Beer's Law Research Articles

Existence, uniqueness, and efficiency of numerically unbiased attenuation pathlength estimators for photon counting detectors at low count rates.

The first step in computed tomography (CT) reconstruction is to estimate attenuation pathlength. Usually, this is done with a logarithm transformation, which is the direct solution to the Beer-Lambert Law. At low signals, however, the logarithm estimator is biased. Bias arises both from the curvature of the logarithm and from the possibility of detecting zero counts, so a data substitution strategy may be employed to avoid the singularity of the logarithm. Recent progress has been made by Li etal. [IEEE Trans Med Img 42:6, 2023] to modify the logarithm estimator to eliminate curvature bias, but the optimal strategy for mitigating bias from the singularity remains unknown. The purpose of this study was to use numerical techniques to construct unbiased attenuation pathlength estimators that are alternatives to the logarithm estimator, and to study the uniqueness and optimality of possible solutions, assuming a photon counting detector. Formally, an attenuation pathlength estimator is a mapping from integer detector counts to real pathlength values. We constrain our focus to only the small signal inputs that are problematic for the logarithm estimator, which we define as inputs of<100 counts, and we consider estimators that use only a single input and that are not informed by adjacent measurements (e.g., adaptive smoothing). The set of all possible pathlength estimators can then be represented as points in a 100-dimensional vector space. Within this vector space, we use optimization to select the estimator that (1) minimizes mean squared error and (2) is unbiased. We define "unbiased" as satisfying the numerical condition that the maximum bias be less than 0.001 across a continuum of 1000 object thicknesses that span the desired operating range. Because the objective function is convex and the constraints are affine, optimization is tractable and guaranteed to converge to the global minimum. We further examine the nullspace of the constraint matrix to understand the uniqueness of possible solutions, and we compare the results to the Cramér-Rao bound of the variance. We first show that an unbiased attenuation pathlength estimator does not exist if very low mean detector signals (equivalently, very thick objects) are permitted. It is necessary to select a minimum mean detector signal for which unbiased behavior is desired. If we select two counts, the optimal estimator is similar to Li's estimator. If we select one count, the optimal estimator becomes non-monotonic. The oscillations cause the unbiased estimator to be noise amplifying. The nullspace of the constraint matrix is high-dimensional, so that unbiased solutions are not unique. The Cramér-Rao bound of the variance matches well with the expected scaling law and cannot be attained. If arbitrarily thick objects are permitted, an unbiased attenuation pathlength estimator does not exist. If the maximum thickness is restricted, an unbiased estimator exists but is not unique. An optimal estimator can be selected that minimizes variance, but a bias-variance tradeoff exists where a larger domain of unbiased behavior requires increased variance.

PARAFAC under non-negativity constraint is adapted to recover the underlying Beer-Lambert law of the excitation-emission fluorescence matrix measurements acquired from analyte-triggered semiconductor QDs photoluminescence modulation. When and why?

BackgroundAnalyte-triggered semiconductor quantum dots (QDs) modulation in the presence of non-consistently responsive fluorescent species represents a challenging analytical issue in concrete multi-way data handling. QDs with heterogeneous sizes and/or uneven distribution of functional moieties on their surfaces exhibit significant fluctuations in the fluorescent response components, known as chemical rank, across different excitation/emission modes. This phenomenon may lead to a substantial deviation from the proportionality prescribed by Beer-Lambert law. Nonetheless, even in the presence of such deviation, a multi-way model may be successfully selected after determining a proper chemical rank in a QDs system. ResultsWe show that in a valid PARAllel FACtor (PARAFAC) model under properly determined chemical rank, meaningfully resolved pure spectral profiles can be reached for each fluorescent responsive constituent in the original excitation-emission fluorescence matrix (EEFM) measurements. This was thoroughly illustrated by applying PARAFAC trilinear decomposition of a three-way data array of two distinct datasets acquired from semiconductor QDs sensing systems with low-rank trilinear assumption. The first dataset, presented here for the first time, comprises EEFM measurements of the ligand-driven quenching of thiomalic acid (TMA)-capped AgInS2 (AIS) QDs by vomitoxin. The second dataset, employed for illustrative purposes, comprises EEFM measurements of the quenching, via cation bridging, of glutathione (GSH)-capped CdTe QDs by Pb(II). The results of this study enabled the determination of vomitoxin at a ppb level in real samples of fish feeds, showcasing the efficacy of the PARAFAC model in resolving spectral signatures (loadings) and pure concentration profiles (scores). SignificancePARAFAC under a properly examined chemical rank can be easily adapted for retrieval the underlying Beer-Lambert law of the original EEFM measurements with a low-rank trilinear structure through the chemically meaningful information either when (i) no deviation of Beer-Lambert law was observed as deeply discussed in connection with the dataset acquired from vomitoxin-driven molecular sensing through TMA-capped AIS QDs, or when (ii) substantial deviations of the Beer-Lambert law are evident, as discussed in connection with the dataset collected from sensing ionic species through Pb(II) bridging of GSH-capped CdTe QDs.

Greenness appraisal and spectrophotometric estimation of carvedilol in pharmaceutical formulations and study kinetic parameters

Numerous studies have established that carvedilol acts as a vasodilator and is effective in managing hypertension. Consequently, this research focuses on the development and validation of analytical methods for the quantification of carvedilol. Various techniques, including UV/Vis spectrophotometric methods, have been investigated alongside innovative, straightforward, accurate, and sensitive approaches. In this study, we established a method based on the interaction between carvedilol and alizarin yellow dye in an aqueous medium, allowing for a reaction time of 20 min for completion. Upon conclusion of the reaction, a purple-colored product is formed, which exhibits maximum absorption at a wavelength of 536 nm. This method adheres to Beer's law within the concentration range of 10–50 µg/mL, with a molar absorptivity of 2.560×103 L·mol−1·cm−1, a Sandel index of 0.158 µg. cm−2, the detection limit of 0.4190 µg/mL, and the quantitative limit is 1.2698 µg/mL. The recovery rate was determined to be 100.7010 %, and the relative standard deviation did not exceed 1.3094 %. The method was applied to estimate the concentration of carvedilol in its pharmaceutical formulation in tablet form CARVEDISAM. Additionally, the kinetics of the resulting complex were studied, revealing that the kinetics are of first order. To assess the environmental impact of contemporary UV spectrophotometric methods, the Green Analytical Greenness Metric (AGREE) software and the Green Analytical System Index (GAPI) were utilized to evaluate the greenness profile. The developed UV method is more sustainable and environmentally friendly.

Characterizing annual leaf area index changes and volume growth using ALS and satellite data in forest plantations

While Leaf Area Index (LAI) is critical for understanding forest canopy, photosynthesis and forest growth, traditional field-based LAI measurements are laborious and costly. Remote sensing offers a practical alternative for extensive assessments. Satellite imagery provides broad-scale, long-term monitoring; however, may lack detail needed to guide specific forest management actions. Conversely, Airborne Laser Scanning (ALS) provides accurate LAI estimates at fine spatial detail but is limited by cost and temporal monitoring constraints. Combining ALS data with satellite observations could enhance plantation management decisions by balancing extensive coverage with detailed observations. This study explores the integration of ALS and satellite remote sensing as a comprehensive alternative for assessing LAI and stand volume growth rate (m3/ha/year) in operational Pinus radiata plantations in central-south Chile. Our approach comprised four major steps. First, we applied the Beer-Lambert law using ALS vertical profiles to estimate LAI across a forest plantation (LAIALS). We found that ALS accurately estimated LAI across 121 plots (R2 = 0.82 and RMSE = 0.51). Second, we built a simple linear regression to link LAIALS with the Normalized Difference Moisture Index (NDMI) derived from surface reflectance information from the Landsat/Sentinel-2 satellites, resulting in an R2 of 0.53 and an RMSE of 1.17. This step showed a higher correlation with satellite data compared to using only ground-based LAI estimates (R2 = 0.38; RMSE = 1.18). Third, we transformed biweekly NDMI time series to LAI, then derived peak annual LAI as an indicator of mean annual increment (MAI) (R2 = 0.51; RMSE = 5.27 m³/ha/year). This allowed us to characterize stand growth and LAI on a yearly wall-to-wall basis. Throughout the modelling steps, we incorporated error propagation, allowing final estimates to be error bounded. This integrated approach serves as a tool for identifying and visualizing growth irregularities, guiding adaptive management strategies to maintain or enhance stand productivity over time.

Heavy Metal Pollution Studies of Soil from the Oti-Dompoase Dumpsite in Kumasi

Waste disposal sites contribute a great deal to environmental pollution. The degree of pollution brought on by heavy metal contamination of soil collected from the Oti-Dompoase dump site in Kumasi of Ashanti region, Ghana was investigated in this study. Twelve (12) composite samples of the surface soil were taken in total at 10 cm depth from the dumpsite to conduct metal analysis. The measurement of heavy metal concentration was done utilizing Atomic Absorption Spectrometer, which uses the absorbance at various wavelength of the electromagnetic spectrum to determine the chemical identity of constituents of the sample and their concentrations with the help of standard solutions and Beer-Lambert law. The mean metal concentrations of soil samples were reported and arranged in terms of magnitude as follows: Iron (2,582.21 mg/kg) &gt; Copper (348.50 mg/kg) &gt; Lead (324.85 mg/kg) &gt; Manganese (192.27 mg/kg) &gt; Zinc (146.24 mg/kg) &gt; Cadmium (7.06 mg/kg). Physiochemical properties such as electrical conductivity (EC), pH and organic matter and water content (%) were also investigated using a PHYWE electrical conductivity meter, pH meter and an oven, respectively. Most of the parameters analysed indicated pollution when compared to baseline values, while human exposure levels were within World Health Organization (WHO) standards. Assessments using geo-statistics of different hazard indicators, including pollution load index, contamination factor (CF), and geo-accumulation, all point to heavy metal pollution of the soil samples. Cadmium contamination was very high based on the pollution indices (CF, geo-accumulation, and pollution load) and manganese has the lowest level of pollution. There is limited data on the extent of pollution caused by the Oti-Dompoase dumpsite and this study will serve to fill this knowledge gap and contribute to the Millenium Development Goal seven (7) by providing data on the extent of pollution of soil around the Oti-Dompoase dumpsite and highlight the need for regular monitoring and on-site remediation strategies to safeguard the site to ensure environmental sustainability.

The Development of a Novel Nitrate Portable Measurement System Based on a UV Paired Diode-Photodiode.

Nitrates can cause severe ecological imbalances in aquatic ecosystems, with considerable consequences for human health. Therefore, monitoring this inorganic form of nitrogen is essential for any water quality management structure. This research was conducted to develop a novel Nitrate Portable Measurement System (NPMS) to monitor nitrate concentrations in water samples. NPMS is a reagent-free ultraviolet system developed using low-cost electronic components. Its operation principle is based on the Beer-Lambert law for measuring nitrate concentrations in water samples through light absorption in the spectral range of 295-315 nm. The system is equipped with a ready-to-use ultraviolet sensor, light emission diode (LED), op-amp, microcontroller, liquid crystal display, quartz cuvette, temperature sensor, and battery. All the components are assembled in a 3D-printed enclosure box, which allows a very compact self-contained equipment with high portability, enabling field and near-real-time measurements. The proposed methodology and the developed instrument were used to analyze multiple nitrate standard solutions. The performance was evaluated in comparison to the Nicolet Evolution 300, a classical UV-Vis spectrophotometer. The results demonstrate a strong correlation between the retrieved measurements by both instruments within the investigated spectral band and for concentrations above 5 mg NO3-/L.

Origin of the anisotropic Beer–Lambert law from dichroism and birefringence in β -Ga2O3

The anisotropic optical absorption edge of β-Ga2O3 follows a modified Beer–Lambert law having two effective absorption coefficients. The absorption coefficient of linearly polarized light reduces to the least absorbing direction beyond a critical penetration depth, which itself depends on polarization and wavelength. To understand this behavior, a Stokes vector analysis is performed to track the polarization state as a function of depth. The weakening of the absorption coefficient is associated with a gradual shift of linear polarization to the least absorbing crystallographic direction in the plane, which is along the a-exciton within the (010) plane or along the b-exciton in the (001) plane. We show that strong linear dichroism near the optical absorption edge causes this shift in β-Ga2O3, which arises from the anisotropy and spectral splitting of the physical absorbers, i.e., excitons. The linear polarization shift is accompanied by a variation in the ellipticity due to the birefringence of β-Ga2O3. Analysis of the phase relationship between the incoming electric field to that at a certain depth reveals the phase speed as an effective refractive index, which varies along different crystallographic directions. The critical penetration depth is shown to be correlated with the depth at which the ellipticity is maximal. Thus, the anisotropic Beer–Lambert law arises from the interplay of both the dichroic and birefringent properties of β-Ga2O3.

Simulation Studies of Interfacial Kinetics of Dye-Sensitized Solar Cells Photoanodes in Scanning Electrochemical Microscopy

Approach curves in the feedback mode of scanning electrochemical microscopy (SECM) were simulated for photoanodes in dye-sensitized solar cells by finite element simulation using COMSOL Multiphysics and compared to experimental data for the sample set with varying the photoanode film thickness (ZnO, cobalt mediator, organic dye). This reveals quantitatively the effect of the mass transport limitation of the mediator diffusion and organic dye regeneration kinetics in the mesoporous photoanode. The simulation of the mesoporous material was made with a pseudo-homogeneous approach in two space dimensions.The simulation allows to extract the maximum information content from the experimental data. The light adsorption was treated as exponential decay of intensity within the photoanode (Lambert-Beer law), electron injection in the conduction band of ZnO photoanode and loss mechanism was explicitly considered. The light illumination is homogeneous over the entire simulation domain of 1 mm in diameter. Just like in the experiment, the built geometry used for the simulation has a conducting blocking layer (0.6 µm in thickness) to prevent the recombination of electrons with the back contact. The porous dye-sensitized layer has a porosity of 50 - 60% and a thickness of 1- 10 µm. The inner surface holds the dye for absorbing light. The mediator diffuses in the pore of the photoanode (internal solution) and in the bulk of the electrolyte (external diffusion). The transparent conducting glass makes the boundary of the simulation domain. The electrolyte-platinum contact is not modelled. The selected boundary conditions are equivalent to the short-circuit operation of the cell.Interestingly, the simulation suggests that built meshes which had earlier been used for porous electrode simulation could not adequately describe the electron concentration profile for thinner electrodes despite providing a correct ME electrode current for limiting cases. The mesh convergence analysis studies were made to optimize the mesh to reduce computation time and memory size. The electrons in the conduction band were quantitatively determined because transport in the semiconducting photoanode is primarily driven by a thermally activated trapping-untrapping mechanism that can be described by transport equations similar to Fick's laws.The unknown parameters (dye absorption coefficient and recombination rate constant) were adjusted to ensure various light intensities in the simulation correspond to the experiment. An accurate description of the electrons within the semiconductor is critical for explaining the time-dependent behavior of the dye-sensitized photoanode in SECM approach curves. After obtaining agreement with experimental approach curves under steady-state conditions, the same parameters are used to study the current transient obtained under intermittent illumination.

Identification of Blood Sugar Based on Non-invasive Measurements UsingPhotoplethysmography Method Signal Decoding in Diabetics in Tasikmalaya

Non-invasive blood sugar testing tools are now in great demand among the public. This research aims to develop a non-invasive blood sugar examination tool with a Photopletysmograph signal decoding system based on data acquisition from a wearable sensor device on the wrist. The tool used for data acquisition uses Near Infra Red Light-emitting Diode NIR LED 880 nm, 660 nm and 537 nm. This acquisition transfers signals from the body via a photodiode to a PC Personal Computer for processing using Matlab. The method used in this research is to look for the height of the systolic and diastolic amplitude of the Photopletysmograph PPG signal and use the peak-to-peak voltage Vpp to implement Beer Lambert's law. This method was tested on 54 people, randomly aged 26-89 years, with normal blood sugar to high blood sugar. The results show an error of 18.37% from the gold standard. In conclusion, the use of the PPG signal decoding method has proven to be significant in producing blood sugar values. Furthermore, this method was developed for real-time remote measurements via wearable sensor devices.

Modeling aerosol transmission spectra from n(λ) and k(λ) infrared optical constants measurements of organic liquids and solids

The effects of light scattering and refraction play significantly different roles for aerosols than for bulk materials, making it challenging to identify aerosolized chemicals using traditional spectral methods or spectral reference libraries. Due to a potentially infinite number of particle morphologies, sizes, and compositions, constructing a database of laboratory-measured aerosol spectra is not a practical solution. Here, as an alternative approach, the measured n/k optical vectors of two example organic materials (diethyl phthalate and D-mannitol) are used in combination with particle absorption / scattering theory (Mie theory and FDTD) and the Beer-Lambert law to generate a series of synthetic infrared transmission / scattered light spectra. The synthetic spectra show significant differences versus simple slab transmission spectra, even for small changes in particle size (e.g., 5 vs. 10 µm) for both single particles and ensembles, potentially serving as useful reference data for aerosol sensing. For spherical single particles with diameters of 1 to 10 µm, FDTD simulations predict changes in the magnitudes of spectral shifts and the shapes of the peaks vs. particle size with only small deviations from Mie theory predictions, yet reliably capture the direction of the shifts. Typical spectral peak shifts in the longwave infrared correspond to Δλ ∼0.20 µm (∼34 cm-1) when compared to corresponding slab transmission spectra. Additionally, synthetic spectra generated from the n/k values derived using two different methods (KBr pellet transmission and single-angle reflectance) are compared using the Mie theory model.

Spectrophotometric-Based Sensor for the Detection of Multiple Fertilizer Solutions

The online detection of fertilizer solution information is a crucial link in the implementation of intelligent and precise variable fertilization techniques. However, achieving simultaneous rapid online detection of multiple fertilizer components is still challenging. Therefore, a rapid detection method based on spectrophotometry for qualitative and quantitative identification of four fertilizers (typical N, P, and K fertilizers: KNO3, (NH4)2SO4, KH2PO4, and K2SO4) was proposed in this work. Full-scan absorption spectra of fertilizer solutions at varying concentrations were obtained using a UV–visible/near-infrared spectrophotometer. By assessing the linear fit between fertilizer concentration and absorbance at each wavelength within the characteristic band, the characteristic wavelengths for KNO3, (NH4)2SO4, KH2PO4, and K2SO4 were identified as 214 nm, 410 nm, 712 nm, and 1708 nm, respectively. The identification method of fertilizer type and the prediction model of concentration were constructed based on characteristic wavelength and the Lambert–Beer law. Based on the above analysis, a four-channel photoelectric sensor was designed with four LEDs emitting wavelengths closely matched to characteristic wavelengths for fertilizer detection. A detection strategy of “qualitative analysis followed by quantitative detection” was proposed to realize the online detection of four fertilizer types and their concentrations. Evaluation of the sensor’s performance showed its high stability, with an accuracy of 81.5% in recognizing fertilizer types. Furthermore, the relative error of the sensor detection was substantially less than ±15% for the fertilizer concentrations not exceeding 80 mg/L. These results confirm the capability of the sensor to meet the practical requirements for online detection of four fertilizer types and concentrations in the field of agricultural engineering.

A temperature-compensated CO2 detection system based on non-dispersive infrared spectral technology.

The concentration of carbon dioxide (CO2) is an important indicator for coal mine safety. Real-time monitoring of CO2 concentration is of great importance for taking actions in advance to avoid the occurrence of potential accidents. To address the issues of poor portability and high cost associated with existing coal mine CO2 detection equipment, this paper develops a miniaturized CO2 detection system based on non-dispersive infrared (NDIR) technology. This sensor integrates an infrared light source and a dual-channel pyroelectric detector into a reflective gas chamber, thereby achieving an extended optical path and higher system sensitivity within limited space. Meanwhile, the noise interference was greatly mitigated by using hardware and software filtering techniques. Based on principle analysis, the Lambert-Beer law was parametrically corrected, and then, a model relationship between the dual-channel voltage ratio and concentration was established. In addition, temperature compensation for zero and span values was introduced to improve the adaptability of the detection results to temperature changes. Testing results indicate that the developed detection system can realize CO2 measurement in the concentration range of 0 to 50 000 ppm within a temperature range of 0-40 °C, with a maximum detection error of less than 0.12% and a repeatability deviation of less than 1.04%. During a stability test for 12h, the maximum concentration drift is 0.07%, indicating that the developed system meets the requirements for monitoring CO2 safety in coal mines.

Laser-induced ultrasound in multiple thin layers-An analytical solution.

Laser-induced ultrasound is based on the thermo-elastic conversion of absorbed short light pulses to pressure pulses. In the work presented here, laser-induced ultrasound in a planar structure of interconnected layers with variations in optical, thermal, and mechanical properties is studied. Layered structures can be used for generating wideband ultrasonic pulses specific to a chosen application. An analytical time-domain solution is derived for the resulting pressure transmitted from the layered structure. The solution is derived for an arbitrary number of layers with an arbitrary optical absorption profile. Free space Green's functions with image sources are used to derive the solution. A solution employing the Beer-Lambert law is also proposed. The simplification with reflections only at the boundaries is in agreement with previous published results. The spectral properties of the generated pulse are derived, where the effects of optical absorption coefficients and layer thicknesses are shown. The analytical solution is compared to one-dimensional (1D) simulations and a three-dimensional (3D) simulation, realised as a two-dimensional (2D) axially symmetric case, using the matlab toolbox k-Wave. The 3D simulation on-axis pressure agrees well with the 1D analytical solution when the diameter of the laser beam is larger by approximately 1 order of magnitude than the thickness of the planar layered structure.

Image post-processing for SILMAS: structured illumination light sheet microscopy with axial sweeping.

In this article, we propose a post-processing scheme for the novel volumetric microscopy technique SILMAS. We demonstrate this scheme on data from an alpha-synuclein transgenic mouse brain. By combining structured illumination and axial sweeping, a SILMAS measurement provides a prerequisite for quantitative data extraction through improved contrast and optical sectioning. However, due to the technique's efficient removal ofb multiple scattered light, image artifacts such as illumination inhomogeneity, shadowing stripes, and signal attenuation, are highlighted in the recorded volumes. To suppress these artifacts, we rely on the strengths of the imaging method. The SILMAS data, together with the Beer-Lambert law, allow for an approximation of real light extinction, which can be used to compensate for light attenuation in a near-quantitative way. Shadowing stripes can be suppressed efficiently using a computational strategy thanks to the large numerical aperture of an axially swept light sheet. Here, we build upon prior research that employed wavelet-Fourier filtering by incorporating an extra bandpass step. This allows us to filter high-contrast light sheet microscopy data without introducing new artifacts and with minimal distortion of the data. The combined technique is suitable for imaging cleared tissue samples of up to a centimeter scale with an isotropic resolution of a few microns. The combination of a thin and uniform light sheet, scattered light suppression, light attenuation compensation, and shadowing suppression produces volumetric data that is seamless and highly uniform.

Heuristic estimation of river bathymetry in braided streams using digital image processing

AbstractMeasurement of river bathymetry has been revolutionized by high‐resolution remote sensing that combines UAV platforms with SfM‐MVS photogrammetry. Mapping inundated and exposed areas simultaneously are possible using either two‐media refraction correction or some form of the Beer–Lambert Law to estimate water depths. If, as in turbid glacially‐fed braided streams, the bed is not visible then traditional survey techniques (e.g. differential GPS systems) are required. As an alternative, here we test whether the spatial distribution of water depths in a shallow braided stream can be modelled from basic planimetric data and used to estimate inundated zone bathymetry. We develop heuristic rules using; (1) distance from the nearest river bank; (2) total inundated width along a line tangential to the local flow direction; (3) local curvature magnitude and direction; and distance from the nearest flow (4) divergence and (5) convergence regions. We parameterize them using a sample of measured water depths in stepwise multiple linear regressions and validate them using independent data. Resulting water depth distribution maps explain between 50% and 60% of the measured water depth spatial variability when compared to independent data. After incorporating modelled water depths into digital elevation models (DEMs) of exposed areas, we show that the developed method is suitable for volumetric change calculations in both dry and inundated areas.

Exploring the use of extended multiplicative scattering correction for near infrared spectra of wood with fungal decay

Extended Multiplicative Signal Correction (EMSC) is a multivariate linear modelling technique for multi-channel measurements that can identify and correct for different types of systematic variation patterns, known or unknown. It is typically used for pre-processing to separate light absorbance spectra, obtained by diffuse reflectance of intact samples, into three main sources of variation: additive variations due to chemical composition (≈Beer's law), mixed multiplicative and additive variations due to physical light scattering (≈Lambert's law) and more or less random measurement noise. The present work evaluates the use of EMSC to pre-process near infrared spectra obtained by hyperspectral imaging of Scots pine sapwood, inoculated with two different basidiomycete fungi and at various degradation stages. The spectral changes due to fungal decay and resulting mass loss are assessed by interpretation of the EMSC parameters and the partial least squares regression (PLSR) results. Including a cellulose (analyte) or bound water (interferent) spectral profile in the EMSC pre-processing model generally improves the predictive performance of the PLS modelling, but it can also make it worse. The inclusion of the additional polynomial baselines does not necessarily lead to a better separation of the physical and chemical effects present in the spectra. The estimated EMSC parameters provide insight into the differences in decay mechanisms. A detailed analysis of the EMSC results highlights advantages and disadvantages of using a complex pre-processing model.

Dynamic spectral extraction method with approximately the same optical path length of non-invasive quantitative analysis of human blood components

The non-invasive quantitative analysis of blood components using spectroscopic methods based on Beer-Lambert law, and dynamic spectroscopic theory needs to meet the four applicable conditions of this law. However, in practical applications, due to the scattering characteristics of human tissue, it is difficult to meet the two conditions (parallel monochromatic light and non-scattering homogeneous system of absorbing substances), which will reduce the accuracy of quantitative analysis. To reduce the principle error caused by scattering, this paper proposes an extraction method for dynamic spectra with approximately the same optical path length. This method extracts approximately the same absorbance values from photoplethysmographic (PPG) spectral signals. A smaller absorbance value corresponds to a thinner blood layer, in which light can be approximated as parallel light, thus maximizing the satisfaction of the conditions of Beer-Lambert law. In the experimental, compared with the traditional single-edge extraction method, the proposed method has higher prediction accuracy. The correlation coefficients of the total cholesterol and triglycerides increased by 31.22% and 38.05%, and the root mean square errors decreased by 29.63% and 37.14%. The results show that the methods can significantly enhance the robustness of non-invasive quantitative analysis of blood components based on dynamic spectral theory.

Experimental Study to Visualize a Methane Leak of 0.25 mL/min by Direct Absorption Spectroscopy and Mid-Infrared Imaging

Tunable laser spectroscopy (TLS) with infrared (IR) imaging is a powerful tool for gas leak detection. This study focuses on direct absorption spectroscopy (DAS) that utilizes wavelength modulation to extract gas information. A tunable interband cascade laser (ICL) with an optical power of 5 mW is periodically modulated by a sawtooth injection current at 10 Hz across the methane absorption around 3271 nm. A fast and sensitive thermal imaging camera for the mid-infrared range between 3 and 5.7 µm is operated at a frame rate of 470 Hz. Offline processing of image stacks is performed using different algorithms (DAS-F, DAS-f and DAS-2f) based on the Lambert–Beer law and the HITRAN database. These algorithms analyze various features of gas absorption, such as area (F), peak (f) and second derivative (2f) of the absorbance. The methane concentration in ppm*m is determined on a pixel-by-pixel analysis without calibration. Leak localization for methane leak rates as low as 0.25 mL/min is accurately displayed in a single concentration image with pixelwise sensitivities of approximately 1 ppm*m in a laboratory environment. Concentration image sequences represent the spatiotemporal dynamics of a gas plume with high contrast. The DAS-2f concept demonstrates promising characteristics, including accuracy, precision, 1/f noise rejection, simplicity and computational efficiency, expanding the applications of DAS.

A new LED-based extinction tomography method for measurement of aerosol surface area

A light-emitting-diode (LED) based optical technique is developed to measure the surface area per unit volume of particles in aerosols and liquid sprays. The technique uses path-integrated measurements of transmittance, T, from two angles to produce a tomographic reconstruction of the local extinction coefficients, K, in the region of interest, using the Beer-Lambert law and a deconvolution algorithm. When the particles in the flow have sufficiently large diameters (existing in the Mie scattering regime), these extinction coefficients can be related to the surface area per unit volume of the particles. The technique has the potential to be applied to a wide range of two-phase flows. In the present study, it is applied to flows through a pharmaceutical inhaler device, where two powders with different particle size distributions are considered.

On the Origin of the Photoplethysmography Signal: Modeling of Volumetric and Aggregation Effects

This study aimed to examine the mechanisms of the photoplethysmography (PPG) signal formation using Monte Carlo simulations of light transport in biological tissues and experimental observations. Based on a three-layer skin model in backscattering geometry, we sequentially simulated volumetric blood changes and the aggregation/disaggregation of erythrocytes in the dermal layer and estimated their contribution to the registered PPG signal. The calculations were conducted for two wavelengths: 525 nm and 810 nm. For green light, absorption predominates over scattering in the formation of a PPG signal, whereas, for near-infrared light, scattering prevails over absorption. This theoretical result was verified using the Modified Beer–Lambert law and clinical in vivo PPG data of seven healthy subjects. Changes in the size of the scatterers during erythrocyte aggregation and disaggregation can significantly contribute to the PPG signal at near-infrared light. Thus, for the green waveband, the classical volumetric model can be considered dominant in the PPG signal formation. In contrast, for the near-infrared range, both volumetric and aggregation effects must be considered as being approximately equal.