## 3 Results and Discussion  
Figure 2(a) shows a LSM image of the final fused silica lens array consisting of 64 lenses. The lenses are designed to have a radius of 4.5 mm resulting in a focal length of 10 mm, calculated by f = R/(n\(-\)1), with R being the lens radius and n = 1.45 the refractive index of fused silica at 1030 nm [32]. Furthermore, the individual lenses reveal a square footprint for both, resulting in a fill factor of 100% and required to generate square shaped Top-Hat beam profiles when used in a beam homogenizer setup. The edge length of the individual lenses is designed to be 1 mm. Apparently, the lens array consists of uniform lenses, while the magnification exemplarily shows the contour of a single lens. Here, the roughness R\({}_{a}\) is 25 nm, measured along lines within an area of 900 \(\upmu\)m \(\times\) 900 \(\upmu\)m (to exclude the corner points). The corresponding cross-section (blue line) also demonstrates the smooth surface contour of the lens, while a circle fit (red area) revealing a radius of 4.5 mm is added to show comparison with the ideal radius. Apparently, the fabricated lens is in excellent agreement with the designed curvature. Smaller roundings are found at the intersection points of two adjacent lenses, which are caused by the melted glass within the polishing process. However, the lens arrays are fabricated with high contour accuracy and a high degree of uniformity overall. Before applying the lens arrays in a beam homogenizer setup, the fabricated optics are tested in a simple setup consisting of a screen, showing the letter \"A\", the fabricated lens array and a USB microscope (VMS-004 Deluxe, Veho, Southampton, England) shown in Figure 2(b). The captured image clearly shows multiple letters \"A\", demonstrating the proper imaging quality and thus the functionality of the tested lens array. To demonstrate the beam homogenizing properties in detail, an optical setup as shown in Figure 4 is used in our experiments. The setup includes a halogen light source (LS 100-130, Instrument Systems, Munich, Germany), a plano-convex collimator lens (CL), an iris diaphragm, the laser-fabricated lens arrays, a Fourier lens (FL) and a CMOS camera (LaserCam-HR, Coherent, Santa Clara, CA, USA). Figure 2(a) shows the beam profile taken behind the iris diaphragm. Obviously, the halogen light source reveals inhomogeneous intensity distribution, which is clearly visible in the cross-sections. Figure 2(b) shows the beam profile taken after beam homogenisation. Apparently, a flat Top-Hat profile is formed, demonstrating the functionality of our lens arrays. The flat Top-Hat is also visible in the cross-sections in both, x- and y-direction, with a marker showing the Top-Hat size of 4.5 mm at full width half maximum. By using two  
Figure 2: Schematic of the all laser-based lens array fabrication process. First, the predefined geometry is generated out of the bulk silica sample in a layer-by-layer ablation process by femtosecond pulsed laser. Second, a CO\({}_{2}\) laser is applied to reduce the previously introduced surface roughness finalizing the optical element. lens arrays with equal focal lengths (10 mm), the theoretical size of the Top-Hat can be calculated by the simplified Equation (2). With the lens pitch being 1 mm, the focal length of the Fourier lens being 50 mm and the distance between the two lens arrays being 11 mm, the Top-Hat is calculated to have a size of 4.5 mm. Based on Equation (2), the Top-Hat size can be easily altered by changing the focal length of the Fourier lens. Obviously, the generated Top-Hat is in excellent agreement with theoretical assumptions. To characterize the generated profile in more detail, the applied laser camera offers calculations of the most important parameters according to ISO 13694:2000(E) for a threshold of 90%, important for the calculation of beam uniformity and flatness factor. The results are summarized in Table 2 with the beam uniformity being 1.8%, the plateau uniformity 2.1%, the flatness factor 95.2% and the edge steepness 32.8%.