Limited interpolative design of lens systems of the triplet type.
Creators: name: Aldersey, ALH
Publisher: name: University Of Tasmania
Year: 2023

description: An extensive study of the Leitz Hektor or type 121 triplet lens has revealed fairly simple relationships between the aberrations and the design parameters at large apertures. These relationships, although more complicated than the direct well known relationships for small apertures of triplet systems, nevertheless, are simple enough to allow the designer to systematically correct the zonal spherical between f/3.5 and f/2.5 in both the monochromatic and chromatic stages of design. The design principles developed for the type 121 triplet have been applied successfully to the type 122 triplet: they have been found by interpolative rather than extrapolative design techniques. Interpolative designis a feature of this work. Initially the 3rd, 5th and 7th order Buchdahl aberration coefficients of the \3rd order type 121 triplets\" have been mapped with respect to all the monochromatic design parameters. This \"limited interpolative study\" has revealed that most of these coefficients approach zero in a small region. In particular in this \"optimum region\" the first three orders of spherical aberration are near zero or pass through zero. This property enables the \"optimum region\" to be located accurately and rapidly with a comparatively small amount of calculation. The spherical aberration (to 7th order) of some systems in the \"optimum region\" is predicted to be zero at two zones (the 0.707 and the marginal zone). This two-zone correction however fails to hold at apertures between 1/3.5 and 1/2.5 due to the presence of 9th order and higher order spherical aberration. However it has been found that these outer zones of the monochromatic system are controlled by the Petzval sum and the spherical aberration residual;thus allowing two zone correction for an aperture of f/2.5 in the presence of higher order aberrations. When correcting the chromatic aberrations of the type 121 a similar situation has been found with the large apertures C. &gt; 1/3.5). The longitudinal chromatic aberration residual in particular is linked to the Petzval sum's influence on the spherical aberration of the zones beyond 1/3.5 and the transverse chromatic aberration residual has a smaller but still significant effect also. Thus it has been found that adjustment of the chromatic aberration leads to a system with a smaller Petzval sum. On the basis of this property it was predicted that the 3rd 5th and 7th order spherical coefficients must converge to a minimum with a small Petzval sum when the chromatic aberration is optimized for all zones. This has been confirmed by repeating the maps of the 3rd 5th and 7th order spherical aberration coefficients with respect to the monochromatic and chromatic design parameters. The aberration coefficients are found to converge to an optimum set in a single region of the entire design space. This model of the system's behaviour explains many published properties of triplets. It has also been predicted from the study of the spherical aberration that the 9th and higher orders of spherical aberration must converge to a minimum in step with the 3rd 5th and 7th orders. This has been confirmed by mapping the 9th and 11th order Buchdahl spherical aberration coefficientswith respect to the design parameters. Thus in the \"optimum region\" the 3rd 5th 7th 9th and 11th order spherical aberration coefficients are near to or pass through zero.' The type 121 with optimum zonal spherical aberration for f/2.5 has been developed and compared with published Pentac f/2.5 designs. Finally the principles developed for correcting the zonal aberrations beyond f/3.5 have been applied to the systematic development of the type 122 triplet. This has resulted in the easy location of two zone correction."