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J. Eur. Opt. Society-Rapid Publ. 22, 42( 2026)
Table 3. Configurations of the five best achromatic cemented doublets and their spot sizes in mm. R1, R2 and R3 are the radius of curvature of sequential surfaces in millimetres. tj are the center thickness of the two lenses in mm and s’ the back focal length of the achromatic cemented doublets in mm.
|
1 |
2 |
3 |
4 |
5 |
Glass 1 |
N-FK58 |
N-PK51 |
N-PK51 |
N-FK51A |
N-PK52A |
Glass 2 |
N-LASF31A |
N-BASF64 |
N-LASF41 |
N-LASF47 |
N-LASF41 |
R1( mm) |
52.256 |
69.622 |
40 |
41.431 |
40 |
R2( mm) |
�50.005 |
�43.523 |
�61.472 |
�55.552 |
�59.612 |
R3( mm) |
�89.575 |
�106.966 |
�492.996 |
�150.846 |
�258.397 |
t1( mm) |
4.087 |
4.541 |
4.264 |
4.326 |
4.306 |
t2( mm) |
6 |
6 |
6 |
6 |
6 |
s 0 |
97.383 |
96.421 |
93.513 |
94.081 |
94.100 |
100 % Spot diameter( mm) |
0.009 |
0.001 |
0.011 |
0.012 |
0.012 |
Table 4. Schott glasses selected after principal component analysis of the Schott catalogue.
LASF35 |
N-KZFS11 |
N-LASF41 |
N-PK51 |
N-SF15 |
N-SF66 |
N-BASF2 |
N-KZFS5 |
N-LASF43 |
N-PK52A |
N-SF2 |
N-SF8 |
N-BASF64 |
N-KZFS8 |
N-LASF45 |
N-SF1 |
N-SF4 |
P-LASF47 |
N-F2 |
N-LAF7 |
N-LASF46B |
N-SF10 |
N-SF5 |
P-SF69 |
N-FK51A |
N-LASF31A |
N-LASF55 |
N-SF11 |
N-SF57 |
|
N-FK58 |
N-LASF40 |
N-LASF9 |
N-SF14 |
N-SF6 |
|
where DG i is the Euclidean distance between the fictitious glass and the real glass i, n dfict; n Ffict and n C fict are the refractive indices of the fictious glass at the wavelength d, F, C, and n glassi, n Fglassi and n C glassi are the refractive indices of the real glass i at the wavelength d, F, C.
The fictitious glass is replaced by each of these 10 glasses one after the other. After a local optimization of the system, the glass leading to the smallest spot diagram is kept. This glass substitution process has been applied using the reduced glass map detailed in Section 4.
The Schott glass map from 2024 contains 120 glasses [ 17 ], which leads to the design of 240 doublets. Extending this method to N lenses needs the design of 120 2 N optical system. For a Tessar lens, this would represent 1920 systems or 122 880 lenses for a 10 lenses objective. To minimize the computational effort, a reduction of the number of glasses is required.
4 Creation of a reduced glass map
Figure 5. Diagram of the full Schott Glass map after principal component analysis.
Multiple attempts at reducing glass maps have been performed in recent decades [ 18 – 22 ]. This is possible since some glasses have very similar optical and chemical properties. The very first step of reducing the glass map would be to select only one glass from multiple glasses with similar optical properties. For instance, the Schott catalogue includes N-SF6, N-SF6HT, and N-SF6HTULTRA, three glasses with identical optical properties that differ mainly in their transmittance characteristics [ 23 ]. In such cases, retaining only one representative glass, typically the most cost-effective, can simplify the selection process. Applying this criterion to the full Schott glass map [ 17 ] and removing the lead containing and radiation resistant glasses, reduces the number of available glasses from 120 to 83. But the resulting set still remains too large for iterative procedures.
In the history of optical design, several dispersion models have been proposed to select glasses for the design of achromatic cemented doublets and apochromats [ 24 – 26 ]. Recently, H. Münz et al. [ 12 ] proposed a new graphical selection of glasses using principal component analysis( PCA) on the normalized index differences d j( k i):