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Figure
13. MTF of the doublets generated with the SPCM,( a) optimized with weights of 5 and 2 for field angles of 0 ° and 2.5 °,( b) optimized with weights of 5 and 1 for field angles of 0 ° and 2.5 °.
reduced glass map. Furthermore, these three glasses have been selected in the reduced glass map in combination with other glasses.
One of the resulting doublet examples is illustrated in Figure 8. This shows the total spot size of the best automatically generated doublet for the axial field, which has a diameter of 8.9 lm, as well as its MTF. The ray aberration diagram Figure 8d shows that for the green and blue wavelengths the curves almost overlap. We can therefore conclude that this generated system is almost diffractionlimited and colour corrected for the axial field.
A Monte Carlo tolerance analysis was performed on the top-performing generated design and on the Thorlabs AC254-100-A achromatic cemented doublet. With typical manufacturing errors of ± 0.05 mm and ± 0.1 ° element tilt, it led to a maximum RMS Spot diameter of 0.8 for the generated achromatic cemented doublet and the Thorlabs AC254-100-A lens( see Fig. 9). This ensure equal performance of the two systems with the same manufacturing conditions.
5.2 Non-axial object field solutions on achromatic doublets
When using achromatic doublets, it is impossible to achieve a0 ° axial object field. They are most often used with a small field of view. To accurately compare our results with catalogue doublets we automatically generated cemented doublets for a field of view of ± 2.5 °.
Using the same method, 68 doublets were generated, and the one with the smallest spot size was selected for this comparison.
As shown in Figure 10, theSPCMcanautomatically generate achromatic cemented doublets with similar performances to catalogue doublets, with a field angle of 2.5 °. These results were achieved by applying weights of 5 and 2 to field angles of 0 ° and 2.5 ° respectively. This produced a system with a comparable spot size for the axial object field and a spot size that is 14 lm smaller for the 2.5 ° angular object field. As shown Figure 11, the spot diameter progressively increases with the field of view without ensuring its performances across the field of view.
By modifying the weight distribution across the field angles, we can minimise one field spot size at the expense of another. For example, setting the weights to 5 and 1 for field angles of respectively 0 ° and 2.5 °, reduces the size of the central field spot, as well as the diameter of the 2.5 ° field spot( see Fig. 12). In addition, the resulting spot for blue and red wavelengths on the axial field are overlapping which is not the case for the doublet shown Figure 10. The overall performance of the two doublets, which were generated with a total FOV of ± 2.5 °, is comparable. How-