J. Eur. Opt. Society-Rapid Publ. 22, 42( 2026) 415
Table 6. Configurations of the two achromatic cemented doublets with non axial field generated with SPCM.
|
1 |
2 |
Thorlabs AC254-100-A |
Glass 1 |
N-PK51 |
N-PK51 |
NBK7 |
Glass 2 |
N-BASF64 |
N-KZFS11 |
SF5 |
R1( mm) |
68.757 |
63.731 |
62.75 |
R2( mm) |
�41.812 |
�40.000 |
�45.71 |
R3( mm) |
�101.802 |
�133.856 |
�128.23 |
t1( mm) |
14 |
11.585 |
4 |
t2( mm) |
14 |
12 |
2.5 |
s 0( mm) |
89.789 |
89.467 |
97.070 |
Effective focal length |
100.000 |
100.000 |
100.070 |
100 % Spot diameter( mm) at 0 ° |
0.015 |
0.01 |
0.140 |
100 % Spot diameter( mm) at 2.5 ° |
0.063 |
0.072 |
0.090 |
Coma |
0.010 |
0.001 |
0.011 |
Spherical aberration |
�0.025 |
�0.025 |
�0.040 |
Axial Color |
�0.013 |
�0.017 |
�0.014843 |
Lateral Color |
�0.005 |
�0.003 |
�0.001 |
ever, diffraction has a stronger impact on the doublet optimised with weights of 5 and 1 for field angles of 0 ° and 2.5 °. Despite having a smaller central spot diameter than the doublet optimised with weights of 5 and 2 for field angles of 0 ° and 2.5 °, its MTF is farther from the diffraction limit( see Fig. 13).
The doublets designed using the SPCM and the selected doublet from Thorlabs show comparable axial chromatic aberrations( see Table 6). The doublet optimised with respective weights of 5 and 1 at 0 ° and 2.5 ° field of view, has a coma 10 times smaller than the first doublet designed with the SPCM and the selected Thorlabs doublet. The SPCM-designed doublets display spherical aberrations half the size of the Thorlabs doublet. However, their lateral chromatic aberration remains slightly stronger than that of the selected Thorlabs doublet.
All simulations have been performed on a 13th Generation Intel Ò Core™ i7-1370P 3.90 GHz CPU computer with a 32 Go RAM using Python 3.11 and Code V 2024.03. The average computation time for the creation of the 34 solutions tree diagrams was about 24 minutes.
6 Conclusion
This article shows the effectiveness of the SPCM combined with a reduced glass map with automatic generation of lens systems. This has been demonstrated through the automatic design of 68 achromatic doublets. These designs respect manufacturing capabilities, with at least five configurations exhibiting superior optical performance for an axial field compared to existing solutions. The five best doublets, which were automatically generated using the SPCM, have a total spot size for an axial field with a diameter half that of the doublets selected in Section 3. When increasing the FOV to 5 °, the doublets generated have similar performance as off-the-shelf doublets.
While glass cost was not considered in the present study, incorporating economic factors could provide an additional parameter for further reduction of the glass map. Moreover, the methodology could be extended to other or combined glass maps to expand the range of available materials. However, this approach currently only uses spherical and on-axis surfaces with a fixed stop aperture position. This is limiting the possibility of designing wide angle or very compact optical systems. By adding the possibility of using aspherical lenses could mitigate this limitation.
Finally, this approach may be generalized to the design of optical systems with a greater number of elements by applying SPCM at a deeper level in the solution tree. These systems could then be used as starting point for further optimisation with aspheres. Colour correction could also be extended to more wavelengths applying the Principal Component Analysis to additional wavelengths.
Acknowledgments
We acknowledge Optiive for its financial support of this work and A. Argy, F. Baumann, J. Belheine, P.-G. Bibal-Sobeaux and B. Brouillet for the first Python script on SPC method developed in IPP Team( ICube laboratory). We thank Paul Montgomery for carefully reading the manuscript.
Funding
This work was funded by Optiive, under a contract with Satt / Conectus.
Conflicts of interest Authors declares no conflict of interest associated to this work.
Data availability statement
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.