A Simple Introduction to Raman Spectral Identification of Organic Materials

Application of Wavelength Dispersive X-ray Fluorescence to Agricultural Disease Research

Challenges of Spectrofluorometry, Part 2

Determination of Elemental Impurities in a Nasal Spray by ICP-MS

A tutorial and spreadsheet for the validation and bottom-up uncertainty evaluation of quantifications performed by instrumental methods of analysis based on linear weighted calibrations were presented by Ricardo J.N. Bettencourt da Silva of the University of Lisbon in Lisbon, Portugal, and colleagues. This software tool was successfully applied to the determination of the mass concentration of Cd, Pb, As, Hg, Co, V, and Ni in a nasal spray by ICP-MS after samples dilution and acidification. Bettencourt da Silva spoke to Spectroscopy about applying this software tool and the implications for a better understanding of quantitative analytical results.

Instrumental methods of analysis are frequently used to determine the level of a compound, class of compounds, or other chemical property on the studied item. The ability to adequately quantify measurement result uncertainty is crucial for the objective that triggered the chemical analysis. A tutorial and spreadsheet for the validation and bottom-up uncertainty evaluation of quantifications performed by instrumental methods of analysis based on linear weighted calibrations were presented by Ricardo J.N. Bettencourt da Silva of the University of Lisbon in Lisbon, Portugal, and colleagues. This software tool was successfully applied to the determination of the mass concentration of Cd, Pb, As, Hg, Co, V, and Ni in a nasal spray by ICP-MS after samples dilution and acidification. Bettencourt da Silva spoke to 

 about applying this software tool and the implications for a better understanding of quantitative analytical results.

Your recent paper (1) describes a tutorial and spreadsheet for the validation and bottom-up uncertainty evaluation for quantitative instrumental methods based on a linear weighted regression model. Why do you believe that there is a need for such a tool? What sort of information or insight does it provide that currently available methods or tools do not?

The developed tool has two merits: the ability to make accessible complex uncertainty evaluations, and the novelty of allowing evaluating the uncertainty from weighted calibrations without the need to collect many replicate signals of calibrators. The paper includes a user-friendly MS-Excel file that can be used to assess the assumptions and evaluate the uncertainty from linear weighted calibrations of instrumental methods of analysis. It is provided with metrological and statistical tools to test the calibrator’s quality and instrumental response linearity where different weighting factors can be selected according to how precision varies in the calibration interval. The disadvantage of weighted regression models of requiring the reliable determination of signal precision in each calibration to better set the weighting factors is overcome by defining precision models that can be updated with the residual standard deviation estimated from daily calibrations based on a few replicate signals.

This tool is particularly useful because most instrumental methods of analysis are calibrated in intervals where the signal varies linearly with the studied quantity, typically the concentration of an analyte, and the signal’s precision varies in that interval. Before the publication of this paper, such a tool was not available that can be easily integrated into the daily activities of test laboratories.

Your spreadsheet tool was successfully applied to the quantitative determination of the mass concentration of Cd, Pb, As, Hg, Co, V, and Ni in a nasal spray by ICP-MS after sample dilution and acidification. What made you decide to choose this particular application to test your tool? What benefits did the utilization of this spreadsheet bring to the analysis?

This application was selected due to the relevance of the quality control of medicines and because these analyses do not include a complex sample preparation that constitutes an additional relevant uncertainty component. In these analyses performed by experts from the Palacky University in Olomouc (Czechia) in their GMP certified laboratory 

, the measurement uncertainty is estimated by combining calibrators’ values uncertainty with the uncertainty from the regression model used to define the calibration curve. Therefore, the experimental application of the developed tool to the analysis of nasal sprays spiked with studied analytes allowed a detailed assessment of the developed uncertainty models.

Briefly discuss your findings and their implications for a better understanding of quantitative analytical results.

The paper presents experimental evidence of the adequacy of the developed measurement uncertainty models and constitutes a relevant contribution to the democratization (making the tool accessible to everyone). of complex measurement uncertainty evaluations. The quantification of measurement uncertainty is crucial to guarantee that performed analyses are fit for purpose and have known quality. Measurement results are only valid for a specific purpose if their uncertainty is adequately low. The measurement uncertainty is also crucial for the sound and objective interpretation of the analytical information.

What are the biggest challenges that you have encountered in developing this tool? What options or alternative developments are available to overcome these challenges or to improve this spreadsheet approach?

The biggest challenges we have faced in developing this tool were making it user-friendly and avoiding the need to collect many replicate signals for the daily calibration of an instrumental method of analysis based on the linear weighted regression model. Some authors have developed software for evaluating the uncertainty of instrumental quantifications that require demanding and not supervised collections of input data. A spreadsheet for the Monte Carlo simulation of instrumental quantification uncertainty was also developed but requires some computational resources for the simulation.

What sort of feedback did you receive from this paper and the study results?

We have received very positive feedback from the pharmaceutical industry that is becoming more interested in measurement uncertainty evaluations to guarantee conformity assessment reliability. However, the developed tool can be applied to any instrumental method of analysis.

What are your next steps regarding this research? Are there any additional analytical approaches or methods where this tool might be beneficial?

We are developing equivalent tools for non-linear regressions and integrating complex sample preparation in analytical methods based on instrumental quantification. These research efforts will involve the development of new metrological tools and their democratization through tutorials and user-friendly software.

(1) T. Pluháček, D. Milde, J. Součková, and R.J.N. Bettencourt da Silva, 

https://doi.org/10.1016/j.talanta.2020.122044

Ricardo Bettencourt da Silva, after working in accredited laboratories as an analyst and consultant for 15 years, started a research and teaching career at the University of Lisbon. Since 2002, collaborates with the Portuguese Accreditation Body, as technical assessor, and trains the staff of laboratories. Ricardo is currently the secretary of CITAC, a member of the executive board, chair of the working group on Qualitative Analysis, and a member of the working group on Measurement Uncertainty and Traceability of Eurachem. He is co-editor of the 

Eurachem/CITAC guide for Setting the Target Measurement Uncertainty

. His research interests are Metrology and Examinology in chemistry, the sciences of measurements, and qualitative analysis in chemistry, respectively. 

Articles

A tutorial and spreadsheet for the validation and bottom-up uncertainty evaluation of quantifications performed by instrumental methods of analysis based on linear weighted calibrations were presented by Ricardo J.N. Bettencourt da Silva of the University of Lisbon in Lisbon, Portugal, and colleagues. This software tool was successfully applied to the determination of the mass concentration of Cd, Pb, As, Hg, Co, V, and Ni in a nasal spray by ICP-MS after samples dilution and acidification. Bettencourt da Silva spoke to Spectroscopy about applying this software tool and the implications for a better understanding of quantitative analytical results. 

Determination of Elemental Impurities in a Nasal Spray Using ICP-MS 

We proposed a new retrieving model (named CAB1) for estimating the chlorophyll content at leaf level using the Prospect radiative transfer (RT) model. CAB1 is built based on multiband information derived from the radiative transfer model. Specifically, a continuous wavelet analysis algorithm was used to find the wavelet coefficients for those spectral characteristics that can highlight the chlorophyll content. Then, the simulated data sets generated by the Prospect model were used to evaluate the sensitivity of CAB1 in chlorophyll and its stability to other biochemical components (leaf structural parameters, water, carotenoids, brown pigment, and dry matter). Finally, CAB1 was verified using the Lopex93 and Angers experimental spectral data sets. Quantitative and qualitative results revealed that the retrieving model was not only more accurate than the traditional spectral index (the highest 

 of the inversion value and the measured value is 0.9), but also more stable.

Chlorophyll is the dominant factor affecting vegetation photosynthesis, and it is closely related to other biochemical parameters such as protein, nitrogen, lignin, and water (1). The chlorophyll content in a crop can be used to indicate the photosynthetic capacity, growth cycles, and degrees of stress (such as disease, insect pests, and heavy metal stress) (2,3). Traditional biochemical methods for measuring the chlorophyll content (such as spectrophotometry, in which samples must be pretreated in the laboratory) are destructive to the vegetation as well as time-consuming and laborious; thus, spectral reflectance is an attractive alternative (4,5).

During the past few decades, many studies have proposed the spectral indices required to estimate chlorophyll contents. By using one of the existing spectral indices or the sensitive bands of chlorophyll, a single or multivariate analysis model can be established. Several studies have successfully estimated the chlorophyll content in vegetation using visible ratios (6), vis-NIR ratios (7–9), red-edge reflectance ratio indices (10,11), and spectral and derivative red-edge indices (12). Yan used the Prospect model to test the applicability of four types of spectral indices, such as visible ratios (eight kinds), vis-NIR ratios (eight kinds), red-edge reflectance ratio indices (six kinds), and derivative red-edge indices (six kinds), to test chlorophyll content extraction. She found that some spectral indices, such as normalized difference vegetation index (NDVI) and the modified chlorophyll absorption in reflectance index (MCARI), are not suitable for retrieving chlorophyll based on the reflectance spectra. Rather, it was necessary to carefully select a spectral index for a specific application (13,14). Using a spectral index to evaluate the chlorophyll content of vegetation is simple and flexible, but there are obvious limitations. One limitation is that the spectral index method does not consider the radiative transfer (RT) mechanism of light in the leaf, which leads to a lack of definite physical meaning (15). The other limitation is that spectral index models are generally adapted to specific databases and are difficult to generalize to other databases.

Therefore, researchers began to consider optical models with geometric meanings, including the radiative transfer performance of light in vegetation, and the effects of vegetation biochemistry on light. The process of light reflection and absorption in vegetation and the interaction process were mathematically described to retrieve the biochemical components of the vegetation. Optical models, such as the Prospect (16), Liberty (17), and Leafmod (18) models, are not limited to the time, location, and other factors, and they are robust to noise. Yan noted that the reflection and absorption spectra simulated using the Prospect model are nearly the same as those of the measured spectra. Jiang used the Prospect model to simulate spectral data of different spectral scales (different bandwidths (5–65 nm)) and analyzed the validity and sensitivity when applied to the estimation of the chlorophyll content (19). Wang used the Prospect model to simulate the spectra of leaves with different biochemical characteristics, and analyzed the influence of different mathematical combinations of the NDVI spectral index on the elimination of interference factors. The spectral index of the dual NDVI ratio vegetation index was established to estimate the carotenoid content in leaves (20). Zhang used the Prospect model to construct a lookup table from which the chlorophyll content of eucalyptus leaves could be retrieved. The spectral data determined using a statistical method, an estimation model linking the chlorophyll, and carotenoid content with spectral characteristic parameters of eucalyptus leaves, were established (21).

The aim of this study was to construct a new spectral index for estimating chlorophyll content at the leaf level with physical implications, robustness, and universality. First, the relationship between the chlorophyll content and the spectral characteristics of vegetation based on the transmission mechanism of the Prospect optical model was analyzed to construct a new specific band. The “Experimental Materials and Methods” section introduces the experimental materials and methods, and describes the establishment of a new inversion model for chlorophyll content with continuous wavelet transform (CWT). The “Results” section reviews the experimental results, which describe the new inversion model validation of comparison with other vegetation indices. The “Discussion” section focuses on the advantages and disadvantages of new spectral index. Finally, the “Conclusion” section summarizes the findings of the study.

The Prospect model, among the most mature RT models, has few required parameters and easy inversion. It can simulate the optical properties of vegetation leaves from 400 nm to 2500 nm (22). The Prospect model is a simple “flat model.” The leaf is composed of 

-1 air layers. In Prospect-5 (23), the total spectral absorption coefficient (

) of each leaf plate layer is a function of leaf structural parameters (

) of a leaf plate layer can be approximately expressed as a function of the leaf structural parameter (

) and a single plate layer absorption coefficient (

 is the refractive index of the basic whitening layer; 

 is the corresponding absorption coefficient spectrum of the leaf chlorophyll; 

 is the corresponding absorption coefficient spectrum of the leaf carotenoid; 

 is the corresponding absorption coefficient spectrum of the leaf brown pigment; 

 is the corresponding absorption coefficient spectrum of the leaf water; and 

 is the corresponding absorption coefficient spectrum of the leaf dry matter.

 were measured and fixed (23). Thus, the Prospect model had six input parameters, including the leaf structure (

). Its output parameters were the reflectivity and spectral transmittance of the leaf ranging from 400 to 2500 nm, and the sampling interval was 1 nm.

According to different experimental purposes, the input parameters of the Prospect model are set, and the simulated data set with different biochemical components can be simulated. Four simulation data used in this paper, named Set_

The sensitivity index, SI, is used for accuracy evaluation (equation 2) (26).

 is the calculated values of the spectral indices and |

| is the absolute value. The smaller the 

, the smaller the influence of the component on the spectral index.

The Lopex93 database was established by the Joint Research Center (JRC) in 1993 (27). Approximately 70 leaf samples representations of more than 50 species were obtained. The database contains 62 samples of spectral data and chlorophyll content data, including 13 monocotyledons and 49 dicotyledons. Spectra were collected over the 400–2500 nm region with a sampling interval of 1 nm. The database not only takes into account the differences of different species, but also the changes of biochemical composition in time. It fully comprises the diversity of biochemical composition content and inner types of leaves. The database cannot only provide a more effective test for spectral index, but also serve as an ideal data source for analyzing the correlation between chlorophyll content and spectral reflectance of mixed species. The Lopex93 data set can be accessed free online (http://opticleaf.ipgp.fr/index.php?page=database).

The Angers database was established at the National Institute for Agricultural Research (INRA) in Angers, France, in June 2003 (23). Approximately 276 leaf samples representations of more than 39 species were obtained. The directional-hemisphere reflectance spectra were measured using an ASD FieldSpec spectrometer with a spectral range of 400–2500 nm and a data interval of 1.4 nm. The biochemical parameters include leaf chlorophyll content, carotenoids, specific leaf weight (SLW), and water content. The Angers data set can also be accessed free online (http://opticleaf.ipgp.fr/index.php?page=database).

Wavelet transform is an effective mathematical tool used to decompose the original spectral signal into multiple scales (28,29). The continuous wavelet transform (CWT) tool can make the wavelet shift smoothly to different positions; thus, each scale component can be compared directly to the input spectral reflectance, and more useful spectral information can be captured (30). In this study, the CWT wavelet analysis method was used in the spectral analysis method. The CWT is defined as follows in equation 3 (31),

 is the signal to be analyzed; Ψ is a chose wavelet basis function, such as biorthogonal (bior), daubechies (db), coiflets (coif), or symlets (sym) (32); Ψa,b (λ) is the prototype to generate child wavelets by adjusting the scale parameter 

 (the corresponding decomposition frequency or band range) and b the translation factor (corresponding to the band position); λ is the wavelength; and dλ is the spectral resolution.

In this study, the spectral reflectance signal was processed by continuous wavelet transform, where f(λ) is the spectral reflectance value or absorption coefficient spectrum of the leaf. Commonly used continuous wavelet decompositions are selected as Ψ; a is the spectrum scale of 100 nm, 150 nm, and 200 nm; 

 is the band position which should be selected by analysis; λ is the wavelength that can be cut down by analysis; and dλ = 1 nm. After the CWT wavelet analysis, the coefficients are obtained, which can be used for singularity detection or periodic analysis. When the signal is projected into the wavelet transform domain, it is advantageous to extract some useful features.

Reconstruction of a New Leaf Spectral Index

To construct the new spectral index for the chlorophyll content of leaves, the relationship between the reflectance and biochemical components of the vegetation is built first. As is known, the summation of the spectral reflectance of the leaf (

), were constantly one. The shape of the leaf reflectance and transmittance were found to be similar in the visible and near- infrared (NIR) radiation, and could be expressed approximately as follows (33):

By combining equation 1 with equation 5, the formula of the leaf spectrum reflectance rate (

Different biochemical components have a different influence on the reflectance in the band 400–800 nm (the sensitive spectrum range of the chlorophyll). In the Prospect model, only one biochemical component was set with different ranges and the other input parameters were fixed to obtain many reflectance spectra, which were used to test the influence of the biochemical component on the reflectance. For example, to test the 

 in the band 400–800 nm influence on the reflectance in the Prospect model, 

). The other input parameters were fixed (

 = 1). Finally, seven reflectance spectra curves were obtained, which were used to find the band region where reflectance is changed with a different 

. The test result is shown in Figure 1. The range of the influence for 

 was 500–750 nm, but the ranges of 400–500 nm and 750–800 nm were not an influence on the spectra. The range of influence for 

 did not change, and the content changes did not affect the spectral shape. We found that, in the range of 550–700 nm, the reflectance spectrum was affected only by chlorophyll 

. Thus, to extract the main influence spectrum range of Cab and minimize the effect of the other components, the final sensitive band range of chlorophyll was determined to be from 550 to 700 nm. Then, equation 6 was further reduced as follows:

 content changes do not affect the reflectance spectra.

FIGURE 1: The chlorophyll sensitive band areas (in nm) of different dataset contents. Abscissa is spectral band (nm) and ordinate is dataset spectra.

In mathematics, the result of CWT computation for constant value is 0. The calculated value of constant coefficients with CWT computation remains unchanged. Therefore, both sides of equation 7 are carried out with the CWT computation. At the same time, we can obtain equation 8

Finally, two factors were considered to determine the scale basis function and band position of the continuous wavelet decomposition in building the new spectral index. One factor was in the range of 550–700 nm, the CWT curve of the 

(a,b) should have a wave valley or wave peak at bands w1 and w2, where the chlorophyll absorption was sensitive. The other factor was that the CWT curve of 

(a,b) should be approximately 0 at bands w1 and w2, eliminating or decreasing the influence of 

 on the reflectance spectrum. Through a large number of comparative experiments, in the selected band range from 550 to 700 nm, with a spectrum scale of 100 nm, 150 nm, and 200 nm, were conducted to 

(a,b). We found that “bior1.1” with a spectrum scale of 150 nm can meet the two factors as shown in Figure 2. Thus, the wavelet base function Ψ was chosen as “bior1.1”, the wave spectrum scale, 

 = 150 nm), the wave-peak w1 position was 699 nm, and the wave-valley w2 position was 613 nm (

 = 150 nm using wavelet function “bior1.1”.

At the wave-peak w1 and wave-valley w2, two formulas can be obtained using Formula 8.

where w1 equals 699 nm, w2 equals 613 nm, 

 equals 150 nm, and the wavelet function is “rbio1.1”. According to Figure 2, we can obtain the wavelet coefficients 

A new leaf chlorophyll content model, termed CAB1 with the wavelet function “rbio1.1,” was obtained as equation 12:

. Then, for the same crop type during the same growth period, 

 was a fixed constant and CAB1 was only affected by the leaf spectrum reflectance rate.

The Spectral Indices Sensitive to Leaf Chlorophyll Contents

To test the established inversion model CAB1, eight commonly used spectral indices (Table II) sensitive to leaf chlorophyll contents were used for comparison, including the spectral index of visible light NPCI, TCARI, and MCARI; spectral indices of visible and infrared light MTCI, TVI, and TCARI/OSAVI; and red-edge spectral index GM and VOG2.

Two aspects should be considered in the spectral index evaluation: The spectral index is sensitive to chlorophyll content, and it can resist the influence of other factors. First, the Prospect optical model was used to simulate the spectral curves with different chlorophyll content, and the advantages and disadvantages of each spectral index were analyzed. According to existing spectral indices (Table II), the band range was selected from 400 to 800 nm. According to the analysis in Figure 1, the influencing factors only included 

. Finally, the Lopex93 and Angers real data were used to analyze the spectral index.

Spectral Indices Sensitivity for Leaf Chlorophyll Content 

 is used for spectral indices sensitivity for leaf chlorophyll content 

. As shown in Figure 3, the values of CAB1, MTCI, and GM monotonously increase with the increase in chlorophyll content, and NPCI, TCARI, MCARI, TVI, TCARI/OSAVI, and VOG2 decrease. They have a good linear relationship with the chlorophyll content, and their 

 = 0.6371) (the first line of Table III)—indicating that these eight spectral indices have good sensitivity to different chlorophyll content. When the chlorophyll content was less than 30 μg/cm

, TVI exhibited an opposite monotonic feature compared to that when the content was greater than 30 μg/cm

), TVI is not suitable for retrieving leaf chlorophyll. Similarly, at a chlorophyll content of 40 μg/cm

, NPCI showed the opposite monotonic characteristics, and the curve gradually changed and usually became smooth, indicating that NPCI was easy to saturate.

FIGURE 3: Sensitivity analysis of hyperspectral vegetation indices on chlorophyll content.

Ability to Resist the Influences of Other Leaf Biochemical Components 

 is shown in Table III (the second line). The influence of 

 on the partial spectral index is large, such as NPCI, TCARI, MTCI, and TCARI/OSAVI. Under the same chlorophyll content, the MTCI value changed approximately 19 times when the N changed from 1 to 3, followed by NPCI, TCARI, and TCARI/OSAVI. The SI of VOG2, GM, and CAB1 are smaller, particularly the SI value of CAB1, which is only 34.87%.

 is shown in Table III (the third line). The influence of 

 on the partial spectral index is small. Only the SI of TVI is over 10%. TCARI/OSAVI, NPCI, and CAB1 had the smallest SI values, particularly for CAB1, which had a SI value of only 0.56%.

 is shown in Table III (the fourth line). The influence of 

 on the partial spectral index is very small. Only the SI of TCARI and TCARI/OSAVI are over 5%. The SI of CAB1, NPCI, MCARI, and TVI are approximately 2%, and the SIs of MTCI, GM, and VOG2 are all approximately 0%.

Spectral Index Verification with Lopex93 and Angers Data 

Using the 190 Lopex93 reflectivity spectral data, the quadratic model of CAB1, TCARI, MTCI, and VOG2 were built. The 80 validation spectral data were used to verify the inversion chlorophyll content accuracy. For Angers data, 69 reflectivity spectral data were used to build the quadratic model of CAB1, TCARI, MTCI, and VOG2, and 60 validation spectral data were used as validation data. Because the structural parameter of the leaf 

 cannot be determined in the Lopex93 and Angers data, 

 is assumed to be the standard value, which is 2. The 

 and RMSE are used to evaluate their accuracy (Table IV). Validation results of chlorophyll estimations are done by the quadratic model of CAB1, TCARI, MTCI, and VOG2, which is shown in Figure 4.

FIGURE 4: Validation results of chlorophyll estimation with Lopex93 data using various approaches: (a) TCARI, (b) MTCI, (c) VOG2, and (d) CAB1; and Angers data: (e) TCARI, (f) MTCI, (g) VOG2, and (h) CAB1.

As shown in Table IV and Figure 4, the quadratic models of CAB1, TCARI, MTCI, and VOG2 with Lopex93 data have low RMSE (RMSE < 3.20). The 

 of MTCI is greater than 0.72, which is better than TCARI and VOG2. The 

 of CAB1 is 0.9108, and the RMSE values are smaller (RMSE = 2.0294). Compared with TCARI, MTCI, and VOG2, CAB1 is more accurate and robust.

The results of CAB1, TCARI, MTCI, and VOG2 estimating chlorophyll with Angers data are shown in Table IV and Figure 4. The quadratic models of CAB1, TCARI, MTCI, and VOG2 with Lopex93 data have high 

 > 0.84), which indicates that they have high accuracy for chlorophyll estimation. The 

 of MTCI is greater than 0.89, which is better than TCARI and VOG2. The 

 of CAB1 is 0.9116, and the RMSE values are smaller (RMSE = 3.6925). Compared with TCARI, MTCI, and VOG2, CAB1 is more accurate and robust.

From the analysis of two sets of data, it was found that the 

 of CAB1 was the highest, and the RMSE was the smallest among the four spectral indexes, indicating that CAB1 performs the best.

The Performance of Wavelet Analysis Method with Prospect Model in the Reconstruction of Leaf Spectral Index 

As shown in equation 8 using the spectral analysis method, the spectral reflectance is limited to 700–800 nm, and the inversion of chlorophyll content has only two important factors: 

. By using continuous wavelet decomposition, the spectral energy can be decomposed to find the band position with the largest 

 effect, thus providing the possibility of constructing a new spectral index for chlorophyll inversion (Figure 2).

The Prospect model starts with spectral and vegetation components and has a strong theoretical basis. Therefore, the spectral index is constructed step-by-step based on the Prospect formula, which has sufficient theoretical basis. However, the results are still affected by 

 (equation 12). Although the experimental results show that the effect of 

 on CAB1 is relatively small, the accuracy of vegetation index would be further improved if the specific value of 

 can be obtained from the measured data. In addition, the model used in this experiment was Prospect-5, which does not separate chlorophyll from anthocyanin, resulting in a greater impact of 

, shown in Table III (the fourth line). With the refinement of the Prospect model, the accuracy of building a new vegetation index is expected to be further improved.

The Performance of the CAB1 Method in the Estimation of Leaf Parameters 

From the Prospect simulation data, CAB1 is in the upper and middle reaches, shown in Table III. Through the aforementioned analysis, the spectral index on the sensitivity of chlorophyll content and ability to resist the influences of other components such as the structure of mesophyll, dry matter, and carotenoids, were summarized to estimate the effectiveness of assessing chlorophyll content. The comprehensive evaluation index (

 is the spectral sensitivity of the biochemical components, as represented by the index trend line fitting degree value 

 (Table III); 1 − SI% is the ability of spectral indices to resist other biochemical components (SI% are selected in Table III); 

 are the influence weights for each biochemical component, which were set at 1. When the 

 of the spectral index is higher, the ability to resist the influence of other components is stronger, indicating that the spectral index comprehensive ability is stronger.

Table III shows that NPCI, TCARI/ OSAVI, and MCARI have the low 

 value and are not suitable for evaluating chlorophyll content in a vegetation leaf. MTCI and TVI comprehensive evaluations are medium, and they have a certain guiding role for the particular vegetation or a certain period of growth of vegetation but are not used for all vegetation. The 

 values of CAB1, GM, and VOG2 are higher (greater than 0.8), and the models are sensitive to chlorophyll content and are relatively stable. The CAB1 integrated capacity evaluations were equivalent to model sensitivity and stability optimum. CAB1 is based on the Prospect model, so using Prospect simulation data can explain the status quo of the vegetation index. Although CAB1 does perform relatively well based on the Lopex93 and Angers data validation, more measured data are needed for further validation.

This study generated a new spectral index, named CAB1, to estimate the chlorophyll content of a vegetation leaf. Based on the Prospect optical model, the continuous wavelet analysis method was used to establish the CAB1 model, in which the “rbio1.1” wavelet basis function with a scale of 150 nm, as well as reflectance spectra for 613 and 619 nm, were selected. The CAB1 model is derived from the Prospect model, so the CAB1 model has a strict physical meaning. The practical adaptability of some spectral indices, which are based on statistics, was the biggest disadvantage. CAB1 is not based on statistics, but instead on the theory of real light propagation, which is more adaptable.

A good chlorophyll vegetation index should be sensitive to chlorophyll while simultaneously not being sensitive to other factors. To verify the adaptability of CAB1, a comparison was made with eight commonly used spectral indices. According to the Prospect model, the data describing the relationship between the leaf spectrum and the content of each component were simulated. A comparison of the chlorophyll sensitivity and resistance to the mesophyll structure, dry matter, and carotenoid content of the CAB1 model and the common chlorophyll spectral indices was examined. MCARI was found to perform the worst (

 = -3.7600). MCARI is very sensitive to the chlorophyll content but also to other components such that it is only suitable for retrieving the chlorophyll content of the same vegetation leaf within a single period. The VOG2, GM, and CAB1 models performed the best (

 > 0.8) because they can retrieve the chlorophyll content of any vegetation leaf with high accuracy. To verify this conclusion, the actual data of Lopex93 and Angers were selected. CAB1 (proposed method), TCARI (spectral index of visible light), MTCI (spectral indices of visible and infrared light), and GM (red edge spectral index) were selected to retrieve the chlorophyll content of vegetation leaves using the Lopex93 and Angers data. Based on the actual data, MTCI, TCARI, and VOG2 were found to have moderate inversion accuracy (the maximal 

 is 0.8), which may be because of noise in the actual data. However, CAB1 offers a high level of accuracy (

 > 0.9), which indicates the CAB1 model is not only more accurate than the other vegetation indexes, but is also very stable. Overall, CAB1 performed well in the leaf layer compared to the commonly used spectral indices NPCI, TCARI, and MCAI in visible regions, and CAB1 is comparable to the red edge spectral index GM and VOG2.

This research was based on the Prospect model simulation data. Because of the influence of the accuracy of the model, and given that the experimental data may be slightly different, the universality of the research results must be further verified. However, the results of this study provide some pointers for combining the physical model and the spectral index method.

This work was supported by the Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources, Shandong Province, and Scientific Research Foundation of Shandong University of Science and Technology under Grant [2014TDJH101]; Scientific and Technological Planning Projects of Colleges and Universities in Shandong Province under Grant [J18KA214]; and Funded by Beijing Key Laboratory of Urban Spatial Information Engineering [2019209].

We thank the SDUST Laboratory for the use of their equipment. The authors also thank the editor and anonymous referees for their insightful comments, which improved this paper.

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Spectral reflectance is a non-destructive method that is applicable to remote sensing and may be used to measure the chlorophyll content in a crop, which indicates the photosynthetic capacity, growth cycles, and degrees of stress (such as disease, insect infestation, and heavy metal stress) on plant ecosystems. This vis-NIR spectral reflectance method measures leaf chlorophyll using a wavelet analysis algorithm approach.

Model for Retrieving Leaf Chlorophyll Using the Wavelet Analysis Algorithm with the Prospect Radiative Transfer Model and Vis-NIR Spectra

In this paper, an effective identification method of wavelength variable selection to rapidly discriminate the grape seed oil adulteration by near-infrared (NIR) spectroscopy is investigated. The extreme learning machine (ELM) is employed to build a stable and accurate model, and a firefly algorithm combined with a successive projections algorithm (FA–SPA) is developed to eliminate redundant wavelengths (The model used throughout is called FA–SPA–ELM). The comparison among different models—the partial least squares discriminant analysis (PLS–DA) model, the support vector machine (SVM) model, the least squares support vector machine (LS–SVM), and the FA–SPA–ELM model—demonstrates that the wavelength number of the FA–SPA model can be effectively reduced with a wavelength variable of 17, and the model of FA–SPA–ELM presents the excellent predictive capability. The experimental results show that the proposed novel method could be used to identify adulterated grape seed oil quickly, effectively, and nondestructively.

Grape seed oil contains high content of lipids and bioactive compounds, such as vitamin E, linoleic acid, and proanthocyanidins, among other components (1,2). The total proanthocyanidins of grape seed oil have been demonstrated to offer benefits for antioxidant, anti-inflammatory, antihypertensive, and hypocholesterolemic activities (3,4). Additionally, grape seed oil has effect on anti-aging, radical-scavenging properties, and the protection against DNA damage (5). The results indicate that grape seed oil is a kind of senior health edible oil that has high nutrition health value and pharmacotherapy efficacy. However, adulterated grape seed oil is sometimes sold with other cheap edible oils by some producers so as to earn larger profits, thus disturbing the market and causing damage to the health of consumers. Therefore, it is of great value to employ rapid detecting techniques to discriminate the quality of grape seed oil.

Conventional methods detecting the quality of edible oils are mainly based on high performance liquid chromatography (HPLC), gas chromatography (LC), and thin-layer chromatography; however, these approaches are expensive, time-consuming, and require a plentiful supply of samples (6). Near-infrared (NIR) spectroscopy primarily measures the molecular vibrations of C-H, O-H, and N-H. Among existing techniques, the NIR spectroscopy technique has been widely applied to the nondestructive and rapid qualitative and quantitative detection of edible oils (7,8). Therefore, this research is intended to provide a potential reference method for detecting adulterated grape seed oil.

However, the full spectrum data measured by NIR contains too much redundant information between adjacent wavelength bands, causing some challenging problems regarding the identification of relevant and effective information, as well as the accuracy of the model. Wavelength selection techniques aim at eliminating the uninformative and interferential wavelength signals, while simultaneously obtaining an optimal subset of informative characteristic wavelength variables from the NIR spectrum (9). Among all different types of wavelength selection techniques, the 

swarm intelligence optimization algorithms

 are more interesting, because they simulate the social behavior of animals and insects to acquire the shortest path between a food source and their nests. Compared with the conventional optimization techniques, these techniques employ a stochastic, probabilistic, and crowd search process rather than a single solution. However, the number of the wavelength selected is still large, and it is easy to fall into a local optimal point through the swarm intelligence optimization algorithms. Hence, a genetic algorithm with a successive projections algorithm (GA–SPA) (10), a uninformative variable elimination with successive projections algorithm (UVE–SPA) (11), and a successive projections algorithm with particle swarm optimization (SPA– PSO) (12) are proposed to assist in rectifying these shortages, and to build a stable model using fewer wavelengths.

A high-quality, high-accuracy, and stable model is required for the qualitative analysis of adulteration by NIR spectroscopy. For the spectroscopy-based classification, chemometricians have developed many valuable algorithms, such as the partial least squares discriminant analysis (PLS-DA) (13), the support vector machine (SVM) (14), and the least squares support vector machines (LS–SVM) (15). Specifically, an algorithm for single-hidden layer feed-forward neural networks called an extreme learning machine (ELM) was proposed (16). Differing from the conventional learning algorithms that require adjusting input weights and hidden layer biases, the ELM arbitrarily assigns input weights and hidden layer biases, and calculates the output weights by a generalized inverse method (17). It is reported that ELM brings a higher learning rate, predictive accuracy, and generalization performance (18). As a rapidly developed technology, a large number of applications of the ELM have emerged in recent years (19,20). On the other hand, the ELM combined with NIR to analyze the adulterated grape seed oils has not been reported.

In this paper, an ELM approach is proposed to demonstrate the feasibility of the combination of NIR spectroscopy and the firefly algorithm combined with a successive projections algorithm ELM (FA–SPA–ELM) model in the quality of grape seed oil. NIR spectra is collected from grape seed oil blended with four kinds of different edible oils. FA–SPA is applied to optimize the characteristic wavelength, and then the ELM is built to determine the adulteration of grape seed oil. Moreover, the predictive performance of ELM is evaluated by a comparison with the conventional modeling methods, including the PLS–DA model, the SVM model, and the LS–SVM model.

This paper also formulates the oil samples, the spectral data collection, and the methods used throughout, as well as provides the experimental comparison and results to verify the effectiveness of the FA–SPA–ELM model.

In this section, the mixing of oil samples, the collection of NIR spectra, and the partition of the samples are described in detail. The flow chart of wavelength selection, and the structure and application of the ELM neural network in the research, are illustrated as well.

The grape seed oil, soybean oil, peanut oil, corn oil, and sunflower oil employed in this study were purchased at the local market. The grape seed oil was mixed with different amounts of soybean oil, peanut oil, corn oil, and sunflower oil to obtain the calibration and prediction set of 31 adulteration samples, respectively. These samples were prepared in volumetric flasks of 200 mL. In the samples of the adulterated grape seed oil, the volume content of the other four oils ranged from 0 mL to 200 mL, with increments of 5 mL, respectively.

The spectra data were acquired by the measurement system consisting of oil samples, the Fourier transform near-infrared (FT-NIR) Antaris II spectrometer, and a laptop. The oil samples were put into the spectrometer to measure spectral information. The spectral data were obtained by the spectrum information acquisition software, and saved as a .csv file (including wavelength values and corresponding absorbance data). Spectral measurement were executed at 25 °C and 60% relative air humidity. The experimental samples were packaged in 10 mm quartz cuvettes. The spectra were scanned in the range of 10,000–4000 cm

 and with 32 replicate scans every time. The spectrum of each sample were analyzed in triplicate, and the average value was taken as the NIR absorption spectrum of the sample.

In this study, 31 samples for each category were divided into a calibration set and a prediction set through the Kennard-Stone (21) algorithm. The calibration set of 21 samples for each category was employed to build the classification model, and the remaining 11 samples were used as a prediction set to evaluate the prediction capability of the model. In the following sections, A1, A2, A3, A4, and A5 represent NIR data of pure grape seed oil, grape seed oil blended with different levels of soybean oil, peanut oil, corn oil, and sunflower oil, respectively.

Selection of Characteristic Wavelength Variables

The full spectral data was weak, owing to the redundant wavelength information. The redundant wavelength information reduced computation speed and accuracy of prediction modeling. Therefore, a firefly algorithm (FA) was applied to screen out characteristic wavelength variables from the NIR spectrum in this work. FA is a swarm intelligence algorithm originally proposed by Yang (22) simulating the social behavior of fireflies that use light to attract mates (23). Yang (24) formulates the following three idealized rules:
(i) All fireflies are unisex, and attract each other;
(ii) Attractiveness is related to their brightness; for any two flashing fireflies, the less brighter one will move towards the brighter one. However, the brightness can decrease as their distance increases. If no one is brighter than a particular firefly, it moves randomly; and
(iii) The brightness of a firefly is determined by the objective function.

where RMSEC is root mean square error of calibration based on partial least squares (PLS) regression, 

 is the number of calibration set samples, 

 is category labels of the oil samples in calibration set, and 

 is predictive category labels through the PLS model.

However, the optimized characteristic wavelengths by FA are still vast, and contain collinear interference. These wavelengths are time-consuming to obtain, and unstable when used to establish classification models. The successive projections algorithm (SPA) is a forward selection method that uses vector projection analysis in the spectral matrix to minimize variable collinearity. SPA is used to extract efficient wavelengths further. The basic principle of SPA starts with one wavelength incorporates another wavelength at each iteration, until a specified number of wavelengths is reached. For each iteration, the combination of wavelength information is selected for constructing multiple linear regression models and calculating the RMSEC. When the value of RMSEC reaches a minimum and tends to be stable, the corresponding preferred wavelength number is the optimal wavelength combination.

Figure 1 shows the flow of the characteristic wavelength selection by FA combined with SPA, where 

 is the wavelength variable matrix for the 

FIGURE 1: The flow chart of FA combined with SPA.

The ELM classification model is a simple and practical single-hidden layer feedforward neural network proposed by Guangbin in 2006 (25). ELM can effectively overcome the issue of traditional neural networks, such as the complexity of training parameters, and the problem of local optimum. Here, there is 

=1 to be employed to establish the classification model between the spectra and category labels, where 

 is the measured spectra absorbance of the 

 = 1,...p are the selected optimal wavelength by the firefly algorithm combined with successive projections algorithm FA–SPA; y

 is the dimension of the category labels, 

 = 1 means the spectral data is labeled as Class 

th sample, the ELM classification model can be mathematically modeled as follows:

(x) is the activation function determined with sigmoid function, i = 1, 2,..., 

 is the input weight vector connecting input nodes with the hide node, 

 is the hidden layer vector bias corresponding to its hidden node, and 

 is the output weight vector connecting the output nodes with the hide node; 

 samples, the equation [2] can be abbreviated as:

 such that the output least-squares error of the model is minimized. It is directly equivalent to solve the following optimization problem:

 is the Moore-Penrose generalized inverse of the hidden layer output matrix 

Given that grape seed oil has shown beneficial effects for consumers, there is a interest in measuring oil quality and potential adulteration. This study demonstrates an effective near-infrared (NIR) spectroscopy method, using a series of machine learning approaches for wavelength variable selection, to rapidly discriminate grape seed oil adulteration.

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