## 2 Holographic Single-Cell Illumination Setup
### Computer-Generated Holograms  
Usage of the FSLM was reported previously [32]. There, a Fourier hologram scheme was employed to steer a focus over mouse retinas. Fourier holograms are utilized when SLM and sample are positioned in the respective focal planes of an objective. They use only one, usually the first, diffraction order. Since binary Fourier holograms result in symmetrical reconstructions, this approach will result in two drawbacks. First, since the 0 th diffraction order and all higher diffraction orders have to be filtered out, it handles light quite inefficiently and it will restrict the number of cells that can be  
Figure 2: (**a**) Turning polarization modulation into phase modulation. The incident polarization is rotated by the ferroelectric liquid crystal on silicon spatial light modulator (FSLM). An appropriately aligned polarizer then projects both the modulated and the unmodulated light onto the same polarization axis but with opposite sign, resulting in a phase modulation of \(\pi\). This also ensures that interference between modulated and unmodulated light is possible. (**b**) Simulated intensity of modulated and unmodulated light transmitted through the polarizer in dependence of the polarizer angle with respect to the incident light, following a \(cos^{2}\)-distribution. The area indicated by the dotted yellow line shows all polarizer rotation angles allowing for opposing polarizations and therefore for an effective phase polarization of \(\pi\). A maximum interference contrast can be expected for equal intensities, here at 25% of the original.  
illuminated simultaneously. As a second consequence, the field of view is halved, which necessitates an objective with a smaller magnification to achieve the same field of view, which in turn limits the minimum spot size.  
We are therefore using free-space computer-generated holograms (CGH) to focus the laser to the desired positions using 0 th diffraction order binary Fresnel zone plates. This way, the modulator itself is acting as the focusing optics. The finite pixel pitch of any SLM, however, leads to a severely limited numerical aperture and therefore to a limited minimal applicable focal length. This limits the minimum focus size that is available for optically activating cells. A Fresnel Zone plate can be represented by the parabolic phase function  
\[\boldsymbol{\varphi}=2\pi*\frac{\boldsymbol{x}^{2}+\boldsymbol{y}^{2}}{2 \boldsymbol{f}\lambda}, \tag{1}\]  
where \(\boldsymbol{x}\) and \(\boldsymbol{y}\) are the SLM coordinates, \(\boldsymbol{f}\) is the focal length of the zone plate, and \(\lambda\) is the wavelength of the light that is used for the illumination of the CGHs. For a parabolic phase function representing a Fresnel zone plate, the minimum focal length can be expressed as [35]  
\[\boldsymbol{f}_{min}=\frac{\boldsymbol{N}*\Delta^{2}}{\lambda}. \tag{2}\]  
Here, \(\boldsymbol{N}\) is the number of pixels along the shorter side of the SLM and \(\Delta\) is the pixel pitch of the SLM. The focal length \(\boldsymbol{f}_{min}\) can be decreased using a telescope comprising the two lenses \(\boldsymbol{L3}\) and \(\boldsymbol{L2}\) (see Figure 1). With the magnification \(\boldsymbol{m}=\boldsymbol{L3}/\boldsymbol{L2}\), the numerical aperture of the overall optical system then becomes  
\[\boldsymbol{N}\boldsymbol{A}\approx\frac{\boldsymbol{N}*\Delta}{2\boldsymbol{ m}*\boldsymbol{f}_{min}}=\frac{\boldsymbol{\lambda}}{2\boldsymbol{m}\Delta}, \tag{3}\]  
resulting in a minimum focus diameter \(\boldsymbol{d}\) of  
\[\boldsymbol{d}=\boldsymbol{0.61}\frac{\boldsymbol{2}\lambda}{\boldsymbol{N} \boldsymbol{A}}=\boldsymbol{2.44}\boldsymbol{m}\Delta. \tag{4}\]  
according to the Rayleigh criterion. To achieve subcellular resolution, the magnification \(\boldsymbol{m}\) can be adjusted to tune \(\boldsymbol{d}\).