## 3 Results and Discussion
### The Construction of CEM Spectra  
The emission spectrum at the optimum excitation wavelength was selected to represent the spectral characteristics of the sample, which was used as the simplified data of the EEM spectrum. The emission spectra at different concentrations were obtained to form the Three-dimensional concentration-emission matrix (CEM).  
The effective excitation wavelengths of oils ranged from 200 nm to 400 nm. For the determination of oils in water, the far ultraviolet (less than 290 nm) was the most widely used wavelength. In this work, the emission spectrum at the excitation wavelength of 266 nm was selected as the characteristic spectrum of the oil. It can be seen that the fluorescence intensities of two oils increased first and then decreased with an increasing concentration. Moreover, the spectra of different oils showed different characteristics as the concentration increased. Figure 2 shows the emission spectra of heavy oil and 92\({}^{\#}\)gasoline measured over a broad concentration range (1.2 ppm-625 ppm).  
These spectra were measured in a wide range of concentrations, leaving considerably long intervals, which causes the CEM to have discrete spectra in the concentration dimension. In order to predict the concentration of oil, a good solution was to use the bicubic interpolation to smooth the CEM spectrum.  
Bicubic interpolation is a new technique for resampling discrete data that can achieve the effect of magnifying images and obtaining high-resolution images [18]. The principle of bicubic interpolation is shown in Figure 3. The bicubic interpolation not only considers the influence of four directly adjacent  
Figure 2: The emission spectra obtained from two kinds of oils in the concentrations range 1.2 ppm to 625 ppm in the excitation wavelength at 266 nm. (**a**) heavy oil; (**b**) 92\({}^{\#}\)gasoline.  
points but calculates the influence factors of 16 points around the sampling point for interpolation. The basic function W(x) of Bicubic was:  
\[\text{W(x)}=\left\{\begin{array}{cc}(a+2)|x|^{3}-(a+3)|x|^{2}+1&\quad\text{ for }|x|\ \leq 1\\ a|x|^{3}-5a|x|^{2}+8a|x|-4a&\quad\text{ for }1\ <\ |x|\ <\ 2\\ 0&\quad\text{ otherwise}\end{array}\right.. \tag{1}\]  
The horizontal and vertical distances from the interpolation B(x, y) to 16 pixels are \(K_{in}\) and \(K_{jn}\):  
\[K_{i0}=1+\mu;\ K_{i1}=\mu;\ K_{i2}=1-\mu;\ K_{i3}=2-\mu;K_{j0}=1+\
u;\ K_{j1}= \
u;\ K_{j2}=1-\
u;\ K_{j3}=2-\
u. \tag{2}\]  
The weight coefficient is:  
\[a_{mn}\ =\ W(K_{in})W\big{(}K_{jn}\big{)}\]  
Finally, the interpolated image is:  
\[\text{B(x, y)}=\ \sum_{i\ =\ 0}^{3}\sum_{j\ =\ 0}^{3}a_{ij}A\big{(}x_{i},\ y_{j} \big{)} \tag{3}\]  
where \(A\) is the original image point, B is the interpolated image point, \(a_{ij}\) represents the weight parameter, and \(i,j\) represent the horizontal and vertical coordinates, respectively.  
To improve the quantitative accuracy of concentration, 19 computing spectra were interpolated in each concentration interval. The spectrum obtained by bicubic interpolation of heavy oil is shown in Figure 4. The X-axis is the logarithmic form of concentration (mg/mL), Y-axis is the emission wavelength (nm), Z-axis is the fluorescence intensity.  
The database of interpolation CEM was constructed by measuring the fluorescence spectra of oil samples at different concentrations. Figure 5 shows the interpolation CEM of six kinds of oils using bicubic interpolation.  
Figure 4: The CEM spectrum of heavy oil with 19 interpolations in the concentrations range of 1.2 ppm to 625 ppm.  
Figure 3: Principle of bicubic interpolation.