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J. Eur. Opt. Society-Rapid Publ. 22, 42( 2026)
Figure 2. Saddle point construction example for the design of a doublet system.
designer to select the most appropriate solution SP _ a _ p where p represents the number of the solution at depth a with p =[ 0, a 2 ]( see Fig. 3).
The selected method enables the automatic generation of new starting points without prior knowledge. This method can be complementary to other AI methods by generating new datasets.
3 Design of achromatic cemented doublets with the SPC method
In the previous section, we explained the principle of the Saddle Point Construction method and its benefits. To validate the effectiveness of the method in optical design, we now apply it to the automatic design of an achromatic cemented doublet.
To evaluate the quality of the generated doublets, we compare them with achromatic doublets designed with a theoretical approach. The selected doublets for this comparison are drawn from [ 16 ], and from Thorlabs and Edmund Optics catalogues. Their common optical characteristics are tabulated in Table 1.
All selected doublets are made using Schott glasses as well as the designed doublets using the Saddle Point Construction Method.
In lens design, it is essential to consider the practical constraints in line with manufacturing capabilities [ 2 ]. The
following constraints were imposed: a minimum center thickness, a minimum edge thickness, a minimum air gap, minimum and maximum curvatures( see values specified in Table 2 where SD is the semi-diameter of the lens). These constraints ensured the achromatic doublets designs remained manufacturable and mechanically robust.
The designing process of the achromat is the following:
Start with a plane-parallel plate made of material M j with a thickness of 4mm.
Optimize this initial configuration into a single lens with fixed focal length, F-number and with d the reference wavelength.
Apply the SPC method to this local minimum to generate two doublet systems integrating a fictitious glass.
Perform a glass substitution by fitting the fictitious glass to real materials, followed by a re-optimization of the optical system with the previous constraints.
The very last optimisation of the optical system is a local optimisation of transverse aberrations. The radii of curvature and the thickness of the lens elements are set as variables to minimise the spot diameter produced by the system.
The Figure 4 shows an example of a tree diagram with resulting RMS spot diameter at each step of the SPCM optimisation process. The initial system used as an example leads to the system 1 in the Table 3. The system 1 is