Microplastics (MPs) have become increasingly common in nearly every natural environment. As their pervasiveness grows, so does the urgency to understand their abundance and origins. Raman spectroscopy has been used to identify MPs in natural environments. However, fluorescence from additives within MPs, other environmental matter, measurement substrates, or other factors can prevent MP identification. Polyethylene (PE) subtypes such as low-density, high-density, and ultra-high molecular weight polyethylene (LDPE, HDPE, and UHMWPE) have widely varying uses and origins (e.g. residential, industrial). In this work, we demonstrate a technique using time-correlated single photon counting (TCSPC) Raman spectroscopy to isolate the Raman signal of microplastics from competing fluorescence. Fluorescence suppression reduces spectral noise and improves quantitative spectral analysis. Decomposing Raman spectra using Voigt profiles enables quantification of PE crystallinity and estimation of its density. In artificially fluorescent and environmental samples, TCSPC Raman spectroscopy improved visualization of weak spectral features and calculation of PE crystallinity compared with continuous-wave (CW) Raman spectroscopy. For an environmental PE MP sample, CW Raman-derived crystallinity estimates often exceeded 100%. These non-physical values were attributed to a significant fluorescence background and low signal-to-noise ratio. In contrast, TCSPC measurements produced crystallinity estimates of 55-70% and 65-80% at two sampled locations on the MP. These results show the potential to quantitatively characterize MPs with TCSPC Raman spectroscopy. The ability to identify the subtype of PE MPs could assist in identifying the sources of microplastic pollution to protect natural environments.
Sum-frequency generation (SFG) spectroscopy is a powerful method for probing molecular composition and organization at interfaces. However, interpretation of SFG spectra in multicomponent systems is complicated because spectral intensities depend on both surface population and molecular orientation. This creates a challenge for analysis of the adsorbed population. Two-dimensional correlation spectroscopy (2D-COS) can aid in spectral interpretation, but molecular reorientation can distort spectral trends and lead to incorrect signs of the cross peaks. In this work, we investigate this problem first using model SFG spectra for a binary system in which the population and reorientation contributions are known, and in which the signal changes in a nonlinear manner with respect to the surface mole fraction. We describe an amplitude-ratio-based spectral reconstruction method where fitted vibrational mode amplitudes are used to calculate intra-component amplitude ratios relative to selected anchor modes. The corrected amplitudes are then used to reconstruct SFG spectra with reduced reorientation-induced artifacts. The reconstructed spectra show suppressed homospectral asynchronous features associated with intra-component reorientation and recover the expected heterospectral 2D-COS signs. The method is then applied to experimental SFG spectra of a binary mixture, further demonstrating that amplitude-ratio reconstruction provides a targeted approach for reducing reorientation artifacts and thereby enables population-based interpretation of SFG data.
Linear regression for quantitative analysis commonly uses a calibration model based on a large global sample set spanning a substantial domain of calibration sample variance. Because of the large variance, determining accurate analyte amounts present in new target prediction samples is challenging. Instead, calibration samples closely matrix-matched to each target sample can be selected to generate localized linear regression models for accurate target sample analyte predictions. The difficulty with local regression in analytical chemistry is how to select calibration samples that bracket each target sample over small respective ranges of innate matrix-matched measured responses and analyte amounts. Recently developed was a robust autonomous local sample selection algorithm called local adaptive fusion regression (LAFR) that can realize the two-goaled sample selection. The method is based on the physicochemical responsive integrated similarity measure (PRISM) algorithm to compute hundreds of similarity measures between a target sample and a global library sample set. Depending on the library size, LAFR can require extensive time-consuming calculations and this paper compares LAFR to an easier more intuitive computer-human hybrid technique using virtual reality (VR) for local model sample selection. Recently explored with VR were successful applications to various chemometric data analysis scenarios relying on the user's lifetime problem-solving training and inherent pattern recognition skills. Like LAFR, these studies and this study use PRISM to compute sample similarity measures. These similarity values are further rendered into VR sample glyph features providing intuitive visualization of sample matrix effects, i.e., based on glyph appearances, the user selects matrix-matched calibration samples in VR localized to each target sample. Presented are partial least squares (PLS) prediction results from LAFR and VR selected calibration sets localized to fifteen target samples across three near infrared (NIR) data sets. By using VR, prediction errors are generally the same or better than LAFR without the lengthy LAFR calculations. Also presented is a discussion on the Rashomon effect supporting the substantial differences between the LAFR and VR regression vector shapes and magnitudes but the models predict similarly. Included in the discussion is the inability to interpret the models.
Cavity ring-down spectroscopy (CRDS) enables highly sensitive detection of trace gases but typically requires high-speed, high-resolution digitizers for exponential fitting of the measured "ring-down" decay signals. This work investigates a simplified signal processing approach based on the Time-over-Threshold (ToT) method, using only threshold crossing times instead of full waveform acquisition. In contrast to the ToT method with static thresholds, dynamic threshold signals are employed to improve linearity and robustness with respect to signal amplitude variations. The proposed dynamic ToT method is implemented using a compact analog circuit and evaluated using a mid-infrared CRDS setup for CO2 measurement. Experimental results demonstrate good agreement with conventional fitting, with improved reliability compared to the ToT method with static thresholds and comparable linearity over a broad range of ring-down decay rates. These findings establish the dynamic ToT method as an accessible and scalable alternative for acquiring decay data in CRDS, particularly suited for simultaneous multi-channel or multi-wavelength measurements.
In this study, a simple procedure to estimate the molecular weight of high-density polyethylene over a very wide range of molecular weights was investigated using Raman spectroscopy with multivariate data analysis. High-density polyethylene samples with viscosity average molecular weights (Mv) [g/mol] ranging from 0.1 to 7.4 million were synthesized, and their Raman spectra in the 3200 to 100 cm-1 region were measured. Using multivariate analysis to develop a calibration model derived from each spectrum and molecular weight, a high correlation coefficient was achieved between the predicted and actual values of the model. Thus, this study shows that Raman spectroscopic method can be employed for estimating the molecular weight of high-density polyethylene. Furthermore, Raman spectroscopy can be implemented in optical systems utilizing optical fibers, enabling operation with the measurement point separated from the main device even in harsh process environments, including high temperatures. Consequently, this technique is highly resistant to environmental conditions and is extremely useful as a measurement method applicable in any measurement environment. In practical applications, the spectroscopic technique will be selected according to the purpose and measurement environment, aiming for industrial application of this method.
Enhancing surgical precision through automated tissue identification requires overcoming the complexities of real operative scenes. Specifically, material detection is complicated by tissue superposition (e.g. thin layer of blood masks underlying structures), intricate anatomical geometries, and lighting instability. These factors manifest as the mixed pixel and spectral variability problems, which remain the foremost challenges for hyperspectral imaging (HSI) in clinical applications.In this context, this paper presents a feasibility study leveraging Visible and Near-Infrared HSI combined with hyperspectral unmixing algorithms to address these complexities. Ex-vivo bovine samples, comprising key orthopedic tissues such as blood, ligaments, cartilage, bone, and fat, were imaged using HSI in a manner that replicates real operative challenges. Subsequently, six state-of-the-art unmixing algorithms selected for their ability to simultaneously resolve mixed pixels and mitigate spectral variability effects are evaluated. Through a comparative analysis, model-based unmixing algorithms demonstrated optimal performance in producing abundance maps that accurately quantify the proportion of distinct tissue types, even within a single pixel subject to variability perturbations. These algorithms successfully decouple environmental variability, such as shadowing, illumination shifts, and shape spectral deformations, from actual material proportions, preventing altered spectral signatures from confusing true abundance quantification.
Calibration by Proxy (CbPx) is applied to the inductively coupled plasma mass spectrometry analysis of seven commercial pipe tobacco samples. Five proxy elements are employed to construct a single calibration curve that applies to every analyte in the sample. Both the preparation of the calibration curve and the multielement analysis of each sample is performed from the analysis of just two solutions. The analysis of a standard reference material (tomato leaves) demonstrates excellent recoveries for 12 test elements, ranging from 77% (Ni) to 104% (Cu), with relative standard deviations averaging 6.6%. Detection limits are in the ppb range (µg analyte per kg leaf). Pipe tobacco samples containing between 0.04 and 700 mg analyte per kg leaf are analyzed for Al, As, Ba, Cd, Cu, Fe, Mn, Mo, Ni, Pb, V, and Zn.
This review presents recent advances in integrated vibrational and X-ray spectroscopic approaches for the characterization of cultural heritage materials. Vibrational techniques, including Raman, Fourier transform infrared (FT-IR), and optical photothermal infrared (O-PTIR) spectroscopy, together with X-ray fluorescence, diffraction, and absorption methods, provide complementary molecular, elemental, and structural information for the analysis of pigments, binders, and degradation products. Emphasis is placed on analytical capabilities, limitations, and the synergistic use of these techniques within multimodal workflows.Vibrational spectroscopy plays a central role in molecular identification and monitoring chemical transformations, whereas X-ray methods provide insight into elemental composition, crystallography, and pigment alteration mechanisms. Their integration establishes a robust framework for materials identification, stratigraphic interpretation, and investigation of degradation pathways in historical objects.Representative case studies discussed in this review illustrate how integrated vibrational and X-ray spectroscopic strategies address key analytical challenges in cultural heritage research, including the characterization of lead-based materials in works attributed to Leonardo da Vinci, compositional layering in paintings by Pablo Picasso, and cadmium yellow degradation in masterpieces by Edvard Munch and Vincent van Gogh. O-PTIR is highlighted as an emerging tool for submicron analysis, while combined Raman and X-Ray spectoscopic methods resolve environmentally driven pigment transformations.This review outlines current advances, practical challenges, and future directions in spectroscopy-driven research on complex materials.
Q355C steel is a critical structural material widely used in offshore wind power facilities, including steel piles and tower cylinders, corrosion caused by marine salt spray poses a serious threat to long term structural integrity. In this study, laser-induced breakdown spectroscopy (LIBS) was employed to assess the corroded characteristics of Q355C steel. A field-deployable LIBS system based on two-dimensional scanning was developed for surface analysis. A quantitative calibration curve was established between the surface salt density of uncorroded Q355C steel and the sodium spectral intensity, achieving a high coefficient of determination (R2=0.94). Subsequently, LIBS measurements were performed on simulated corrosion specimens, revealing variations in elemental distribution within the corrosion zone with depth. Since surface corrosion products primarily consist of iron oxide whose thickness varies with corrosion severity, the ratio of manganese to iron spectral intensities (IMn/IFe) was identified as a potential indicator for distinguishing corrosion severity. By exploiting the spectral differences between genuine corrosion areas and pseudo-corrosion areas (areas covered by flow rust), accurate differentiation between the two was achieved. The accuracy of the LIBS binarization method was approximately 24% higher than that of traditional visual methods.
Absorbance spectroelectrochemistry is a powerful in situ technique utilized to investigate redox changes and charge carrier properties in electronic materials, such as mixed ionic-electronic conducting polymers. In this method, the absorption spectrum of the material is obtained as a function of applied potential, and the results are used to understand its electrochemical behavior. The standard approach uses chronoamperometry, in which a constant potential is applied, and an absorption spectrum is measured at electrochemical equilibrium for a series of potentials selected across the electrochemical window of the sample. However, this method is limited by slow, labor-intensive data acquisition and lack of time-resolved absorbance information. Herein, we describe an automated absorbance spectroelectrochemical method that couples a high-speed, broadband optical absorbance instrument with normal pulse voltammetry to capture full absorbance spectroelectrochemistry spectra in a single measurement. The instrument measures absorption spectra over a 400 - 2500 nm window at a maximum spectral acquisition rate of 200 Hz (5 ms response time). We demonstrated the capability of this spectroscopy technique to automatically obtain a full set of potential-dependent absorbance spectra and absorbance transients by applying it to study the electrochemical charging behavior of a polythiophene electrode, which was time-resolved at 1 spectrum/s.
A highly sensitive method has been developed for the determination of bisphenol A (BPA) in beverages (juice, beer, carbonated soft drinks) using surface-enhanced Raman spectroscopy (SERS) coupled with solid-phase extraction (SPE), in situ synthesis of silver nanoparticles (AgNPs), and surface modification with tetraoctylammonium bromide (TNOAB). SPE showed high BPA recovery rates (>90%) from complex food matrices. The crucial factor for achieving maximum sensitivity was the in situ synthesis of AgNPs directly in the presence of the analyte, as the use of pre-synthesized nanoparticles led to an approximately 100-fold decrease in signal intensity. Investigation of cationic modifiers with different structures revealed that the efficiency of SERS signal enhancement correlates with alkyl chain length. TNOAB (C8) provided a 7-fold increase in signal compared to the unmodified system, significantly outperforming the effects of tetrabutylammonium bromide (C4, 1.7-fold enhancement) and triethylamine (C2, 1.3-fold enhancement). The limit of detection for BPA was 0.077 ppb with a signal enhancement factor of 1.87×108. For quantitative analysis, a PLS calibration model was applied in the range of 1-100 ppb (R2 = 0.9986, RMSEC = 1.75 ppb, RMSEP = 1.95 ppb). The simplicity of the developed approach makes it suitable for routine monitoring of BPA content in beverages.
As a traditional Chinese medicinal material, the quality of Poria cocos (PC) significantly affects its pharmacological efficacy. However, adulteration of PC in the market has been frequently observed. Adulterated PC not only compromises its medicinal value but also poses potential risks to public health. Conventional identification methods are often labor-intensive, destructive, and insufficiently sensitive to complex adulteration scenarios. In this study, a rapid and nondestructive strategy for both qualitative and quantitative analysis of PC adulteration is developed by integrating near-infrared (NIR) two-dimensional correlation spectroscopy (2DCOS) with deep learning algorithms. NIR spectra in the range of 960-1600 nm are collected from pure PC and samples adulterated with 5 common adulterants at concentration gradients of 5%. Specifically, to enhance spectral resolution, a systematic 2DCOS dataset is established by combining 5 representative spectral preprocessing methods with 2 types of 2DCOS. Furthermore, a bidirectional long short-term memory network with an attention mechanism (BiLSTM-Attn) is proposed to fully exploit the sequential dependency of correlation features embedded in 2DCOS maps. Compared with experiments involving convolutional neural network (CNN), gated recurrent unit (GRU), long short-term memory (LSTM), and bidirectional LSTM (BiLSTM) models, the proposed BiLSTM-Attn achieved 100% classification accuracy and superior regression performance, with a mean coefficient of determination (R2) of 0.9920, a low root mean squared error (RMSE) of 2.41, and a high mean residual predictive deviation (RPD) of 12.85. Extended experiments demonstrate that the combination of NIR 2DCOS and deep learning algorithms enables accurate and robust detection of PC adulteration. The proposed framework offers valuable support for quality control in traditional Chinese medicine, and has a wide range of applications.
This work utilized terahertz time-domain spectroscopy (THz-TDS) and Fourier Transform Infrared (FTIR) spectroscopy to characterize epoxy blends. The epoxy blends were prepared by blending a virgin DER-332/LC-100 epoxy system with Recovered Epoxy Polymer (REP) at 1-10 wt%, and were compared with references of virgin epoxy and REP. The REP was obtained via peracetic acid digestion of Carbon Fibre Reinforced Polymer (CFRP), followed by purification. Using THz-TDS amplitude-phase analysis, five optical parameters were obtained: refractive index (n), extinction coefficient (κ), absorption coefficient (α), and the real and imaginary of the dielectric constant (ε' and ε″). Under ambient conditions, these parameters extracted from THz-TDS were unable to distinguish low REP content 0-10% REP but were able to clearly differentiate 100% REP from all other epoxy blends. Compared to the other blends, 100% REP shows markedly increased n, κ, α, ε', and ε″, attributed to oxidation, formation of polar groups, chain scission and microvoid-induced scattering. To distinguish low REP-content blends using THz-TDS, external perturbation was applied. Under perturbation, linear concentration-dependent trends in Δn, Δκ, Δα, Δε' and Δε'' were observed. The external perturbation enhanced the interaction between the samples and the THz wave, likely due to amplification of dipole relaxation. Additionally, the transmission spectra (3500-7500 cm⁻1) obtained from FTIR increased as the REP content increased from 0-10%. This concentration dependent trend can be attributed to partial network dilution and reduced overtone absorption. However, the transmission of 100% REP showed strong attenuation due to structural disorder and enhanced scattering.
Efficient monitoring of solvent extraction processes is essential for the safe and sustainable operation of nuclear fuel reprocessing, particularly under conditions where radiolysis and solvent degradation can affect separation efficiency and phase stability. We investigate an integrated optical approach that combines Raman spectroscopy of the organic phase with laser-induced breakdown spectroscopy (LIBS) of the aqueous phase for simultaneous control of extractant composition and raffinate elemental content. Raman spectroscopy was applied to tributyl phosphate (TBP) in a hydrocarbon diluent over a range of concentrations selected to mimic changes in extractant loading and degradation. Using closely spaced bands in the 1000-1200 cm-1 region, a simple ratiometric indicator yielded an excellent linear correlation with TBP concentration (R2 = 0.996) and a median prediction error of about 1.0%. LIBS measurements were performed on aqueous solutions containing Zr, La, Ce and Sr as fission-product surrogates in concentration ranges representative of late extraction stages (1-40 g L-1). Despite shot-to-shot fluctuations associated with breakdown in liquids, internal standardization to solvent oxygen lines or a major solute element provided linear calibration curves with mean absolute percentage errors of 4-8% and limits of detection on the order of a few grams per liter. The combined Raman-LIBS scheme thus offers a promising basis for a reagent-free in situ monitoring of solvent extraction operations in nuclear fuel reprocessing.
Foodborne illnesses pose a serious threat to food safety and cause substantial economic losses. Hyperspectral imaging (HSI) has emerged as a powerful tool for rapid and non-destructive identification of foodborne pathogens. However, the high chemical similarity among different pathogen categories presents a challenge for accurate discrimination. To address this issue, we developed an optimized machine learning framework integrated with HSI that incorporates multimodal learning and a multi-head attention mechanism, enabling deeper extraction and fusion of spectral profiles and intensity images features. In visualization analyses, the deeply fused features demonstrated excellent inter-species separability, and the proposed multimodal multi-head attention fusion (MMAF) strategy achieved a high identification accuracy of 96.29%, representing an improvement of 4.17% over the single-modal approach. These results indicate that the optimized HSI approach, driven by advanced machine learning, holds great potential as an effective tool for rapid detection of microbial contamination in food products.
Mid-infrared spectroscopy is a powerful technique for probing molecular structure and composition, yet its application to aqueous systems remains limited by strong solvent absorption and the dynamic range of mid-IR detectors, which restrict the usable optical pathlength. Here, we present a quantum cascade laser-based spectroscopic setup that enables simultaneous acquisition of absorption spectra measured in transmission across a continuum of optical pathlengths using a custom-made wedge-shaped flow cell and a pyroelectric detector array. This design eliminates the need for mechanical adjustments or sample dilution, allowing direct analysis of complex liquid samples. We introduce the pathlength-to-noise ratio as a novel metric for determination of the optimal pathlength region for every wavenumber. By weighing detector signals based on this ratio, we achieve robust integration of multi-pathlength data into a single coherent mid-IR absorption spectrum. The system was validated using aqueous protein solutions of bovine serum albumin and β-lactoglobulin in the range of 1 to 25 mg mL-1. Characteristic amide I and II bands were successfully resolved, and secondary structure differences were detected. This work establishes a flexible approach to mid-IR absorption spectroscopy, aiming to eliminate the limitations of detectors with a small dynamic range and to get a better understanding of the optimal pathlength for complex samples.
Advanced ALD (atomic layer deposition) precursors are designed to deposit thin films that must be reliable, clean and free of contaminants. This created a need for analytical methods to measure contaminants and ensure the purity of the starting compounds used in ALD. However, accurate analysis of multiple trace impurity elements in high purity copper precursors is extremely challenging. The paper presents a comparison of analytical performances of the inductively coupled plasma optical emission spectrometry (ICP-OES) and the inductively coupled plasma mass spectrometry (ICP-MS) for the trace analysis of copper(II) acetylacetonate. A detailed study of the copper matrix effect and its influence on the intensity of the analytical signals was performed. The limits of detection for ICP-OES and ICP-MS analysis ranged from 0.1 to 100 ng g-1 for more than 60 trace elements. The capabilities of the ICP-MS technique were expanded by the use of a reaction/collision cell. The combination of the developed ICP-OES and ICP-MS methods allows monitoring 62 impurities in copper(II) acetylacetonate with a purity of 6N (99.9999 wt%). The accuracy was rigorously validated through spike recovery experiments and the analysis of a high-purity copper certified reference materials, demonstrating the absence of significant systematic errors. The methodology's applicability was further confirmed by analyzing additional copper precursors, showcasing its utility for quality control of copper ALD materials.
Photoacoustic imaging is an emerging imaging modality with unique features that have attracted significant interest for clinical translation. Spectroscopic photoacoustic (sPA) imaging acquires photoacoustic images at multiple wavelengths, enabling the differentiation of chromophores at greater depths than conventional optical imaging while maintaining spatial resolution comparable to ultrasound. It is a straightforward integration with ultrasound imaging that provides a powerful diagnostic platform for structural, functional, and molecular imaging. This capability makes it somewhat analogous to combined X-ray computed tomography (CT) and positron emission tomography (PET), but without ionizing radiation, offering a safer and more accessible alternative for a broader patient population. While spectroscopic photoacoustic imaging, with or without exogenous contrast agents, has shown great potential in various preclinical applications, its clinical translation faces several technical and practical challenges. These include limitations in light penetration, spectral unmixing complexities, and the need for improved image reconstruction techniques. Additionally, standardization and regulatory considerations must be addressed to facilitate widespread clinical adoption. In this review, we introduce spectroscopic photoacoustic imaging, highlighting its significant potential to address critical gaps in biomedical diagnostics. We further discuss the key technical and practical limitations hindering its clinical implementation and explore recent advancements aimed at overcoming these barriers.
Cadmium sulfur selenide and cadmium zinc sulfide pigments have been widely employed by artists of the twentieth century. A deep knowledge of these artworks, also in view of their conservation and/or restoration, relies on comprehensive and robust databases of reference materials of the pigments to easily detect their composition and their tendency and routes to deterioration. In this work, we initiate the construction of such a database by applying exclusively non-invasive techniques, X-ray fluorescence (XRF) and fiber optics reflectance spectroscopy (FORS) in the visible to shortwave (Vis-SWIR) range, to two sets of historical pigments: a group of pure commercial tube paints and a mixed palette representative of artistic practice. To strengthen the interpretative framework, mock-up samples were prepared using modern Cd-based pigments. These reference materials were first analysed using the same non-invasive protocols to ensure full data compatibility. In addition, they were further characterized through synchrotron-based techniques, namely high-hesolution X-ray powder diffraction (HR-XRPD) and X-ray absorption spectroscopy (XAS), providing additional structural and phase information not accessible through laboratory non-invasive methods alone. The integration of non-invasive and synchrotron-based data on the modern reference materials enables a more rigorous interpretation of the spectra collected on historical pigments. This combined approach enhances phase discrimination, compositional assessment, and the understanding of pigment variability, thereby increasing the reliability and internal consistency of the historical database. The resulting dataset establishes a solid foundation for future non-invasive studies of twentieth-century Cd-based pigments in complex stratigraphic and binding media contexts.
Accurate wavelength characterization is essential for high-precision spectral measurements, particularly in applications such as solar-induced chlorophyll fluorescence (SIF) retrieval, where weak spectral signals are highly sensitive to instrument performance. In array spectrometers, characteristic wavelengths can be defined by peak, center, or centroid positions, whereas spectral resolution is commonly represented by full width at half-maximum (FWHM) or equivalent rectangular width (ERW). This study systematically investigates the influence of sampling conditions on wavelength characterization using a crossed Czerny-Turner array spectrometer operating over the 650-800 nm spectral range. The concept of sampling ratio is employed to define near-limit sampling conditions, in which monochromatic spectral peaks are represented by only 2-5 detector pixels. Experimental results show that the spectrometer predominantly operates within this regime. Under these conditions, significant discrepancies arise among different characteristic wavelength definitions owing to the combined effects of discrete sampling and spectral peak shape. Peak-based wavelength estimation is primarily affected by local sampling variations, whereas centroid-based definitions are more sensitive to energy distribution and peak asymmetry. Furthermore, a systematic divergence between ERW and FWHM demonstrates that spectral resolution metrics depend not only on geometric peak width but also on spectral energy distribution, particularly under non-ideal imaging conditions. These results show that wavelength characterization should be regarded as a coupled problem involving sampling conditions, spectral peak representation, and resolution metrics rather than as independent parameters. The proposed multi-parameter characterization approach establishes a practical framework by clarifying the relationships among sampling ratio, characteristic wavelength definitions, and spectral resolution, introducing two deviation metrics to quantify inconsistencies among wavelength definitions, and revealing the complementary physical significance of FWHM and ERW from geometric and energy-distribution perspectives. This approach provides a physically interpretable basis for wavelength calibration, spectral resolution evaluation, and performance assessment of array spectrometers operating under near-limit sampling conditions.
