J. Eur. Opt. Society-Rapid Publ. 22, 42( 2026) 409
Figure
3. Tree diagram example for a saddle point construction of depth a, where a corresponds to the number of elements added to the system. The root system is a N elements optimized system, and the final system have( N + a) elements.
Table 1. Characteristics of the selected doublets used for the comparison.
Optical characteristics |
Value |
EFL( mm) |
100 |
F # |
4 |
Wavelengths |
d, F, C |
FOV(°) |
0 |
represented by the bottom branch of the tree diagram with an RMS spot size of 0.004 mm.
This routine is applied to the j materials of the Schott map, enabling to find 2 j achromatic doublets.
To control the whole process, the Code V glass fitting algorithm was not used, but rather with a bespoke glass substitution Python algorithm. We then performed a search for the 10 closest real glasses to the fictitious glass. These 10 glasses minimise their distance to the fictitious glass as:
DG i ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 2 2 n dfict � n dglassi þ nFfict � n Fglassi þ nC � n fict C; glassi ð1Þ
Table 2. Design constraints applied to the design of an achromatic doublet with the SPC method, where SD is the semi-diameter of the lens.
Constraint type |
Value |
Minimum edge thickness |
1 mm |
|
Minimum center thickness
Minimum air gap
|
SD
15
1 mm
|
Effective focal length |
100 mm |
|
Minimum curvature
Maximum curvature
|
� 1
2SD
1
2SD
|
Figure 4. Example of RMS spot diameter evolution during the SPCM optimisation process, from initial system to final doublet after glass fitting.