# Optical Design and Stray Light Analysis of Underwater Spectral Radiometer
## 5 Experiment and Results  
### Wavelength Calibration  
A tunable laser was used to calibrate the laboratory spectrum of an underwater spectrometer. The tunable laser adopts EKSPLA NT242, which can output a continuously tunable laser wavelength in the spectral range of 210-2600 nm, covering all bands required for wavelength calibration. The repetition frequency of the laser is 1 kHz, and the line width is better than 5 cm\({}^{-1}\). In the process of spectral calibration, the laser spectrum analyzer is used to monitor the change in laser output wavelength. The spectral calibration system is shown in Figure 14. After passing through the reflector, the Laser beam is divided by the beam splitter, one beam enters the Laser Spectrum Analyzer (LSA) for wavelength monitoring, the wavelength measurement accuracy is better than 0.01 nm, and the other beam passes through the integrating sphere and is measured by the underwater spectrometer. The main control computer controls the switching of the laser wavelength and the data acquisition of the spectrometer. Once the laser's output wavelength stabilizes, the measurement parameters from the laser spectrum analyzer are read, providing the true emission wavelength of the laser. Figure 13: Irradiance received by the detector. (**a**) The irradiance on the detector surface in an ideal optical system; (**b**) The irradiance on the detector surface after surface blackening treatment; (**c**) The irradiance on the detector surface after adding the extinction screw thread and the light-shielding ring. Based on the spectral mode of the underwater spectrometer, the dispersion has a certain uniformity. Twelve groups of spectral lines were selected equally in 400-950 nm for wavelength calibration. For the measurement of each beam of monochromatic light, the corresponding pixel position is obtained by Gaussian fitting of the response value of each spectral channel, and the corresponding relationship between the spectral pixel number and the detection wavelength is determined. Specific data are shown in Table 3.  
The wavelength and central pixel in the above table were fitted by using the origin. After multiple fitting analyses, the residual sum of squares of the 5 th-degree polynomial fitting was the smallest, so the 5 th-degree polynomial was chosen as the final fitting result. The specific expression is shown as follows:  
\[\lambda = 1.13536\times 10^{-14}n^{5}-5.12284\times 10^{-11}n^{4}+9.32479 \times 10^{-8}n^{3}-\ 2.13197\times 10^{-4}n^{2} \tag{24}\] \[+0.85011n+290.97428\]  
Figure 15 shows the histogram of the residual distribution of the quintic multinomial fitting model. Fitting residuals of 12 calibration wavelengths are given. The results show that the wavelength scaling residuals of the center coordinates fitted by Gaussian are distributed within \(\pm 0.11\) nm. \begin{table}
\begin{tabular}{c c c} \hline
**Numerical Order** & **Wavelength/nm** & **Central Pixel** \\ \hline
1 & 399.916 & 132.298 \\
2 & 449.895 & 195.813 \\
3 & 499.849 & 261.162 \\
4 & 549.789 & 328.254 \\
5 & 599.740 & 397.166 \\
6 & 649.612 & 468.180 \\
7 & 699.526 & 541.292 \\
8 & 751.034 & 618.966 \\
9 & 801.193 & 696.694 \\
10 & 851.443 & 777.586 \\
11 & 901.524 & 860.939 \\
12 & 951.564 & 947.142 \\ \hline \end{tabular}
\end{table} 
Table 3: Mapping between wavelength and pixel serial number. Figure 14: Wavelength calibration system. After the wavelength calibration, the spectral resolution of the underwater spectrometer is verified. As shown in Figure 16, the response code values of each spectral channel and the half-peak full width of the response curve can be expressed as the spectral resolution of the spectrometer at this wavelength when three groups of specific wavelengths of monochromatic light incident. According to Table 4, the spectral resolution of the spectroradiometer at 400-950 nm is better than 3 nm. Figure 16: Spectral bandwidths. (**a**) Spectral bandwidth at wavelength 400 nm. (**b**) Spectral bandwidth at wavelength 650 nm. (**c**) Spectral bandwidth at wavelength 950 nm.