Abstract

In an ordinary varifocal or zoom lens system one or more lenses are moved back and forth along the optical axis. But lateral movements can also cause a zoom effect. The refractive or diffractive elements to be moved are no longer rotationally symmetrical. The elements can be made out of transparent material or as a grating with curved lines or as a special version of a kinoform. The zoom systems with lateral motion are very compact.

© 1970 Optical Society of America

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References

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  1. A. W. Lohmann, Brit. Patent998,191.
  2. A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1567 (1967).
    [Crossref] [PubMed]
  3. L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
    [Crossref]
  4. L. W. Alvarez, U.S. Patent3,305,294.
  5. J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, Appl. Opt. 9, August (1970).

1970 (1)

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, Appl. Opt. 9, August (1970).

1969 (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

1967 (1)

Alvarez, L. W.

L. W. Alvarez, U.S. Patent3,305,294.

Hirsch, P. M.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, Appl. Opt. 9, August (1970).

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

Jordan, J. A.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, Appl. Opt. 9, August (1970).

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

Lesem, L. B.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, Appl. Opt. 9, August (1970).

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

Lohmann, A. W.

Paris, D. P.

Van Rooy, D. L.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, Appl. Opt. 9, August (1970).

Appl. Opt. (2)

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 1567 (1967).
[Crossref] [PubMed]

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, Appl. Opt. 9, August (1970).

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Dev. 13, 150 (1969).
[Crossref]

Other (2)

L. W. Alvarez, U.S. Patent3,305,294.

A. W. Lohmann, Brit. Patent998,191.

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Figures (2)

Fig. 1
Fig. 1

Two basic refractive elements t1 and t2. Together they form a cylindrical zoom system with lateral x motion. t(x, y) is thickness as function of x and y.

Fig. 2
Fig. 2

Diffractive zoom lens system with spatial carrier frequencies in the two masks M1 and M2.

Equations (14)

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t 1 ( x , y ) = t 0 + A x 3 .
t 2 ( x , y ) = t 1 ( x , y ) ; t 1 ( x Δ , y ) + t 2 ( x + Δ , y ) = 2 t 0 6 A x 2 Δ 2 A Δ 3 .
ϕ = ( 2 π / λ ) ( n 1 ) ( t 1 + t 2 ) .
ψ = ψ 0 π x 2 / λ f ,
1 / f = 12 A ( n 1 ) Δ .
t 1 ( x , y ) = A x 3 ; t 2 ( x , y ) = t 1 ( x , y ) ; t 3 ( x , y ) = t 1 ( y , x ) ; t 4 ( x , y ) = t 1 ( y , x ) ; t 1 ( x Δ ) + t 2 ( x + Δ ) + t 3 ( y Δ ) + t 4 ( y + Δ ) = 6 A ( x 2 + y 2 ) Δ + .
M ( x , y ) = + C n exp [ i n ϕ ( x , y ) ] ; C 0 = 1 2 ; C n = sin ( n π / 2 ) / n π ; ϕ ( x , y ) = ( 3 x y 2 + x 3 ) / a 3 .
M ( x Δ , y ) M ( x j + Δ , y ) = C n C m exp [ i n ϕ ( ) + i m ϕ ( + ) ] = C n C m exp [ i ( n + m ) [ ϕ ( ) + ϕ ( + ) ] / 2 + i ( n m ) [ ϕ ( ) ϕ ( + ) ] / 2 ] .
ϕ ( ) ϕ ( + ) = 6 ( x 2 + y 2 ) Δ / a 3 2 ( Δ / a ) 3 .
1 / f = 6 λ Δ / π a 3 .
C 0 = 0 ; C n = 2 sin ( n π / 2 ) / n π ; C 1 4 = ( 2 / π 4 ) .
M 1 = C n exp ( i n ϕ 1 ) ; ϕ 1 = ( 3 x y 2 + x 3 ) / a 3 + 2 π x / d ; M 2 = C m exp ( i m ϕ 2 ) ; ω 2 = ( 3 x y 2 + x 3 ) / a 3 + 2 π y / d .
M 1 ( x , y ) = exp [ i ϕ ( x , y ) ] ; M 2 = exp [ i ϕ ] ; ϕ ( x , y ) = ( 3 x y 2 + x 3 ) / a 3 .
M 1 ( x Δ , y ) M 2 ( x + Δ , y ) = exp [ i 6 ( x 2 + y 2 ) Δ / a 3 i 2 ( Δ / a ) 3 ] ; 1 / f = 6 λ Δ / π a 3 .

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