Abstract

A technique for accurately figuring very thin, lightweight lenses is discussed. The phase change required to focus a plane wave into a point is calculated and photographically plotted with exposure proportional to phase (scaled from 0 to 2π). The plot is photoreduced and the photoreduction is etched, with the depth of etch approximately proportional to the exposure. The result is a kinoform lens. Photographs taken with a kinoform lens are included.

© 1970 Optical Society of America

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References

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  1. L. B. Lesem, P. M. Hirsch, J. A. Jordan, IBM J. Res. Develop. 13, 150 (1969).
    [CrossRef]
  2. K. Miyamoto, J. Opt. Soc. Amer. 51, 17 (1961).
    [CrossRef]
  3. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), p. 151.
  4. We are indebted to P. Kruythoff for clarification of this idea.
  5. A. Lohmann, UCSD; private communication.
  6. J. Tsujiuchi, U.S. Patent3,045,530 (U.S. Government Printing Office, Washington, D.C., 1962).
  7. J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, IBM Publication 320.2351 (1968).
  8. J. Camus, F. Girard, R. Clark, Appl. Opt. 6, 1433 (1967).
    [CrossRef] [PubMed]

1969 (1)

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

1967 (1)

1961 (1)

K. Miyamoto, J. Opt. Soc. Amer. 51, 17 (1961).
[CrossRef]

Camus, J.

Clark, R.

Girard, F.

Hirsch, P. M.

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

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, IBM Publication 320.2351 (1968).

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), p. 151.

Jordan, J. A.

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

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, IBM Publication 320.2351 (1968).

Lesem, L. B.

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

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, IBM Publication 320.2351 (1968).

Lohmann, A.

A. Lohmann, UCSD; private communication.

Miyamoto, K.

K. Miyamoto, J. Opt. Soc. Amer. 51, 17 (1961).
[CrossRef]

Tsujiuchi, J.

J. Tsujiuchi, U.S. Patent3,045,530 (U.S. Government Printing Office, Washington, D.C., 1962).

Van Rooy, D. L.

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, IBM Publication 320.2351 (1968).

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), p. 151.

Appl. Opt. (1)

IBM J. Res. Develop. (1)

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

J. Opt. Soc. Amer. (1)

K. Miyamoto, J. Opt. Soc. Amer. 51, 17 (1961).
[CrossRef]

Other (5)

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1950), p. 151.

We are indebted to P. Kruythoff for clarification of this idea.

A. Lohmann, UCSD; private communication.

J. Tsujiuchi, U.S. Patent3,045,530 (U.S. Government Printing Office, Washington, D.C., 1962).

J. A. Jordan, P. M. Hirsch, L. B. Lesem, D. L. Van Rooy, IBM Publication 320.2351 (1968).

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Figures (12)

Fig. 1
Fig. 1

Photographic plot of the phase retardation required for a kinoform lens. This plot can be photoreduced and the photoreduction bleached to form a lens.

Fig. 2
Fig. 2

Pattern projected from a kinoform in 6328-Å light. This picture was taken on Kodak Tri-X film using an f/15 kinoform lens. The exposure time was 1 10 sec. Cause of the noise in this image is primarily scattering from imperfections in the bleached emulsion.

Fig. 3
Fig. 3

Pattern shown in Fig. 2, taken in the same camera, using a Goerz Artar lens stopped to f/15. The exposure time was 1 10 sec on Kodak Tri-X film.

Fig. 4
Fig. 4

Scene taken using a f/15 kinoform lens. This picture was taken on Polaroid color film. The color prints exhibit considerable chromatic abberration.

Fig. 5
Fig. 5

Geometry of the calculation of the phase of a wavefront at the plane z = 0. The spherical wave emerging from the z = 0 plane is assumed to focus at the image point (0, 0, L).

Fig. 6
Fig. 6

Cross section of the relief on a kinoform lens showing the first few zones out one radius. The depth of etch is the distance dmax.

Fig. 7
Fig. 7

A technique for color correction of kinoform lenses. Rays passing through the annulus at radius R subsequently pass through the region P in the second kinoform lens and are brought to the focus F. Rays passing through the annulus with radius R pass through region P and are also brought to a focus at F. The focal lengths in regions R and P differ from those in regions R and P, respectively.

Fig. 8
Fig. 8

Color correction using a quartz lens and a kinoform lens. The blur circle radius is plotted as a function of Δλ = λ/λ0, where λ0 is the design wavelength, in this case 4000 Å. Two systems are shown. The circles indicate an 80-cm diam f/1.15 system, while the squares indicate an 80-cm diam f/6.8 system. The Rayleigh limits for the two systems are shown as L and L, respectively. For comparison, the blur circle of the uncorrected quartz lens is shown as Q.

Fig. 9
Fig. 9

Maximum spatial frequency required to form a 40-cm diam lens, as a function of focal length. Design wavelength is 1 μ, and it is assumed that four samples are required to adequately represent a zone. The required spatial frequency response is inversely porportional to the design wavelength.

Fig. 10
Fig. 10

Transfer function used in the calculations to simulate a real material.

Fig. 11
Fig. 11

Comparison of the diffraction limited image of a perfect 10-cm focal length f/12.2 lens with the computed image for a kinoform made with the material represented by Fig. 10. The stars are the computed image points, while A is the Airy distribution. The numerical techniques do not include the diffraction limitation. Thus a real kinoform lens would yield an image distribution which is the convolution of the Airy function with the computed image.

Fig. 12
Fig. 12

Photographic plot for a cylindrical lens.

Equations (4)

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ϕ = ( 2 π / λ ) [ ( L 2 + x 2 + y 2 ) 1 2 L ] .
d ( x , y ) = ( d max / 2 π ) ( Δ ϕ mod 2 π ) ,
f = R 2 / 2 N λ ,
s = [ R / λ ( f 2 + R 2 ) 1 2 ] 1 .

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