# Optical Design and Stray Light Analysis of Underwater Spectral Radiometer
## 5 Experiment and Results
### Uncertainty Analysis  
From Equation (25), it can be seen that the uncertainty sources in laboratory radiation calibration mainly include the uncertainty of the calibration source itself and the uncertainty introduced by instrument measurements. The uncertainty of the calibration source is provided by the calibration certificate, and by consulting the calibration certificate, it can be determined that the uncertainty of the spectral irradiance of the calibration source is better than 1% in the range of 400-950 nm. The uncertainty of the spectral irradiance caused by the stable current driving the spectral irradiance standard lamp is 0.1%.  
The spectral irradiance received by the instrument is influenced by the distance between the instrument and the standard lamp, following the inverse square law. Utilizing a high-precision laser ranging sensor to measure the distance between the center of the filament of the standard lamp and the optical detection point of the instrument, when the distance between them is 500 mm, the maximum error value observed during three measurement sessions is 1 mm. Hence, the uncertainty caused by the calibration distance is less than 0.4%.  
During spectral irradiance calibration, the calibration device is placed on an optical experimental platform. The reflection of light from the optical experimental platform and other instruments entering the probe of the spectral radiometer is one of the important sources of spatial background stray light. To assess the impact of this stray radiation on measurement results, first, the standard lamp is observed using the spectral radiometer, and the output code value of the radiometer is recorded. Then, the standard lamp light source is blocked using a black shield, and the output code value of the instrument is recorded currently. The ratio of these two measurement results represents the response of the radiometer caused by spatial background stray light. For this calibration system, the uncertainty introduced by spatial background stray light is approximately 0.2%.  
The measurement stability of the spectral radiometer system is primarily influenced by the signal-to-noise ratio (SNR) of the output signal, which is determined by the relative standard deviation of multiple measurements during calibration (measurement standard deviation/measurement mean). By taking multiple measurements of the calibration light source within a short period of time to obtain the sample's mean and standard deviation, the signal-to-noise ratio (SNR) of the instrument, denoted as \(R_{SN}\), can be represented by Equation (26). The reciprocal of the signal-to-noise ratio represents the uncertainty introduced by the system noise.  
\[R_{SN}=\frac{x_{p}}{S_{\sigma}} \tag{26}\]  
Figure 18: Spectral irradiance scaling coefficient curve.  
In the above equation, \(x_{p}\) represents the mean value of the sample data, and \(S_{\sigma}\) represents the standard deviation of the sample data. According to the evaluation, the calibration uncertainty introduced by the system noise is about 0.3\(\sim\)0.9% in the calibration band. According to the uncertainty synthesis formula, the laboratory calibration uncertainty of the instrument ranges from 1.14% to 1.42% in the 400-950 nm band. The uncertainties of irradiance calibration of underwater spectroradiometer are shown in Table 5.