Abstract

Figures of merit for comparing various holographic storage media are defined and discussed. These figures of merit are based on the dynamic range of the medium. Formulas for these figures of merit are derived for photographic film.

© 1970 Optical Society of America

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References

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  1. G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966), p. 116.
  2. L. J. Cutrona, E. Leith, C. Palermo, and L. Porcello, IRE Trans. IT-6, 139 (1964).
  3. D. Falconer, J. Soc. Phot. Sci. Eng. 10, 133 (1966).
  4. A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
    [Crossref]
  5. A. Vander Lugt and R. H. Mitchel, J. Opt. Soc. Am. 57, 372 (1967).
    [Crossref]
  6. J. W. Goodman, J. Opt. Soc. Am. 57, 483 (1967).
    [Crossref]
  7. A. Kozma, J. Opt. Soc. Am. 58, 436 (1968).
    [Crossref]
  8. O. Bryngdahl and A. Lohmann, J. Opt. Soc. Am. 58, 1325 (1968).
    [Crossref]
  9. The object length XB− XA must be no greater3than (XB+ XA)/3. This requirement is equivalent to limiting the fractional spatial-frequency bandwidth of the hologram to two thirds.
  10. Additional ghost images appear in the reconstruction but they may be shown to have negligible irradiances.
  11. A. A. Friesem, A. Kozma, and G. F. Adams, Appl. Opt. 6, 851 (1967).
    [Crossref] [PubMed]
  12. We assume, in this small-signal calculation, that the term (4H0/K1)[K2 + 3K3(HR+ 3H0)] ≪ 1 [see Eq. (5)].
  13. We note, however, that the effect of the assumption is to yield a value of Hmax that is somewhat larger than it ought to be. This, in turn, leads us to interpret Eq. (12) as an upper bound on dynamic range.

1968 (2)

1967 (3)

1966 (2)

D. Falconer, J. Soc. Phot. Sci. Eng. 10, 133 (1966).

A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
[Crossref]

1964 (1)

L. J. Cutrona, E. Leith, C. Palermo, and L. Porcello, IRE Trans. IT-6, 139 (1964).

Adams, G. F.

Bryngdahl, O.

Cutrona, L. J.

L. J. Cutrona, E. Leith, C. Palermo, and L. Porcello, IRE Trans. IT-6, 139 (1964).

Falconer, D.

D. Falconer, J. Soc. Phot. Sci. Eng. 10, 133 (1966).

Friesem, A. A.

Goodman, J. W.

J. W. Goodman, J. Opt. Soc. Am. 57, 483 (1967).
[Crossref]

Kozma, A.

Leith, E.

L. J. Cutrona, E. Leith, C. Palermo, and L. Porcello, IRE Trans. IT-6, 139 (1964).

Lohmann, A.

Mitchel, R. H.

Palermo, C.

L. J. Cutrona, E. Leith, C. Palermo, and L. Porcello, IRE Trans. IT-6, 139 (1964).

Porcello, L.

L. J. Cutrona, E. Leith, C. Palermo, and L. Porcello, IRE Trans. IT-6, 139 (1964).

Stroke, G. W.

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966), p. 116.

Vander Lugt, A.

Appl. Opt. (1)

IRE Trans. (1)

L. J. Cutrona, E. Leith, C. Palermo, and L. Porcello, IRE Trans. IT-6, 139 (1964).

J. Opt. Soc. Am. (5)

J. Soc. Phot. Sci. Eng. (1)

D. Falconer, J. Soc. Phot. Sci. Eng. 10, 133 (1966).

Other (5)

We assume, in this small-signal calculation, that the term (4H0/K1)[K2 + 3K3(HR+ 3H0)] ≪ 1 [see Eq. (5)].

We note, however, that the effect of the assumption is to yield a value of Hmax that is somewhat larger than it ought to be. This, in turn, leads us to interpret Eq. (12) as an upper bound on dynamic range.

The object length XB− XA must be no greater3than (XB+ XA)/3. This requirement is equivalent to limiting the fractional spatial-frequency bandwidth of the hologram to two thirds.

Additional ghost images appear in the reconstruction but they may be shown to have negligible irradiances.

G. W. Stroke, An Introduction to Coherent Optics and Holography (Academic Press Inc., New York, 1966), p. 116.

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Figures (4)

Fig. 1
Fig. 1

Recording geometry of hologram. S is an opaque screen with pinholes for the reference and object points.

Fig. 2
Fig. 2

Reconstruction geometry. The hologram is placed in an optical spectrum analyzer and the image is reconstructed in the back focal plane of the lens.

Fig. 3
Fig. 3

Reconstructed-image details. As expected for a Fourier-transform hologram, a pair of image distributions is formed in the Fourier-transform plane. Each image is perturbed by the presence of ghosts, generated by the film nonlinearity.

Fig. 4
Fig. 4

Experimental system. This configuration superimposes three plane waves on the film. Spatial frequencies in the interference pattern are precisely controlled by rotation of beam splitters B3 and B4.

Equations (13)

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E ( ξ , η ) = { E R exp [ j π λ D ( ξ 2 + η 2 ) ] + E A exp ( j π λ D [ ( X A - ξ ) 2 + η 2 ] ) + E B exp ( j π λ D [ ( X B - ξ ) 2 + η 2 ] ) } exp [ j 2 π D λ ] .
H ( ξ , η ) = H R + H A + H B + 2 ( H R H A ) 1 2 cos ϕ A + 2 ( H R H B ) 1 2 cos ϕ B + 2 ( H A H B ) 1 2 cos ϕ A B ,
T a ( H ) = K 0 + K 1 H + K 2 H 2 + K 3 H 3 ,
I p = I 0 M 2 ( w ) K 1 2 H R H 0 ( P Q / λ F ) 2 · { 1 + ( 4 H 0 / K 1 ) [ K 2 + 3 K 3 ( H R + 3 H 0 ) ] } 2 .
I g = I 0 M 2 ( w ) H R H 0 3 ( P Q / λ F ) 2 · 4 [ K 2 + 3 K 3 ( H R + 4 H 0 ) ] 2 .
SNR = I d I N [ 1 1 + 2 ( I d / I N ) ] 1 2 ,
I N ( w ) = I 0 [ N ( w ) / ( λ F ) 2 ] P Q ,
H min = ( 1 + 2 ) N ( w ) / H R M 2 ( w ) K 1 2 P Q .
H max 3 [ 2 K 2 + 6 K 3 ( H R + 4 H max ) ] 2 = ( 1 + 2 ) N ( w ) H R M 2 ( w ) P Q .
H max K 2 / 12 K 3 + H R / 4.
H max = [ ( 1 + 2 ) N ( w ) H R M 2 ( w ) ( 2 K 2 + 6 K 3 H R ) 2 P Q ] 1 3 .
Δ ( w ) = [ H R M 2 ( w ) P Q K 1 3 4.8 N ( w ) ( K 2 + 3 K 3 H R ) ] 2 3 .
μ ( w ) = Δ ( w ) / H L P Q .