Limited interpolative design of lens systems of the triplet type.

摘要

An extensive study of the Leitz Hektor or typeud121 triplet lens has revealed fairly simple relationshipsudbetween the aberrations and the design parameters at largeudapertures. These relationships, although more complicatedudthan the direct well known relationships for small aperturesudof triplet systems, nevertheless, are simple enough toudallow the designer to systematically correct the zonaludspherical between f/3.5 and f/2.5 in both the monochromaticudand chromatic stages of design. The design principlesuddeveloped for the type 121 triplet have been appliedudsuccessfully to the type 122 triplet: they have been foundudby interpolative rather than extrapolative design techniques.udInterpolative designis a feature of this work. Initially the 3rd, 5th and 7th order Buchdahludaberration coefficients of the "3rd order type 121 triplets"udhave been mapped with respect to all the monochromaticuddesign parameters. This "limited interpolative study" hasudrevealed that most of these coefficients approach zero inuda small region. In particular, in this "optimum region"udthe first three orders of spherical aberration are nearudzero or pass through zero. This property enables theud"optimum region" to be located accurately and rapidly withuda comparatively small amount of calculation. The spherical aberration (to 7th order) of someudsystems in the "optimum region" is predicted to be zero atudtwo zones (the 0.707 and the marginal zone). This two-zoneudcorrection, however, fails to hold at apertures betweenud1/3.5 and 1/2.5 due to the presence of 9th order and higherudorder spherical aberration. However, it has been foundudthat these outer zones of the monochromatic system areudcontrolled by the Petzval sum and the spherical aberrationudresidual;thus allowing two zone correction for an apertureudof f/2.5 in the presence of higher order aberrations.udWhen correcting the chromatic aberrations of theudtype 121 a similar situation has been found with the largeudapertures C. > 1/3.5). The longitudinal chromatic aberrationudresidual, in particular, is linked to the Petzval sum'sudinfluence on the spherical aberration of the zones beyondud1/3.5 and, the transverse chromatic aberration residualudhas a smaller but still significant effect also. Thus itudhas been found that adjustment of the chromatic aberrationudleads to a system with a smaller Petzval sum. On the basis of this property, it was predictedudthat the 3rd, 5th and 7th order spherical coefficientsudmust converge to a minimum with a small Petzval sum whenudthe chromatic aberration is optimized for all zones.udThis has been confirmed by repeating the maps of the 3rd,ud5th and 7th order spherical aberration coefficients with respect to the monochromatic and chromatic design parameters.udThe aberration coefficients are found to converge to anudoptimum set in a single region of the entire design space.udThis model of the system's behaviour explains many publishedudproperties of triplets.udIt has also been predicted from the study of theudspherical aberration that the 9th and higher orders ofudspherical aberration must converge to a minimum in stepudwith the 3rd, 5th and 7th orders. This has been confirmedudby mapping the 9th and 11th order Buchdahl spherical aberrationudcoefficientswith respect to the design parameters.udThus in the "optimum region" the 3rd, 5th, 7th, 9th and 11thudorder spherical aberration coefficients are near to, or passudthrough, zero.'udThe type 121 with optimum zonal spherical aberrationudfor f/2.5 has been developed and compared with publishedudPentac f/2.5 designs.udFinally the principles developed for correctingudthe zonal aberrations beyond f/3.5 have been applied to theudsystematic development of the type 122 triplet. This hasudresulted in the easy location of two zone correction.