## Appendix A Transmit Optical Power  
In VLP, LED luminaires are used for both illumination and localization. Therefore, it is important to ensure that the transmitted optical power translates into the recommended level of illuminance when designing a VLP system. The relation between the optical power and the illuminance depends on the optical power spectrum of the light source and the human eye perception to brightness. In this appendix, we show how the transmitted optical power is chosen to satisfy the illumination requirement in a typical workplace room.  
The luminous flux of a light source depends on the spectral power distribution of the light source and is given by  
\[\Phi=P_{\text{opt}}\Phi_{0} \tag{1}\]  
where \(P_{\text{opt}}\) is the transmit optical power and \(\Phi_{0}\) is the optical flux that corresponds to a normalized optical power spectrum, \(\int_{380}^{780}P_{o}\left(\lambda\right)d\lambda=1\), and it is given by \[\Phi_{0}=k_{\mathrm{m}}\int\limits_{380}^{780}P_{0}\left(\lambda\right)V\left( \lambda\right)d\lambda \tag{2}\]  
where \(k_{\mathrm{m}}=683\,\mathrm{Lm/w}\) is the maximum spectral luminous efficacy at \(\lambda=555\,\mathrm{nm}\), and \(V\left(\lambda\right)\) is the luminosity function, which describes the average spectral sensitivity of human visual perception of brightness. Figure 11a shows the normalized optical spectrum of a typical white LED. The luminosity function is represented by the photopic curve shown in Figure 11b.  
The brightness of an area is usually expressed by the illuminance, \(E\), in lux, which is the incident luminous flux, \(\Phi\), per unit area. The illuminance depends on the radiation pattern of the light source, the direction of the incident light and distance between the light source and the illuminated area. For a Lambertian light source of order \(m\) with the light coming from \(\left(\varphi,\theta\right)\) and an area that is parallel to the plane on which the light source is located, the illuminance is given by  
\[E=\Phi\times\frac{m+1}{2\pi l^{2}}\mathrm{cos}^{m}\phi\mathrm{cos}\varphi \tag{3}\]  
By substituting Equation (1) in Equation (3), the transmit optical power of the light source is calculated using  
\[P_{\mathrm{opt}}=\frac{2\pi l^{2}E}{\left(m+1\right)\times\Phi_{0}\times \mathrm{cos}^{m}\phi\mathrm{cos}\varphi} \tag{4}\]  
Figure 11a shows the illuminance level for a transmitter with a transmit optical power of 1 W. The illuminance is at maximum at the area directly below the transmitter at 120 lx and it decreases until it reaches zero lx for \(\left|x\right|>2\) or \(\left|y\right|>2\)  
According to the Australian illumination standard, AS/NZS 1680.1:2006, in a workplace with simple to moderate illumination requirements, the recommended illuminance is between 160 lx and 400 lx [43]. By considering a typical room configuration similar to the room shown in Figure 11. From Equation (3), the transmit optical power required by each luminaire to provide a maximum illuminance of 400 \(\mathrm{lx}\) at the center of the room at a table height of 0.7 m is 1.57 W. Figure 10 illustrates the distribution of the illuminance level over the room. It demonstrates that the considered transmit optical power is sufficient to provide levels of illuminance that are within the recommended levels over the room.