Theory of the Thesis
2.5: Optical Properties of Seawater
2.5.4: Optimum transmission wavelength
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able to reach the receiver. However, this situation is likely to induce ISI, as discussed above.
Recently, a modified version of the Beer’s law for a Lambertian source, such as a light-emitting diode (LED), which includes an exponential function with weighting coefficients, has been proposed by Liquet al. [36]. The exponential function is obtained by numerical fits from data in the scientific literature for typical values of various seawaters.
As anticipated in Section 2.1.2, Morel in 1991 [52] modelled the dependence of the scattering coefficient, , as a function of the chlorophyll concentration
(2.5)
where is the scattering coefficient for pure seawater. As one would expect, the value of the scattering coefficient Equation (2.5) increases as the wavelength increases. This behavior is shown in Figure 2.7. Also, similarly to Equation (2.3), there is a non-linear dependence between and .
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United Kingdom across the year. As described above Sections 2.1.2 and 2.1.3, both absorption and scattering are wavelength dependent processes. This section focuses on the selection of the transmission wavelength which is less absorbed by the medium, a key parameter in any FSO.
The main assumption in this frequently used bio-optical model for the absorption and scattering coefficients is that the mean chlorophyll-a concentration is the main agent influencing the optical properties of seawater. Chlorophyll is a family of similar molecules that absorb photons to initiate the process of photosynthesis. It absorbs mainly in the blue and red range of wavelengths thus it greatly influences the absorption and scattering underwater. An analysis of how the values of the optical coefficients discussed so far, , change with wavelength and chlorophyll-a concentration is presented in Figure 2.11.
In seawaters characterized by a very low chlorophyll-a concentration , the total attenuation coefficient c is mainly the consequence of the absorption contribution. For increasing chlorophyll-a concentration, the relative weight of the scattering part becomes preponderant in the final value of although its trend is shaped by the absorption curve. When operating in seawater characterized by a moderate/high chlorophyll-a concentration , it is interesting to note how the minimum of the total spectral attenuation curve redshirts. Thus, the transmission wavelength that corresponds to the minimum number of optical losses moves roughly from the blue to the green/yellow region of the spectrum.
The analysis of the optimal transmission wavelength in various circumstances, such
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as the period of the year and geographic location, has been integrated and developed in a MATLAB algorithm. A. Morel [50] and L. Prieur & S. Sathyendranath [51] published the coefficient values with a 5nm-spacing. This discrete set of Equi spaced data points have been post-processed in MATLAB by performing the cubic spline interpolation using an interplant with a step size an arbitrary resolution of 1nm. This technique produces a color map of the optimal wavelength in each seawater in a given period (see Figure 2.4, as shown in Figure 2.9.
From the results in Figure 2.7 and Figure 2.12, it is evident how the amount of solar energy incident on the sea surface is directly correlated with the distribution of photosynthesizing organism concentration. This, in turn, determines the optical properties of seawater and thus the optimum transmission wavelength. The latter may naturally change across the year, which is something that must be taken into account in the design of a UOCS.
In addition, the analysis presented so far is referring only to the concentration at sea surface derived from satellite remote sensing. The solar radiation propagates through water only in the upper layer, known as the euphoric zone. For this reason, the depth distribution of chlorophyll-a and other light-dependent organisms is also dependent on the type of seawater and the vertical gradient of concentration. The equations proposed in the literature for the chlorophyll profiles at a given depth, in the literature
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Follow a Gaussian distribution from the sea surface, such as [64
(2.6)
where is the background chlorophyll concentration at sea surface , S is the vertical gradient of concentration ,, h is the total chlorophyll above background levels is the depth, is the depth at which the maximum concentration of chlorophyll occurs and is the standard deviation of concentration. These parameters are specific for each season and region, so often average values are chosen to estimate the vertical distribution of chlorophyll concentration in a specific scenario. Even if the precise value depends on the type of seawaters and the period of the year, at a depth the photosynthesizing organism concentration is usually greatly reduced. This results in a lower total attenuation coefficient (i.e., fewer losses), thus improving the performance of a UOCS [65]. In conclusion, I presented a model of seawater attenuation coefficients that I developed in order to estimate the optimum transmission wavelength for the design of a UOCS. This finding will help the system design process during the selection of the most suitable optical source for a given water type and time of the year. As already pointed out earlier in Section 2.1.2, the model presented here should be applied only to phytoplankton-dominated seawater types since its most important pigment, chlorophyll- a, is used to convert light energy into chemical energy (photosynthesis). I will present a patent pending novel beamforming technique that I helped to model and develop for the minimization of the detrimental effect due to the underwater photon scattering in Chapter 6