Abstract

A method of encoding multiple asymmetric symbols into a single thin binary Fourier hologram is presented. It assumes a combination of a spatial segmentation and carrier frequencies in order to achieve multiple reconstructed images selectable by the angle of the incident laser beam. The proper segmentation function with an optimized period allows us to encode a number of different objects with little loss of reconstruction quality. A special sequence of phase encoding steps and a binarization enable recording of asymmetric symbols into a binary hologram. The description of the design procedure is given, followed by the experimental results confirming the conclusions conceived from numerical simulations. The method can be used practically for the design of simple translucent holographic head-up displays.

© 2009 Optical Society of America

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References

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  1. G. C. Larsen and T. S. Gleghorn, “Hologram methods for signature security consolidated content and an accelerometer,” U.S. patent application 2007/0127096 A1 (7 June 2007).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  5. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).
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    [CrossRef]
  9. A. Ramsbottom, S. Sergeant, and D. Sheel, “Holography for automotive head-up-displays,” Proc. SPIE 1667, 146-164(1992).
    [CrossRef]
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    [CrossRef]
  11. www.holosight.com.
  12. “Lightweight holographic sight,” U.S. patent 6,490,060(3 December 2002).

1996 (1)

T. Matsumoto, S. Eguchi, F. Yamagishi, and M. Nakashima, “Compact holographic head-up display,” Proc. SPIE 2652, 341-344 (1996).
[CrossRef]

1993 (1)

1992 (1)

A. Ramsbottom, S. Sergeant, and D. Sheel, “Holography for automotive head-up-displays,” Proc. SPIE 1667, 146-164(1992).
[CrossRef]

1990 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

1971 (1)

J. W. Goodman, “Holography,” Proc. SPIE 59, 1292-1304(1971).

1970 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2947 (1969).

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Curran, R. K.

Eguchi, S.

T. Matsumoto, S. Eguchi, F. Yamagishi, and M. Nakashima, “Compact holographic head-up display,” Proc. SPIE 2652, 341-344 (1996).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Gleghorn, T. S.

G. C. Larsen and T. S. Gleghorn, “Hologram methods for signature security consolidated content and an accelerometer,” U.S. patent application 2007/0127096 A1 (7 June 2007).

Goodman, J. W.

J. W. Goodman, “Holography,” Proc. SPIE 59, 1292-1304(1971).

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2947 (1969).

Larsen, G. C.

G. C. Larsen and T. S. Gleghorn, “Hologram methods for signature security consolidated content and an accelerometer,” U.S. patent application 2007/0127096 A1 (7 June 2007).

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Matsumoto, T.

T. Matsumoto, S. Eguchi, F. Yamagishi, and M. Nakashima, “Compact holographic head-up display,” Proc. SPIE 2652, 341-344 (1996).
[CrossRef]

Mok, F. H.

Nakashima, M.

T. Matsumoto, S. Eguchi, F. Yamagishi, and M. Nakashima, “Compact holographic head-up display,” Proc. SPIE 2652, 341-344 (1996).
[CrossRef]

Ramsbottom, A.

A. Ramsbottom, S. Sergeant, and D. Sheel, “Holography for automotive head-up-displays,” Proc. SPIE 1667, 146-164(1992).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Sergeant, S.

A. Ramsbottom, S. Sergeant, and D. Sheel, “Holography for automotive head-up-displays,” Proc. SPIE 1667, 146-164(1992).
[CrossRef]

Shankoff, T. A.

Sheel, D.

A. Ramsbottom, S. Sergeant, and D. Sheel, “Holography for automotive head-up-displays,” Proc. SPIE 1667, 146-164(1992).
[CrossRef]

Wyrowski, F.

Yamagishi, F.

T. Matsumoto, S. Eguchi, F. Yamagishi, and M. Nakashima, “Compact holographic head-up display,” Proc. SPIE 2652, 341-344 (1996).
[CrossRef]

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909-2947 (1969).

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

Opt. Lett. (1)

Optik (Jena) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Jena) 35, 237-246 (1972).

Proc. SPIE (3)

J. W. Goodman, “Holography,” Proc. SPIE 59, 1292-1304(1971).

A. Ramsbottom, S. Sergeant, and D. Sheel, “Holography for automotive head-up-displays,” Proc. SPIE 1667, 146-164(1992).
[CrossRef]

T. Matsumoto, S. Eguchi, F. Yamagishi, and M. Nakashima, “Compact holographic head-up display,” Proc. SPIE 2652, 341-344 (1996).
[CrossRef]

Other (4)

www.holosight.com.

“Lightweight holographic sight,” U.S. patent 6,490,060(3 December 2002).

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

G. C. Larsen and T. S. Gleghorn, “Hologram methods for signature security consolidated content and an accelerometer,” U.S. patent application 2007/0127096 A1 (7 June 2007).

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Figures (7)

Fig. 1
Fig. 1

Symbols encoded in the hologram.

Fig. 2
Fig. 2

Improvement in the quality of a numerical reconstruction against the number of iterations of the Gerchberg–Saxton algorithm: (a) after 1 iteration, (b) after 10 iterations, (c) after 100 iterations.

Fig. 3
Fig. 3

Ghost images caused by the segmentation function: (a)  a = b = 0 , 1 mm ; (b)  a = b = 1 mm .

Fig. 4
Fig. 4

Method of distributing six subhologams on the surface of the final hologram: (a) input images, (b) iterated phase distributions, (c) mosaic mask defined by shifted functions f ( x , y ) from Eq. (1), (d) masked phase distributions, (e) sum of the masked phase distributions—the final hologram. Images are magnified, and three are omitted for clarity.

Fig. 5
Fig. 5

Optical reconstruction of multiple symbols in the Fourier configuration.

Fig. 6
Fig. 6

Optical reconstruction setup with a variable angle of incidence of the plane wave. The angle of incidence is marked as α.

Fig. 7
Fig. 7

Results of the optical reconstruction of the six encoded symbols.

Tables (2)

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Table 1 Periods and Orientations of the Sawtooth Diffractive Gratings Used

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Table 2 Influence of the Array Size and the Size of an Elementary Square (a) on the Diffractive Efficiency of a “Gas Station” Subhologam

Equations (2)

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f ( x , y ) = [ rect ( x / a ) × rect ( y / b ) ] [ comb ( x / M a ) × comb ( y / N b ) ] ,
F { h ( x ) × f ( x ) } = F { h ( x ) × [ rect ( x / a ) comb ( x / M a ) ] } = M a 2 H ( ν x ) [ comb ( M a ν x ) × sinc ( a ν x ) ] ,

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