# Optical Camera Communication as an Enabling Technology for Microalgae Cultivation +
## 4 Methodology
### Experiments
#### 4.2.1 Indoor Experiment  
In this experiment, the radiance emitted by specific regions from the container's surface is evaluated. The aim is to determine how the radiance profile changes as the biomass concentration increases for different camera viewing angles. At the same time, the SNR of the channel is measured, and the bit error rate (BER) is estimated. The selected species for this experiment was _BEA 0007B Arthrospira platensis (A. platensis)_.  
Regarding the evaluation methods, the experiment was based on acquiring nine images at different viewpoints with respect to the azimuthal angle \(\theta\), keeping the link range constant. The radiance for vertical angles was not evaluated because camera translations in the vertical axis were not considered in the theoretical analysis, and for symmetry reasons, a similar behaviour was expected. For each discrete angle, the camera was aligned in the direction to the centre of the container. Figure 6a shows the experimental setup. The biomass concentration was increased in steps of \(20\,\mathrm{mg}\,\mathrm{l}^{-1}\), starting from \(0\,\mathrm{mg}\,\mathrm{l}^{-1}\) and reaching \(100\,\mathrm{mg}\,\mathrm{l}^{-1}\).  
After capturing the image samples, they were processed offline to obtain the radiance and SNR, from two different regions, the centre and the boundaries of the container's surface, to analyse the skewness phenomenon in the outermost regions of the surface.  
The radiance was measured indirectly by averaging the pixel values in a tiny window no higher than \(50\,\times\,50\) pixels. For the area projected in this window and considering the distance and the size of the container, it can be assumed that the radiance pattern varies very smoothly within this region. The original horizontal and vertical window's length was established at the start of the experiment when \(\theta=0^{\circ}\). Afterwards, the horizontal size must decrease as a function of the cosine of the angle, \(\theta\). Consequently, only the radiance contribution of the same original area was evaluated for each angle. The vertical length would remain unaltered as there were no vertical translations. We highlight that because the camera points to the centre of the containers, the windowed area located at the boundaries would decrease not only as a function of the cosine of the view angle, but also as a function of the distance, which varies very slightly for more acute angles. However, the area reduction factor due to this distance increment is considerably lower than the factor due to the view angle, and it can be neglected.  
In addition, the SNR was computed within the same window by measuring the mean, \(\mu_{\mathrm{chan}}\), and the standard deviation, \(\sigma_{\mathrm{chan}}\), of each independent colour channel, Equation (42), taking into account that there was no other source of light during the experiment. Furthermore, the expected theoretical BER for an on-off keying (OOK) signal can be estimated from Equation (43) using the complementary error function \(\mathrm{erfc}(\cdot)\)[3].  
\[SNR=20\cdot log_{10}(\frac{\mu_{chan}}{\sigma_{chan}}) \tag{42}\]  
Figure 6: Pictures of the indoor experiment. (**a**) shows the experimental setup, and (**b**) depicts exemplary images captured at different angles for different biomass concentrations.  
\[BER=\frac{1}{2}\text{erfc}\left(\sqrt{\frac{SNR}{2}}\right) \tag{43}\]  
The key parameters of this experiment are summarised in Table 2. Figure 6b shows some image samples for different biomass concentrations. It can be anticipated by the images obtained that at the borders, the radiance decreases abruptly for internal view angles (in the case of low biomass concentration). This suggests that the initial assumption about the radiance's skewness phenomenon at the surface's borders is valid.