## 4 Spatial Pattern Formation and Correction of System Aberrations  
The light power of the system in the sample plane was measured to be 280 \(\upmu\)W for the blue beam path and 680 \(\upmu\)W for the yellow beam path. The field of view and spatial resolution of the setup were determined by scanning a single focus in the sample plane by displaying sets of phase gratings on the SLMs. Foci in the sample plane were magnified onto a camera using a telescope with a measured magnification of 3.95. The camera was mounted on a manual translation stage to allow axial scanning. Beam parameters were determined according to ISO 11146 using the \(D_{4\sigma}\) beam widths of the intensity distributions on the camera and a fit of a hyperbolic function to the resulting data. System aberrations were corrected by iteratively optimizing a predefined set of Zernike polynomials (ZP). The ZP are displayed on the same ferroelectric SLMs that are used to generate the light patterns. The radius \(r\) of the polynomials was normalized to the diagonal \(r_{max}=\frac{\sqrt{2048\text{-}1563}}{2}\).8.2 \(\upmu\)m of the SLMs. The amplitudes at \(r=r_{max}\) were normalized to 1 before multiplication by a scanning factor times \(\pi\) to minimize the mean \(e^{-2}\) beam area of all foci, defined by the number of pixels with values bigger than \(e^{-2}\) times the maximum pixel value per focus. ZP were tested in ANSI order from index 3 (oblique astigmatism) to index 25, determining the scan factor which minimizes the area covered by the focus for each polynomial. Before testing the next ZP, the result of the previous test was added as a phase mask to the SLM to compensate this specific aberration. The process of testing each ZP was executed twice to overcome possible cross-talk between the individual ZP. Figure 3d shows an example of this optimization process from the center of the FOV for the blue beam path. Blue bars represent the amplitude of the respective Zernike polynomial, and the orange line shows the drop in focus size by applying the respective polynomial to the overall aberration correction. It is obvious that lower order polynomials like astigmatism dominate the overall system aberrations. Correcting these, a near diffraction-limited \(e^{-2}\) width can be achieved, assuming a perfect Airy disc according to Equation (8). The shown optimization result does reach the diffraction limit assuming a Gaussian beam according to Equation (5). Figure 3a,b demonstrates the result of aberration correction over the whole field of view. Both plots show focus diameters along the major axes of the individual potentially astigmatic beams as ellipses centered at the position of a generated focus in the field of view. Red circles indicate the diffraction limit according to Equation (5). The relative amplitudes with respect to the maximum in the observed field of view are encoded in color. In Figure 3a, one can observe almost diffraction-limited focus sizes in some areas. Over most of the FOV, however, beam waists are much larger with no clear tendency where these deviations occur. After correction, as demonstrated in Figure 3b, foci over the whole field of view are significantly smaller, with deviations occurring mostly along the edges of the FOV, which might be the result of some remaining field curvature. Figure 3c summarizes these findings as box plots. With aberration correction, focus diameters are pushed toward the diffraction limit, and the standard deviation and outliers are greatly reduced. We calculated the mean values of focus diameters for the edges of the FOV as well as for the central 9 foci. In comparison, foci on the edges are 23% larger, which also results in a larger extent in axial direction. Similar analyses have been performed for the 589 nm beam path, as depicted in Figure 3e,f.