J. Eur. Opt. Society-Rapid Publ. 21, 12( 2025) 139
same parameters, there is a notable discrepancy in the levels of initial waviness and roughness. This is likely a result of the dressing condition and successive wear of the grinding tool, as the samples were ground in the order of their respective numbering.
While the overall waviness values Sq W of the ground samples are lower than the roughness values Sq R, they cannot be reduced by the same extent during PJP. However, an improvement in the Sq W range from 50 nm to 15 nm was achieved.
The mean isotropic PSD functions in Figure 23 allow a more precise look at the measurement of each sample regarding the process steps and the two distinct measurement position, which were shown in Figure 21( A). First, it is obvious that after grinding more peaks occur at position“ P”( see Fig. 23( A)) compared to position“ V”. Both PSD functions also reveal that peaks located at higher spatial frequencies can be reduced more efficiently. The peaks at spatial frequencies higher than 0.01 lm �1 have largely disappeared. Hence, low frequency errors must be avoided in the grinding process since they cannot be corrected later in the thermal polishing step. It is obvious that PJP parameters T = 2050 ° Candv = 0.5 mm / s are beneficial to achieve the best values here( see # S5). This is also evident from the overall lowest Sq W values given in Figure 22( A).
As presented in Figure 22( B), the roughness of the ground samples is Sq R =( 179.6 ± 23.0) nm. Applying PJP, the roughness of the Alvarez lenses can be reduced very effectively. The slower scanning velocity of the PJ( v = 0.5 mm / s, see Table 2) seems to enable a more uniform smoothing of the sample. The areal measurements given in Figure 24. clarify this finding for sample # S2 which was the worst of the optimization batch and # S5 which was the best overall. The damage, which probably resulted from micro-chipping caused by the abrasive grain, is no longer apparent after the PJP. However, the Sq R values can be improved for all samples to less than 1 nm by applying PJP. This indicates the stronger impact of the PJP to higher spatial frequency errors.
It was shown that the PJP with an increased temperature of 2050 ° C in combination with a reduced scan velocity of the PJ( v = 0.5 mm / s) is beneficial. Considering both roughness and waviness, the best PJP results have been obtained for sample # S5. The birefringence due to internal stresses was also in accordance with the requirements for precision optics.
For the best sample mentioned above, the experimental results are compared with the corresponding theoretical polishing, applying the convolution function to the ground initial surface. So far, the predictability of the PJP result has been demonstrated for planar samples [ 29 ]. A more precise look at the mean isotropic PSD functions is given in Figure 25. The PSD curve obtained after PJP fits very well with the graph resulting from the filtered ground state, in the spatial range, where the convolution function can be applied. The comparison of the initial graph( black) and the PSD after PJP( blue) demonstrates the efficacy of the smoothing process in the higher spatial frequency range. Additionally, the application of PJP to the freeform
Figure 25. Predictability of PJP result applying a filter function on the initial ground state for sample # S5: Comparison of mean isotropic PSD of the initial ground( black), filtered ground( golden) and the experimental PJP( blue).
element has been shown to result in a notable reduction in waviness( see ranges in Fig. 5).
It can be stated that the predictability of the polishing result is also sufficient for the freeform lenses and can therefore be applied for future optimization of the process chain, especially with regard to the linking of grinding and PJP.
5 Conclusion
As part of the investigations described above, it was possible to develop and systematically investigate a new type of process chain for freeform production using a combination of machining processes( grinding) and a beam-based thermal process( PJP). Both of these technology types were examined in detail and optimized for the specific application of an Alvarez lens.
With regard to the grinding processes, it was possible to identify influences on surface deviations in the complex process of freeform production and thus optimize the process step by step. After several improvement steps, sufficient shape accuracies of the freeform geometry between approx. 3 – 6 lm PV value were achieved. Among other things, different kinematic approaches, the machine accuracy and CAM program solution have a major influence on the resulting surface deviations and offer a high potential for optimization. Ultra-fine grinding with resin-bonded tools can achieve low roughness and good surface qualities suitable for the final PJP process regarding workpieces out of fused silica. They can be polished in one step while retaining their original form. High-frequency defects in particular can be removed so that roughness of Sq R < 0.5nmcanbe achieved. Grinding marks having longer wavelengths can only be removed to a limited extent( Sq W < 20nm). Here, the grinding process should be further optimized according to the target specifications of the desired optics. The application of the convolution function to theoretically assess the outcome of a PJP process can be helpful to minimize the amount of sample material used. It was shown that freeform manufacturing of the chosen Alvarez design can be performed within 150 min processing time.