Abstract

A new type of computer-generated hologram (CGH) is described in this research. Upon the base of a two-channel CGH, it can generate four independent images in four different directions with the addition of positive or negative quadratic phase factors on the object spectrum; it has the character of self-focus. Results of the experiment are provided.

© 1997 Optical Society of America

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References

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  1. B. R. Brown, A. W. Lohman, “Complex spatial filter with binary mask,” Appl. Opt. 5, 967–969 (1966).
    [CrossRef] [PubMed]
  2. A. W. Lohman, D. P. Paris, “Binary Fraunhofer holograms generated by computer,” Appl. Opt. 6, 1739–1749 (1967).
    [CrossRef]
  3. W.-H. Lee, “Binary computer-generated holograms,” Appl. Opt. 18, 3661–3669 (1979).
    [CrossRef] [PubMed]
  4. D. Mendlovic, I. Kiryuschev, “Two-channel computer-generated hologram and its application for optical correlation,” Opt. Commun. 116, 322–325 (1995).
    [CrossRef]

1995 (1)

D. Mendlovic, I. Kiryuschev, “Two-channel computer-generated hologram and its application for optical correlation,” Opt. Commun. 116, 322–325 (1995).
[CrossRef]

1979 (1)

1967 (1)

1966 (1)

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Figures (4)

Fig. 1
Fig. 1

Sample unit of CGH.

Fig. 2
Fig. 2

Setup for reconstructing four-channel self-focus CGH. Input illumination is coherent and collimated.

Fig. 3
Fig. 3

Part of CGH, magnified 80 times.

Fig. 4
Fig. 4

Result of experiment. Images of four objects are reconstructed in four different directions.

Equations (12)

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ηmnμ=Pmnμ+Wmnμ/2,ξmnμ=Pmnμ-Wmnμ/2,ηmnν=Pmnν+Wmnν/2,ξmnν=Pmnν-Wmnν/2,
Hμ, ν=mnrectμ-m+ηmnμδda×rectν-n+ηmnνδda+rectν-m+ηmnμδdarectν-n+ξmnνδda+rectν-m+ξmnμδdarectν-n+ηmnνδda+rectν-m+ξmnμδdarectν-n+ξmnνδda.
hx, y=F-1Hμ, ν=mnexpj2πδdλfxηmnμ+yηmnν+expj2πδdλfxηmnμ+yξmnν+expj2πδdλfxξmnμ+yηmnν+expj2πδdλfxξmnν+yξmnν×sincax sincay×expj2πδdλfxm+yn,
x1δdλf=1,  y1δdλf=1.
h+1,0x, y=mncos πWmnμ expj2πPmnμ×expj2πδdλfxm+ynx=x-x1,h-1,0x, y=mncos πWmnμ exp-j2πPmnμ×expj2πδdλfxm+ynx=x+x1,h0,+1x, y=mncos πWmnν expj2πPmnμ×expj2πδdλfxm+yny=y-y1,h0,-1x, y=mncos πWmnν exp-j2πPmnν×expj2πδdλfxm+yny=y+y1,
H+1,0=mncos πWmnμ expj2πPmnμ,H-1,0=mncos πWmnμ exp-j2πPmnμ,H0,+1=mncos πWmnν expj2πPmnν,H0,-1=mncos πWmnν exp-j2πPmnν.
h+1.0=F-1H+1.0, h-1.0=F-1H-1.0,  h0,+1=F-1H0,+1, h0.1=F-1H0,-1.
Fxmδd, nδd=mnAmnx expjΦmnX,  Fymδd, nδd=mnAmny expjΦmny,
Amnx=cos πWmnμ, Φmnx=2πPmnμ  Amny=cos πWmnν, Φmny=2πPmnν.
mnAmnX+1 expjΦmnX+1, mnAmnX-1 expjΦmnX-1,  mnAmnY+1 expjΦmnY+1, mnAmnY-1 expjΦmnY-1.
Fxmδd, nδd=mnAmnX+1 expjΦmnX+1×exp-jπλfm2+n2δd2+AmnX-1 exp-jΦmnX-1×expjπλfm2+n2δd2.
Fymδd, nδd=mnAmnY+1 expjΦmnY+1×exp-jπλfm2+n2δd2+AmnY-1 exp-jΦmnY-1×expjπλfm2+n2δd2.

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