# Optical Design and Stray Light Analysis of Underwater Spectral Radiometer
## 4 Stray Light Suppression and Simulation Analysis
### Sources of Stray Light and Inhibition Assessment Methods  
The underwater spectral radiometer's overall opto-mechanical structure is depicted in Figure 7, consisting primarily of the front-end optical system and the spectroscopic system. Solar radiation entering the water is collected by the front-end optical system, guided through fiber optic bundles into the micro-spectrometer module. After passing through an optical slit, the light is diffracted by a flat-field concave holographic grating, and the dispersed spectrum is detected on the surface of the spectroscopic detector. Due to the small size of the optical slit in the micro-spectrometer module and the coupling of light through fiber optics, extraneous stray light outside the field of view entering the micro-spectrometer module is minimal and can be neglected. Therefore, the stray light in the spectrometer mainly originates from light other than the required order diffraction, reaching the detector surface, and is considered as system stray light.  
As shown in Figure 8, spectral distributions of different diffraction orders are given. By analyzing the propagation path of light in the micro-spectrometer, it can be inferred that the stray light in this system mainly comes from two sources. The detected wavelength range of the system is 400-950 nm, according to the grating diffraction Equation (12) as follows:  
\[m\lambda=d(\sin\theta_{i}\pm\sin\theta_{d}) \tag{12}\]  
In the Equation, \(m\) represents the diffraction order, \(\lambda\) is the wavelength of the incident light; \(d\) is the groove spacing of the grating; \(\theta_{i}\) is the angle of incidence; \(\theta_{d}\) is the diffraction angle; \(\pm\) depends on the positive or negative diffraction order.  
From Formula (12), it can be inferred that the second-order diffraction spectrum in the 400-475 nm range of the underwater spectral radiometer will overlap with the first-order diffraction spectrum in the 800-950 nm range on the detector image plane. They cannot be distinguished in the detector pixel space. This part of stray light is referred to as direct stray light, and it severely affects the system, necessitating means to eliminate it. Another portion of stray light results from diffraction orders that are not actively used by the grating. After multiple reflections and scatterings within the optical elements and the mechanical structure's inner walls of the instrument, this stray light reaches the detector image plane.  
Figure 7: The mechanical structure of the underwater spectral radiometer.  
This type of stray light is known as indirect stray light, and it may be distributed at various locations on the detector surface. For this system, measures must also be taken to suppress this indirect stray light.  
When an optical system undergoes stray light suppression design, it is necessary to calculate the stray light energy entering the system and assess the performance of the stray light. The common evaluation methods include measuring the system's stray light coefficient \(V\), using the Point Source Transmittance (PST) from the stray light model, and conducting radiance distribution analysis. With the accurate design of surface properties for various materials in the simulation model, the stray light coefficient of the system is calculated using radiance distribution analysis graphs output by ray tracing analysis software. This is used to assess the level of stray radiation in the system. Specifically, we represent this performance as the ratio of the energy of stray light radiation \(E_{S}\) from unexpected optical paths to the total energy reaching the image plane \(E_{T}\).  
\[V=\frac{E_{S}}{E_{T}} \tag{13}\]