Abstract

Expressions for the quantization error in Hsueh-Sawchuk holograms are presented. These expressions suggest that the Hsueh-Sawchuk algorithm may be improved using a technique called prequantization. We demonstrate that the addition of prequantization reduces the quantization error in Hsueh-Sawchuk holograms by ∼25%.

© 1981 Optical Society of America

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References

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  1. C. K. Hsueh, A. A. Sawchuk, Appl. Opt. 17, 3874 (1978).
    [CrossRef] [PubMed]
  2. N. C. Gallagher, IEEE Trans. Inf. Theory IT-24, 156 (1978).
    [CrossRef]
  3. J. P. Allebach, Appl. Opt. 20, 290 (1981).
    [CrossRef] [PubMed]

1981 (1)

1978 (2)

C. K. Hsueh, A. A. Sawchuk, Appl. Opt. 17, 3874 (1978).
[CrossRef] [PubMed]

N. C. Gallagher, IEEE Trans. Inf. Theory IT-24, 156 (1978).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Inf. Theory (1)

N. C. Gallagher, IEEE Trans. Inf. Theory IT-24, 156 (1978).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Implementation of one cell in a Hsueh-Sawchuk hologram.

Fig. 2
Fig. 2

Comparison of quantization performance for Hsueh-Sawchuk holograms with and without prequantization as a function of input variance.

Fig. 3
Fig. 3

Hsueh-Sawchuk hologram.

Fig. 4
Fig. 4

Prequantized Hsueh-Sawchuk hologram.

Equations (15)

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A exp ( i θ ) = 1 2 exp [ i ( θ + ψ ) ] + 1 2 exp [ i ( θ ψ ) ] ,
ψ = cos 1 A , 0 A 1 .
γ 1 = θ + ψ , γ 2 = θ ψ .
d 1 = γ 1 d / 2 π d 2 = γ 2 d / 2 π
α 1 = γ 1 γ ̂ 1 , α 2 = γ 2 γ ̂ 2 .
α 1 = 2 N n = 1 ( 1 ) n n sin ( n N γ 1 ) , α 2 = 2 N n = 1 ( 1 ) n n sin ( n N γ 2 ) .
θ = 1 2 ( γ 1 + γ 2 ) , ψ = 1 2 ( γ 1 γ 2 ) .
θ ̂ = 1 2 ( γ ̂ 1 + γ ̂ 2 ) , ψ ̂ = 1 2 ( γ ̂ 1 γ ̂ 2 ) ,
e θ = θ θ ̂ , e ψ = ψ ψ ̂ .
 = cos ψ ̂ .
e θ = 1 2 ( α 1 + α 2 ) , e ψ = 1 2 ( α 1 α 2 ) .
e θ = 2 N n = 1 ( 1 ) n n sin ( n N θ ) cos ( n N ψ ) , e ψ = 2 N n = 1 ( 1 ) n n cos ( n N θ ) sin ( n N ψ ) .
E { e ψ 2 } 1 N 2 n = 1 1 n 2 ( 1 + E { cos 2 nN θ } ) .
θ = θ = k π N + π 2 N ,
γ 1 = θ + ψ , γ 2 = θ ψ .

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