Abstract

An analysis is presented of the intensity variations in the Fourier transform plane resulting from the use of a bilevel random phase mask for holographic data recording as suggested by Burckhardt. To maintain a fixed ratio of peak intensities between in-phase amplitude components and out-of-phase components for an imperfect phase mask, the permissible error in the phase shift varies as 1/N, where N is the number of apertures in the data mask. A factor of 212 reduction in the rms intensity fluctuations in both the Fourier transform plane where the hologram is recorded and in the retrieved image may be obtained by using four levels of phase shift. No further improvement is obtained with additional levels.

© 1972 Optical Society of America

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References

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  1. C. B. Burckhardt, Appl. Opt. 9, 695 (1970).
    [CrossRef] [PubMed]
  2. J. P. Waters, J. Opt. Soc. Am. 58, 1284 (1968).
    [CrossRef]
  3. L. B. Leselm, P. M. Hirsch, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
    [CrossRef]
  4. Y. Takeda, Y. Oshida, Y. Miyamura, IEEE/OSA Conf. on Laser Engineering and Applications (Washington, 2–4 June 1971) [(digest) IEEE J. Quantum Electron. QE-7, 311 (1971)].

1970 (1)

1969 (1)

L. B. Leselm, P. M. Hirsch, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

1968 (1)

Burckhardt, C. B.

Hirsch, P. M.

L. B. Leselm, P. M. Hirsch, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Jordon, J. A.

L. B. Leselm, P. M. Hirsch, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Leselm, L. B.

L. B. Leselm, P. M. Hirsch, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

Miyamura, Y.

Y. Takeda, Y. Oshida, Y. Miyamura, IEEE/OSA Conf. on Laser Engineering and Applications (Washington, 2–4 June 1971) [(digest) IEEE J. Quantum Electron. QE-7, 311 (1971)].

Oshida, Y.

Y. Takeda, Y. Oshida, Y. Miyamura, IEEE/OSA Conf. on Laser Engineering and Applications (Washington, 2–4 June 1971) [(digest) IEEE J. Quantum Electron. QE-7, 311 (1971)].

Takeda, Y.

Y. Takeda, Y. Oshida, Y. Miyamura, IEEE/OSA Conf. on Laser Engineering and Applications (Washington, 2–4 June 1971) [(digest) IEEE J. Quantum Electron. QE-7, 311 (1971)].

Waters, J. P.

Appl. Opt. (1)

IBM J. Res. Dev. (1)

L. B. Leselm, P. M. Hirsch, J. A. Jordon, IBM J. Res. Dev. 13, 150 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (1)

Y. Takeda, Y. Oshida, Y. Miyamura, IEEE/OSA Conf. on Laser Engineering and Applications (Washington, 2–4 June 1971) [(digest) IEEE J. Quantum Electron. QE-7, 311 (1971)].

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Figures (3)

Fig. 1
Fig. 1

(a) Perfect 0–π random phase component of imperfect random phase data mask and (b) π/2 equiphase component of imperfect random phase data mask.

Fig. 2
Fig. 2

(a) Autocorrelation function of perfect 0–π random phase data mask and (b) Fourier transform of this autocorrelation function.

Fig. 3
Fig. 3

(a) Autocorrelation function of equiphase component of random phase data mask and (b) its Fourier transform.

Tables (2)

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Table I Central Spot Intensity Probabilities for a Two-Level Random Phase Data Mask

Tables Icon

Table II Central Spot Intensity Probabilities for a Four-Level Random Phase Data Mask

Equations (21)

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R = N sin 2 ( δ / 2 ) / cos 2 ( δ / 2 ) .
p ( n ) = C n 4 ( 1 2 ) 4 n ( 1 2 ) n = 4 ! ( 1 2 ) 4 / n ! ( 4 n ) ! .
A k = j = 1 N a j exp ( i ϕ k j )
I k = | A k | 2 = j = 1 N l = 1 N a j a l * exp [ i ( ϕ k j ϕ k l ) ] .
I = j = 1 N | a j | 2 ,
I k 2 = j = 1 N l = 1 N m = 1 N n = 1 N a j a l * a m a n * × exp [ i ( ϕ k j ϕ k l + ϕ k m ϕ k n ) ] .
I 2 = S 1 + S 2 + S 3 ( 2 levels ) = S 1 + S 2 ( > 2 levels ) ,
S 1 = j = 1 N l = 1 N | a j | 2 | a l | 2 ,
S 2 = j = 1 N l = 1 l j N | a j | 2 | a l | 2 ,
S 3 = j = 1 N l = 1 l j N a j a j a l * a l * .
I ˜ 2 = I 2 I 2 ,
I 2 = S 1 ,
I ˜ 2 / I 2 = ( S 2 + S 3 ) / S 1 ; ( 2 levels ) = S 2 / S 1 ( > 2 levels ) .
t k ( x ) = j = 1 N rect [ ( x j L ) / d ] exp ( i ϕ k j ) ,
A k ( ξ ) = j = 1 N exp ( i ϕ k j ) exp ( i 2 π L ξ j ) d sin ( π ξ d ) / π ξ d ,
A k ( ξ ) = j = 1 N exp ( i ϕ k j ) exp ( i 2 π L ξ j ) .
I k ( ξ ) = j = 1 N l = 1 N exp [ i 2 π L ξ ( j l ) ] exp [ i ( ϕ k j ϕ k l ) ] ,
I k 2 ( ξ ) = j = 1 N l = 1 N m = 1 N n = 1 N exp [ i 2 π L ξ ( j l + m n ) ] × exp [ i ( ϕ k j ϕ k l + ϕ k m ϕ k n ) ] .
I ( ξ ) = N ,
I ˜ 2 ( ξ = 0 , ± p / 2 L ) / I ˜ ( ξ = 0 , ± p / 2 L ) 2 = 2 ( 1 N 1 ) ( 2 levels )
= ( 1 N 1 ) ( > 2 levels ) .

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