The PDS method was developed and described in detail in the papers by Kowalski et al^[17], In PDS, the relationship between the spectra measured by two different spectrometers can be established. The spectra measured on one spectrometer Z_m can be transferred to match the spectra of another spectrometer Z_s, by a transformation matrix F, to construct the transformation matrix, each data length of the target spectrum Z_{m, n} is regressed on the corresponding spectral window of the transfer spectrum Z_{s, n}=[Z_{s, n-k}, Z_{s, n-k+1}, …, Z_{s, n+k-1}, Z_{s, n+k}] according to the PLS regression model: Z_{m, n}=Z_{s, n}b_n, the regression vectors b_n (n=1, …, q) are obtained, then set bnas the diagonal element of the transformation matrix, and the other elements are 0, the diagonal matrix F=diag ( b1T, b2T, …, biT, …, bqT) can be developed. The transfer spectra X_S can be converted into the X_{S, Std} to match the target spectra according to X_{s, std}=F× X_s.

According the principle of PDS, three key parameters of PDS method including the number of transfer factor (N_lv), the number of transfer samples (N_s), and the half-width of the window (k) will seriously affect the performance of matrix F, therefore, in the process of model transfer, to obtain optimal F, three parameters need to be selected according to certain rules.

In this paper, SA which can evaluate the similarity between spectra or the difference between the spectral vector and the shape of the spectral curve is used as a criterion for optimization of parameters of PDS.

In SA method, the representativeness of the transfer and validation samples is also very important to optimization, thus, Rank-KS method is used to select validation set and transfer set of having great representativeness and wide coverage.The spectra were pre-treated with multivariate scatter corrected (MSC)^[18] to remove noise, baseline drift and wavelength drift.

The specific steps to determine the optimum N_lv, N_s and k according the criterion are as follows:

(1) Determine the optimum N_lv

Step 1: Set the k value of the default value of 7, N_s value is the number of transfer samples originally collected, change the N_lv in the range of 1~X (X less than 15), a series of transformation matrix {F_p1, F_p2, …, F_pX} can be obtained by PDS method;

Step 2: Correct the spectra of m validation samples Z_test by {F_p1, F_p2, …, F_pX} according to formula (4), {Z_p1, Z_p2, …, Z_pX} can be obtained.

Step 3: Calculate the angle between target spectrum Z_m and the transferred spectrum Z_t for each validation sample according to formula (5). A series of spectra angles {θ _p1, θ _p2, …, θ _pm} can be acquired. And the average value of angles { θ̅p1, θ̅p2, …, θ̅pX} is taken as the spectra angle between the target spectra and corrected spectra.

θp=arccos(zm, zt)=arc< zm, zt> < zm, zm> < zt, zt> (5)θ̅p=1m∑i=1mθpi(6)

Where < , > presents the inner product of two vectors, arc presentsthe inverse trigonometric function.

Step4:Select the smallest θ̅p, the corresponding N_lv value is the optimum N_lv determined.

(2) Determine the optimum N_s

Set the k value of the default value of 7, N_lv is the optimum N_lv value determined, !change the number of transfer samples in the range of 2~S (S is the number of transfer samples original collected), a series of transformation matrix {F_s2, F_s3, …, F_ss} can be obtained by PDS method, the spectra angle between target spectra and the transferred spectra { θ̅s2, θ̅s3, …, θ̅ss} or validation samples can calculated according to formula (5) and (6), then the smallest θ̅pare selected, the corresponding N_s value is the optimum N_s determined.

(3) Determine the optimum k

Set N_lv and N_s are the optimum value determined respectively, change the k in the range of 1~Y (Y is less than 20), a series of transformation matrix {F_k1, F_k2, …, F_kY} can be obtained by PDS method, the same as the process of determining the optimum N_lv and N_s, the spectra angle { θ̅k1, θ̅k2, …, θ̅kY} are calculated, then select the smallest θ̅p, the corresponding k value is the optimum k determined.

2.1.1 Materials and Instruments

208 tobacco samples from the Yunnan province were provided by the China Tobacco Yunnan industrial Co. Ltd, as shown in Fig.1(a). They include different varieties and grades of tobacco. The glycosides content which is one of properties tested routinely was utilized for building multivariate model and determined according to “ Tobacco and tobacco products-water soluble sugars-Continuous flow method” (YC/T 159-2002). The glycosides contentof the samples ranges from 7.1% to 41.6%. The first and second generation of NICOLET ANTARIS FT-NIR spectrometers were used to collect the NIR spectra of the tobacco samples as shown in Fig.1(b).

Fig.1

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	Fig.1 Samples and spectrometer (NIR) (a): Tobacco samples; (b): NICOLET ANTARIS FT-NIR

2.1.2 Spectra measurement

In experiments, the tobacco leaves were ground to 40 meshes, then about 6 g powders of the samples were taken and put into the rotating quartz cup accessory. The diffused reflectance spectra were collected at room temperature (22~25 ℃) from 4 000 to 10 000 cm^-1 with a resolution 8 cm^-1 and with 72 scans, further, each sample was measured at least 3 times and their average was used as the spectrum of the sample.

2.1.3 Calibration model development

50 samples were selected as the validation set, remaining 158 samples served as a calibration set. The spectra of calibration samples measured on master spectrometer are used to develop PLS calibration model. In PLS, the number of latent variables (LV) was chosen according to the curve of prediction residual error sum of squares (PRESS). For the NIR of tobacco, the entire wavelength range of the spectra was pre-processed to the first derivative using the Savitzky-Golay(S-G) method with a 25-point window and a second-order polynomial, and theglycosides content model were built.

2.2.1 Materials and Spectrometers

162 substrate asphalt samples were collected from Jiangsu province, Urumqi city, Liaohe, Qinhuang Island and Karamay, China as shown in Fig.2(a). The samples of substrate asphalt are dark and solid at room temperature. The wax content of asphalt samples were determined by “ Test method for wax content of asphalts” (SH/T 0425-2003), and they were distributed from 1.50% to 2.64%. Their mid-infrared spectra were obtained with two Agilent 5500 FTIR spectrometers equipped with ATR accessory as shown in Fig.2(b).

Fig.2

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	Fig.2 Samples and spectrometer (MIR) (a): Asphalt samples; (b): Agilent 5500 FTIR

2.2.2 Spectra measurement

In this study, about 0.5 g of asphalt was taken and put on the crystal surface of ATR accessory, the sample was heated using a homemade heater at 70 ℃ to melt and spread over all the surface. The spectra were acquired from 650 to 4 000 cm^-1 with a resolution 4 cm^-1 and with 32 scans. Each sample was measured at least 3 replicates of spectrum and their average was used as the spectrum of sample.

2.2.3 Calibration model development

134 samples were selected as the calibration set and 28 samples served as a validationset. The spectra of calibration samples measured on master spectrometer are used to develop PLS calibration model.For MIR data of asphalt, the spectra pre-treated with SG method (1st derivative, the order of the polynomial was 2, and window width was 35) was used to develop the wax content PLS model.

The transfer direction depends on need of the specific application. Usually, there are two directions, that’ s slave spectrometer to master one, or in the reverse direction. In most cases, the original model built on master spectrometer is shared by slave ones, the spectra of slave spectrometers are modified to match the spectra of the master spectrometer. Sometimes, in the beginning the new spectrometer needs an initial model which is transferred from master spectrometer, then the model is updated by supplementing new calibration sample on slave spectrometer continually in application.The evaluation of model transfer usually was based on comparison of the prediction results of the corrected spectra by original model with their reference data. However, not only it will be expensive to determine the reference data anddifficult to collect the validation samples sometimes, but also the error in reference data will affect the optimization of parameters of PDS. In this study, SA was proposed as the criterion to optimize the parameters of PDS without using reference data so that the limitations would obviously be reduced for the model transfer. The new model transfer method also easily allows both transfer directions between master spectrometer and slave ones because of no need of reference data.

In PDS, three parameters including N_lv, N_s and k need be determined to obtain the transfer matrix F. The F was used to establish the mathematical relationship between the spectra measured on master and slave spectrometers, therefore, the optimization of transfer parametersis crucial for any direction of model transfer. In SA-PDS method, the selection of parameters was based on the spectral angles between thetarget spectra and corrected spectra. The smaller the angle, the higher the similarity of spectra. For two transfer directions of MIR and NIR spectra, the spectral angles of different N_lv, N_s and k were calculated respectively, the evolution of the spectralangles with the three parameters of PDS, shown in Fig.3, indicates the direct effect of N_lv, N_s and k on the results of spectra transfer. Specific analysis is discussed as follows:

(1) Number of transfer factors. It was shown in Fig.3 that the angle varies significantly with the change of N_lv. A too small N_lv may cause the process to become under fitting, and a too large N_lv will lead to the process over fitting. According to the criterion for optimization of parameters, the optimal N_lv locates at the lowest point of the curve. For two transfer directions of NIR, the optimal N_lv is 4, for MIR, the optimal N_lvis 2. It is also found that the change range in angle for NIR is larger than for MIR.

(2) Number of transfer samples. The N_s is a crucial transfer parameter. In general, the larger the N_s the higher the probability that nice results will be achieved. However, more samples mean higher costs and added work. Therefore, in practice, using fewer transfer samples to achieve satisfactory results is preferred. In order to select transfer sample set which has representative in spectral space spanned by all the samples, the transfer samples were chosen by Rank-Kennard-Stone (Rank-KS) algorithm. As shown in Fig.3(b), only few transfer samples are needed to reach quite low angle value.

(3) Half-width of the window. From Fig.3(c), it is seen that the angle decreases with the increase of k, however, at a certain value of k, the angle value cannot reduce significantly.

Fig.3

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	Fig.3 Spectral angle versus number of transfer factors (a), number of transfer samples (b) and half-width of the window (c) circle: transfer from slave to master of MIR, triangle: slave to master of NIR, square: transfer from master to slave of MIR, diamond: master to slave of NIR; Red color: MIR data, blue color: NIR data

According to the criterion of the minimum spectra angle, the optimum values of N_lv, N_s and k were chosen, identified and shown in Table 1.

Table 1

Table 1

Table 1 The determination of parameters in SA-PDS standardization Samples Directions Nlv Ns k Spectral Angle Asphalt (MIR) Slave to master Master to slave 2 2 11 16 11 12 0.021 4 0.022 3 Tobacco (NIR) Slave to master Master to slave 4 4 15 16 9 12 0.039 8 0.030 5

Table 1 The determination of parameters in SA-PDS standardization

The effect of the new method will be shown by the similarity between the spectra of master spectrometer and the spectra of slave spectrometer after being transferred, and comparison of the prediction results of master spectra, slave spectra and transferred spectra by original model. The similarity is represented by SA between the spectra, the smaller the angle, and the higher similarity.

3.3.1 Spectra transfer results of NIR

A tobacco sample is random chosen for comparing the similarity of spectra before and after spectral transfer. The values of N_lv, N_s and k as shown in table 1 are used. Fig.4 and Fig.5 depictthe changes of first derivative NIR spectra of this sample measured on the master and slave spectrometers before and after corrected. It is clear that the dramatic spectral differences between two spectrometers were greatly reduced after the spectral correction. The SA reduced from 0.082 8 to 0.032 9, showing the considerable effects of SA-PDS method. Further, the validation samples were used to test the performance of the transfer method, the calibration model built by master spectrometer were employed to predict the content of glycosides in tobacco, for comparison, the prediction results of master spectra, slave spectra and transferred spectra were all calculated, RMSEP and bias as the criteria of precision and accuracy of the prediction results.

Fig.4

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	Fig.4 The first derivative NIR spectra of a sample measured on the master and slave spectrometer

Fig.5

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	Fig.5 The first derivative NIR spectra of a sample measured on the master and slave spectrometer after corrected

The plot of reference versus predicted values for different spectra is shown in Fig.6. In the figure, the points on the straight line signify that the predicted values are equal to the reference ones. From the figure, the blue points are evenly distributed on both sides of the straight line. The distribution of these points shows that the original model can predict the spectra measured on master spectrometer with high accuracy. However, the green points are deviated from the straight line seriously and distributed above the line, it indicates that the original calibration model cannot be applied to the slave spectrometer directly, the differences of spectrometers caused significantdeviations in the prediction of slave spectra. The red points in the figure represent the predicted results of the spectra transferred by SA-PDS method, they are symmetrically distributed of the straight line and close to the blue points. The variation in the distribution indicates that the differences of spectrometers were significantly reduced, and the calibration model can successful applied to the spectra after transferred by SA-PDS method.

Fig.6

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	Fig.6 The predicted results of the spectra measured on master spectrometer and slave spectrometer before and after transfer (NIR)

3.3.2 Spectra transfer results of MIR

MIR and NIR belong to molecular spectroscopy which can describe the sample information in both composition and properties at molecular level. MIR (4 000 to 400 cm^-1) assigned to the fundamental vibrations differs obviously from NIR (700~2 500 nm) assigned to the vibrations of the overtone or combination in the contour of their peaks. The MIR peaks usually are relatively sharp and the NIR ones vice versa. The clear difference in their peak contour will challenge applicability of model transfer method built based on one kind of spectra. Hence, the transfer method adapting both MIR and NIR spectra simultaneously is needed to develop.

The process of model transfer in MIR is akin to transferring in NIR, anasphalt sample is random chosen for comparing the spectral similarity, the MIR spectra collected respectively from the master and slave spectrometer before and after corrected are shown in Fig.7 and Fig.8. It can be seen that the spectrumof slave spectrometer is corrected to match that of master spectrometer well, and the SA decreases from 0.121 7 to 0.028 9.

Fig.7

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	Fig.7 The MIR spectra of a sample measured on the master and slave spectrometer

Fig.8

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	Fig.8 The MIR spectra of a sample measured on the master and slave spectrometer after corrected

The calibration model built by master spectrometer was used to predict the content of wax in asphalt, as such, for comparison, the prediction results of the spectra of samples in validation set measured on master, slave spectrometer and transferred were all calculated. The reference versus predicted values for three kinds of spectra are shown in Fig.9, it can be seen that the green points above the straight line, showing the predicted concentration for the spectra of slave spectrometer most lower than reference value, the model is invalid for the salve spectrometer. However, the red points are tightly distributed on the both side of line and close to blue points. Itindicates that the predicted values of the transferred spectra are very close to the values of the original spectra, the calibration model is valid to the spectra after transferred by the SA-PDS method.

Fig.9

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	Fig.9 The predicted results of the spectra measured on master spectrometer and slave spectrometer before and after transfer (MIR)

The new transfer method allows the spectra collected by themaster spectrometer transferred to the spectra as if they were measured on slave spectrometer. A new model applicable to the slave spectrometer can be established by the transferred spectra. Thus, the effect of the transfer method is demonstrated via the performance of the new model. In this work, the spectra of calibration samples measured on master spectrometer were all transferred by SA-PDS method, the process of transfer from master to slave spectrometer is similar to that from slave to master spectrometer, and the parameters of PDS are also shown in Table 1. The spectra of validation samples measured by slave spectrometer were used to test the performance of the model. For NIR spectra of tobacco, the new calibration model is built to predict the glycosides content in tobacco. The plot of reference versus predicted values of the calibration and prediction spectra isshown in Fig.10, the points also closely distributed on both sides of the line, indicating that the calibration model is valid and performance well. For MIR spectra of asphalt, the new calibration model of wax content is established by transferred spectra, the prediction results for calibration and validation spectra via this new model are presented in Fig.11.The distribution of the points indicates there are no significant differences between the reference and the prediction values. Thus, the calibration model developed by the transferred spectra can be successfully applied to the slave spectrometer. Therefore, the SA-PDS method led to successful model transfer from master to slave spectrometer.

Fig.10

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	Fig.10 Results of the model built by transferred spectra for calibration and prediction (NIR)

Fig.11

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	Fig.11 Results of the model built by transferred spectra for calibration and prediction (MIR)

In the absence of sufficient spectra of salve spectrometer to develop a model, the traditional PDS method cannot correct the spectra of master spectrometer to match the spectra of slave spectrometer accurately. In the proposed SA-PDS method, the angle between spectra was proposed as the criterion to optimize the parameters of PDS, no need of reference data and model. Thus, for comparison, the transfer results from slave to master spectrometer of PDS method that using RMSEP as the criterion to choose parameters in the process of model transfer are also calculated. The prediction accuracy (RMSEP, Bias) of RMSEP-PDS method and SA-PDS method using NIR andMIR data are calculated and presented in Table 2 and Table 3, respectively, they indicate that the SA-PDS method achieve the better results whether for the transfer of near infrared or infrared.

Table 2

Table 2

Table 2 Results of different model transfer methods (NIR) Prediction set SA-PDS method RMSEP-PDS method RMSEP Bias RMSEP Bias master 1.087 3 0.153 0 1.087 3 0.153 0 slave/before* 5.257 4 -4.963 1 5.257 4 -4.963 1 slave/after* 1.337 1 0.577 4 1.350 3 0.695 3

Table 2 Results of different model transfer methods (NIR)

Table 3

Table 3

Table 3 Results of different model transfer methods (MIR) Prediction set SA-PDS method RMSEP-PDS method RMSEP Bias RMSEP Bias master 0.121 0 -0.036 8 0.121 0 -0.036 8 slave/before* 0.525 1 0.492 2 0.525 1 0.492 2 slave/after* 0.186 9 -0.069 8 0.219 4 0.078 0 after * denotes the results of the slave spectra after correction; before * denotes the results of the slave spectra before correction.

Table 3 Results of different model transfer methods (MIR)