Abstract

Investigation of the thin lens theory of zoom lenses results in a general statement concerning conjugate points, a simple proof of the maximum number of crossing points, and an algorithm for computing component focal lengths of a five-component symmetrical zoom lens. The three-component optically compensated zoom lens is discussed in detail. Results of applying the algorithm are given. A prototype of the five-component zoom lens has been built and is briefly discussed.

© 1965 Optical Society of America

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References

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  1. T. Smith, Proc. Phys. Soc. (London) 57, 558 (1945).
    [Crossref]
  2. The substitution of 1 for A is justified since we are interested in the highest powers of Δ resulting from multiplication. Multiplying some power of Δ by either 1 or A gives the same result as far as the highest power of Δ is involved.

1945 (1)

T. Smith, Proc. Phys. Soc. (London) 57, 558 (1945).
[Crossref]

Smith, T.

T. Smith, Proc. Phys. Soc. (London) 57, 558 (1945).
[Crossref]

Proc. Phys. Soc. (London) (1)

T. Smith, Proc. Phys. Soc. (London) 57, 558 (1945).
[Crossref]

Other (1)

The substitution of 1 for A is justified since we are interested in the highest powers of Δ resulting from multiplication. Multiplying some power of Δ by either 1 or A gives the same result as far as the highest power of Δ is involved.

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Figures (9)

Fig. 1
Fig. 1

Number of possible crossing points with one-, three- and five-component optically compensated zoom lenses.

Fig. 2
Fig. 2

Three-component zoom lens with negative fixed component.

Fig. 3
Fig. 3

Solutions for a three-component zoom lens with crossing points occurring at the midposition and at the two ends of travel (negative fixed component) A2=−10D, t1=t2=60 mm, shift ±50 mm.

Fig. 4
Fig. 4

Three-component zoom lens with positive fixed component.

Fig. 5
Fig. 5

Solutions for a three-component zoom lens with crossing points occurring at the midposition and at the two ends of travel (positive fixed component), A2=7.5 D, t1=t2=60 mm, shift ±50 mm.

Fig. 6
Fig. 6

Symmetrical five-component zoom lens with negative fixed components.

Fig. 7
Fig. 7

Five-component system with two motions linearly related, magnification range ×8.13, maximum focusing error=0.0026, f1=289.16, f2=−229.57, f3=215.14.

Fig. 8
Fig. 8

Optically compensated zoom lens with same over-all length from object to image as system in Fig. 7, magnification range ×8.39, maximum focusing error=0.0081.

Fig. 9
Fig. 9

Prototype of five-component optically compensated zoom lens with auxiliary end components (housing removed).

Tables (2)

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Table I Five-component zoom—positive components movable.

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Table II Five-component zoom—negative components movable.

Equations (17)

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( 1 - t 0 0 1 ) ( 1 0 A 1 1 ) ( 1 - t 1 0 1 ) ( 1 0 A 2 1 ) × ( 1 - t 2 0 1 ) ( 1 0 A 3 1 ) ( 1 - t 3 0 1 ) = ( B D A C ) ,
( 1 - t + Δ 0 1 )
( 1 Δ 0 1 ) .
( 1 0 A 1 )
( 1 0 1 1 )
( 1 Δ 0 1 ) ( 1 0 1 1 ) = ( 1 + Δ Δ 1 1 ) ( Δ Δ 1 1 ) .
( 1 Δ 0 1 ) ( 1 0 1 1 ) ( 1 Δ 0 1 ) ( 1 0 1 1 ) ( 1 Δ 0 1 ) × ( 1 0 1 1 ) ( 1 Δ 0 1 ) ( Δ 3 Δ 4 Δ 2 Δ 3 ) .
( Δ 3 Δ 4 Δ 2 Δ 3 ) ( 1 0 1 1 ) ( 1 Δ 0 1 ) ( 1 0 1 1 ) ( 1 Δ 0 1 ) ( Δ 3 Δ 4 Δ 2 Δ 3 ) ( Δ Δ 2 Δ Δ 2 ) ( Δ 5 Δ 6 Δ 4 Δ 5 ) .
( 1 - t - a Δ 0 1 ) .
( 1 Δ 0 1 ) .
( B D A C ) .
( 1 0 A 0 1 ) ( B D A C ) = ( B D A 0 B + A A 0 D + C ) .
( B D A C ) .
( A 0 D + C ) / ( A 0 B + A ) .
( A 0 D + C ) / ( A 0 B + A ) = ( A 0 D + C ) / ( A 0 B + A ) .
( B D A C )
( C D A B ) .