSW046ibtjYtJlNND3WVK7IxQA+n6jnVqvyyqFJkHuuQdyxynhvMWce9WclD+etyqKGFxaLVKjkPHLjHLvcEdn2T7fLX86oK4PNll0Rz8hFaHlfJOaDeolHm7FI625VL6UM5ur0LX6Rmt4FeidhDTj47rezkzHxEvZHPDucCP8jHarN9oLNuz3IXZNRLDXcOuceLWdUTqctokzxqf9sMHWU3uN3X4626+Q6b7N0XB5VsiKfaDftozbGPyb31HVocl08bcvbR9qF9ieN9OfZJrtskjq3SqxU3SsqkylgxoNxRVYi+wkLU4/FQQZz22bvmKS3UErxZtBoEmv8V0U1VC6u2vuegUra1ZsjWO1vepe/E5dGGV9jWI3eo4Px3KL7GSR0fbx78Sloacdlmg+d1hv7tgVkgAAKhJ6C2hbG+/pLr9VXnImtvvuO6E5nJhXnvVubVPmTmv5q/WvB3qnEu799jb8WNpL330af8GtC2cDWVGSRifQqBGvotxYwgAAJzjQD/IRcpOo2KitK8S7+6i2xXvf+0XZknFo0qsatW0T3OP7cuW+tJSLYLHUN5qU0fdlD2jsNaW5ph7+nCPxR6Tj/nEQ4vm36PatOmdKrgwjkNXNAo0LzT4XNxvG+JVFi0ZOSYjC5idLyvT7IanPKZNkVMPFuutcQRHukYtCvZYn25V6g5z3kGzZkWcXTvVH/PnFopd7iIEpdRourdu4aHkKLTuLjS0FZ+xj//zPsbtquH7SIxsZ7tMrBd59guGm2XrNnVzhWAq/30oGpFkSiV0tLUr9Gr6aerfGaGjhN9cIVF5rIX3fHmNqnD6XWyN52+TlnbD9GbpwRNTKo/47xk95mVbunPA9LIz7Sbl/2YSpKN9J8Ht1C0nosujZqKWwfprIVFd3/y2R6aN/Qd74uO98Vd36ZIiWcOkb1d1OU90nG7TcmSzhzKZc+toKNzntvmzHRp5yg71Me9Xk5B2tfxGn3B9520eW3057Id79M9YeV9meAhtbDS3fPVF8G2Dp75lHSJH/6cLvxWjMhTOm61UZbuw5/nkqQTI4Qm+Rbbqst792KE+SbCgv3ZC9wLAiAwRwgse532/usC2n/oNXIN6mnFqGVzalHUjp0TcHD9Yswv7udtRYjvHDlDWCYIgED4ElCacjx7hDeplYUoh5mOhPZemVcs6q+w2L0yvWt7kfNODVreaTkNsPgKJHzVrxWo/VG5uq9jqcDVfVWPGLejyd6htX5RMp2D5+oEMfNoDLEjlxz+Fw/2y5QxN587w3aVkGMZ28W/cPZ8yQ053xxll6jZpbnBQ2RX9SOvuL8t7KAnqk6NCavlNw+66Kt7KHrcajUvanO3m1KMUs3qevfunTvVDxx8a1+j7gt70DuWsRd0eF+yeF+4YJFS8+TtsjpRWvMe55gynOF9UcVpyvpaKf7Mx2T/gsXySf/FaUAb1nSGjiTto+ts61dqsPSBL0nJ2k7Ll1+MUJpibx08JerWHIkh4bdGuslhwbhAAARAAATGEtC8qB996aJnFkSezKh2rdnCrzU6b66pr6w0cZp9KjKm5hL96fY3ovhh7VkIVF8J4j4QAAEQmA4C3QdoUV08VTUvHdE1w/msea1Z1ODx5qhOV04qh33KkqVNNJd0Tzrv1Fe8Wn/UxJVadV8l80kWpJ+KWW9wMSW18pRWKCeR3ojppZ4yp/wCCyz2Oge1HcxEdmqCVLNrWCj/enrt6j5IKXVxHFK7jNpFgUWhjfMv1Sq8RimvdSOdHeQc1fvkpA6LVGPZXmlDipO2f7LZ7UuP1eF9iftBnSZIz9X9Wtr4xhL6y4CmAKm2LZG28b44y5xudV+Eg4spZd9q2na0mVwGH0Wwr4fkIfc5u1mQJi6nuIxhQfprXdZPltDvJH5bpNrKZ+gn/9xLvRd+O/jCmzupVxQQ5hsk9hgGBEBg9hAYFqmGd0sjX3nmK9p66VUXv16MCfedaLVqEaXv7lsdWXDoI4p+XBfVOCROIVBnz/nASkAABGYZATUseGGC4smrJaGrZfOY0F71d9aqUk/NPqMwvuBSKDF4806LRIUL/9j117gg0YkpbwXjLUZULJpXx1Kr5qdsok67mbgyvfeKNVAiFVBGikJnq7SQ6JCI09F25WqGdN/frkVs1/tTa5cqMBcmeNz5tSQ5mrmQE+d7sjjVwmY18VlV6q7da5DeZ8/mPcWKhjCq9xH7V9PS+ujq3fDmCY+Xt0iSTUpaHcOhwWoH0iZytCVRQoxA0eq3vFfzeV+Wp3h4X8rpmuqVvZkqp0b302ccohzKy1skyaZLej6W/iGBE1OphzrbzBTHvVO1b2ONlChsoeWLPVTPtvZeZHF6GTmoodwjzAUCIBA+BFSRSvQ4/duz/fT5z97y2XBO54n6bvRf6fOat+jzcU/Bg+ozRtwIAiAAAqEloIbwFs3rpxO77n0DrxaVofiq0Bo0ajb2xMlliwxihYe9uOXLaGDIQ+ePQd6qv/mcS+pWW8n4FBqs5WKmFlJafzV/aYWYpOjCNOqr3k19qgDjXNBoLsRQxP9Whc9Qfqg/ZgV072i7HDPALjWEt1A/Jnd2ZF29jSf57BzzVlAK0sXr11GqlfeEx/aun3NCeV9OjuzLSI7oZ7xX03mxrRH07JCt6pmxUcQTO1OpfyhP1XZZ/d6qnaHfTLOt08kJc4MACIDAdBGAQJ0u8pgXBEAABCZBoKfDTonPxVKLV5SF/Oo98BLlseeypPtw4Hmn3BakjduCrGHPleYMnY6FhJzc9E/YrZ6dlTH059HJoNNvFiwAARAAARAAAY0ABCoOAgiAAAiEGQEOrfXkiC8Lqw5Pj+F38067KP9aHYf2OgIK7dVyFnGFlACfHfcruk3Sip8LpKaGhrSIVEhXislAAARAAATClQAEarjuHOwGARCYswScTR9SRXIibZkGAtYXOSzXUCR6RvJOAxOn3vDeNtGjZJGR80cHpmEtc3HKXq60W5GUQPkP6Yk6F9lgzSAAAiAAAjODAATqzNgHWAECIAACDyUwXL3XeCGLSqrGFk566MNBuGE479SucKebSgt/kextu+3/NdSv2/8H8URABIar9xoubKSSY6+N6Yka0IB4CARAAARAAASmiAAE6hSBxbAgAAIgEGwCavVeSivSirf0cwGgUKdsNm2K5bxTopFGrMFeIMabMgJaVV4uLqWdHS78M3/KZsLAIAACIAACIDA5AhCok+OHp0EABEBgThDwek+LRFK9p8G8khMINZKCCRRjgQAIgAAIgEB4E4BADe/9g/UgAAIgEBIC7IGTNO9tWrCn41Yo92mjE+xZMB4IgAAIgAAIgEB4EIBADY99gpUgAAIgAAIgAAIgAAIgAAIgMOsJQKDO+i3GAkEABEAABEAABEAABEAABEAgPAhAoIbHPsFKEAABEJhRBF589IJsqM0Uu5pz6ZogSA6bzadeqFyJWD6fs05MV7aT8uxAwD1UZxQMGAMCIAACIAACIBA0AhCoQUOJgUAABEBg7hD4oG+JVJTWTyf8yB9d++jX8qJNe8XE61wKGGVk585hwUpBAARAAARAwA8CEKh+wMKtIAACIDDXCQz3Qs1rNVNJdwvprwlSZmbTYI5kESs8yn1b0GQ3ypQ6IErHHTYpTU+0NsEsH+kkMcj1gOf61mD9IAACIAACIDArCECgzoptxCJAAARAIDQE1Gq+1vdL5RpDp2iMIRowENlsV6ToQm9/1vteV3eTIzTmYRYQAAEQAAEQAIEwJwCBGuYbCPNBAARAIOQEujup7eWVZDlVhxzSkMPHhCAAAiAAAiAwuwlAoM7u/cXqQAAEQCDoBJpOV5A5YSu10jVtbKt1oexLiK/D4VshpaAbjAFBAARAAARAAATChgAEathsFQwFARAAgekn4M1BLRITV8bQsZ4m2blzJ9WSoIb4eoomMm9UiK+3im8x5592U9eaXNnIFYBtPlYAnv7VwwIQAAEQAAEQAIGpJgCBOtWEMT4IgAAIzEIClZYUUhqrKLWuTnI4HD61mFnLrWkksVDkWkp85ZOpIp+SS7tke7yVQ4XhXZ2FxwRLAgEQAAEQAAG/CUCg+o0MD4AACIDA3CWgFkmiNC6IlMYMrp7wq/jRcW5NU1i0ZCy8/mpa0j93eWLlIAACIAACIAACYwn8P7j852oz9aRrAAAAAElFTkSuQmCC\" alt=\"image\"\u003e\u003c/p\u003e\n\u003cp\u003eWith respect to the horizontally arranged beams: \u003cimg width=\"119\" height=\"14\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e; and with respect to the longitudinally arranged beams:\u0026nbsp;\u003cimg width=\"161\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPIAAAAVCAYAAAB8KbOeAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAAjLSURBVHhe7Vs7j+JIEC6jydmcFBMg0jlpIV0JDZNMxEokXAQhTsiQEYiMYE0I0ZEgLREJoJUuNReQckiHSSdf/gB9X7cxT4MNmMfsYmmSoR/V1VX11aufSqUSPb4HBx4c+NgcePrY5D+of3DgwQHOgYciP+TgwYFfgAN3r8iq+syyUoIaFrOjGhl6jlrlsvQL8P/gEVL+H0xWBssxmR6jwPDXP/e171VVU6xfq1KlHaYCZGt4h7KV+vRjnv43KRXyOUoEyVcql9k6n+5ekVf6a1B81oLyzrgSL8/AL6EWk0mh+1Zw9fmdwR5Rj9VdC0prFpdKpTipKT+Lycq15fu32M+Sn3ayR039ZQcgnt+LLDG6vWy1fsZ9el6ax9IxKVPQ58Wi6iuVVsr8YRR5v1QZNAZoRbXXq6F06tnPqpU2hZs6zVruELLfaYBGY6nEXICm/S5VKwo1LNCNZkhr1l2veWlNO+Wc59KUgsFLVxo0WDoiUcpoTQoII+7tt1JiEyRa5eHGBubvRaJI6CaypWwhb7n106c3v85joZikTfS5IkOZF8j84RW5XB5KAWTecdHe3rLNamoKbn46QTLulihDvSDR5tXbk2AiapSSRhBKao7pZ2VKIF7I9AwqDVuSWFtOkCIL1GZeuHeWoI4Lx7nkp55z/fSn7C1CCXgtnCdx8ISvxxVbTsjcCDLTI/Pw61dJGeAe9SAM7O665TL2i5eo5OqWz6PLjud2K3Jlbmo0D/1ZkyZ6bi6rqq8MZf7winwe+9zPFspYnVChySjfjdExnm6/qtAg06P4Nnrjf4GFwJZbQymvRVlDaVCnX6eAe9I8HXnOOc8hZIl+azzh67WGAamXIZZod+H6qsyr3IhlaGA1XIc655zv0NxjeR5MfKXPynfqGTlh+HkB+UkE+tk00EH4pyKRBLigNOBiQHBrejrVX6b412IM/qcZ7l3KSx2eryviF5EFg1U9IvY8haZyaybFoV3DVplkP20kGhwvCWisGS9A4xV+DwMladvSB0MRLLVKbp1C57lzTj3nufs6zvfavZ12qQ1WZwovuNRdv2qVaLxD2QomKPlZoTY8F0uTn6bI1k3yOrG3LEmJMXVrWRqH8qSzPIkkUqVG4c6YiI+p94lnkNvdKcUdOX/5AS91g7QRaIy83dyq7jvttNsGGhd20dhmAo+juVF6s5etyzP0hjtwN1YtZJiSSNB7z2CWpyJc6+KuIbQjVSBbmoDcLqoaxlgAVRKINrOJj3iisZcZINEVJgy5gnPtnvngle+PCJsPxlOEGiFMLNFTaxaQEMnT1D8CygyoTWZ8wuP+5wiQp6GQiLG4W4hSkJvtVkjpNNobdI+G99yG0/YX/t0snRXh1ThrphlH8/jQfVb7wuRfffky3Gijp7E0YmKYNCFrRRce4PP7D9YJF2iKnEWEJkTTPvnxv/GbfnK57haJrqMZPprQhLE5xMa3jJENnvoFGhRyZuC/GbMsMrPTCY0wKhI6nOURbqPLzk9kfY+mfzXBzFhHCofpubZhseib1irU4OEK9HjNq9457zJeQ1b7nDrx9jmLRZGVI0qIHNGaEfbGgK4fxIu9l2U28KG0SGwJF1eWYOAYUNq+QjAMxKV8aMKq2TaNIA/pdISSBWS6D9TcpxMhybRflBfVkH2QvTj8rWRrW4iEIltKG9XyKxfVLoYQ7giU3RlgzlDOI6b2O7DcEEoHQL6eYVnRbvEUNb+DpYtlHTzSWwrvERzYGLp9zkOZ4/MM6C6F5+5t0Trghg9gYtn3YK5JWtsM8Yw9yS6roWPEdTMK9YyEKSQDkA6UFMx8xIgm0z3cFqAF1/t1VWmwG3kL2bKjw0TkhdJuIJtNDCFiODDaKWa4lpVytqqnqoQH86zShoPR42UoBUps1Hkzgptilge03eUSJgJSZrNmy2NnM8QbI+iz/3githNukq4blI1NKJ8PUbcao/c3fS+KO7FA5DaA2A7OntMyl/0dCcCQJKExpLQoP9ko7baSHBMzXMNKrVz/wt0luix0WW8AsbtR4Tb+4JWCVUcR7wCLTfKLLrbLysF9rS5TGGhKiPtSdZsyU3R/0om71qKPYOpnHJQpiApBAP0FdsVh69ByGHjboDGsg12pT4Sa0aQjaN2Ch6r6xzzrIyn6LQhjwyOmsvlowg7Zdg+yihnU1wlqqiGKg1m3OIi5p7sY5nL0HXDLHBoNOE1WcktDLdCqjZqlQPg74fzlyD565QPnPHqt/RM48qaSUaYoCqVrIWqqpjKbWWt3nXuidIZyynoL794dg6+UjCqkdPpU2tLkddAKisSZn73WXWTCPePHgudI/dh+ltuPpOAA1WLosVlHFm1oKJFY3URmtnWTebyD6i3DGxZkio01at7aFXSZePOKt4JPcOHaqLcvUkgo4XEmRVkmudlCuN2OaUeDaBLBDwO+hpWhXSSnEL3c7DvmnF4TyUs+Ri+CFk10zylidVbkbauol84WjTNe7bkqd3XoeauTbmVUEiSNUEdG26xXjSh29B/g+fwdstVQght91dPed/rnc5L+gs1f6DE92bWh7Wt75C4Mb+LffrjgFXOPWceMYfbXAY9Zy81YwadAHB17+NuesNYeateOabf+wfDDo3ZT624PuphbxLk9pxPPTtmbr8k7ueJoi+TIan1QYqftTvv9JU9aVKZKDaHM1grWgxX+b94EdMnPiefrFSA19Qm91iR9+y/HK8gfv9fadP01QlKRLnTNJ93d3nbMk1Z7TLokBwQq6wYjFPDx+ok1c7uvny65/7FrCyVOf5ciXZ2UEJT4I75+GsClh+oyrrx/F8b0hUcDvWvGLc5st9B4ux3Teab9CKtN0CoH84LJ4/OWA5Yyh9DhmEbGu4ASlxcPVrylEo9H8B45VsV7ZLy4E++R15SY73X3jyYsN5/3l5hvehX6UuE94Oc1T3jNaL6eSLbA9faqRrvu3gl6D2VhL3Gg32RN4doidx2Pz3ie6C5Pzd8jxwOgD26+Xa/V/3K1BAr/iR6fAAAAAElFTkSuQmCC\" alt=\"image\"\u003e. Because laser beams of different wavelengths traversing the same grid have distinct\u0026nbsp;\u003cimg width=\"24\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACQAAAAVCAMAAAAZ+LyiAAAAAXNSR0IArs4c6QAAAGxQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZjoAZjo6ZrbbZrb/kDoAkGY6kNv/tmYAtpA6tpBmttv/tv//25A62////7Zm/9uQ/9u2//+2///bS3LZtAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA40lEQVQ4T8VS2RLCIAwE6121VYtFKwXL//+jObjUGcc380CTdLPZBIT4p/lbfS/6m93wqcarw/iSdZsuxI+TlHILNV41kPIKQjIAuFVPKLeEclNBG4uHmNoGcl34b+bErfHj6hEoFhhbOM2sp1Sk8oqxSBkFcCEZSxBanjm2UM42tcRJpsmdjnJPdRlUcEZSf5HETuLfOINkzBqJjTOTTvACxBoSKIyZNRnkwNUU07klTRRmAF9Xg/BMnwgM7joYrfy6hv2He+SNC8s3whY2nori4nIi312R+/IKStQP76lsVPhPG5wQipyEpCUAAAAASUVORK5CYII=\" alt=\"image\"\u003e\u0026nbsp;values, Eq. (2) constitutes an ill-posed inversion problem for retrieving spatially resolved parameters.\u003c/p\u003e\n\u003cp\u003eConventional flame field reconstruction techniques typically combine two-line temperature measurements with iterative tomography to obtain temperature distributions\u003csup\u003e17,29,39\u003c/sup\u003e. Despite their effectiveness, these methods require the precise synchronization of multiple lasers and detectors, resulting in complex system setups and challenging optical path alignment\u003csup\u003e40\u003c/sup\u003e. In contrast, our approach exploits the multi-line characteristics of broadband MIR DCS for spectral path encoding and uses a single-detector architecture with optimized reconstruction algorithms, eliminating the need for multiple transceivers and synchronization. This configuration not only simplifies the optical setup but also improves system stability, rendering it suitable for practical and dynamic combustion environments. Additionally, a modified fully convolutional neural network (D-FCNN) was developed and optimized based on the FCNN architecture to address the ill-posed problem of the reconstruction process. The network connects neurons across layers through fully connected mappings, enabling robust and accurate reconstruction of spatial temperature fields. As shown in Fig. 2, the D-FCNN model consists of one input layer, thirteen hidden layers, and two output layers. The integral absorption value vectors \u003cimg width=\"14\" height=\"14\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e\u0026nbsp;and \u003cimg width=\"13\" height=\"14\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e\u0026nbsp;represent the network input, whereas the reconstructed temperature distribution vector \u003cimg width=\"7\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAVCAMAAACnruT/AAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjqQOpDbZgAAZrb/kDoAkNv/tmYAtv//25A62////7Zm/9uQ//+2///bTuYxdwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAU0lEQVQYV6WPSRKAMAgEJ+7ZI0n+/1VRQ/Rq2ReoopkC4AfVqYZFMRp5scirB81AGjzytl/pYborUwzPGqcuEOtCGKO01b113ZWk+irxCU/Ol28OLpwCOJYrqlsAAAAASUVORK5CYII=\" alt=\"image\"\u003e\u0026nbsp;represents the output.\u003c/p\u003e\n\u003cp\u003eA total of 300,000 samples were randomly generated based on a random mixture of Gaussian functions, representing various states within the flame region. Each sample was assigned distinct flame center positions and physical parameters, replicating the multimodal and asymmetric flame distributions typically observed in practical combustion devices. Specifically, the integrated absorbance \u003cimg width=\"107\" height=\"14\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e\u0026nbsp;of each laser beam was calculated with Eq.\u0026nbsp;(2) based on the assumed temperature matrix\u0026nbsp;\u003cimg width=\"79\" height=\"14\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e\u0026nbsp;and concentration matrix\u0026nbsp;\u003cimg width=\"79\" height=\"14\" src=\"data:image/png;base64,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\" alt=\"image\"\u003e. Together, these components form the D-FCNN sample dataset\u0026nbsp;\u003cimg width=\"105\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJ4AAAAVCAMAAACALKdSAAAAAXNSR0IArs4c6QAAAJxQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjoAOjo6OjpmOjqQOmaQOma2OpC2OpDbZgAAZgA6ZjoAZjpmZpDbZrbbZrb/kDoAkDo6kGY6kJA6kJC2kLa2kLbbkNv/tmYAtmY6tpBmtrZmttv/tv/btv//25A625Bm27Zm27aQ29u22////7Zm/9uQ/9u2//+2///b+3UJTgAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACZElEQVRIS+1Wa1fbMAy1W0oDYzAohTV0gwbY6gJ1mvz//zZJfsmNDWThC+egD3Udydb11cMW4ks+EwObb3J0DYDbZTRmpqKZSXm4RfuH03XPc6qzP+9eoaSUC/BycyeeRish1HRbH4UxMwV4F+SiLc8RZD+pT8Dje6UurDHCamYLcHnhxsxUOHho6qQtic6U7KuIACttCQSRBMxPhRyvUQG7O3i75U9wewkLq6kbM1MPT49DZJWJdko6KhVMMQ4IgUMWFQZSS4yMhVfJg97w2nLq0TRXv3LwuiqGRcMWCtDUp+xwpAeWQHxwn+EM/YLrl8I29wvFqIw47Kp4UoBptX8w1CuDl3xgFOkPWBroZsxMbe5pjIEROHwOXkplmLHSzPiMPqrDR8umoWBTmIbSzOUIguzGzLQDr71ZUYgSklRFfPEguNMWLhQJZSbDowNjyQa+NEwZl3yDpCqCl1iopCN0ADy/L3ZpKZPsBZVmpR3BqzpJq8cPH8Ceh6eQS806V6CPqarQJHnu8fq3iXy0cn0/VO7bIeXZjK4c8fUxtr9kGJiqLX3j9c6pqooAmzxg+/DVPCC49tx22GCTF9DxD76v4eqh5OGq5vJ2TiaACJuDY0151s0X8+sKbQA8QbcGPhvguJqST4/u4N52PiJVXfzY2muGbg0LD9Y5fPSlKTFHd3M5oRtpCLy99oouMS5AEQUoFsRk4JlLo2uSWDQIXufFQs8KvLfvsXnGgqipJOyLpWuSWPS/8NLvPYC3Wx7//Z0oM6TGvNn6v/f6VO1rtpBsZy+zSeq9WZ8UcpK8Vz7KudvnHyvpWarbB4nQAAAAAElFTkSuQmCC\" alt=\"image\"\u003e. Of these, 70% of the samples were allocated for model training,\u0026nbsp;whereas the remaining 30% were reserved for testing. In addition, the reconstruction error was defined as the ratio between the norm of the difference and the norm of the true flame parameter values and served as a quantitative measure of the reconstruction accuracy. The reconstruction results of the D-FCNN model for three representative flame field distributions\u0026mdash;unimodal (a\u0026ndash;c), bimodal (d\u0026ndash;f), and flat-topped concave (g\u0026ndash;i)\u0026mdash;at an integrated absorbance signal-to-noise ratio (SNR) of 20 are presented in Fig. 3. In our experiments, achieving an integrated absorbance SNR of 20 required an acquisition time of ~9 ms. When the acquisition time was reduced to the sub-ms level, the corresponding SNR decreased to ~6, leading to reconstruction errors of about 10%. Therefore, 9 ms was selected as the optimal acquisition time. Even under low SNR conditions, the temperature distributions of different flame shapes are accurately reconstructed, with reconstruction errors within 4%. The simulation results indicate that the D-FCNN model achieves high-precision temperature reconstruction, strong noise robustness and excellent reconstruction accuracy. Future work will focus on increasing the number of measurement paths and extending the reconstruction model to enable simultaneous reconstruction of multiple flame parameters (i.e., \u003cimg width=\"7\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAAVCAMAAACnruT/AAAAAXNSR0IArs4c6QAAAEJQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjqQOpDbZgAAZrb/kDoAkNv/tmYAtv//25A62////7Zm/9uQ//+2///bTuYxdwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAU0lEQVQYV6WPSRKAMAgEJ+7ZI0n+/1VRQ/Rq2ReoopkC4AfVqYZFMRp5scirB81AGjzytl/pYborUwzPGqcuEOtCGKO01b113ZWk+irxCU/Ol28OLpwCOJYrqlsAAAAASUVORK5CYII=\" alt=\"image\"\u003e, \u003cimg width=\"8\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAVCAMAAABFcv+GAAAAAXNSR0IArs4c6QAAAEtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOpDbZgAAZrb/kDoAkGYAkLbbkNv/tmYAtmY6tv//25A62////7Zm/9uQ//+2///bnOTBDAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWklEQVQoU6VOSRKAMAgDd+tSXGr5/0uFUu3ZMQcmJJMAwH8EVDSrNR2VB15kpKXeAQJOynnuzneJbhSJ1DaNN1RFIlrW5jLSSEZ0ffn1GlKngezAE8+3i/+F3YVUArk/PsVbAAAAAElFTkSuQmCC\" alt=\"image\"\u003e\u0026nbsp;and \u003cimg width=\"8\" height=\"14\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAwAAAAVCAMAAABFcv+GAAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjqQOpC2OpDbZgAAZjoAZrb/kDoAkNv/tmYAtpBmtrZmtv//25A627Zm2////7Zm/9uQ/9u2//+2///bPezQtwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAAFiUAABYlAUlSJPAAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAaklEQVQoU6WPyxaAIAhEh6ystOyhleX/f2doHVt3YgUD3AHgf6yShA2GSEXWVIzATt0WC99wMdW3RzAKrk06h6uWnMNLYfMhjp4FVnYx5w7DTp08gFMPDK4SLJg476IvYIjFo6fy5X368AL+TgPrvEDciwAAAABJRU5ErkJggg==\" alt=\"image\"\u003e).\u003c/p\u003e\n\u003cp\u003eExperimental Setup\u003c/p\u003e\n\u003cp\u003eThe flame field was generated with a commercial butane lighter. The lighter consists of a grinding wheel, a flint, a spark aperture, and a gas nozzle. Rapid friction between the spark pin and the grinding wheel produces sufficient heat, melting metal particles on the wheel surface and generating sparks. These sparks ignite the nearly pure butane gas emitted through the aperture, resulting in the formation of a flame with an irregular spatial distribution. The flame has three regions: the flame core near the nozzle, the inner flame, and the outer flame. Owing to oxygen deficiency, the core exhibits incomplete combustion and a relatively low temperature, whereas the outer flame is well oxygenated and reaches a higher temperature. In this experiment, the flame tip was selected as the target region, and a measurement volume of 8\u0026times;8\u0026times;21 mm\u0026sup3; was set up with it as the center. Afterward, the lighter was mounted on a precision z-axis displacement stage, enabling fine positional adjustments to scan various sections of the flame field.\u003c/p\u003e\n\u003cp\u003eMIR DCS Frequency-domain Encoding System\u003c/p\u003e\n\u003cp\u003eThe flame field reconstruction system based on the MIR DCS is shown in Fig. 4. The system employs two MIR frequency comb sources with slightly different repetition rates. The output of the first MIR comb is divided into two beams by a pellicle beam splitter (BP145B4, Thorlabs). Each beam passes through a modular optical delay line before it is combined with the second comb, resulting in the formation of a DCS pair with an adjustable temporal delay. The DCS beams subsequently entered the frequency-domain encoding module for spectral filtering and beam alignment. This module consists of an MIR grating, a CaF₂ prism, a lens assembly, a square reflector, and an aperture. First, the dispersive elements spatially separate the beams according to their wavelength components, producing a beam footprint larger than the target detection area. Second, the long- and short-wavelength components were spatially filtered and aligned via reflector and aperture assembly. This configuration enables the precise selection of spectral components and allows the two beams to be parallel and symmetrically distributed. Stray-wavelength interference in gas absorption is effectively suppressed in this configuration, resulting in increased accuracy in gas-molecule detection.\u003c/p\u003e\n\u003cp\u003eThe MIR spectral region has strong CO₂ absorption features, where even small molecular variations induce obvious spectral changes, which is an advantage over near-infrared CO₂ absorption sensors. Consequently, a 4.2 \u0026mu;m MIR DCS system was selected for flame field temperature sensing\u003csup\u003e41,42\u003c/sup\u003e. The spectral resolution of the system is 160 MHz, which is sufficient to resolve CO₂ absorption lines with gigahertz-level linewidths. To avoid spectral aliasing and achieve a high refresh rate, the repetition rate difference was 20 kHz, yielding a temporal resolution of 50 \u0026mu;s, which is suitable for probing the kinetics of the combustion reaction. To increase sensitivity to low-temperature regions, the DCS beams were spatially arranged in alternating \u0026ldquo;long-wave/short-wave\u0026rdquo; and \u0026ldquo;short-wave/long-wave\u0026rdquo; sequences, where purple and red denote long-wavelength components and short-wavelength components, respectively. The grating and prism positions were optimized to produce an 8 mm beam diameter, covering the flame tip region. Last, all the signals were collected by a single detector and digitized with a 12‑bit acquisition card at 500 MS/s.\u003c/p\u003e\n\u003cp\u003eThe single-cycle time-domain signal recorded by the system is presented in Fig. 5(a). The first and third interference peaks originate from one group of symmetrically arranged, parallel DCS beams, whereas the second and fourth peaks belong to the orthogonal beam group. The delayed optical paths separate the four interference signals in time, enabling high temporal resolution and distinct isolation of identical spectral components. This optical‑path configuration enables the complete acquisition of all spectral information with a single detector. The spatial resolution of the system is characterized by an optical filtering module. By translating the displacement platform, the spectral components of the same beam at different spatial positions are sequentially filtered, as shown in the lower panel of Fig. 5(b). The spectral components of each beam group exhibit a symmetric distribution, allowing the entire measurement plane to be divided into an 8 \u0026times; 8 grid and discrete flame‑field temperature measurements.\u003c/p\u003e\n\u003cp\u003eReconstruction of 3D Temperature Distribution in Flame Field\u003c/p\u003e\n\u003cp\u003eWe evaluated the ability of the MIR DCS system to reconstruct 3D flame field temperature distributions by sequentially obtaining two-dimensional slices at different flame heights. Each slice was recorded within 50 ms, and the flame was moved upward in 1 mm increments with a precision z-axis stage, yielding a total of 21 slices for 3D reconstruction. The reconstructed flame temperature reached values near 2100 K, which is consistent with the expected temperature of complete butane combustion. Figures 6(a) and 6(b) show one representative slice of the reconstructed temperature field, clearly indicating the flame structure and that the temperature decreased from the core to the periphery. To further confirm the reconstruction accuracy, a cold aluminum plate was positioned at a 45\u0026deg; angle relative to the laser beam on one side of the flame. The convective interaction between hot and cold air caused the flame tip to tilt toward the plate, which is clearly observed in the reconstructed temperature distributions at multiple heights, as shown in Fig. 6(c). The progressive leaning of the flame tip in the y=8 direction along each measurement plane is consistent with the effect of the cold aluminum plate. These results indicate that the reconstruction accurately reveals the characteristic structure of the flame and validates the reliability of the MIR DCS system for 3D flame‑field temperature mapping.\u003c/p\u003e\n\u003cp\u003eReconstruction of Temperature Distribution in Dynamic Flame Field\u003c/p\u003e\n\u003cp\u003eSpatio-temporal measurement of flame temperature parameters is scientifically important for dynamic combustion, because it provides essential data for understanding and controlling complex physical and chemical phenomena during combustion. To determine the spatio-temporal resolution capability of the MIR DCS frequency-domain encoding system, an experimental setup for generating dynamic flames under acoustic excitation was designed and constructed. First, an acoustic excitation system consisting of a loudspeaker and a power amplifier was placed near the flame to modulate the flame using a fixed‑frequency acoustic signal, as shown in Fig. 7(a). The sinusoidal signal was increased by the power amplifier and then delivered to the loudspeaker, which generated acoustic waves that acted on the flame. Under acoustic excitation, the flame exhibited periodic oscillations at the harmonic frequency, revealing the phenomenon of flame disturbance induced by the acoustic field. To obtain high‑accuracy temperature measurements, the extracted absorption spectral lines were fitted with Voigt profiles. Numerical simulations indicate that a signal-to-noise ratio (SNR) of the integrated absorbance above 20 is sufficient to keep the reconstruction error below 4%. In our experiments, the raw spectral intensity data collected within a 9 ms time window achieved a single-point SNR of approximately 500. Considering the line depth and the number of independent resolution elements across the absorption feature, this corresponds to an integrated absorbance SNR exceeding 20, thus meeting the requirement. Therefore, a temporal resolution of 9 ms was used to analyze the dynamic evolution of the 2D flame temperature distribution. Within a 1 s time window, the temporal evolution of the flame cross‑sectional temperature is shown in Fig. 7(b), which clearly shows the dynamic response of the flame under acoustic excitation. The corresponding dynamic process is further described in the\u0026nbsp;Supplementary Information.\u003c/p\u003e\n\u003cp\u003eFurthermore, the temporal evolution of the temperature distribution across a representative cross-section is presented in Fig. 8(a). The figure displays the temperature variations over time across a 1 \u0026times; 8 spatial grid. Under external perturbation, the flame clearly exhibits dynamic temperature fluctuations over time. A specific pixel within this cross-section was then selected for detailed analysis, as indicated by the black dashed line in Fig. 8(a). The temporal evolution of the temperature of this pixel is extracted and shown in Fig. 8(b), where obvious periodic oscillations directly reflect the dynamic response of the flame to the acoustic field. To quantitatively analyze this periodic variation, a Fourier transform was performed on the temperature variation over a 1-second period to extract the dominant frequency information representing the temperature variation, as shown in Fig. 8(c). The red curve represents the scenario where the loudspeaker output frequency is 10 Hz, with the reconstructed frequency exhibiting a slight offset of 0.09 Hz. To avoid randomness, the acoustic excitation frequency was increased to 15 Hz, and the reconstructed dominant frequency (blue curve) shows a 0.01 Hz offset. These results indicate that the frequency of the reconstructed temperature variation is consistent with the applied acoustic excitation, fully confirming the spatiotemporal resolution capability of the DCS frequency-domain encoding system for measuring dynamic flame-field temperature distributions.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eWe propose a novel method for spatio-temporal flame temperature measurement based on MIR DCS. Integrating spatial frequency-domain coding with a single-detector configuration simplifies conventional multi-detector architectures and enables efficient acquisition of combustion data. We developed the D-FCNN model to reconstruct the flame field temperature distribution with an accuracy of less than 4%, enabling accurate 3D temperature reconstruction of flame fields. Additionally, the dynamic flame temperature variations under acoustic excitation were obtained with a temporal resolution of 9 ms, demonstrating the ability of the system for spatio-temporal resolution diagnostics. Overall, this technique provides a robust, scalable solution for high-precision, high-resolution measurements in combustion fields, and a powerful tool for advancing combustion modeling, optimizing energy systems, and improving emission control strategies.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe code employed in this study for reconstructing flame temperature from integrated absorbance is available from the corresponding author.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported in part by the National Natural Science Foundation of China (12274141, 12134004, 62425503, 12574436, 62505086).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eJanbozorgi, M., Far, K. 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Unlike conventional techniques that often require complex multi-detector configurations, we present a single-detector method for three-dimensional (3D) flame temperature reconstruction based on mid-infrared dual-comb spectroscopy. By employing frequency-domain spectral encoding, the system simplifies implementation while enhancing stability and spatiotemporal resolution. This method integrates laser-spectrum optimization and time-division multiplexing, eliminating the need for detector arrays and synchronization. Simulations and experiments confirmed that an acquisition time of ~\u0026thinsp;9 ms provides sufficient accuracy (SNR\u0026thinsp;\u0026asymp;\u0026thinsp;20, error\u0026thinsp;\u0026lt;\u0026thinsp;4%), whereas sub-ms acquisition reduces the SNR to ~\u0026thinsp;6 and increases errors to ~\u0026thinsp;10%. Guided by this finding, we achieved high-precision 3D temperature reconstruction of flames fields and determined the dynamic evolution of acoustically perturbed combustion with a temporal resolution of 9 ms, highlighting the potential of this high-resolution, multi-line absorption approach for rapid combustion-field diagnostics. This work demonstrates the ability of this technology to obtain full-field, high-spatiotemporal-resolution measurements, offering new opportunities for investigating transient phenomena and optimizing combustion systems.\u003c/p\u003e","manuscriptTitle":"Rapid Three-Dimensional Flame Temperature Reconstruction Using Mid-Infrared Dual-Comb Spectroscopy","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-08 09:20:51","doi":"10.21203/rs.3.rs-7722786/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"0a711f39-64bb-4476-ac56-a3b2a7cbf255","owner":[],"postedDate":"October 8th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":55917048,"name":"Physical sciences/Optics and photonics/Other photonics/Frequency combs"},{"id":55917049,"name":"Physical sciences/Optics and photonics/Optical techniques/Optical spectroscopy/Infrared spectroscopy"}],"tags":[],"updatedAt":"2025-11-07T16:56:11+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-08 09:20:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7722786","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7722786","identity":"rs-7722786","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}