## 3 Results
### Setup Specifications
#### 3.1.3 Generation of Multiple Foci  
We also conducted experiments to determine the number of individual foci that can be generated using our setup. Since the object of our investigations will be random neural networks, we generated patterns of random equally distributed foci. We then evaluated the mean peak-to-background ratio  
Figure 5: Cross-sections of a single focus observed using a 20\(\times\) objective. The fits reveal an average focus diameter of about 8 \(\upmu\)m.  
Figure 6: Raster scan of an area of (1.5 \(\times\) 1.5) \(\upmu\)m at 961 positions. The raster positions are indicated in (**a**). The time taken to scan the positions is depicted in (**b**). The overall scan takes 0.568 s, which results in a framerate of 1.7 kHz or a temporal resolution of 0.59 ms.  
(PBR) \(r\) of the resulting illumination pattern, including the speckled background. The corresponding PBR in dependence on the number of spots is shown in Figure 7b. Ideally, the available light power distributes equally among all of the spots with no increase in background noise, leading to an \(n^{-1}\)-distribution with \(n\) being the number of generated spots. We fit an exponential function \(r=A*n^{-b}+c\) to the measured data in Figure 7b, with the maximum PBR \(A\). It shows an exponent \(b\) of \(-1.4\), which reveals a proportionality of background noise with a rising number of spots. Furthermore, we executed simulations to compare the approach of binary phase-only modulation that we are using in our setup with binary amplitude modulation, which can be realized e.g., using DMDs. We calculated holograms for an increasing number of simultaneously generated foci as described in Sections 2.2 and 2.3 using the physical parameters of our setup and binarized them using bidirectional error diffusion. The holograms were computationally propagated to the sample plane to obtain the image of the desired foci. The resulting images were evaluated, as explained above. The resulting PBR curves are depicted in Figure 7a. As can be seen, in our case, the PBR using binary phase-only modulation is on average six times higher than when using binary amplitude modulation, e.g., when using a DMD for holographic illumination. Also, both of the fitted PBR curves show a dependency on \(n^{-a}\) with a \(>1\) and \(a_{amplitude}>a_{phase}\). This reveals that in both cases there is an increase of background noise with increasing spot number, which is more pronounced in the case of binary amplitude modulation. Therefore, the intensity decrease per spot with an increasing number of simultaneously illuminated spots cannot simply be circumvented by increasing the power of the light source. Since the peak-to-background ratio should not fall below a certain threshold in order to avoid the unwanted stimulation of neurons with random background noise, the useful number of stimulation spots should be restricted. Since a higher pixel count will enable the representation of higher spatial frequencies in the holograms, an increase in PBR for multiple foci can be expected for SLMs with a higher pixel number.  
Due to the design of the modulator and the overall setup, only \(11.1\%\) of the light arriving on the modulator is available on the sample surface. The maximum available power density in one spot, however, can be estimated to \(1.5\) W/mm\({}^{2}\). This is three orders of magnitude above the EC50 for activating ChR2, which is \(1\) mW/mm\({}^{2}\)[40]. For stimulating one or only a few neurons, the maximum power density can be easily adjusted using neutral density filters.  
Figure 7: Mean peak-to-background ratio in dependence of the number of foci created on the sample. (**a**) Comparison of simulated binary phase-only modulation as with our FSLM and simulated binary amplitude modulation as with a digital micromirror devices (DMD). On average, binary phase-only modulation yields an about 6 times higher PBR as well as a lower increase in background noise with higher spot number as indicated by the lower exponent of \(n\). (**b**) Measured Data using the fast FSLM.