Abstract

A method is described whereby the focal distance of a lens can be varied digitally using electrooptics or other means without changing the magnification or spot size. The device is limited to lenses with half-angles less than 15°. Pairs of polarization switches and passive birefringent elements are used. A total of 2N equally spaced focal positions can be achieved with N switches. If a total length L of birefringent material (indices of refraction n and n + Δn) is used, the total shift in focal distance can be as high as LΔn/n2. A ten-stage (1024-position) device falls within the limitations set by material and depth-of-field considerations. The shift in focal distance can be magnified optically to arbitrary distances, but the image or spot size is also magnified in the process. Several practical applications of this device are discussed.

© 1967 Optical Society of America

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References

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  1. W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Develop. 8, 64 (1964).
    [CrossRef]
  2. T. J. Nelson, Bell System Tech. J. 43, 821 (1964).
  3. E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).

1964 (2)

W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Develop. 8, 64 (1964).
[CrossRef]

T. J. Nelson, Bell System Tech. J. 43, 821 (1964).

1951 (1)

E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).

Harris, T. J.

W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Develop. 8, 64 (1964).
[CrossRef]

Kosanke, K.

W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Develop. 8, 64 (1964).
[CrossRef]

Kulcke, W.

W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Develop. 8, 64 (1964).
[CrossRef]

Max, E.

W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Develop. 8, 64 (1964).
[CrossRef]

Nelson, T. J.

T. J. Nelson, Bell System Tech. J. 43, 821 (1964).

Wolf, E.

E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).

Bell System Tech. J. (1)

T. J. Nelson, Bell System Tech. J. 43, 821 (1964).

IBM J. Res. Develop. (1)

W. Kulcke, T. J. Harris, K. Kosanke, E. Max, IBM J. Res. Develop. 8, 64 (1964).
[CrossRef]

Proc. Roy. Soc. (London) (1)

E. Wolf, Proc. Roy. Soc. (London) A204, 533 (1951).

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Figures (3)

Fig. 1
Fig. 1

Passage of light through a dielectric slab.

Fig. 2
Fig. 2

A two-stage (four-position) depth controller using electrooptical switching.

Fig. 3
Fig. 3

Auxiliary lens to magnify the depth changes.

Equations (13)

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F = h cot θ - L cot θ tan ϕ .
Δ F = L ( n Δ n / n 2 - sin 2 θ ) ( 1 - sin 2 θ / n 2 - sin 2 θ ) ½ .
Δ F = L ( Δ n / n 2 ) .
l n = n n - 1 l 1 .
l 1 = L / ( 2 N - 1 ) .
Δ L m = m l 1 Δ n / n 2 ,
u = k ( N A ) 2 Z
v = k ( N A ) r ,
3 = k ( N A ) 2 d 0
d 0 = 3 / k ( N A ) 2 .
Δ L = L Δ n / n 2 .
D = ( α / α - 1 ) f .
Δ α = - ( Δ L ) / f .

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