J. Eur. Opt. Society-Rapid Publ. 21, 12( 2025) 131
Figure 10. Calculated error topography obtained by measurement with telecentric WLI showing unwanted surface structures.
characterized by a positional dependency of the component in the machine room or on the mounting plate used for fixing, respectively. This surface deviation occurs if the component positioning is eccentric in relation to the center of the table axis. Possible causes include influences of axis stability and deviations in path planning with off-center sample fixation. If the sample is fixed centrical, the formation of such a structure in the grinding process can be prevented. In the areal measurement given in Figure 11( A) no arch-like structure can be recognized. As a result, central positioning was always used for the following freeform generation on the CNC machine employed.
The cause for the vertically aligned ripple structures, however, is to be found way earlier in the freeform generation chain, namely in CAM program settings. In the CAM parameters, the so-called tolerance setting determines the accuracy and number of coordinate points that map the grinding path. The setting accuracy of the grinding machine used is one micrometer. It was experimentally found and evaluated that if the tolerance is set to 1 lm, the ripple structures appear on the machined surface. A coarser tolerance leads to an increase of the ripple wavelength, while a tolerance setting of 0.1 lm, i. e. an order of magnitude finer than the machine accuracy, prevents the formation of such ripples, as shown in Figure 11( B) The finer resolution generates more reference points in the CNC program, which are then interpolated to apparently form a more continuous and smoother tool path. However, the finer resolution also increases the size of the machine data files significantly which can complicate data handling.
Therefore, one aspect of Section 4.2 deals with the initial condition of the ground surface regarding tolerance setting that is required or suitable for the final PJP.
The iterative surface improvements are also apparent by observing the PSD function of Alvarez lenses with different optimization grades. Figure 12 compares the resulting surface deviations in dependency of their spatial frequency measured with the telecentric WLI for two fine ground Alvarez samples shown before. The sample seen in Figure 10, ground without process optimizations, is characterized by rather high deviations in the low spatial frequency region and distinct peaks in the mid- to highspatial region, representing periodic errors in Figure 12( A) compared to a more flat and uniform PSD curve in Figure 12( B) for the sample shown in Figure 11( B) which was produced in an optimized process.
After carrying out the process optimizations described, it is furthermore possible to achieve sufficient shape accuracies of the freeform geometry between approx. 3 – 6 lm PV value with the grinding machine used, which is expressly not an ultra-precision machine.
4.1.2 Ultra-fine grinding for roughness reduction
After fine grinding the Alvarez samples are ultra-fine ground as described above, using a resin bond tool with fine grain size D16. The tool paths are not changed for this, only the removal depth( a p = 10lm), feed rate( v f = 100 mm / min) and cutting velocity( v c = 13.1 m / s) are adapted to the changed grinding regime. It is possible to achieve the