Comparison Of Linear And Non-Linear Calibration Models For Non-Destructive Firmness Determining Of ‘Mazafati’ Date Fruit By Near Infrared Spectroscopy

Abstract

The selection of calibration method is one of the most important factors affecting the measurement accuracy with near infrared spectroscopy. In this research, the performance of two general calibration methods, namely, linear partial least squares regression and nonlinear back propagation artificial neural networks for firmness predicting of ‘Mazafati’ date fruit was investigated. A total of 175 date samples harvested during fruit ripening were selected as the data set. Optical scanning was performed with a fiber optic near infrared spectrometer with a range of 900–1700 nm. The inputs of back propagation artificial neural networks were the first five principal components resulting from the principal component analysis, namely, principal component analysis artificial neural network modeling or the first six latent variables obtained from partial least squares regression, namely, latent variable artificial neural network modeling. Both the leave-one-out cross validation and test set validation showed the priority of latent variable artificial neural network model with respect to partial least squares and also principal component analysis artificial neural network models. The best latent variable artificial neural network model could predict the firmness of Mazafati date fruits with R_p ² of 0.90, RMSEP of 1.30 N, and SDR_p of 3.28. The results also recommended the adoption of nonlinear latent variable artificial neural network modeling for applying light scattering properties of fruits in order to predict indirect property of firmness with near infrared spectroscopy.

Keywords:

• Date fruit
• Firmness
• Near infrared spectroscopy
• Linear modeling
• Artificial neural networks

INTRODUCTION

Date fruit (Pheonix dactylifera L.) is one of the most important commercial fruits in the Middle East. The major countries in producing this fruit are Egypt, Iran, and Saudi Arabia, respectively, with the production of 1,350,000, 1,088,040, and 1,052,400 tons in 2009.[1] There are a large number of date varieties which can be divided in three main groups including soft or wet (e.g., Mazafati), semi-dry (e.g., Zahedi), and dry (e.g., Dayri). In Iran, Mazafati variety is considered as the most famous soft variety that is usually harvested at an unripe stage. After harvesting, Mazafati dates are stored in a cooled condition until marketed. Generally, date is a climacteric fruit that can be ripened even after harvesting. One of the main factors that can determine the maturity of date and influences its proper future ripening is firmness. For instance, Mazafati dates reached the optimal eating ripe stage, the end of Kharak stage,[2] at a firmness of around 6 N; after that they are considered to be matured dates even though they can ripen after harvesting. The firmness is especially important for wet varieties of dates like Mazafati. For this group of dates, the accurate assessment of firmness in sorting lines allows the optimization of appropriate storage periods and adequate transport and packaging conditions.[3]

Date fruit firmness relates to the texture properties of the flesh and can be judged either by humans or, more accurately, by mechanical tests. Human estimation of firmness is not accurate and may cause a bruise or deformation in dates, while the mechanical test is usually based on the destructive Magness-Taylor penetrometer test, which is time-consuming and unsuitable for application to a single date. Hence, development of a rapid and non-destructive method to estimate the firmness of date fruit can be useful in optimization of harvest time and would also be a good substitution for hand sorting in the processing stream.

On the other hand, near infrared spectroscopy (NIRs) has been applied to determine firmness in a wide range of fruits, such as apples, [4,5] kiwifruits,[6,7] mandarins,[8] cherries,[9] pears,[10,11] watermelons,[12] and tomatoes.[13] Our previous works have proved the ability of NIRs in non-destructive and rapid estimation of compositional properties, such as moisture and soluble solids content of ‘Mazafati’ date fruits.[2] However, NIRs has not yet been used to measure firmness of date fruit, which is an indirect and more complicated quality index of date.

Generally, during the interaction of light with a biological material, absorption and scattering are two basic phenomena. Light absorption is related to certain chemical constituents in the fruit, such as sugar, acid, water, etc.,[14] while scattering is a physical phenomenon that depends on the size, density, and extra- and intra-cellular matrices of fruit tissue.[4] Therefore, light scattering seems to be more useful than absorption for quantifying such certain mechanical or textural properties of fruits as firmness. On the other hand, date fruit softening, like every climacteric fruit, has a clear chemical basis in the solubilization of the intercellular pectic substances.[15] Since these substances include polar CHx and OH type chemical structures, they will absorb NIR light. Thus, from this point of view, absorption is expected to be more efficient than scattering for determining firmness in climacteric fruits. These two different aspects play an important role in selecting the suitable approach for developing firmness calibration models. If we try to develop firmness calibration models from absorption, for the reason of the presence of substantial non-linearity, which is due to the light scattering or inherent non-linearity in the absorption bands, first we have to apply methods for removing or correcting non-linearity effects, i.e., mathematical pre-processing of absorbance spectra, and then use the common multivariate regression methods, such as partial least squares (PLS) method. But, if we prefer the physical point of view, i.e., determining firmness from light scattering, it is not necessary to remove non-linearity effects from spectra and, thus, the best way for solving the problem seems to be the application of non-linear calibration methods, such as artificial neural networks (ANNs). The wide range of applications of ANNs is largely due to their ability to deal with complex functions, enabling the modeling of non-linear relationships.[16] This method has been usually implemented based on principal components (PCs) obtained from principal component analysis (PCA) and sometimes wavelet components (WTs) obtained from wavelet transform.[17,18] However, no literature about combining the PLS with ANN for firmness determination of fruits with NIR spectroscopy have been carried out so far. The objective of this study was to compare the abilities of the linear chemometrics method and nonlinear ANN approach in estimating the firmness of date fruits (cv. Mazafati) from NIR spectral data. The linear modeling will use the common PLS method while the nonlinear ANN analyses will be based on PCs obtained from PCA, namely PCA-ANN modeling, and latent variables (LVs) obtained from PLS, namely LV-ANN modeling.

MATERIALS AND METHODS

Sample Selection

Some bunches of Mazafati date fruits were harvested on September 10, 2009 and October 20, 2009 from different trees of two orchards in Jiroft (Kerman province, Iran). At the first harvest time, dates were in the primary stages of ripening called Kimri and Kharak stages, while in the second harvest time the bunches included dates with more advanced stages of ripening referred to as Rutab and Tamr stages. After each harvest, fruits were stored at 2°C for a maximum of 10 days. Totally, 175 samples of date were selected from all bunches specified by the following ripening stages: Kimri (20%), Kharak (30%), Rutab (30%), and Tamr (20%). Before spectra acquisition, fruits were equilibrated for about 6 h to room temperature of approximately 22°C.

Spectral Recording

NIR spectra were taken using a portable EPP2000 NIR spectrometer (StellarNet, Inc., Oldsmar, FL, USA). The indium gallium arsenide (InGaAs) detector of spectrometer with 512 pixels could acquire the spectra in the range of 900–1700 nm and 2.5 nm resolution. The illumination source was a 20 W dc tungsten halogen light (SL1-CAL, StellarNet, Inc.). The spectra of dates were recorded in the interactance mode by using a bifurcated cable (R400-7-VISNIR, StellarNet, Inc.). This cable consisted of six optical fibers for illumining the sample, one fiber for detecting the diffuse reflection of the sample, and one metal probe (88.9 mm length and 6.35 mm outer diameter) to collect the fibers at the head of the cable. Each spectrum was the average of 10 scans and all measurements were performed on two opposite positions on the equator of each date marked with a circle. In this way, all spectral and firmness measurements were performed at exactly the same position on the fruit. The dataset included 350 observations in total (175 dates, two measurements per fruit). They were all considered independent for further analysis.[11]

Firmness Measurements

Immediately after spectral acquisitions, each date fruit was cut into two halves at the direction of the major axis and the inside seed removed. Then, the firmness of each half was measured using a universal-testing machine (STM5, SANTAM Inc., Iran) with a 2-mm diameter stainless-steel round probe. The testing machine was connected to a computer to obtain continuous force-deformation curves. The loading rate of the crosshead was 25.4 mm min⁻¹ and the depth of penetration was 3 mm. The maximum value recorded by the probe while passing through the fruit, in N, was regarded as the firmness of the date.

Data Analysis

Linear regression method

As explained earlier, in this study, the firmness predictive models were obtained using two different approaches: linear chemometrics method and non-linear ANN approach. In the linear method, the models were developed by partial least squares (PLS). For this purpose, the spectra were first transferred to the Unscrambler Version 9 (CAMO Process AS, Oslo, Norway) for pre-processing and model construction. Then, the spectra were reduced to 920–1680 nm, in order to eliminate noise at the edges of each spectrum. Pre-treatments of NIR spectra included Savitsky-Golay smoothing (gap size 9) and constant offset elimination (COE). Other data pre-treatments, such as multiplicative scatter correction (MSC), vector normalization, first and second derivation, straight line subtraction, and a combination of the mentioned methods, were also tried. However, no advantage was found in using such procedures and COE yielded the best results in PLS modeling of firmness.

PLS model validation procedures were based on the leave-one-out cross-validation and test set validation methods. From the total sample set, 263 measurements (75%) were randomly used for calibration and leave-one-out cross-validation with 87 remaining (25%) for external or test set validation. The optimum number of latent variables (LVs) of PLS for a model was selected by examining a plot of leave-one-out cross-validation residual variance against the number of latent variables obtained from PLS regression. For this purpose, the number of latent variables of the first minimum value of residual variance was selected.[19] Outlier detection was based on performing principal components analysis (PCA) on the pre-processed spectra. The score plot of the first two PCs presents two-dimensional diagrams showing the relation between data. Data points lying outside the ellipse (with 95% confidence level) were considered as strong outliers and were removed from the data set.[20]

Non-linear regression method

Artificial neural networks (ANNs) were used to build the models for non-linear regression. ANN is a powerful computational modeling tool, consisting of a large number of interconnected simple processing elements (artificial neurons), that can model complex, parallelism, and non-linear systems. In particular, back propagation (BP) networks are the most common and appropriate networks for spectroscopic applications.[14] A BP network is a feed-forward multilayer perceptron network consisting of one input layer with the neurons as independent variables, one or more hidden layers, and one output layer with the neurons as dependent variable, namely, firmness of dates.[21] In the feed-forward networks, error minimization can be achieved by a number of methods, such as gradient descent (GD), Levenberg-Marquardt (LM), and conjugate gradient (CG). The standard BP applies the GD technique, which is very stable when a small learning rate is used; however, it has slow convergence properties.[22] Several methods have been used for speeding up BP algorithms, such as GD with momentum (GDM) and a variable learning rate. In this article, GDM learning rule, which is an improvement of the straight GD rule, was used to avoid local minima, speed up learning, and stabilize convergence.

The input of BP-ANN was selected from either PCs obtained from PCA, or LVs obtained from PLS. Both PCA and PLS have been applied on the raw spectra. These two possibilities, namely PCA-ANN and LV-ANN, were tested and the results were compared. Adopting PCs or LVs as input for BP-ANN is an effective way of reducing the dimensionality of the spectral data by reserving the major spectral information.[23] The optimum number of PCs in the PCA-ANN models was based on the cumulative percentage of explained data variance. The optimum number of LVs in LV-ANN models was obtained at the first minimum value of residual variance, as explained by Brown et al.[19]

The tan-sigmoid function and a linear function were used in the hidden and output layers, respectively. The learning rate and momentum in the networks were 0.1 and 0.3, respectively, and the number of epochs was equal to 1000 times. In order to avoid over-fitting of ANN models, the cross validation option was adopted. The NIR spectra of 350 samples were assigned to the training (50%), validation (25%), and test (25%) subsets. The optimum number of nodes in the hidden layer was determined by examining several networks with different numbers of nodes in the hidden layer. For this purpose, the number of neurons of the first minimum value of root mean squared errors of cross-validation (RMSECV) was selected in the hidden layer.[24] In this study, all ANN analyses were performed using Statistica neural networks software (StatSoft, Inc., USA).

Statistical parameters used to assess the performance of calibration models

To compare different regression methods, the performance of each model was evaluated by coefficient of determination (R ²) between the predicted and measured firmness, root mean squared errors of cross-validation (RMSECV), and prediction (RMSEP). We have also calculated the standard deviation ratio (SDR) for both leave-one-out cross-validation (SDR_cv = σ _cv /RMSECV, where σ _cv is the standard deviation of the calibration or leave-one-out cross-validation set) and test set validation (SDR_p = σ _p /RMSEP, where σ _p is the standard deviation of the test set validation). SDR (or RPD, in some reference texts), known as the best index to evaluate the regression models performance, is the factor by which the prediction accuracy increases compared to use the mean of the original data.[14,25]

RESULTS AND DISCUSSION

The statistics of the firmness for samples in both linear and non-linear analysis are summarized in Table 1. It is clear that the firmness of samples in both calibration (leave-one-out cross validation) and test data sets in linear regression (PLS method), as well as in training, verification, and testing data sets in non-linear regression (ANN approaches), is appropriately distributed. Also, the mean value and standard deviation (SD) of firmness in the data sets at each modeling method are very close to each other.

Relationship Between Reflectance Spectra and Date Softening

The firmness determined by destructive testing showed a uniform decreasing during ripening stages of dates, i.e., from Kimri to Kharak, Rutab, and Tamr stages, respectively (data not shown). The firmness data also showed that at the end of Kharak stage, the dates had a firmness of around 6 N. Therefore, date fruits with the firmness less than 6 N could be considered as matured dates.

Table 1 Distributional statistics of data sets used for linear and non-linear modeling of ‘Mazafati’ date firmness (N)

		Sample indices
Modeling	Data set	N	Min.	Max.	Mean	SD	%CV
Linear regression	Calibration/LOOCV	262	0.3	14.4	7.2	4.0	56
	Test	88	0.3	12.9	7.3	3.8	52
Non-linear regression	Train	175	0.3	13.2	7.3	3.9	54
	Verification	87	0.3	14.4	7.1	4.1	58
	Test	88	0.3	13.5	7.2	4.1	57
LOOCV: leave-one-out cros validation.

In order to understand how date fruit ripening contributes to the reflectance spectra, the correlation spectrum r(λ) between the date firmness (F) and the reflectance (R) is depicted in Fig. 1. Correlation spectrums were drawn for three cases: (1) all date samples (solid line); (2) only for date samples with firmness more than 6 N (high-F range shown with open circles); and (3) only for date samples with firmness less than 6 N (low-F range shown with black circles).

Figure 1 Correlation of Mazafati date firmness with the raw reflectance spectra at each wavelength, r(λ). (–) Correlation made with the total set. (•) Correlation made only with samples having firmness lower than 6 N. (○) Correlation made only with samples having firmness higher than 6 N.

As shown in Fig. 1, firmness showed a positive correlation with diffuse reflectance for three sets and all wavelengths (except for low-F values in the narrow range of 1420–1480 nm). This is due to the softening process in climacteric fruits, such as dates. Softening results mainly from progressive cell wall modification and disassembly by enzyme action, leading to the solubilization and depolymerization of pectins and hemicelluloses.[26] The consequence of this process is lower flesh opacity, increasing light penetration depth, and decreasing the level of diffuse reflectance. This effect is directly correlated with firmness for all sets and wavelengths.

Correlation diagrams for all three sets remained nearly constant between 900 and 1380 nm. After that, the correlation values decrease dramatically around 1460 nm (especially for total and low-F samples) being related to the strong water absorption band. The low correlation around 1460 nm may be partially explained by the fact that the moisture content does not have any correlation with firmness. This was also highlighted by Cavaco et al.[10] for ‘Rocha’ pear, which is also a climacteric fruit. However, Peirs et al.[27] held that cell wall deterioration may lead to relocation of water molecules, changing relative refractive indices and, consequently, the scattering and reflectance properties. After all, this means that a correlation between the water absorption band, such as 1460 nm and firmness, is reasonable. But the problem is that water absorption in date fruit had such a dominant influence on light absorption that the effect of firmness was diminished greatly.

Compared to the total samples and low-F sets, high-F set has a better correlation at the vicinity of 1460 nm. The higher opacity of high-F samples caused decreasing of light penetration depth in all wavelengths including 1460 nm. Therefore, the light reflectance at the vicinity of 1460 nm is less influenced by moisture content of whole date flesh and is more affected by texture property, i.e., firmness of dates.

Linear PLS Model for Firmness

In linear modeling of firmness, the PCA was first performed on the pre-processed spectra to identify and eliminate the outliers. In total, seven data points were located outside the ellipse (with 95% confidence) in the first two PCs diagram and were considered as the outliers and removed from the data set. Afterwards, the PLS regression method was carried out for modeling the firmness of dates. The scores plot of the samples for the first two PLS components (the first component u[1] of firmness score and the first component t[1] of spectra score) is illustrated in Fig. 2. The scores were determined after mean centering and log transformation. Data points were then grouped in the two categories including low firmness (Firmness < 6 N) and high firmness (Firmness > 6 N) samples. As shown, these two groups are obviously separated from each other indicating that PLS models at least have the ability to discriminate between low and high firmness samples.

Figure 2 The scores plot of the samples for the first two PLS components.

Figure 2 also indicates the possibility of obtaining better results through separate modeling of low firmness and high firmness groups. This was the main hypothesis followed in the work of Cavaco et al.,[10] who revealed that for a climacteric fruit ripening, a segmented model possibly produces better results as far as firmness prediction is concerned. However, this hypothesis was not valid for the present work regarding firmness prediction of date fruit, i.e., we found even slightly better results with full-range modeling of firmness.

The best PLS calibration model parameters for the firmness using the full range of data are presented in Table 2. The model was then applied to the test sets. As shown in Table 2, the PLS model built for firmness prediction of ‘Mazafati’ date fruits was fairly acceptable in terms of coefficient of determination (R_p ² = 0.85), but the respective SDR gave a 2.59 value. The respective scatter plots of predicted versus measured firmness obtained by destructive method for the calibration, leave-one-out cross-validation and the test set validation, are shown in Fig. 3a. The model performance verifies that in the linear modeling; only a coarse quantitative prediction for firmness is possible. This result was also found by McGlone and Kawano,[7] Cavaco et al.,[10] and Nicolaï et al.[11] for firmness prediction of kiwifruits, pears, and apples, respectively. The relative coarse results in the linear modeling may be explained by the fact that the complex physical structure of date fruit tissue produces an optically compact material that is difficult to penetrate and change the pathlength traveled by the light. Therefore, the amount of tissue inspected is not known with certainty. On the other hand, the PLS models for prediction of firmness are not generally based on the physical measures directly related to firmness but in the measurement of other parameters, such as water and pectin, that like firmness, may change during ripening. In other words, in the PLS modeling, firmness cannot be determined as a single analyte like sugar.

Table 2 The results of linear PLS and non-linear PCA-ANN and LV-ANN models in firmness predicting of Mazafati date fruit

		Calibration/training		Cross validation/verification			Test
Analysis	LV/NHL	R ^2	RMSE (N)	R ^2	RMSE (N)	SDR	R ^2	RMSE (N)	SDR
PLS	9	0.88	1.34	0.86	1.43	2.75	0.85	1.55	2.59
PCA-ANN	7	0.90	1.24	0.89	1.38	2.94	0.86	1.56	2.63
LV-ANN	6	0.91	1.19	0.90	1.27	3.37	0.90	1.30	3.28
LV: number of latent variables; NHL: number of neurons in hidden layer; RMSE: root mean squares error.

Figure 3 Scatter plots of predicted versus measured firmness in (Δ) calibration (training), (○) leave-one-out cross-validation (verification), and (■) test set samples for (a) PLS, (b) PCA-ANN, and (c) LV-ANN models.

When results were compared with some recent investigations for other fruits, the results of PLS model can be deemed good and acceptable. The best statistical parameters for comparison are prediction coefficient R_p ² and SDR_p values because they do not depend on populations’ statistics. With regard to other fruits, Vis/SWNIR (400–950 nm) was used for ‘Rocha’ pears^[10] with a similar correlation (R_p ² = 0.85) and a lower prediction capability (SDR_p  = 2.48 versus 2.59). For ‘Satsuma’ mandarin,^[8] full spectral range (400–2350 nm) resulted in R_p ² and SDR of worse than our results (R_p ² = 0.68 and SDR = 1.7). Kiwifruit firmness was predicted by McGlone and Kawano^[7] in the range of 800 – 1100 nm and the best results were R_p ² = 0.76 and SDR = 2.0. The results for ‘Royal Gala’ (R_p ² = 0.59 and SDR = 1.6) reported by McGlone et al.,^[28] and for ‘Idared’ and ‘Golden Delicious’ apples (R_p ² = 0.81 and SDR ≈ 1.8), obtained by Zude et al.,^[5] were also worse than ours. Lammertyn et al.[29] and Nicolaï et al.^[11] failed to provide a satisfactory prediction model for firmness of ‘Jonagold’ apples (R_p ² between 0.53 and 0.56) and ‘Conference’ pears (R_p ² = 0.65), respectively. The only better results were reported for ‘Heatwave’ tomato,^[13] that had a lower correlation coefficient (R_p ² = 0.69) but a higher prediction capability (SDR = 3.5).

Nonlinear ANN Models for Firmness

In order to reduce the dimensionality of the spectral data and the number of inputs in ANN models, PCA and PLS analysis were performed. In PCA analysis, the first principal component (PC1) could explain 97.4% of the original variables while with five PCs, the explained variance was 99.2%. These five PCs were enough to ensure that all variability would be considered by the analysis. With these PCs as the inputs, BP-ANN models with three layers were developed. One input layer consisted of five neurons for five PCs, one hidden layer and one output layer with one neuron for firmness prediction. The trial and error procedure was used to ensure that the number of five PCs as the inputs to ANN is effective and enough for modeling of firmness. ANN models with a lower number of five PCs had a lower regression power and with the higher number of five PCs, the models had more complexity without meaningful regression power. In order to determine the optimum number of neurons in the hidden layer, several networks with different numbers of neurons in a hidden layer were established. The considered PCA-ANN models provided different prediction performances of the studied date firmness; however, the PCA-ANN model with seven neurons in the hidden layer resulted in the best accuracy. The results of the best PCA-ANN model are summarized in Table 2 and the respective scatter plot of predicted versus measured firmness is depicted in Fig. 3b for training, verification, and test set samples. The PCA-ANN model shows slightly better results in firmness prediction of date fruits compared to linear PLS model (SDR_p  = 2.63 versus SDR_p  = 2.59), however, the difference is not significant.

In PLS analysis, the first LV could explain 97.38% of X-variable (NIR data) and 53.09% of Y-variable (firmness), while with six LVs, 99.97% of X-variable and 76.30% of Y-variable could be explained. ANN models with a lower number of six LVs had a lower prediction power, while by using a larger number of LVs, the models resulted to more complexity without considerable prediction power. Considering the coefficients of determination (R ²) and RMSE for training, verification, and testing, the best LV-ANN model for firmness prediction was achieved by six neurons in the hidden layer. As indicated in Table 2, the LV-ANN model led to the best performance compared to PLS and PCA-ANN models with R_p ² = 0.90, RMSEP = 1.30 N, and SDR_p  = 3.28. Figure 3c shows the scatter plot of predicted versus measured firmness for LV-ANN model.

One of the highest reported accuracy of firmness measurements of fruits with a Vis-NIR spectroscopy is that reported by Shao et al.^[13] They arrived at a R_p ² value of 0.61, RMSEP of 2.24 N, and SDR_p  = 3.5, by conducting common PLS analysis on spectra of 138 tomato samples. Comparing these results with those of the present study, for both correlation (0.90 versus 0.61) and RMSEP (1.30 versus 2.24) values, the LV-ANN model for date fruit firmness had a better performance than the PLS model for tomato firmness, but in terms of SDR values (3.23 versus 3.5) the LV-ANN model was slightly worse than PLS model. This comparison reveals that nonlinear LV-ANN modeling is a better method with respect to the common linear PLS models, since the number of samples used in the latter study was larger, and due to the existence of a large seed inside date fruits, the optical properties and destructive firmness measurements of date fruit are more complicated than those of tomato. The priority of the nonlinear LV-ANN model, as compared to the linear PLS model in firmness prediction, may show that light scattering is a better phenomenon than light absorption for prediction of structurally related properties, such as fruit firmness. In other words, it seems that the changes in scattering of light with tissue structure influence firmness estimation more than changes in absorption of light with CHx and OH type chemical structures resulting from hydrolyzing of insoluble cell wall propectin. With that being said, firmness is a combination of changes in several factors, such as changes in the structure of cells, the state of the pectin, and also turgor pressure. These facts make it difficult to quantify firmness by using common PLS models in the way that is usually possible for chemical attributes. Therefore, it may better to use nonlinear modeling, such as LV-ANN.

CONCLUSIONS

In the present study, the common linear chemometrics methods and nonlinear ANN approach were applied to estimate the firmness of date fruits (cv. Mazafati) from NIR spectral data. The comparison among linear PLS and nonlinear PCA-ANN and LV-ANN methods showed that the LV-ANN model outperformed PLS and PCA-ANN models for firmness prediction of the tested date fruits. Therefore, it was concluded that in prediction of structurally related properties, such as fruit firmness by NIRs, scattering of the light with tissue structure may be a better phenomenon than absorption of light with chemical functional groups resulting from fruit softening.

Notes

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ljfp.