Abstract

In a holographic page-oriented memory the information is stored in an array of holograms. It is advantageous to record the Fourier transform of the original data mask because the minimum space bandwidth is then required and the information about any one data bit is spread over the hologram plane. In the Fourier transform plane most of the light is concentrated in an array of bright “spikes” because the data mask consists of an array of equidistant data spots. Some means is needed to distribute the light more evenly. We report here on the use of a phase mask which imparts a phase shift of 180° to half the data spots chosen at random. An analysis shows that the intensity in the Fourier transform plane is now proportional to the intensity of the Fourier transform of one single data spot.

© 1970 Optical Society of America

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References

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  1. F. M. Smits, L. E. Gallagher, Bell System Tech. J. 46, 1267 (1967).
  2. L. H. Lin, H. L. Beauchamp, Bell Telephone Laboratories; unpublished work.
  3. S. O. Rice, Bell System Tech. J. 23, 282 (July1944).
  4. R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Book Company, New York, 1965).
  5. Considerations analogous to the ones just made also show that our phase mask has the same effect as a phase mask where the phase in each square has a constant random value, uniformly distributed between 0° and 360°.
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Company, New York, 1968).
  7. “Applications Data for Kodak Photosensitive Resists,” Kodak Publication P-91.
  8. C. B. Burckhardt, E. T. Doherty, Appl. Opt. 9 (1970).
    [CrossRef]
  9. J. T. LaMacchia, C. J. Vincelette, Bell Telephone Laboratories; unpublished work.
  10. It might be thought that it is possible to form near Fourier transform holograms by illuminating the lens with a collimated beam and moving the photographic plate toward the lens. A little reflection will show that this is not possible because in that case the hologram will not remain centered within the aperture upon translation of the lens and aperture

1970 (1)

C. B. Burckhardt, E. T. Doherty, Appl. Opt. 9 (1970).
[CrossRef]

1967 (1)

F. M. Smits, L. E. Gallagher, Bell System Tech. J. 46, 1267 (1967).

1944 (1)

S. O. Rice, Bell System Tech. J. 23, 282 (July1944).

Beauchamp, H. L.

L. H. Lin, H. L. Beauchamp, Bell Telephone Laboratories; unpublished work.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Book Company, New York, 1965).

Burckhardt, C. B.

C. B. Burckhardt, E. T. Doherty, Appl. Opt. 9 (1970).
[CrossRef]

Doherty, E. T.

C. B. Burckhardt, E. T. Doherty, Appl. Opt. 9 (1970).
[CrossRef]

Gallagher, L. E.

F. M. Smits, L. E. Gallagher, Bell System Tech. J. 46, 1267 (1967).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Company, New York, 1968).

LaMacchia, J. T.

J. T. LaMacchia, C. J. Vincelette, Bell Telephone Laboratories; unpublished work.

Lin, L. H.

L. H. Lin, H. L. Beauchamp, Bell Telephone Laboratories; unpublished work.

Rice, S. O.

S. O. Rice, Bell System Tech. J. 23, 282 (July1944).

Smits, F. M.

F. M. Smits, L. E. Gallagher, Bell System Tech. J. 46, 1267 (1967).

Vincelette, C. J.

J. T. LaMacchia, C. J. Vincelette, Bell Telephone Laboratories; unpublished work.

Appl. Opt. (1)

C. B. Burckhardt, E. T. Doherty, Appl. Opt. 9 (1970).
[CrossRef]

Bell System Tech. J. (2)

F. M. Smits, L. E. Gallagher, Bell System Tech. J. 46, 1267 (1967).

S. O. Rice, Bell System Tech. J. 23, 282 (July1944).

Other (7)

R. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill Book Company, New York, 1965).

Considerations analogous to the ones just made also show that our phase mask has the same effect as a phase mask where the phase in each square has a constant random value, uniformly distributed between 0° and 360°.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill Book Company, New York, 1968).

“Applications Data for Kodak Photosensitive Resists,” Kodak Publication P-91.

L. H. Lin, H. L. Beauchamp, Bell Telephone Laboratories; unpublished work.

J. T. LaMacchia, C. J. Vincelette, Bell Telephone Laboratories; unpublished work.

It might be thought that it is possible to form near Fourier transform holograms by illuminating the lens with a collimated beam and moving the photographic plate toward the lens. A little reflection will show that this is not possible because in that case the hologram will not remain centered within the aperture upon translation of the lens and aperture

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Figures (11)

Fig. 1
Fig. 1

Recording of holograms in the exact Fourier transform plane.

Fig. 2
Fig. 2

Portion of the phase mask.

Fig. 3
Fig. 3

Phase mask and data mask superposed.

Fig. 4
Fig. 4

Previous recording method where the hologram is recorded without the use of a phase mask and a small distance away from the exact Fourier transform plane.

Fig. 5
Fig. 5

Photograph of the intensity in the Fourier transform plane. In order to show the outer ring the central area was overexposed.

Fig. 6
Fig. 6

Decomposition of phasors with an inaccurate phase shift.

Fig. 7
Fig. 7

Arrangement for the alignment of the phase mask and data mask.

Fig. 8
Fig. 8

Intensity distribution in the Fourier transform plane.

Fig. 9
Fig. 9

Image of the data mask–phase mask combination formed in the arrangement of Fig. 7.

Fig. 10
Fig. 10

Photograph of a reconstruction with an efficiency of 11%.

Fig. 11
Fig. 11

Hologram writer.

Equations (9)

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A ( ξ , η ) = + + a ( x 1 , y 1 ) exp ( 2 π i ξ x 1 ) exp ( 2 π i η y 1 ) d x 1 d y 1 .
ξ = x 2 / λ d ,
η = y 2 / λ d .
I ( ξ , η ) = A ( ξ , η ) A * ( ξ , η ) .
r ( x 1 , y 1 ) = + + a * ( u , υ ) a ( u + x 1 , υ + y 1 ) d u d υ .
I ( ξ , η ) = { 2 [ J 1 ( π b ν ) / π b ν ] } . 2
| a 1 | = | b 1 | = | a | cos ( δ / 2 ) ,
| a 2 | = | b 2 | = | a | sin ( δ / 2 ) .
P 2 = P sin 2 ( δ / 2 ) ,

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