Measuring the tensile strain of wood by visible and near-infrared spatially resolved spectroscopy

Strain measurement is critical for wood quality evaluation. Using conventional strain gauges constantly is high cost, also challenging to measure precious wood materials due to the use of strong adhesive. This study demonstrates the correlation between the light scattering degrees inside the wood during tension testing and their macroscopic strain values. A multifiber-based visible-near-infrared (Vis–NIR) spatially resolved spectroscopy (SRS) system was designed to rapidly and conveniently acquire such light scattering changes. For the preliminary experiment, samples with different thicknesses, from 2 to 5 mm, were measured to evaluate the influence of sample thickness. The differences in Vis–NIR SRS spectral data diminished with an increase in sample thickness, suggesting that the SRS method can successfully measure the wood samples' whole strain (i.e., surface and inside). Then, for the primary experiment, 18 wood samples were each prepared with approximately the same sample thickness of 2 mm and 5 mm to construct strain calibration models, respectively. The prediction accuracy of the 2-mm samples was characterized by a determination coefficient (R2) of 0.81 with a root mean squared error (RMSE) of 343.54 με for leave-one-out cross-validation; for test validation, the validation accuracy was characterized by an R2 of 0.76 and an RMSE of 395.35 με. For the validation accuracy of the 5-mm samples, R2val was 0.69 with 440.78 με RMSEval. Overall, the presented calibration results of the SRS approach were confirmed to be superior to the standard diffuse reflectance spectroscopy.

spectral data diminished with an increase in sample thickness, suggesting that the SRS method can successfully measure the wood samples' whole strain (i.e., surface and inside). Then, for the primary experiment, 18 wood samples were each prepared with approximately the same sample thickness of 2 mm and 5 mm to construct strain calibration models, respectively. The prediction accuracy of the 2-mm samples was characterized by a determination coefficient (R 2 ) of 0.81 with a root mean squared error (RMSE) of 343.54 le for leave-one-out cross-validation; for test validation, the validation accuracy was characterized by an R 2 of 0.76 and an RMSE of 395.35 le. For the validation accuracy of the 5-mm samples,

Introduction
Wood is a natural material with multi-layered elongated cells. Due to the variability of its mechanical properties, the tensile strain evaluation of each structural wooden member is critical for quality management (Wang et al. 2020). The strain (e) is defined as the ratio of the change in length to the original length; it is a unitless quantity (Ambrose 1993). The wood cell wall is a macromolecular composite formed of cellulose, hemicelluloses, and lignin (Hon and Chang 1984). Cellulose is the primary component in bearing tensile stress (Salmén and Bergström 2009). In contrast, hemicelluloses function as a coupling agent to hold the cellulose (Burgert 2006). The conventional method for wood strain measurement is to use a strain gauge, which is high cost (either disposable or reusable ones) in constant use (Yang et al. 2005). In addition, it is challenging to measure precious wood materials due to the use of a strong adhesive, which can destroy the wood after removal. For example, the heritage community generally does not apply strain gauges on genuine objects of art (Anaf et al. 2020). Moreover, difficulties arise when strain gauges are used in an environment where the electromagnetic wave interference is extensive. Such an environment can affect the measurement accuracy or even damage the experimental instruments (Liu et al. 2015; Barr et al. 2017).
In addition to the strain gauge, the wood strain can also be evaluated by monitoring the displacements that occurred during deformation, i.e., digital image correlation (DIC) techniques (Samarasinghe and Kulasiri 2000;Ozyhar et al. 2012). X-ray diffraction (Kamiyama et al. 2005) and infrared (IR) spectroscopy (Å kerholm and Salmén 2001;Salmén and Bergström 2009) can detect wood structure-function relationships at the nano-and microstructural levels. Near-IR (NIR) spectroscopy (wavelength: 800-2500 nm or wavenumber: 12500-4000 cm -1 ) is another wellsuited method in wood research, mainly in combination with multivariate mathematical techniques (Tsuchikawa 2007;Watanabe et al. 2012;Hein et al. 2017). When NIR light illuminates and transmits through an object, the energy of the incident electromagnetic wave changes due to the stretching and bending vibrations of chemical bonds, such as O-H, N-H, and C-H. Subsequently, the quality and quantity of an object can be evaluated non-destructively, rapidly, and cost-effectively by analyzing the light reflectance and transmittance values (Tsuchikawa and Kobori 2015;Ma et al. 2020). Compared with microtomed sections needed for IR spectroscopy, NIR spectroscopy can non-destructively measure wood samples up to several millimeters thick without special sample pretreatments. It is essential when focusing on practical applications, as thin samples prepared in lab behave differently than solid wood, e.g., including stress relaxation in the former (Yu et al. 2009). Taking the advantages of NIR spectroscopy, Guo and Altaner (2018) analyzed band shifts and band assignments on NIR light absorbance characteristics during the wood tension test, the results of which suggest that the observed band shifts correlate with wood tension levels. Their study is impressive and has reference value for future use of NIR spectroscopy (Guo et al. 2019). However, since the molecules are influenced by neighboring molecules, actual peaks generally overlap on the NIR spectra (Okazaki 2012). Although advanced curve-fitting approaches could be used to predict the small-signal peak shift, the band shift may also vary among specimens, which has been confirmed by the IR method (Eichhorn 2001). Additionally, the spectral information of such long-wave sensitive spectrometers is relatively rich, and, as such, it requires expensive equipment, such as detectors and light sources (Xing et al. 2008). Accordingly, there is still room to develop and improve NIR spectra collection and data analysis methods, especially for on-site application purposes.
The most likely to be neglected is that bulk wood is a highly scattering medium. Studies show that the reduced light scattering coefficient (l 0 s ¼ 10 À 100cm À1 ) is much larger than the absorption coefficient (l a ¼ 0:05 À 1:00cm À1 ) in the wavelength range of 700-1040 nm for both softwood and hardwood species treated in different ways (dry, wet and degraded) (D'Andrea et al. 2007). The light scattering degree inside the wood cell wall highly correlates with the microstructure (Ban et al. 2018;Ma et al. 2018aMa et al. , 2019. The deformation under longitudinal tension includes macromolecule deformations in the layers and interlaminar slippages. The former is related to the structure, orientation, and interaction of the polymers in the wood, and the latter slippage deformation results from the structural differences between cell-wall layers (Keckes et al. 2003;Adler and Buehler 2013). For example, the misalignment between the cellulose fibrils to the strain direction could be amplified by bending and shearing (Montero et al. 2012;Salmén 2015). Moreover, the weak interfaces of wood cells or annual rings could deflect transverse cracks into the longitudinal plane (Smith et al. 2003;Marthin and Kristofer Gamstedt 2019;Guo et al. 2020). Hence, effective utilization of the light scattering degrees (i.e., microstructure changes) inside the wood during tension testing should predict strain levels accurately. This method also can reduce costs associated with equipment because shorter wavelengths are scattered more strongly than longer wavelengths in the visible (Vis)-NIR optical range (Ma et al. 2018a).
Conventional Vis-NIR spectrometry has the potential to gather information on both molecular and anatomical strain. However, since it generally acquires spectral data from a single sample point based on the collective effects of light absorption (due to chemical components such as water and cellulose content) and scattering (due to physical structures such as cell size and intercellular spacing) (Vanoli et al. 2020); studies have mainly relied on performing further spectral pretreatments, such as baseline offset correction or standard normal variate (SNV), to reduce light scattering effects before training calibration models (Zude et al. 2011). By contrast, spatially resolved spectroscopy (SRS) requires relatively strong, steady-state spotlights for illumination; its diffusely reflected light pattern is collected at multiple distances for light absorption and scattering evaluation (Farrell et al. 1992;Qin et al. 2009;Lu et al. 2020). SRS has two main measurement configurations: spectral imaging and fiber probing. On the one hand, the SRS based on spectral imaging is a non-contact method that measures spatially resolved diffuse reflectance over a broad spectral range (Peng and Lu 2008;Qin and Lu 2008;Zhu et al. 2015). The measurement system mainly consists of a hyperspectral imaging (HSI) camera, a prime lens, and a small broadband beam as illumination. However, the distance between the light beam and the source-detector is required to be carefully considered in this configuration, as they determine the measured results (Cen and Lu 2010;Lu et al. 2020). On the other hand, the fiber probe-based SRS is a contact method, which is often inconvenient for rapid online quality assessment (Ma et al. 2018a). However, due to the easy-to-operate design with a strong light reflectance, fiber probebased SRS portable systems are desirable alternatives for on-site applications. Additionally, the contact measurement is more convenient to predict the tension strains of wood samples. This paper reports on wood strain prediction results obtained by evaluating the changes in Vis-NIR SRS spectral data collected from wood samples during tension testing. The objectives of this paper are as follows: (1) acquire light scattering characteristics in wood samples during tension testing by a newly designed multifiber-based Vis-NIR SRS system; (2) examine the relationship between SRS signals and wood strains by principal component analysis (PCA); (3) construct wood strain calibration models by partial least squares (PLS) regression; and (4) benchmark against standard diffuse reflectance spectroscopy to quantify the added value of the SRS method. This study should provide new insights to predict the tensile strain of wood samples conveniently and costeffectively.

Sample preparation
Wood samples (Hinoki cypress) with a length of 120 mm (longitudinal), a width of 10 mm (radial), and various thicknesses (tangential: 2 mm, 3 mm, 4 mm, and 5 mm) were sawn from air-dried wood board that commercially purchased from a local wood processing company. Specimens were selected from mature wood parts sufficiently far from the pith to neglect ring curvature.
For the preliminary experiment, samples with different thicknesses (2 mm, 3 mm, 4 mm, and 5 mm) were measured to evaluate the influence of sample thickness. Then, for the primary experiment, 18 wood samples were each prepared for approximately the same thickness 2 mm and 5 mm to construct strain calibration models, respectively. The samples were selected based on the wood fiber directions, which were as parallel as possible to the longitudinal direction. Before the experiment, all the pieces remained in a desiccator, where relative humidity (RH) was controlled at 59% with a saturated salt solution of sodium bromide. Subsequently, the sample weights were measured using a digital balance (accuracy of 0.0001 g). A digital caliper (0.01 mm accuracy) was used to measure the sample dimensions. From the measured weights and dimensions of the raw data, sample moisture content (MC) and density were calculated according to the following equations: Density where W is the sample weight before spectral data acquisition and W d is the sample weight after ovendrying, and V is the sample volume under the equilibrated condition.

Tensile testing
Each prepared wood sample was placed in a bending testing machine (either Shimadzu AG-100KNI, Shimadzu, Japan or SVZ-50NA, IMADA-SS Corporation, Japan was used depending on the sample thickness and experiment schedule). The bending machine was suspended several times manually during the tension test to obtain strain measurements and Vis-NIR SRS data. The strain was recorded with strain gauges (FLAB-5-11, Tokyo Sokki Kenkyujo, Japan) glued to one side of each sample with instant adhesive (CN, Tokyo Sokki Kenkyujo, Japan) and connected to a strain-meter (TC-32 K, Tokyo Sokki Kenkyujo, Japan). A Vis-NIR measurement system was used to collect light scattering characteristics on the other sample side ( Fig. 1a and b).
Visible and near-infrared spatially resolved spectroscopy measurements Figure 1c and d show the measurement part (i.e., the fixator of light illumination and detection fibers) of the proposed Vis-NIR SRS system and a diagram of the internal structure. A 5-W halogen lamp initially provided light illumination. An optical fiber (SOG-70S, Sumita Optical Glass, Inc., Saitama, Japan) translated the light source onto each wood sample. Then, 30 silica fibers (Vis-NIR type, Core: 100 lm, Clad: 110 lm, Fiberguide Industries, New Jersey, USA) were separated into five groups (1, 2, 3, 4, and 5 mm from the light illumination point) to collect the diffusely reflected light and transfer the light to the Vis-NIR HSI camera (SPECT-100nir1F, Spectral Application Research Laboratory Co., Ltd. Shizuoka, JAPAN). A fiber connecter was used to order the 30 silica fibers horizontally at the side of the HSI camera. Then, the light beam was dispersed by a spectrometer into spectral components (vertical axis) while preserving spatial information (horizontal axis), and the two-dimensional light signals were collected. The shutter speed and framerate were set at 15 ms and 8 fps, respectively. In this study, the fixator was pasted parallelly to the sample grain direction with a doublesided tape, which can be easily removable after   (3): where k denotes the wavelength, S and B are the sample and a white reference spectrum, respectively, and D is the dark spectrum. A digital camera took photos (16 9 amplification) of another wood sample (thickness of 2 mm) before and after the tensile test to understand the submicroscopic changes.

Spectra pretreatments and principal component analysis
The Vis-NIR SRS raw spectra were smoothed by a Savitzky-Golay filter (polynomial order: 2; frame length: 15). The spectral data, collected before tension testing subtracted from various strain levels, were tested to correct the natural variability of physical structure among wood samples. Then, PCA with the mean center was used to reduce the dimensionality of the Vis-NIR spectral data while minimizing information loss; the purpose of this was to examine the correlation between measured strain reference values and the spectral data changes. Principal component (PC) loadings are the weights for each variance value of spectral data when calculating the PC scores (Martens and Tormod 1992). Generally, the first PC score accounts for the most variability in the original data, and each successive component accounts for as much of the remaining variability as possible (Ma et al. 2020). It is noteworthy that no other spectra pretreatments (e.g., SNV (Cuesta Sánchez et al. 1995) and the second derivative (Gorry 1991)) were used in this study to keep the maximum light scattering information.

Partial least squares regression analysis
To achieve the initial value correction purpose, the Vis-NIR difference spectral data obtained by subtracting the spectrum collected at strain 0 from others were used to calibrate with the measured strain values via PLS regression (Martens and Tormod 1992). To against overfitting, the wavelength range from 900 to 1000 nm was selected from each fiber group (FG). In addition, 70% of measured data was randomly selected as the calibration set, leaving 30% for the test set in developing the PLS regression models. Leave-one-out cross-validation was used to optimize the number of latent variables (LVs). The coefficients of determination ( R 2 ) and the root mean squared error (RMSE) characterized the constructed calibration model's performance: where n is the number of measurements, y is the reference strain values, b y is the strain value predicted by PLS regression analysis, and y is the mean value of y. To quantify the added value of the SRS approach, the PLS calibration results earned by using the total five FGs were also benchmarked against either using the first three FGs or the standard spectroscopy analysis that only using one FG. Data analysis was performed by MATLAB (The MathWorks Inc., Natick, MA). Figure 2 shows the raw spectral image of 2-mm wood sample taken by the Vis-NIR HSI camera before the tensile test. This image data contains the spatial information of the 30 silica fibers (horizontal axis) and the spectral information of the measured wood sample (vertical axis). The main difficulty with conventional SRS methods is associated with quickly collecting the spectral data with a high signal-to-noise ratio. One way is to repeat the same data measurements and to average the results, which is time-consuming (Tkachenko 2006). This study is desirable for the spectral data acquisition time to be short of excluding other relaxation phenomena (Burgert 2006;Altaner et al. 2014). This was achieved by a two-step signal averaging process: (i) each fiber occupies 34 pixels of the HSI camera, and the central 30 pixels were averaged for spectral data collection, after which, (ii) the signals of six fibers in the same group were averaged. Figure 3 shows the Vis-NIR SRS spectra with standard deviations of the 18 wood samples with approximately the same 2 mm and at various tension levels. It is logical that the overall spectral intensity quickly falls with an increase in distance from the light illumination. The wavelength at 925 nm corresponds to the third overtone of C-H absorption (Mohammadi-Moghaddam et al. 2018), which can be attributed to the chemical components of the wood samples. The wavelength at approximately 930 nm has the highest light reflectance when the FG is 3-4 mm away from the light illumination, suggesting that the light at said wavelength was less absorbed and transmitted further from the light illumination than other wavelengths along the wood grain direction. It is noteworthy that the optical scattering was not isotropic within each wood sample. The light propagated further in the parallel direction because the scattering coefficient along the cylinders is much smaller than that in the perpendicular direction to the grain direction (Ma et al. 2018b(Ma et al. , 2019. Figure 4 shows the Vis-NIR spectral data for various strain measurements for wood samples with different thicknesses (vertical) by different FGs (horizontal), respectively. The wavelength range was selected to 900-950 nm to expand the image size. In this study, the Vis-NIR light could transmit through the hinoki wood samples with an thickness of approximately 5 mm, then be reflected by the white plate and detected by the SRS system (see supplementary, Fig. S1). The light reflectance increased with an increase in wood strain. Light absorption at 925 nm is the most obvious at the spectra collected by the 1-mm FG. The signal quality decreases with an increase in distance between the light illumination and light-detection fibers, suggesting that different FGs can collect spectral data with different light absorption and scattering degrees. Light reflectance is also affected by sample thickness. The differences in the Vis-NIR spectral data, caused by sample strains, diminished in thicker samples, especially at far FGs. This could be due to the light transmission depth is different among the wood samples at various thicknesses. Since thicker wood samples have a more profound light transmission, which affected light propagates in parallel; stronger noise was associated with the collected spectra at more extended FGs.  Except for signal quality, because the strain gauge was stuck on the opposite side of the SRS fixator, less transmission light could also reduce the correlation between SRS data and strain reference values. Further improvements could be considered to construct strain prediction models for thicker samples, such as reducing the distance between FGs and introducing a method to measure the strain changes where the spectral data were collected. Figure 5b and c show the digital photos of wood samples before and after tension testing with a strain of 3410 le. The stretched wood cell wall could decrease the amount of material in the measured area and increase the light transmissivity on the cell wall between the light source and the five FGs of the SRS fixator. Hence, the light reflectance values increased during the tension test.

Results and discussion
To check the correlation between measured strain reference values and the spectral data changes. The SRS data collected from the total five FGs at a wavelength range of 660-1002 nm were concatenated, resulting in 2555 variance values (Fig. 6a 1 : 2-mm sample, b 1 :3-mm sample, c 1 : 4-mm sample, and d 1: 5-mm sample). Figure 6a 2 -d 2 shows their first two PC loadings. The PC loadings can be understood as the weights for each variance value when calculating the PC score. The accumulated contribution rate of the frist two scores is approximately 99.64, 99.15, 97.47, and 94.48% for a sample thickness of 2, 3, 4, and 5 mm, respectively. The PC1 and PC2 scores of the SRS are shown in Fig. 6a 3 -d 3 , where the Y-axis shows the PC2 score and the X-axis shows the PC1 score. There is a strong correlation between PC1 loading and light scattering differences, i.e., vertical baseline shift. As expected from Fig. 4 (i.e., the differences in the Vis-NIR spectral data diminished in thicker samples), the contribution rate of the PC 1 score decreases with an increase in sample thickness. Moreover, PC2 loading has relatively high absolute values at light wavelengths close to water specific band at 970 nm. It suggests a meaningful correlation between the light absorption by hydrogen bonds and wood strain changings, but the contribution rate was much lower than the light scattering differences. It could be supported by the knowledge that wood becomes more ductile with increased MC (Ozyhar et al. 2012;Mvondo et al. 2017), which also affects the light scattering degree (Konagaya et al. 2016). This also suggests that MC effects much be fully valued, to build individual calibration models depends on sample MC may be the best way to reduce the MC effects. Figure 7a 1 shows the strain calibration results of the 18 wood samples with approximately the same thickness of 2 mm from the PLS regression method with the five FGs. The wavelength range of 900-1000 nm was selected from each FG.  Table 1 shows the detailed density and MC values of all the wood samples. Overall, the PLS calibration model has a high prediction accuracy: the R 2 and RMSE of the calibration set were 0.81 and 343.54 le, respectively. For the validation set, the R 2 and RMSE were 0.76 and 395.35 le, respectively. Differences in the RMSE could be attributed to the strain gauge measured the strain reference values from the wood surface. By contrast, the SRS method measured the light scattering degrees mainly affected by the sample inside structures. Hence, there is a possibility that the SRS method could estimate the wood sample strain more accurately than the conventional strain gauges, but further studies are required to prove this. Figure 7b 1 -3 shows the calibration results of the same wood samples with the first three FGs (i.e., 1-mm FG, 2-mm FG, and 3-mm FG) and LV numbers 7. Figure 7c 1 -3 shows the calibration results of the same wood samples with only the first FG (i.e., 1-mm FG) and LV numbers 5. It is evident that the prediction accuracy was improved by increasing the number of FGs, suggesting the effectiveness of the SRS method compared to the conventional NIR spectrometry. Figure 8a 1-3 shows the strain calibration results of the 18 wood samples with 5 mm thickness from the PLS regression method with the five FGs and LV numbers 7. The same wavelength range of 900-1000 nm was selected from each FG. Table 1 shows the detailed density and MC values of all the samples. Overall, the PLS calibration model had a good prediction accuracy: the R 2 and RMSE of the calibration set were 0.8 and 348.81 le, respectively. For the validation set, the R 2 and RMSE were 0.69 and 440.78 le, respectively. Figure 8b 1 -3 shows the calibration results of the same wood samples with the first three FGs and LV numbers 4. Figure 8c 1 -3 shows the calibration results of the same wood samples with only the first FG and LV numbers 2. Overall, the strain prediction accuracy of the 5-mm samples was lower than that of the 2-mm wood samples, which agrees that the differences in the Vis-NIR spectral data, caused by sample strains, diminished in thicker pieces. Nevertheless, that does not mean the SRS method can not be  Fig. 8 (a 1 -c 1 ) Scatter plot of measured and predicted strain values of 5-mm wood samples using; (a 2 -c 2 ) RMSE of the predictors and response; (a 3 -c 3 ) PLS regression coefficients used to assess thicker structural timbers. The maximum measurable depth of the hinoki wood samples was confirmed to be approximately 5 mm using the designed Vis-NIR SRS system (see supplementary, Fig. S1); Hence, for thick timbers, the stain prediction would be achieved by estimating the light scattering changes in the sample subsurface layers.

Conclusion
This study aims to demonstrate the correlation between light scattering changes inside the wood samples during tension testing and their macroscopic strain values. Spatially resolved diffuse reflectance was collected by designing a portable and costeffective measurement system based on fiber probes. For the preliminary experiment, samples with different thicknesses (2 mm, 3 mm, 4 mm, and 5 mm) were measured to evaluate the influence of sample thickness. Then, for the primary experiment, each 18 wood samples with the same thickness of 2 mm and 5 mm were tested to construct a strain calibration model. The prediction accuracy for the 2 mm samples was characterized by an R 2 of 0.81 and an RMSE for 343.54 le for leave-one-out cross-validation, 0.76 and 395.35 l for test validation. The R 2 and RMSE of the calibration set for the 5-mm samples were 0.8 and 348.81 le, respectively. For the validation set, the R 2 and RMSE were 0.69 and 440.78 le, respectively. The designed SRS measurement system does not require sophisticated measurement techniques. Moreover, it has a cost-effective design due to the Vis-NIR HSI camera with short-wave sensitivity, which is much cheaper than long-wave sensitivity cameras. Further research should focus on extending the applicability of the SRS approach to a broader database of wood types and larger sample numbers with various thicknesses. The intervals between FGs should be changed to test the strain prediction of thicker wood samples. This research also references further research to measure growth strain in trees nondestructively. However, because light scattering degree is also affected by MC, this would require more in-depth spectral pretreatments.