Abstract

The cross talk for image plane holograms is calculated and compared with previously derived results for Fourier plane holograms. Image plane storage is found to have significantly smaller cross talk.

© 1994 Optical Society of America

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References

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  1. C. Gu, J. Hong, I. McMichael, R. Saxena, F. H. Mok, J. Opt. Soc. Am. A 9, 1978 (1992).
    [CrossRef]
  2. K. Curtis, C. Gu, D. Psaltis, Opt. Lett. 18, 1001 (1993).
    [CrossRef] [PubMed]
  3. A. Yariv, Opt. Lett. 18, 652 (1993).
    [CrossRef] [PubMed]

1993

1992

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Figures (5)

Fig. 1
Fig. 1

Recording and readout geometry for angle multiplexing.

Fig. 2
Fig. 2

NSR versus position on the output plane for angle-multiplexed Fourier plane (the valley-shaped curve) and image plane (flat plane) holograms.

Fig. 3
Fig. 3

SNR versus hologram number (i) for angle-multiplexing case.

Fig. 4
Fig. 4

NSR versus position on the output plane for wavelength-multiplexed Fourier plane (the bowl-shaped curve) and image plane (flat plane) holograms.

Fig. 5
Fig. 5

Worst-case SNR for Fourier plane and image plane holograms versus total number of holograms stored.

Equations (6)

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E ( x 2 , y 2 ) m = - M M - 1 F m ( - x 2 λ F 3 - Δ K m i x 2 π , - y 2 λ F 3 - Δ K m i y 2 π ) × sinc { t 2 π [ Δ K m i z + 1 F ( Δ K m i x x 2 + Δ K m i y y 2 ) + λ 4 π ( Δ K m i x 2 + Δ K m i y 2 ) ] } ,
E ( x 3 , y 3 ) m = - M M - 1 d x 2 d y 2 ( d x d y f m ( x , y ) × exp { - i 2 π [ - x 2 λ F x + ( - y 2 λ F - Δ K m i 2 π ) y ] } ) × sinc [ t λ f ( y i - y m ) + t y 2 2 λ f 3 ( y m 2 - y i 2 ) ] × exp ( - i 2 π x 3 x 2 λ F ) exp ( - i 2 π y 3 y 2 λ F ) .
E ( x 3 , y 3 ) m = - M M - 1 1 A exp ( - i 2 π y 3 B A ) - A / 2 - y 3 / A A / 2 - y 3 / A × d y f m ( x 3 , y ) exp [ i 2 π ( B A + Δ K m i 2 π ) y ] ,
NSR = m i sinc 2 [ t λ f ( y i - y m ) + π t 4 λ f 4 ( y m 2 - y i 2 ) 2 ] .
E ( x 2 , y 2 ) m = - M M - 1 F m ( - x 2 λ i F , - y 2 λ i F ) × sinc [ - 2 t ( 1 λ m - 1 λ i ) + t ( x 2 2 + y 2 2 ) 2 F 2 ( λ m λ i 2 - 1 λ i ) ] .
I i ( x 3 , y 3 ) m = - M M - 1 | d w x d w y × sinc [ - 2 t ( 1 λ m - 1 λ i ) + t ( λ m - λ i ) ( w x 2 + w y 2 ) ] | 2 ,

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