## 5 Results
### Accuracy of Numerical Computations
To test the accuracy of the numerical integration over the particle diameter range (Figure 1, N\({}^{\circ}\)S3), we ran the ScattnLay code for DS1 case studies and compared \(\tilde{F}(\theta)\) and \(C_{sca}\) rebuilt from Equation (2) with Lorentz-Mie computations as the Lorentz-Mie code provides the polydisperse phase functions and cross section as outputs (Figure 1, N\({}^{\circ}\)M1). Note that even a narrow polydispersion washes out the interference and resonance features, which explains why most natural particulate assemblages do not exhibit such patterns [26; 42] (Figure 3). A perfect match is obtained between the ScattnLay-rebuilt-polydisperse and Lorentz-Mie-polydisperse \(\tilde{F}(\theta)\) and \(C_{sca}\) values when the integration step (\(\Delta D\)) is set to 0.01 \(\upmu\)m for \(D\) in the range [0.03, 2 \(\upmu\)m]; 0.1 \(\upmu\)m for \(D\) in the range [20, 20 \(\upmu\)m]; and 10.0 \(\upmu\)m for \(D\) in the range [200, 500 \(\upmu\)m]. Using the DS1 data set, the impact of the angular integration on the backscattering ratio \(\widetilde{b_{bp}^{a}}\) is examined as a function of the hyperbolic slope \(\xi\) for different values of the real refractive index and two values of total angular steps (i.e., N\({}_{\theta}\) = 750 and 3600) (Figure 4). The impact of the integration is noticeable only for \(\xi\) values lower than about 3 and relatively high \(n_{r}\) values. When the number of angular steps increases, the curves become flatter at low \(\xi\) values. Differences in the curve shape are reduced if we increase the angular step. For \(\Delta\theta\) = 0.24\({}^{o}\) (N\({}_{\theta}\) = 750), the present results of the Lorentz-Mie calculations (solid lines in Figure 4) perfectly match those previously obtained by [PERSON] et al. [5] (not shown). However, in this case (N\({}_{\theta}\) = 750), the numerical integration is not accurate enough as the integration of Equation (1) gives values between 1.999 (\(\xi\) = 4.9) and 1.04 (\(\xi\) = 2.5). In the following, \(\Delta\theta\) is set to 0.05\({}^{o}\) (N\({}_{\theta}\) = 3600) and Figure 4 (dashed lines) will be the reference figure for homogeneous spheres. Figure 3: Interference and resonance features observed for the scattering phase function of monodisperse particles (light green). The major low-frequency maxima and minima are called the “interference structure”. The high-frequency ripples are resonance features. The interference and resonance feature are washed out for a polydisperse assemblage of particles (dark green). Impact of the Structural Heterogeneity of Phytoplankton Cells on the Bulk Particulate Backscattering Ratio  
The impact of phytoplankton cell structural heterogeneity on \(\widetilde{b_{bp}^{a}}\) is examined as a function of \(\xi\) for the three previously described water bodies (oligotrophic-like, phytoplankton bloom, coastal-like) considering the 80%-20% phytoplankton morphological model (Figure 5a). The real and imaginary bulk refractive indices for oligotrophic-like, phytoplankton bloom, and coastal-like case studies, vary with \(\xi\) as the relative proportions of the different particle components, having different \(n_{r}\) and \(n_{i}\), vary with \(\xi\) (Tables 1-5 and Figure 5b,c). For the no-mineral water bodies (oligotrophic-like and phytoplankton bloom), \(n_{r}\) stays around 1.04 \(\pm\) 0.007 (Figure 5b). In contrast, \(n_{i}\) shows large variation with \(\xi\) for both oligotrophic-like and phytoplankton bloom water bodies (Figure 5c). In bloom conditions, \(n_{i}\) increases as the relative proportion of phytoplankton increases as compared to the no bloom conditions. In agreement with typical values of the oceanic bulk imaginary refractive index [43], the \(n_{i}\) values for the particulate populations considered here are always lower than 0.002. In the presence of mineral particles (coastal-like), \(n_{r}\) increases as MIN have a higher \(n_{r}\) than VIR, BAC, PHY and DET. Its values are between 1.103 (\(\xi=2.5\)) and 1.145 (\(\xi=4.9\)).