Abstract

The random phase shifter method for Fourier transformed holograms is discussed. It is shown that by adopting the random phase shifters of the phase quantization levels beyond 2 (4, for example), the effectiveness becomes about twice that of 2, and that the reduction of the effectiveness by the coincidence between a pattern of the information and a phase shifter can be withdrawn under the probability of 10−10. Hologram memories of information storage density of 105 bits/mm2 and 2.0 × 103 characters/mm2 are demonstrated.

© 1972 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Takeda et al., Proc. of Annual Meeting of Electronic and Communication Engineers of Japan, 777 (1971).
  2. C. B. Burckhardt, Appl. Opt. 9, 695 (1970).
    [CrossRef] [PubMed]
  3. F. Spitzer, Principles of Random Walk (Van Nostrand, Princeton, N.J., 1964).
    [CrossRef]
  4. E. D. Cashwell, C. J. Everett, Monte Carlo Method (Pergamon Press, London, 1959).
  5. Y. Takeda et al., Oyo Butsuri 40, 41 (1971).
  6. L. H. Lin, Appl. Opt. 8, 863 (1969).
    [CrossRef]

1971

Y. Takeda et al., Oyo Butsuri 40, 41 (1971).

1970

1969

L. H. Lin, Appl. Opt. 8, 863 (1969).
[CrossRef]

Burckhardt, C. B.

Cashwell, E. D.

E. D. Cashwell, C. J. Everett, Monte Carlo Method (Pergamon Press, London, 1959).

Everett, C. J.

E. D. Cashwell, C. J. Everett, Monte Carlo Method (Pergamon Press, London, 1959).

Lin, L. H.

L. H. Lin, Appl. Opt. 8, 863 (1969).
[CrossRef]

Spitzer, F.

F. Spitzer, Principles of Random Walk (Van Nostrand, Princeton, N.J., 1964).
[CrossRef]

Takeda, Y.

Y. Takeda et al., Oyo Butsuri 40, 41 (1971).

Y. Takeda et al., Proc. of Annual Meeting of Electronic and Communication Engineers of Japan, 777 (1971).

Appl. Opt.

Oyo Butsuri

Y. Takeda et al., Oyo Butsuri 40, 41 (1971).

Other

Y. Takeda et al., Proc. of Annual Meeting of Electronic and Communication Engineers of Japan, 777 (1971).

F. Spitzer, Principles of Random Walk (Van Nostrand, Princeton, N.J., 1964).
[CrossRef]

E. D. Cashwell, C. J. Everett, Monte Carlo Method (Pergamon Press, London, 1959).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

The concepts of the systems to be discussed. (a) Random phase shifter; (b) information of dot matrix; (c) setup making hologram memory.

Fig. 2
Fig. 2

P(G < G0) vs G0: for parameter W.

Fig. 3
Fig. 3

P′(G > G0′) vs G0′: for parameter W.

Fig. 4
Fig. 4

Distribution patterns of the information of 5 × 103 bits on the holograms made by (a) the previous defocusing method and (b) the random phase shifter method.

Fig. 5
Fig. 5

Reconstructed images from the holograms of the Fig. 4; (a) and (b) correspond to (a) and (b) in Fig. 4. The reconstruction efficiencies are, respectively, 8% and 20% for a SNR of 30.

Fig. 6
Fig. 6

Reconstructed image (2 × 104 bits) from a hologram of 0.5-mm diam. The information storage density of the hologram is 105 bits/mm2.

Fig. 7
Fig. 7

Reconstructed image (800 characters) from a hologram of 0.7-mm diam. The information storage density of the hologram is 2.0 × 103 characters/mm2.

Tables (2)

Tables Icon

Table I Calculated Values of 0 vs W

Tables Icon

Table II Calculated Values of Gmax vs W

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

F ( x , y ) = 1 = 0 M m = 0 M f 0 ( ξ l p , η m p ) exp [ i Ө ( l , m ) ] × exp ( i 2 π λ ξ x + η y f ) d ξ · d η = f 0 ( ξ , η ) exp ( i 2 π λ ξ x + η y f ) d ξ d η × 1 = 0 M m = 0 M g ( l , m ) exp [ i 2 π λ ( l p x + m p y f ) + i Ө ( l , m ) ] ,
f 0 ( ξ l p , η m p ) = { 1 : [ ( ξ l p ) 2 + ( η m p ) 2 ] 1 2 < ¯ d D 2 , 0 : [ ( ξ l p ) 2 + ( η m p ) 2 ] 1 2 > d D 2 ,
G = | F ( x , y ) | max 2 / { M 2 [ f 0 ( ξ , η ) d ξ d η ] 2 } .
G = 1 M 2 { l M m M exp [ i Ө ( l , m ) ] } 2 .
P ( G < G 0 ) = G 0 M 0 J 1 ( G 0 M t ) [ J 0 ( t ) ] M 2 d t .
g ( l , m ) = 1 , for θ 0 < ¯ Ө w ( l , m ) < θ 0 + π , g ( l , m ) = 0 , for θ 0 + π < ¯ Ө w ( l , m ) < θ 0 + 2 π ,
G = 1 M 2 | l M m M g ( l , m ) exp [ i Ө ( l , m ) ] | 2 .
P ( G > G 0 ) = 1 2 N l 1 l 2 l W [ ( N / W ) ! ] 2 l 1 l 2 ! l W ! [ ( N / W ) l 1 ] ! [ ( N / W ) l 2 ] ! [ ( N / W ) l W ] ! . l 1 l 2 l W
P ( G > G 0 ) = 2 l 1 = 0 ( N / 2 ) ( G 0 N ) l 2 = ( G 0 N ) + l 1 ( N / 2 ) × [ 1 2 N [ ( N / 2 ) ! ] 2 l 1 ! l 2 ! [ ( N / 2 ) l 1 ] ! [ ( N / 2 ) l 2 ) ! ] ,
P ( G > G 0 ) = { k 1 = G 0 N / 2 K A k 2 = { [ ( G 0 N ) 2 K 1 2 ] 1 2 } k 1 + k 1 = ( G 0 N ) ( N / 4 ) k 2 = 0 k 1 } 2 N ( k 1 k 2 ) K 1 = k 1 ( N / 4 ) K 2 = k 2 ( N / 4 ) × [ ( N / 2 ) ! ] 4 2 N K 1 ! K 2 ! [ ( N / 4 ) K 1 ] ! [ ( N / 4 ) K 2 ] ! ( k 1 K 1 ) ! [ ( N / 4 ) k 1 + K 1 ] ! ( k 2 K 2 ) ! [ ( N / 4 ) k 2 + K 2 ] !
N ( k 1 , k 2 ) = { 0 ( k 1 = k 2 = 0 ) 2 ( k 1 = 0 or k 2 = 0 or k 1 = k 2 0 ) 3 ( k 1 k 2 , k I × k 2 0 ) , K A = { ( G 0 N ) ; ( G 0 N ) < ( N / 4 ) ( N / 4 ) ; ( G 0 N ) = ( N / 4 ) .

Metrics