Abstract

We present what is to our knowledge the first experimental observation of controlled intensity fluctuations of Fresnel holograms of 8 μm × 8 μm pixel size by using a function for calculation of optical phase errors from the pixel area of an aperture of synthetic Fresnel holograms derived without approximation.

© 1996 Optical Society of America

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References

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    [CrossRef]
  2. M. K. McGaugh, C. M. Veber, R. P. Kenan, Appl. Opt. 34, 1562 (1995).
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    [CrossRef] [PubMed]
  4. J. A. Davis, D. M. Cottrell, R. A. Lilly, S. W. Connely, Opt. Lett. 14, 420 (1989).
    [CrossRef] [PubMed]
  5. M. Rossi, R. E. Kunz, Opt. Commun. 112, 258 (1994).
    [CrossRef]
  6. T. Matsumoto, T. Tanji, A. Tonomura, Optik 97, 169 (1994).
  7. J. A. Davis, A. M. Field, D. M. Cottrell, Appl. Opt. 34, 790 (1995).
    [CrossRef] [PubMed]
  8. A. Yoshida, T. Asakura, Opt. Commun. 109, 368 (1994).
    [CrossRef]
  9. R. Silvennoinen, J. Uozumi, T. Asakura, J. Opt. xx, xxx (1995).
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    [CrossRef] [PubMed]
  11. F. S. Roux, Opt. Eng. 33, 2843 (1994).
    [CrossRef]
  12. R. A. Robers, C. T. Mullis, Digital Signal Processing (Addison-Wesley, Reading, Mass., 1987), p. 112.

1995 (3)

1994 (7)

F. S. Roux, Opt. Eng. 33, 2843 (1994).
[CrossRef]

L. N. Hazra, Y. Han, C. Delisle, J. Opt. Soc. Am. A 11, 2750 (1994).
[CrossRef]

M. Rossi, R. E. Kunz, Opt. Commun. 112, 258 (1994).
[CrossRef]

T. Matsumoto, T. Tanji, A. Tonomura, Optik 97, 169 (1994).

A. Yoshida, T. Asakura, Opt. Commun. 109, 368 (1994).
[CrossRef]

D. P. Hamblen, Opt. Lett. 19, 1687 (1994).
[CrossRef] [PubMed]

J. A. Davis, A. M. Field, D. M. Cottrell, Appl. Opt. 33, 8194 (1994).
[CrossRef] [PubMed]

1989 (1)

Asakura, T.

R. Silvennoinen, J. Uozumi, T. Asakura, J. Opt. xx, xxx (1995).

A. Yoshida, T. Asakura, Opt. Commun. 109, 368 (1994).
[CrossRef]

Connely, S. W.

Cottrell, D. M.

Davis, J. A.

Delisle, C.

Field, A. M.

Hamblen, D. P.

Han, Y.

Hazra, L. N.

Kenan, R. P.

Kunz, R. E.

M. Rossi, R. E. Kunz, Opt. Commun. 112, 258 (1994).
[CrossRef]

Lilly, R. A.

Matsumoto, T.

T. Matsumoto, T. Tanji, A. Tonomura, Optik 97, 169 (1994).

McGaugh, M. K.

Mullis, C. T.

R. A. Robers, C. T. Mullis, Digital Signal Processing (Addison-Wesley, Reading, Mass., 1987), p. 112.

Robers, R. A.

R. A. Robers, C. T. Mullis, Digital Signal Processing (Addison-Wesley, Reading, Mass., 1987), p. 112.

Rossi, M.

M. Rossi, R. E. Kunz, Opt. Commun. 112, 258 (1994).
[CrossRef]

Roux, F. S.

F. S. Roux, Opt. Eng. 33, 2843 (1994).
[CrossRef]

Silvennoinen, R.

R. Silvennoinen, J. Uozumi, T. Asakura, J. Opt. xx, xxx (1995).

Tanji, T.

T. Matsumoto, T. Tanji, A. Tonomura, Optik 97, 169 (1994).

Tonomura, A.

T. Matsumoto, T. Tanji, A. Tonomura, Optik 97, 169 (1994).

Uozumi, J.

R. Silvennoinen, J. Uozumi, T. Asakura, J. Opt. xx, xxx (1995).

Veber, C. M.

Yoshida, A.

A. Yoshida, T. Asakura, Opt. Commun. 109, 368 (1994).
[CrossRef]

Appl. Opt. (3)

J. Opt. (1)

R. Silvennoinen, J. Uozumi, T. Asakura, J. Opt. xx, xxx (1995).

J. Opt. Soc. Am. A (1)

Opt. Commun. (2)

A. Yoshida, T. Asakura, Opt. Commun. 109, 368 (1994).
[CrossRef]

M. Rossi, R. E. Kunz, Opt. Commun. 112, 258 (1994).
[CrossRef]

Opt. Eng. (1)

F. S. Roux, Opt. Eng. 33, 2843 (1994).
[CrossRef]

Opt. Lett. (2)

Optik (1)

T. Matsumoto, T. Tanji, A. Tonomura, Optik 97, 169 (1994).

Other (1)

R. A. Robers, C. T. Mullis, Digital Signal Processing (Addison-Wesley, Reading, Mass., 1987), p. 112.

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Figures (4)

Fig. 1
Fig. 1

Geometric setup for the integrated-optical path difference ΔIo and the phase difference Δ from an object point in the O plane to a pixel domain in the H plane.

Fig. 2
Fig. 2

Photos recorded with an optical microscope from the aperture of the binary-phase FH that produces the two off-axis spots on the focal plane: A, 1 mm × 1 mm aperture; B, magnified area from A.

Fig. 3
Fig. 3

Simulated and reconstructed intensity distributions of the off-axis Fresnel lens 24.5 × 103 μm from the element, which is designed to have its spot image located at (900, 0, and 25 × 103 μm) from the midpoint of the element: a, corner point of the pixels; b, pixel phase-error function. The experimental image recorded by the CCD camera is shown in the inset.

Fig. 4
Fig. 4

(a) Simulated tangential intensity distribution of the two bright focal points at (630, 0, and 25 × 103 μm) and (670, 0, and 25 × 103 μm) from the midpoint of the off-axis Fresnel test element: curve a, corner point of the pixels; curve b, pixel phase-error function considered for the 25 × 103 μm image distance; curve c, experimental intensity distribution recorded along the one row of the CCD array through the midpoints of the images of the two point sources. The complete intensity distributions of the point images are shown in the inset in ( b).

Equations (7)

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Δ I o ( x i , y j , ξ , η ) = 1 X H Y H x i x i + 1 y j y j + 1 Δ o ( x , y , x i , y j , ξ , η ) d x d y ,
Δ I o 1 = α x α y R 3 - X H Y H D 3 X H Y H ,
α x = tan - 1 ( x i + X H - ξ D ) - tan - 1 ( x i - ξ D ) ,
α y = tan - 1 ( y i + Y H - η D ) - tan - 1 ( y i - η D ) .
Δ I o 2 = R - R .
Δ I o 3 = α x α y ( R 3 - R 3 ) 3 X H Y H ,
Δ I ϕ = 2 π Δ I o / λ o ,

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