Abstract

A method is described in which arbitrary images are formed via Fresnel diffraction. In this method, a multifacet hologram is used to deflect small square areas of light from a given spatial location in the input plane to an arbitrarily prescribed location in the output plane, producing an image composed of small square patches of light. Five different variations of multifaceted holography are presented. Volume phase holograms are used in the deflection process resulting in nearly 100% efficiency.

© 1983 Optical Society of America

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References

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  1. W.-H. Lee, in Progress in Optics, Vol. 16, E. Wolf, Ed. (North-Holland, Amsterdam, 1978), Chap. 3.
    [CrossRef]
  2. W. J. Dallas, in The Computer in Optics Research, B. R. Frieden, Ed. (Springer, New York, 1980), Chap. 6.
  3. It has been shown that the efficiency of a CGH can be improved by copying the bandpass filtered output of a CGH to form a volume phase hologram in a material such as dichromated gelatin,H. O. Bartelt, S. K. Case, Appl. Opt. 21, 2886 (1982).
    [CrossRef] [PubMed]
  4. L. B. Lesem, P. M. Hirsh, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  5. D. C. Chu, J. R. Fienup, J. W. Goodman, Appl. Opt. 12, 1386 (1973).
    [CrossRef] [PubMed]
  6. S. K. Case, P. R. Haugen, O. J. Loekberg, Appl. Opt. 20, 2670 (1981).
    [CrossRef] [PubMed]
  7. S. K. Case, P. R. Haugen, Opt. Eng. 21, 352 (1982).
    [CrossRef]
  8. H. O. Bartelt, S. K. Case, Opt. Eng. 22, 497 (1983). In this paper, a calculation of the possible space–bandwidth product for our multifacet hologram method is given.
    [CrossRef]
  9. R. E. Haskell, Opt. Eng. 14, 195 (1975).
    [CrossRef]
  10. S. K. Case, “Multiple Exposure Holography in Volume Materials,” Ph.D. Thesis, U. Michigan (1976) (Xerox University Microfilma 76-27461).
  11. B. J. Chang, C. D. Leonard, Appl. Opt. 18, 2407 (1979).
    [CrossRef] [PubMed]

1983

H. O. Bartelt, S. K. Case, Opt. Eng. 22, 497 (1983). In this paper, a calculation of the possible space–bandwidth product for our multifacet hologram method is given.
[CrossRef]

1982

1981

1979

1975

R. E. Haskell, Opt. Eng. 14, 195 (1975).
[CrossRef]

1973

1969

L. B. Lesem, P. M. Hirsh, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Bartelt, H. O.

Case, S. K.

H. O. Bartelt, S. K. Case, Opt. Eng. 22, 497 (1983). In this paper, a calculation of the possible space–bandwidth product for our multifacet hologram method is given.
[CrossRef]

It has been shown that the efficiency of a CGH can be improved by copying the bandpass filtered output of a CGH to form a volume phase hologram in a material such as dichromated gelatin,H. O. Bartelt, S. K. Case, Appl. Opt. 21, 2886 (1982).
[CrossRef] [PubMed]

S. K. Case, P. R. Haugen, Opt. Eng. 21, 352 (1982).
[CrossRef]

S. K. Case, P. R. Haugen, O. J. Loekberg, Appl. Opt. 20, 2670 (1981).
[CrossRef] [PubMed]

S. K. Case, “Multiple Exposure Holography in Volume Materials,” Ph.D. Thesis, U. Michigan (1976) (Xerox University Microfilma 76-27461).

Chang, B. J.

Chu, D. C.

Dallas, W. J.

W. J. Dallas, in The Computer in Optics Research, B. R. Frieden, Ed. (Springer, New York, 1980), Chap. 6.

Fienup, J. R.

Goodman, J. W.

Haskell, R. E.

R. E. Haskell, Opt. Eng. 14, 195 (1975).
[CrossRef]

Haugen, P. R.

Hirsh, P. M.

L. B. Lesem, P. M. Hirsh, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Jordon, J. A.

L. B. Lesem, P. M. Hirsh, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Lee, W.-H.

W.-H. Lee, in Progress in Optics, Vol. 16, E. Wolf, Ed. (North-Holland, Amsterdam, 1978), Chap. 3.
[CrossRef]

Leonard, C. D.

Lesem, L. B.

L. B. Lesem, P. M. Hirsh, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Loekberg, O. J.

Appl. Opt.

IBM J. Res. Dev.

L. B. Lesem, P. M. Hirsh, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Opt. Eng.

S. K. Case, P. R. Haugen, Opt. Eng. 21, 352 (1982).
[CrossRef]

H. O. Bartelt, S. K. Case, Opt. Eng. 22, 497 (1983). In this paper, a calculation of the possible space–bandwidth product for our multifacet hologram method is given.
[CrossRef]

R. E. Haskell, Opt. Eng. 14, 195 (1975).
[CrossRef]

Other

S. K. Case, “Multiple Exposure Holography in Volume Materials,” Ph.D. Thesis, U. Michigan (1976) (Xerox University Microfilma 76-27461).

W.-H. Lee, in Progress in Optics, Vol. 16, E. Wolf, Ed. (North-Holland, Amsterdam, 1978), Chap. 3.
[CrossRef]

W. J. Dallas, in The Computer in Optics Research, B. R. Frieden, Ed. (Springer, New York, 1980), Chap. 6.

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Figures (13)

Fig. 1
Fig. 1

Image formation via multifacet holography.

Fig. 2
Fig. 2

Recording apparatus to produce multifacet holograms.

Fig. 3
Fig. 3

Intensity profile of two pixels placed next to each other recorded with (a) a plane wave object beam and (b) a slightly expanding object beam.

Fig. 4
Fig. 4

(a) Hologram recorded in Kodak 649-F and (b) resulting image from the hologram recorded in dichromated gelatin.

Fig. 5
Fig. 5

Redistribution of light from multifacet hologram.

Fig. 6
Fig. 6

Characters produced by multiexposure single-facet holograms.

Fig. 7
Fig. 7

Principle of duplex image formation with one image in the zero order and one image in the first order.

Fig. 8
Fig. 8

Zero order and first order from duplex hologram of the type shown in Fig. 7.

Fig. 9
Fig. 9

Principle of a hologram used to produce images in two different planes.

Fig. 10
Fig. 10

Redistribution of light from 67-facet hologram made to produce two images in two different planes.

Fig. 11
Fig. 11

(a) Histogram of number of facets per intensity for an arbitrary picture and (b) histogram of a picture matched to a Gaussian intensity distribution.

Fig. 12
Fig. 12

(a) Original image; (b) reduced resolution image; (c) image after histogram redistribution; (d) actual gray level image from hologram.

Fig. 13
Fig. 13

Gray level image of an airplane.

Equations (5)

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U ( x 0 ) = exp ( j k z ) j λ z e [ j k 2 z ( x 0 x 1 ) 2 ] d x 1 ,
Δ x = ν ( λ z 2 ) 1 / 2 ,
I = I 0 exp ( k 1 r 2 ) ,
I = I 0 exp ( k 3 N 2 ) ; k 3 = ( k 1 ) / ( k 2 2 ) .
N = k 3 ln ( I / I 0 ) ,

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