# YAG Laser Rod 3D Corrective Process Optimization through Tool Influent Function Shape Inspection
## 3 Results and Discussion  
The results of the spot experiments performed on the YAG samples for the FEM tool are shown in Figures 3 and 4, which confirm a significant difference in the real behavior of the tool from the theoretical model, manifested by ripple formation. Such complicated forms of the spots are difficult to fit mathematically and are, therefore, unsuitable for dwell time correction. The experiments also showed that an increase in tool speed led to an increase in material removal but had almost no effect on the shape of the polishing spot. In addition, it was evident that with an increase in pressure, the shape of the removal function changed. Consequently, it was deduced that the assumption that this tool design would ensure constant pressure was faulty. This was likely an effect associated with the small tool radius (necessary to control the spot size) and the inherent rigidity of the polyurethane polishing pad. Figure 3: _Cont._  
Figure 2: Example of white light interferometry (WLI) analysis results (FEM tool at 700 rpm with a pressure of 0.7 bar). Two variants were tested for the VEH tool: a tool with a radius of R10 and a tool into whose head a planar surface with a diameter of 5.5 mm had been machined for the purpose of gluing on the polishing pad (R0). From the experiments performed (Figure 5), it was evident that in all cases, material removal increased when the tool speed rotation increased; however, this had no effect on the final shape of the polishing spots. Furthermore, in the case of the R10 spherical tool (Figure 5a), the material was polished out primarily by a very narrow ring, as the central part of the tool nearly failed to remove the material due to low circumferential speed and low polish penetration. The interaction between the pressure, the circumferential speed, and the distribution of the polishing slurry then resulted in the observed undulation, which was unsuitable for mathematical modeling of TIF using the Gaussian function. Figure 4: FEM R10 tool at 800 rpm for pressures of 0, 0.7, and 1.5 bar. Figure 5: VEH R10 **(a)** and R0 **(b)** tools. Figure 3: FEM R10 tool at 0 bar **(a)**, 0.7 bar **(b)**, and 1.5 bar **(c)**. In the case of the R0 tool, the situation was simpler, as the component of the variable pressure distribution was eliminated and, therefore, the resulting spot did not have such a tendency to ripple. However, a certain complication was caused by the increased sensitivity of the geometry of the planar tool-planar workpiece surface to mutual plane parallelism, where a small angular deviation led to a violation of uniformity in pressure distribution and material removal in the wedge (Figure 5b). Despite this complication, the planar tool option was considered more suitable for the YAG 3D shape correction. Finally, the variant in which the spherical R10 tool was inclined by \(15^{\circ}\) from the normal of the polished surface was tested. In this arrangement, the tool rotary axis did not pass through the polishing spot, which led to a smaller decrease in the removal rate toward the center of the polishing spot. However, there was a rotationally asymmetrical distribution of circumferential speeds, which resulted in a characteristic deformation of the spot shape (Figure 6a) and thus unsuitability for the accurate fitting necessary for the dwell time correction. However, this phenomenon could be suppressed by sequential tilting of the tool rotation axis in the +X, +Y, -X, and -Y axes of the polishing device coordinate system (the so-called dynamic mode) [5], thus symmetrizing the shape of the polishing spot. This was confirmed by the results of the experiments performed using this method (Figure 6b). For example, if we compare the results of the TIF mathematical fitting obtained by the Zeeko Precessions software for the FEM tool spot and for the VEH tool spot generated in dynamic mode with sequential tilting \(15^{\circ}\) in the +X, +Y, -X, and -Y axes, there was a significant reduction in the residual error of the TIF (Figure 7).