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Limited interpolative design of lens systems of the triplet type.


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Aldersey, ALH 1967 , 'Limited interpolative design of lens systems of the triplet type.', PhD thesis, University of Tasmania.

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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. > 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.

Item Type: Thesis - PhD
Authors/Creators:Aldersey, ALH
Keywords: Lenses
Copyright Holders: The Author
Copyright Information:

Copyright 1967 the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
would be pleased to hear from the copyright owner(s).

Additional Information:

Thesis (Ph.D) - University of Tasmania, 1967. Includes bibliographies

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