Issue 
Ann. For. Sci.
Volume 67, Number 4, June 2010



Article Number  403  
Number of page(s)  10  
DOI  https://doi.org/10.1051/forest/2009123  
Published online  12 March 2010 
Original article
Rapid prediction of shrinkage and fibre saturation point on teak (Tectona grandis) wood based on nearinfrared spectroscopy
Prédiction rapide du retrait et du point de saturation des fibres pour le bois de teck (Tectona grandis) par spectroscopie proche infrarouge
^{1}
Laboratoire de Botanique et Ecologie Végétale, Faculté des Sciences,
Université de Lomé, BP1515, Lomé, Togo
^{2}
CIRAD, PERSYST Department, Production and Processing of Tropical Woods Unit,
Montpellier,
France
^{3}
CIRAD, BIOS Department, Genetic Diversity and Breeding of Forest Species
Unit, BP 5035,
34398
Montpellier Cedex 5,
France
^{*} Corresponding author:
gilles.chaix@cirad.fr
Received:
14
April
2009
Accepted:
9
October
2009
• Dimensional stability, along with the natural durability and colour of the wood, is one of the most important characteristics of teak used as timber. However, it is very timeconsuming to take measurements of this kind. For the purposes of selection for the production of improved varieties, the number of samples to be measured rapidly exceeds the capacity of a traditional laboratory.
• Nearinfrared spectroscopy, based on a set of reference data, is a tool enabling many of the chemical properties of wood to be predicted and the number of laboratory measurements to be reduced exponentially. The issue here is a question of checking the effectiveness of NIRS tool to build models and predict the shrinkage and fibre saturation point of teak wood from Togo.
• The results show the possible use of NIRS to measure the dimensional stability of teak wood and that it is appropriate to choose the type of wood and type of surface to be measured by NIRS. The best prediction models for radial and tangential shrinkage and fibre saturation point give R^{2} values of 0.72, 0.83 and 0.87 respectively with ratios of performance deviation of 1.8, 2.4 and 2.8.
• Consequently, after verification on other sets of teak samples, which may or may not be included in the prediction model, NIRS can be used to predict shrinkage and fibre saturation point values accurately for a large number of samples, making it possible to include these characteristics in the selection criteria for classifying wood and high throughput phenotyping.
Résumé
• La stabilité dimensionnelle avec la durabilité naturelle et la couleur du bois, est l’une des plus importantes caractéristiques pour le teck utilisé en bois d’œuvre. Néanmoins, les mesures de ce caractère sont longues et coûteuses en temps. Pour les besoins de la sélection pour la production de variétés améliorées, le nombre d’échantillons à mesurer devient vite supérieur aux capacités d’un laboratoire traditionnel.
• La spectroscopie proche infrarouge, sur la base d’un jeu de données de références, est un outil qui permet de prédire de nombreuses propriétés chimiques du bois et de réduire le nombre de mesures de laboratoire de façon exponentielle. La question ici est de vérifier l’efficacité de l’outil NIRS pour construire des modèles et prédire les retraits et le point de saturation des fibres du bois de teck provenant de plantations du Togo.
• Les résultats démontrent la possible utilisation de la SPIR pour mesurer la stabilité dimensionnelle du bois de teck et qu’il a y lieu de choisir le type de bois et le type de face que l’on mesure par SPIR. Les modèles de prédiction pour les retraits radial et tangentiel et le point de saturation des fibres montrent des R^{2} de 0,72, 0,83, 0,87 respectivement avec des rapports d’efficacité de 1,8, 2,4 et 2,8.
• En conséquence, et après vérification sur d’autres jeux d’échantillons de teck, qu’il conviendra ou non d’intégrer dans le modèle de prédiction, la SPIR permet de prédire des valeurs de retrait et de PSF avec efficacité pour un grand nombre d’échantillons rendant possible l’intégration de ces caractères dans les critères de sélection pour le classement des bois et pour le phénotypage à grande échelle.
Key words: shrinkage / fibre saturation point / teak / NIRS
Mots clés : retrait / point de saturation des fibres / teck / SPIR
© INRA, EDP Sciences, 2010
1. INTRODUCTION
Teak (Tectona grandis) has been selected for sustainable production of high quality timber in the tropics (Bhat and Priya, 2004). It is often used for outdoor purposes (e.g. boat decks, bridge building, and garden furniture) and traditional indoor uses such as parquet and furnishings. Its timber qualities include a golden brown colour with typical features and grain, resistance to fungus and termites. Teak wood possesses very interesting technological properties such as medium specific gravity, high strength (Bhat and Priya, 2004; Kokutse et al., 2004), good dimensional stability and high durability (Baillères and Durand, 2000). The main wood quality factors related to dimensional characteristics are shrinkages (tangential and radial) and sorption properties such as fibre saturation point (FSP). Moisture can exist in wood as liquid water (free water) or water vapor in cell lumens and cavities, or as water held chemically (bound water) within cell walls. Conceptually, the moisture content at which only the cell walls are completely saturated (all water is bound) but no water exists in cell lumens is called the FSP. It is normally assumed that the FSP is the moisture content (MC) below which the physical and mechanical properties of wood change as a function of moisture content (Berry and Roderich, 2005; Simpson and TenWold, 1999). FSP is affected by the presence of wood extractives, which can behave as hygroscopic, hydrophobic or neutral entities (Stamm, 1971). Teak has been reported as presenting shrinkage, from the green state to ovendry condition, of 2.5 to 3.0% in the radial direction and 3.4 to 5.8% in the tangential direction (Simatupang and Yamamoto, 2000; Trokenbrodt and Josue, 1999). Several authors have shown the relationships between the presence of extracts in the heartwood, e.g. anthraquinones and tectoquinones, and teak wood durability (Haluk et al., 2001; Pahup et al., 1989; Simatupang and Yamamoto, 2000; Yamamoto et al., 1998). The good dimensional stability of teak wood is mainly due to the bulking effect of the ethanol and hot water soluble wood extractives located in the cell wall (Simatupang and Yamamoto, 2000). Some results have been published on the shrinkage of teak wood (Bhat, 1998; Sanwo, 1987; Simatupang and Yamamoto, 2000) but no studies have been carried out on FSP. Determination of shrinkage and FSP are based on tests that require destructive sampling and extensive sample preparation. The industry would benefit from employing a more rapid, nondestructive technique for the estimation of these properties.
An option for the estimation of these wood properties is near infrared (NIR) spectroscopy. This is based on vibrational spectroscopy that monitors changes in molecular vibrations intimately associated with changes in molecular structure. Spectra within the NIR region consist of overtone and combination bands of fundamental stretching vibrations of functional groups that occur in the middle infrared region, mainly CH, OH and NH, which represent the backbone of all biological compounds. The potential application of NIR spectroscopy to predict wood characteristics has been reported in the literature (Kelley et al., 2004; Tsuchikawa, 2007). It offers a rapid method for estimating many important wood properties including density, microfibril angle, stiffness (Cogdill et al., 2004; Hein et al. 2009; Schimleck et al., 2005; 2007), and prediction of the longitudinal tensile modulus and strength (Hedrick et al., 2007). Gierlinger et al. (2003) have shown that NIR spectroscopy is an accurate and fast method for nondestructive determination of natural durability. The effect of biological deterioration on the physical, mechanical and chemical properties of wood has also been characterized through spectroscopy (Edwin and Ashraf, 2006). In the forest products industry, NIR spectroscopy is used mainly for rapid prediction of pulp yield and pulping characteristics (Alves et al., 2006; Boeriu et al., 2004; Brinkmann et al., 2002; Monrroy et al., 2008; Raymond et al., 2001; Schimleck and Michell, 1998; Schimleck et al., 1997; Wright et al., 1990). In addition, a few studies have used NIR spectroscopy to assess physical properties such as shrinkage (Baillères et al., 2002; Taylor et al., 2008). For studies concerning forest product, there is no reference in which NIR spectroscopy is used to assess characteristics such as FSP. This paper evaluates the potential of NIR spectroscopy for the assessment of some major physical wood characteristics for Teak. Our objective was to measure the prediction accuracy under actual operational conditions and to use the prediction model for selection according to nondestructive sampling methods of core samples.
2. MATERIALS AND METHODS
2.1. Site description
The study site was situated in the central part of Togo (1° 00′ E, 8° 21′ N), West Africa. This central area of Togo is covered by Guinean woody savannas and is situated at an altitude of 200–400 m. In this area, two major seasons exist in a year, one long rainy season lasting 6–8 months, followed by a long dry season. Mean annual precipitation is 1400–1600 mm and temperatures vary from 25 °C to 40 °C (Ern, 1979).
2.2. Wood samples
Twenty trees were selected for analysis from two plots, namely Tchorogo (established in 1972) and Oyou (established in 1966). The description of the study sites is presented in Table I. Planks were cut radially (500 mm in the longitudinal axis and 50 mm in the tangential axis) between a height of 1 and 1.5 m. Four beams were cut per plank along the diameter (20 × 20 × 500 mm) and lastly, 5 wood samples of dimensions 20 × 20 × 10 mm (in radial, tangential and longitudinal directions) were cut per beam. The samples were stabilized to a theoretical MC of 12% in a climate chamber at 20 °C and 65% humidity. A total of 393 remaining samples were used for measuring dimensional stability, FSP and NIR absorbance. For each sample, 2 NIR measurements were recorded (longitudinalradial (LR) and tangentialradial (TR) surfaces). All the samples were then ground into wood meal (with a 4 mm filter) to compare the prediction accuracy based on ground wood samples and solid wood samples.
Site characteristics. A: altitude (m); D: density (tree.ha^{−1}); MD: mean diameter (cm) at height 1.3 m; MH: mean height (m).
2.3. Determination of FSP
FSP was obtained by measuring the weight and the dimensions of wood samples placed in different conditions of air temperature and relative humidity (Ruelle et al., 2007). Initially, the samples were immersed in water until saturation. Next, each sample was oven dried in appropriate temperature and air humidity conditions, until the theoretical moisture content had reached 18%, 12% and 6% successively. When each state had been reached, all samples were weighed and the radial and tangential dimensions were then measured with a displacement transducer. Ink marks were printed on the samples to ensure correct repositioning between successive measurements. Finally, the samples were brought to the anhydrous state, by oven drying them at 103 ± 2 °C. The FSP is the constant coefficient (Eq. (2)) of the linear regression between the variation of transverse area (VTA, Eq. (1)) and the moisture content (MC) (Guitard, 1987): (1)with DR: radial dimension, DT: tangential dimension, SAT: fully saturated sample and MC: moisture content after conditioning (18%, 12%, 6% and 0%). (2)with b_{1}: slope coefficient and ε: random error.
2.4. Measurement of shrinkages
Radial shrinkage (RS) and tangential shrinkage (TS) were obtained using equation (3 between the saturation state and the final oven dried state: (3)with S: shrinkage, D_{SAT}: saturated dimension, D_{0%}: dried dimension.
2.5. Near infrared spectra collection
Nearinfrared spectra were collected in the NIR region from 12 500 to 3 800 cm^{−1} (800–2 850 nm) on solid wood and ground wood with an NIR spectrometer (Bruker model Vector 22/NI) in diffuse reflectance mode at a spectral resolution of 8 cm^{−1} (each spectrum consisted of 2 335 absorption values). Spectra taken from TR and LR surfaces of solid wood (sample used for dimensional stability) were used in the calibration modelling. Each spectrum was obtained with 32 scans, and means were calculated and compared to the standard in order to obtain the absorption spectrum of the sample. Wood meal spectra were also collected in diffuse reflectance mode using a spinning cup module. Each spectrum was obtained with 64 scans. Temperature and relative humidity were kept constant (20 °C, 65% respectively) throughout the NIR processing.
2.6. Data processing
In a first step, a validation set was established by a selection of 100 samples among the 393 samples based on the sample distances calculated on five components after a principal component analysis (PCA) of the spectral data. We assumed that these covered the FSP and shrinkage ranges. In a second step, the spectra data from 293 remaining samples were regressed against the FSP, TS and RS, and by means of 5 random cross validation groups, a significant number of Partial Least Squares (PLS) components (rank) was obtained using OPUS Quant 2 software (Bruker) and Unscrambler 9.8 (Camo). This step allowed the preprocessing to be compared and outliers to be detected. Different data treatments were evaluated for the spectral data: first derivative (D1), second derivative (D2), standard normal variate (SNV), detrend (DT), and combinations of all. SNV is a transformation usually applied to spectroscopic data, which centers and scales each individual spectrum (i.e. a sampleoriented standardization). DT is a transformation which seeks to remove nonlinear trends in spectroscopic data. Like SNV, it is applied to individual spectra. DT and SNV are often used in combination to reduce multicollinearity, baseline shift and curvature in spectroscopic data. Derivatives of spectral data are used to remove or suppress lowfrequency background noise and globalline variations. Derivatives also provide a resolution enhancement that helps to identify weak peaks that are not apparent in the original spectrum. The PLS models were then used to predict data of the validation set, evaluating their predictive ability. The number of outsiders (samples whose predicted value lies outside the calibration range) and the number of outliers (samples whose Mahalanobis distance is too large, meaning that the similarity of the spectra compared to the calibration spectra is too low) of the models were compared. The quality and the final selection of the models were assessed by: coefficient of determination (R^{2}) from reference values and predicted values by the models, standard error of calibration (SEC) and standard error of crossvalidation (SECV). The best results for each pretreatment considering either the minimum SEC or SECV were noted. When the best models were determined, a validation set (established by random selection from within the batch and not used for the calibration process) was used to test their performances. The performance of models was controlled by the coefficient of determination (R^{2}) from reference values and predicted values obtained by the models and the standard error of prediction (SEP, Eq. (4)). (4)with : estimated value, y_{p}: measured value, n: number of samples in the validation set.
Models were tested by the Ratio of Performance Deviation (RPD) which is the ratio of the standard error SD (deviation for the reference method values) of sample validation divided by SEP.
3. RESULTS
3.1. Solid wood calibration
The FSP of the 393 samples ranged from 16.2% to 26.0% with an average of 20.4% and a standard deviation of 1.8% (Tab. II). For all samples, the radial and tangential shrinkages varied from 1.7% to 5.4% and from 2.3% to 9.3% respectively, with a standard deviation of 0.7 and 1.3 (Tab. II). Shrinkage properties are more variable than the FSP. The coefficient of variation for radial and tangential shrinkage is 22% and 24% compared to 9% for the FSP. This reading is not due to measurement error as the error relating to shrinkage (1.6% error for RS and 0.9% for TS) is smaller than that for FSP (7.6%). The measurement error calculations are detailed in the annex. In the absence of other considerations, high variability and low measurement error favour the statistical estimation of shrinkage variables with respect to the FSP variable.
Number of samples (N) and descriptive statistics of reference values. M: mean (%). SD: standard deviation (%). CV: coefficient of variation (%). Min: minimum value (%). Max: maximum value (%).
Solid wood – PLS results of the calibration and crossvalidation on detrend, SNV (standard normal variate) and derivate 2 preprocessing spectral data. N: number of sample. M: mean. SD: standard deviation. SEC: standard error of calibration. SECV: standard error of cross validation.
The calibration results for solid wood are given in Table III. Whatever the estimated property and the transverse section, the best pretreatment is detrend followed by SNV and D2. All the models are highly significant with determination coefficients greater or equal to 0.74. The models calculated on the TR surface absorbance perform better than the model based on LR surface. The r^{2} are systematically higher (1 significant latent value higher for TR surface). In addition, the TS models are better than the RS models, irrespective of the TR surface under consideration. The laboratory standard deviation (SEL of 0.53 calculated in the annex) is very close to the calibration standard deviation (SEC of 0.65 and 0.53) for the FSP. Of the three properties studied, the FSP is the best estimated (r^{2} = 0.90 for the TR surface). With respect to the shrinkage properties, the SEC is 10 times higher than the SEL which is equal to approximately 0.026 (SEL estimated in the annex).
3.2. Solid wood validation
The validation results for solid wood are shown in Figure 1 and Table IV. The population used to validate the models has statistical characteristics similar to those of the calibration population, irrespective of the property being studied (Tab. IV). The variability percentages explained by the validation models are lower than those for calibration but the difference is slight (from 1–3 points for FSP, to 7–14 points for RS). The findings for calibration are also found in the validation population; i.e. (a) the models for the TR surface are higher than the models on the LR surface, (b) the TS models are better than the RS models, (c) FSP is the property with the best estimation. The value found for the RPD to FSP shows that this model may be used for rough screening according to the reference gave by Williams and Sobering (1993).
Figure
1 Near Infrared – Partial Least Square predicted versus laboratory determined radial shrinkage, tangential shrinkage and fibre saturation point for Tectona grandis solid woods (A: NIR data from LongitudinalRadial surface, B: NIR data from TangentialRadial surface). 
Solid wood – PLS Model results of test validation. N: number of sample. M: mean. SD: standard deviation. SEP: standard error of prediction. RPD: ratio performance to deviation.
3.3. Wood meal calibration
Table V and Figure 2 show wood meal calibration and crossvalidation results. As for solid wood (Tab. III), the best pretreatment obtained is D2 followed by SNV and detrend. The ranks relating to the models for powders are lower than those relating to solid woods. The variability percentages explained by the powder samples are lower than those obtained for solid woods. As with solid wood, the estimation for tangential shrinkage is better than for radial shrinkage. FSP is the best estimated property, with an r^{2} very close to that obtained for solid wood (Tab. III).
Powder samples – PLS results of the calibration and crossvalidation on detrend, SNV (standard normal variate) and derivate 2 preprocessing spectral data. N: number of sample. M: mean. SD: standard deviation. SEC: standard error of calibration. SECV: standard error of cross validation.
Figure 2 Near Infrared – Partial Least Square predicted versus laboratory determined radial shrinkage, tangential shrinkage and fibre saturation point for Tectona grandis ground wood. 
An additional analysis was then conducted using the models for powders on solids and vice versa. The findings cannot be used when the “solid” models are used for powders and if the “powder” model is used on the TR section of solids. However, if the “powder”model is used to predict data from the spectra measured on the LR section of solid samples, results that can be used with an r^{2} of 0.81 for the FSP and a RPD of 2.3 is obtained (Tab. VI).
Models developed for powders and used for prediction purposes on the LongitudinalRadial surface spectra of solid samples. N: number of sample. M: mean. SD: standard deviation. SEP: standard error of prediction. RPD: ratio performance to deviation.
4. DISCUSSION
The findings show that, in the case of solid wood, the models developed for the TR section are better than the models developed for the LR section (Tabs. III and IV). It is thought that this observation may be explained, firstly by the fact that the width of the LR surface of the sample corresponds to the dimension of the infrared beam (10 mm). Operational errors in positioning the samples may therefore have added noise to the experiment measurements. Furthermore, the infrared beam touches all the anatomical elements directly on the TR surface while the same elements are measured by diffuse reflection inside the material in the LR surface.
With respect to the shrinkage properties, the TS models are systematically better than the RS models (Tabs. III–V). This phenomenon is explained by the fact that the measurement error for TS (0.9%, see annex) is lower than the RS measurement error (1.6%, see annex). It is also thought that there is an operational effect, the measurements were always taken in the same order: tangential then radial. It is possible therefore that additional humidity between the two measurements may have affected the radial measurements.
Of the three properties studied for solid samples and powders, FSP is the bestestimated property (Tabs. III–V). However, there is a higher measurement error for FSP (7.6%) than for tangential and radial shrinkages and a lower variability (coefficient of variation of 9%) than for TS and RS (variation coefficients of 24% for TS and 22% for RS). The number of anomalies detected (outliers) is always higher for FSP than for shrinkages. This finding does not appear to be sufficient to explain the fact that the FSP is the best estimated by the models. It would appear to be due to the way in which the FSP is calculated: the surface variation calculation takes into account the radial and tangential dimensions, the use of linear adjustment also tends to reduce experimental error (the laboratory errors calculated in the annex are maximum theoretical errors).
The ranks relating to the models for powders (rank 2 and 3 models, Tab. V) are lower than those relating to solid woods (rank 4 and 5 models, Tab. III). This finding shows that the information necessary for estimating the properties is more condensed in the case of powders. It is thought that the measurement noise due to structural heterogeneity and irregularities on the surface of the solid wood is lessened in the case of powders. In this form the material is homogenised with respect to the measurement surface (dimension of the ground particles: 4 mm; dimension of the measurement beam: 10 mm). During the measurement of powders the range recorded for each sample is the average of several scans which, if a spinning cup is used for measurement, includes a larger exchange volume between the beam and the material. Consequently, the information found on the powders is certainly more complete than that obtained for solid woods.
The models developed for powders may be used only on the LR surface of solid woods (Tab. VI). This phenomenon can be explained by the mathematical distances being very short between the powder ranges and the solid wood ranges for the LR surface. It can therefore be presumed that the data within these ranges is similar. It is thought that this phenomenon may be explained purely by the grinding: the grade of grinding used and the structure of the material favours the formation of powder in the form of flakes, the larger axis of which coincides with the lengthwise axis of the solid wood.
The statistical models obtained by NIRS calibration demonstrate highly significant levels of correlation between the predicted values and the reference values. The differences of absorption of the near infrared rays depend on the nature and concentration of the chemical components of the material (Hein et al., 2009). In the case of the water/wood material relationship and its consequences on dimensional variations, the bound water (which defines the FSP) is absorbed on the surface of the cell cavities in polymolecular layers and in the internal walls of the ligneous matter at the polysaccharides hydroxy sites. To reach the hydrogen bridge sites, some of the water molecules enter the cell wall with a definite propensity for hemicelluloses causing dimensional variations or shrinkage (Guitard, 1987). The FSP may also be affected by the extractives (Arevalo Fuentes, 2002; Brémaud, 2006; Chafe, 1987; Hernandez, 2007). The anatomy of the material does not however appear to play a determining role in adsorption (Hernandez, 2007).
5. CONCLUSION
The findings of this study demonstrate the possible use of NIRS to measure the dimensional stability of teak wood. The precision of the models developed is slightly lower than the reference measurement but its value and the rapidity of measurement undisputedly show advantages for this approach. In accordance with the reference list commonly adopted, the RPD values obtained after validation for the best prediction models, whether from ranges of solid woods or powders, are sufficient for screening for shrinkages and an approximate prediction of FSP.
These models remain to be tested on other samples of different origins and ages. The inclusion of additional samples other than those studied will lead to stronger prediction models which may be used on a wide range of woods of different plantation origins and enable a shift away from traditional shrinkage measurements on large sets of samples requiring measurement capacities which go well beyond the possibilities of a reference laboratory, particularly in the case of genetic studies which require highthroughput phenotyping. Nevertheless, this will always be necessary for developing existing equations and conducting regular controls.
Additional studies will be conducted on the variability of extractives in teak wood samples. There is no doubt that comparing the results presented here with future results will give matter for discussion on controlling the dimensional stability of teak wood when drying.
ANNEX  SEL ESTIMATION
1 Definition of relative uncertainty and SEL estimation
Relative uncertainty (RU) is the ratio of the absolute uncertainty (ΔX) of a measurement to the best estimate (mean of X). It expresses the relative size of the uncertainty of a measurement (its precision): (5)Assuming a normal distribution of the measurement error, the standard error of laboratory (SEL) can thus be estimated as (with a confidence level of 95%): (6)
2 Uncertainty of shrinkage computation
Using (Eq. (3)) and (Eq. (5)), the relative uncertainty can be written as: (7)The absolute uncertainty  ΔD  is equal to 0.005 mm, the mean value of D_{SAT} is 20.21 mm for radial measurements and is equal to 20.50 mm for tangential measurements. The mean of the dimension difference is 0.64 mm (R axis) and is 1.13 mm (T axis). Using Equation (7), the S uncertainty values are thus equal to: (8)
3 Uncertainty of moisture content computation
Moisture content of wood (MC) is assessed using the formula:(9)With W_{H}: weight of the sample, W_{0}: weight of the ovendry sample. From Equation (5) and Equation (9), the relative uncertainty can be expressed as follows: (10)The absolute uncertainty  ΔW  is equal to 0.005 g, the mean weight of the ovendry samples is 3.00 g and the mean of the weight difference is 0.40 g. Using Equation (10), the MC uncertainty value is thus equal to: (11)
3 Uncertainty of FSP determination
The variation of transverse area (VTA) between full saturation and a given MC is written below: (12)With DR: radial dimension, DT: tangential dimension, _SAT: fully saturated sample and _MC: moisture content after conditioning. From Equation (5) and Equation (12), the relative uncertainty can be expressed as follows: (13)Equation (13) can be simplified assuming the equality between radial and tangential dimensions (D in Eq. (14)) and also small values of transverse shrinkages: (14)The measurement error  ΔD  is 0.005 mm, the dimension D is set to 20 mm and the mean value of VTA is closed to 40 mm^{2}. The VTA uncertainty is thus equal to: (15)
5 Uncertainty of area computation

•
The FSP corresponds to the constant coefficient of the linear regression equation between VTA and MC:

•
The question can be expressed as: assuming a perfect linear relationship between two variables X and Y: Y = b_{1}·X + b_{0}. If perturbations are added in X and Y, what will the corresponding error ε be?

•
From Equations (16), (18) and (19), the SEL associated to FSP can be determined as follows:
The data set used for numerical application is VTA {24; 36; 48; 60} associated with MC {18; 12; 6; 0}. The relationship between VTA and MC is strictly linear with coefficients b_{1}{–0.5} and b_{0}{30}. This example represents the ideal case of FSP determination.
Acknowledgments
Thanks due to the International Foundation of Science (IFS), Sweden, and to the Agence Universitaire de la Francophonie for funding our research on teak plantation in Togo.
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All Tables
Site characteristics. A: altitude (m); D: density (tree.ha^{−1}); MD: mean diameter (cm) at height 1.3 m; MH: mean height (m).
Number of samples (N) and descriptive statistics of reference values. M: mean (%). SD: standard deviation (%). CV: coefficient of variation (%). Min: minimum value (%). Max: maximum value (%).
Solid wood – PLS results of the calibration and crossvalidation on detrend, SNV (standard normal variate) and derivate 2 preprocessing spectral data. N: number of sample. M: mean. SD: standard deviation. SEC: standard error of calibration. SECV: standard error of cross validation.
Solid wood – PLS Model results of test validation. N: number of sample. M: mean. SD: standard deviation. SEP: standard error of prediction. RPD: ratio performance to deviation.
Powder samples – PLS results of the calibration and crossvalidation on detrend, SNV (standard normal variate) and derivate 2 preprocessing spectral data. N: number of sample. M: mean. SD: standard deviation. SEC: standard error of calibration. SECV: standard error of cross validation.
Models developed for powders and used for prediction purposes on the LongitudinalRadial surface spectra of solid samples. N: number of sample. M: mean. SD: standard deviation. SEP: standard error of prediction. RPD: ratio performance to deviation.
All Figures
Figure
1 Near Infrared – Partial Least Square predicted versus laboratory determined radial shrinkage, tangential shrinkage and fibre saturation point for Tectona grandis solid woods (A: NIR data from LongitudinalRadial surface, B: NIR data from TangentialRadial surface). 

In the text 
Figure 2 Near Infrared – Partial Least Square predicted versus laboratory determined radial shrinkage, tangential shrinkage and fibre saturation point for Tectona grandis ground wood. 

In the text 