# Light Transmission in Fog: The Influence of Wavelength on the Extinction Coefficient
## 5 Discussion  
This study showed that the literature models (here Mie and MODTRAN) and direct measurements of the extinction coefficient showed the same trends even if there was a difference between them. On the other hand, a limit to the use of the Mie model was shown, which is, however, the most widespread. More complex models such as those used in MODTRAN may reveal local behavior. For example, MODTRAN solves the radiative transfer equation including the radiative energy gain due to in-scattering (involving the phase function of the Mie theory) and molecular scattering, which can lead to local spectral behavior. These complementary elements to the Mie model (which takes into account only single particle scattering according to Mie theory) were important in refining the model. The question then arises as to which elements have the greatest impact in refining the model. This may be the subject of further study. Wavelengths from 350 nm to 1000 nm had the same behavior in fog, regardless of fog density or type. On the other hand, above 1000 nm, differences may occur. For very dense fogs (\(V<30\) m) and in particular advection fogs, fog had an impact about 10% higher for wavelengths in the near-infrared range (1000 nm-2400 nm) than for visible wavelengths (400 nm-800 nm). This kind of fog has larger drops, having a greater impact at higher wavelengths. On the other hand, for light radiative fog (\(V>100\) m), the impact of the fog was equal, or even lower, for wavelengths above 1000 nm. For light fog, therefore, we have the same conclusion as that given in the literature [2]. This is very positive and confirms the validity of the work presented. It is therefore essential to take into account the DSD of the fog when comparing extinction coefficients above 1000 nm. This calls into question the use of some models of the extinction coefficient as a function of wavelength proposed in the literature [3] without verifying the similarity of the DSD. However, some models [4] give several possible DSDs, which is a good point. Regarding possible tests of near-infrared sensors in fog conditions within the PAVIN BP platform, it is essential to always test these systems on advection fog or very dense radiation fog (\(V<30\) m). These fogs contain larger droplets, at least larger than 2 um. These droplets have a much higher impact on the near-infrared domain than droplets with a diameter of 1 um or less. Two main questions are still pending and deserve to be addressed in further research. Firstly, it seems important to compare the advection and radiation fogs produced on the PAVIN BP platform with natural fogs. This study showed the importance of the DSD on the extinction coefficient for near-infrared wavelengths. It is then necessary to measure the DSD of natural fogs and compare it to that of fogs produced in the PAVIN BP platform. Secondly, the good correlation between the measurements of the coefficient correlation made with a spectroradiometer and the combination model + PSA suggests that we might consider posing the problem the other way around. It would then be  
Figure 10: \(H_{2}\)Oabsorption spectrum, with a wavelength step greater than 0.5 nm. possible to use the spectroradiometer as a PSA, by optimizing a theoretical DSD to obtain the measured extinction coefficient as a function of wavelength. Concerning LiDAR technologies, it appears that the choice of wavelength, 905 nm vs. 1550 nm, should not be justified by the fog criterion. This is because these two wavelengths have close extinction coefficients (systematically, a ratio between 1.0 and 1.1), while the eye-safe emitted power is at least 20-times greater in the case of 1550 nm [1]. It should be noted, however, that care should be taken to avoid the ranges 1340 nm-1440 nm and 1910 nm-1950 nm, which have been identified as potentially disturbed due to strong H\({}_{2}\)O molecular absorption (according to MODTRAN modeling). These conclusions are the same for time-of-flight cameras and for other active sensors working in the near-infrared spectral band.