Abstract

The holographic storage of diffraction patterns in a three-dimensional media is described from a vector viewpoint derived from the Kirchhoff diffraction integral. The sensitivity of the reconstruction to wavelength and to the orientation of the readout beam is calculated, and experimental results are given.

© 1966 Optical Society of America

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References

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  1. D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Phys. Soc. (London) B64, 449 (1951).
    [CrossRef] [PubMed]
  2. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962); J. Opt. Soc. Am. 53, 1377 (1963); J. Opt. Soc. Am. 54, 1295 (1964).
    [CrossRef]
  3. K. Stetson has reported the construction of a hologram on such media (private communication, 1964). More recently, similar work has been reported by Carson Laboratories (private communication, 1965).
  4. Y. N. Denisyuk, Opt. Spectry. 15, 279 (1963).
  5. P. J. van Heerden, Appl. Opt. 2, 393 (1963).
    [CrossRef]
  6. K. S. Pennington, L. H. Lin, Appl. Phys. Letters 7, 56 (1965).
    [CrossRef]
  7. A. Friesem, Appl. Phys. Letters 7, 102 (1965).
    [CrossRef]
  8. H. Fleisher, P. Pengelly, J. Reynolds, R. Schools, G. Sincerbox, in Optical and Electro-Optical Information ProcessingJ. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanerburgh, Eds. (MIT Press, Cambridge, Mass., 1965).
  9. A. Kozma, J. Opt. Soc. Am. 56, 428 (1966).
    [CrossRef]
  10. A. S. Hoffman, J. G. Doige, D. G. Mooney, J. Opt. Soc. Am. 55, 1559 (1965)
    [CrossRef]
  11. C. Schwartz, Battelle Memorial Institute, private conversation, Nov.1965. [Note added in proof: G. W. Stroke has also recently reported producing halograms of this type and has noted the white light reconstructions. G. W. Stroke, Washington meeting of the Optical Society of America, 15–18 March 1966; see also, G. W. Stroke and A. E. Labeyrie, Phys. Letters 20, 368 (1966)].
  12. C. F. Quate, C. D. Wilkinson, D. K. Winslow, Proc. IEEE 53, 1604 (1965).
    [CrossRef]
  13. M. G. Cohen, E. I. Gordon, Bell System Tech. J. 44, 693 (1965).
  14. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 593, 608.
  15. This result is the same, within a proportionality constant, as that obtained from the ultrasonic scattering theory (Ref. 14). This situation also arises in the theory of the phase contrast microscope where small refractive index variations are converted to intensity variations. For a discussion of the validity of the approximation see F. D. Kahn, Proc. Phys. Soc. (London) (B), 86, 1073 (1955).
    [CrossRef]

1966

1965

A. S. Hoffman, J. G. Doige, D. G. Mooney, J. Opt. Soc. Am. 55, 1559 (1965)
[CrossRef]

C. F. Quate, C. D. Wilkinson, D. K. Winslow, Proc. IEEE 53, 1604 (1965).
[CrossRef]

M. G. Cohen, E. I. Gordon, Bell System Tech. J. 44, 693 (1965).

K. S. Pennington, L. H. Lin, Appl. Phys. Letters 7, 56 (1965).
[CrossRef]

A. Friesem, Appl. Phys. Letters 7, 102 (1965).
[CrossRef]

1963

Y. N. Denisyuk, Opt. Spectry. 15, 279 (1963).

P. J. van Heerden, Appl. Opt. 2, 393 (1963).
[CrossRef]

1962

1955

This result is the same, within a proportionality constant, as that obtained from the ultrasonic scattering theory (Ref. 14). This situation also arises in the theory of the phase contrast microscope where small refractive index variations are converted to intensity variations. For a discussion of the validity of the approximation see F. D. Kahn, Proc. Phys. Soc. (London) (B), 86, 1073 (1955).
[CrossRef]

1948

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Phys. Soc. (London) B64, 449 (1951).
[CrossRef] [PubMed]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 593, 608.

Cohen, M. G.

M. G. Cohen, E. I. Gordon, Bell System Tech. J. 44, 693 (1965).

Denisyuk, Y. N.

Y. N. Denisyuk, Opt. Spectry. 15, 279 (1963).

Doige, J. G.

Fleisher, H.

H. Fleisher, P. Pengelly, J. Reynolds, R. Schools, G. Sincerbox, in Optical and Electro-Optical Information ProcessingJ. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanerburgh, Eds. (MIT Press, Cambridge, Mass., 1965).

Friesem, A.

A. Friesem, Appl. Phys. Letters 7, 102 (1965).
[CrossRef]

Gabor, D.

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Phys. Soc. (London) B64, 449 (1951).
[CrossRef] [PubMed]

Gordon, E. I.

M. G. Cohen, E. I. Gordon, Bell System Tech. J. 44, 693 (1965).

Hoffman, A. S.

Kahn, F. D.

This result is the same, within a proportionality constant, as that obtained from the ultrasonic scattering theory (Ref. 14). This situation also arises in the theory of the phase contrast microscope where small refractive index variations are converted to intensity variations. For a discussion of the validity of the approximation see F. D. Kahn, Proc. Phys. Soc. (London) (B), 86, 1073 (1955).
[CrossRef]

Kozma, A.

Leith, E. N.

Lin, L. H.

K. S. Pennington, L. H. Lin, Appl. Phys. Letters 7, 56 (1965).
[CrossRef]

Mooney, D. G.

Pengelly, P.

H. Fleisher, P. Pengelly, J. Reynolds, R. Schools, G. Sincerbox, in Optical and Electro-Optical Information ProcessingJ. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanerburgh, Eds. (MIT Press, Cambridge, Mass., 1965).

Pennington, K. S.

K. S. Pennington, L. H. Lin, Appl. Phys. Letters 7, 56 (1965).
[CrossRef]

Quate, C. F.

C. F. Quate, C. D. Wilkinson, D. K. Winslow, Proc. IEEE 53, 1604 (1965).
[CrossRef]

Reynolds, J.

H. Fleisher, P. Pengelly, J. Reynolds, R. Schools, G. Sincerbox, in Optical and Electro-Optical Information ProcessingJ. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanerburgh, Eds. (MIT Press, Cambridge, Mass., 1965).

Schools, R.

H. Fleisher, P. Pengelly, J. Reynolds, R. Schools, G. Sincerbox, in Optical and Electro-Optical Information ProcessingJ. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanerburgh, Eds. (MIT Press, Cambridge, Mass., 1965).

Schwartz, C.

C. Schwartz, Battelle Memorial Institute, private conversation, Nov.1965. [Note added in proof: G. W. Stroke has also recently reported producing halograms of this type and has noted the white light reconstructions. G. W. Stroke, Washington meeting of the Optical Society of America, 15–18 March 1966; see also, G. W. Stroke and A. E. Labeyrie, Phys. Letters 20, 368 (1966)].

Sincerbox, G.

H. Fleisher, P. Pengelly, J. Reynolds, R. Schools, G. Sincerbox, in Optical and Electro-Optical Information ProcessingJ. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanerburgh, Eds. (MIT Press, Cambridge, Mass., 1965).

Stetson, K.

K. Stetson has reported the construction of a hologram on such media (private communication, 1964). More recently, similar work has been reported by Carson Laboratories (private communication, 1965).

Upatnieks, J.

van Heerden, P. J.

Wilkinson, C. D.

C. F. Quate, C. D. Wilkinson, D. K. Winslow, Proc. IEEE 53, 1604 (1965).
[CrossRef]

Winslow, D. K.

C. F. Quate, C. D. Wilkinson, D. K. Winslow, Proc. IEEE 53, 1604 (1965).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 593, 608.

Appl. Opt.

Appl. Phys. Letters

K. S. Pennington, L. H. Lin, Appl. Phys. Letters 7, 56 (1965).
[CrossRef]

A. Friesem, Appl. Phys. Letters 7, 102 (1965).
[CrossRef]

Bell System Tech. J.

M. G. Cohen, E. I. Gordon, Bell System Tech. J. 44, 693 (1965).

J. Opt. Soc. Am.

Nature

D. Gabor, Nature 161, 777 (1948); Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Phys. Soc. (London) B64, 449 (1951).
[CrossRef] [PubMed]

Opt. Spectry.

Y. N. Denisyuk, Opt. Spectry. 15, 279 (1963).

Proc. IEEE

C. F. Quate, C. D. Wilkinson, D. K. Winslow, Proc. IEEE 53, 1604 (1965).
[CrossRef]

Proc. Phys. Soc. (London) (B)

This result is the same, within a proportionality constant, as that obtained from the ultrasonic scattering theory (Ref. 14). This situation also arises in the theory of the phase contrast microscope where small refractive index variations are converted to intensity variations. For a discussion of the validity of the approximation see F. D. Kahn, Proc. Phys. Soc. (London) (B), 86, 1073 (1955).
[CrossRef]

Other

C. Schwartz, Battelle Memorial Institute, private conversation, Nov.1965. [Note added in proof: G. W. Stroke has also recently reported producing halograms of this type and has noted the white light reconstructions. G. W. Stroke, Washington meeting of the Optical Society of America, 15–18 March 1966; see also, G. W. Stroke and A. E. Labeyrie, Phys. Letters 20, 368 (1966)].

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), pp. 593, 608.

K. Stetson has reported the construction of a hologram on such media (private communication, 1964). More recently, similar work has been reported by Carson Laboratories (private communication, 1965).

H. Fleisher, P. Pengelly, J. Reynolds, R. Schools, G. Sincerbox, in Optical and Electro-Optical Information ProcessingJ. T. Tippet, D. A. Berkowitz, L. C. Clapp, C. J. Koester, A. Vanerburgh, Eds. (MIT Press, Cambridge, Mass., 1965).

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Figures (12)

Fig. 1
Fig. 1

The readin process. The vectors designate the normals to the impinging wavefronts; θs and θr designate angles within the emulsion. The broken lines show the constant density surfaces produced within the emulsion as a consequence of interference between the two waves.

Fig. 2
Fig. 2

The readout process. The readout beam enters the plate at an angle θi. The point P(xs, xy) is the point at which the diffracted field is calculated. P(x,y) is a point within the emulsion. s is the distance between the two points.

Fig. 3
Fig. 3

Vector diagram of the effect of altering the direction of the readout wave. The vectors ki and kψ are shown for the solution v-1. When the readout wave direction θi is altered by Δθi, the diffracted wave changes direction by Δψ in such a way that the residual vector is parallel to the real axis.

Fig. 4
Fig. 4

Plot of the change Δθi in readout angle needed to extinguish the diffracted wave (solution v-1) as a function of θr, for θs = 0. The parameters are for Eastman Kodak type 649F emulsion coated on a glass plate: λ = 6328 Å and the emulsion thickness L = 15.5 μ. Also shown is the change Δψ of the diffraction angle resulting from the change Δθi. Several experimentally determined points corrected for emulsion thickness are given (designated by x’s). The angles are those within the emulsion (refractive index 1.52). The hatched area represents a region that is not readily accessible; that is, an angle of 41° within the emulsion corresponds to an angle of 90° for the beam in air.

Fig. 5
Fig. 5

Vector diagram showing Δθi and Δψ as the readout wavelength λ′ is varied, always reorienting the plate to produce maximum intensity of a first-order diffraction. In (a), the readout wavelength is longer than the wavelength used for hologram construction, i.e., λ′ > λ. In (b), the situation is reversed: λ′ < λ.

Fig. 6
Fig. 6

Vector diagram showing diffraction sensitivity when the incident beam angle θi is maintained constant as the readout wavelength is varied. The vectors ki and kψ are for p = 1 and for p < 1, corresponding to readout with a longer wavelength than is used in making the hologram. The diagram is for the solution v − 1.

Fig. 7
Fig. 7

Plot of the wavelength change Δλ needed to extinguish the diffracted wave (solution v − 1) while maintaining the readout angle θi constant. The parameters are for Eastman Kodak type 649F emulsion coated on glass plate: λ = 6328 Å and L = 15.5 μ. Also shown is the variation of the diffraction angle associated with change Δλ, and some experimentally determined points (designated by small x’s). The calculated angles are those that exist within the emulsion (assumed to have index of refraction 1.52). The hatched area is normally inaccessible, as explained in the caption of Fig. 4.

Fig. 8
Fig. 8

Sequence of superimposed holographic images, each one readin at a different orientation of the recording plate. Readout is done by rotating the plate in the illuminating beam, thus reproducing each image in succession as a hologram movie.

Fig. 9
Fig. 9

Virtual image from a hologram illuminated with white light from a zirconium concentrated arc source. The reference beam was introduced at θr = 160° (external angle). The hologram was made at 6328 Å; the reconstruction ranges from violet to green, depending on the angle of incidence of the white light. Emulsion shrinkage precludes a reconstruction at wavelengths longer than green, unless the plate remains unfixed, whereupon reconstructions up to orange-red are obtainable.

Fig. 10
Fig. 10

Theoretical curves and experimental points showing the relative intensity of the diffracted wave as a function of the incidence angle of the readout wave for θs = 0 and three values of θr: (a) θr = 15.6°, (b) θr = 40°, and (c) θr = 70°. Experimental points are shown as x’s.

Fig. 11
Fig. 11

Intensity of the zero-order spectrum as θi is varied. A peaking occurs at the angle that maximizes the light in the first order. In (a), the polarization of the readout beam is parallel to the fringe contours. In (b), the polarization is rotated by π/2.

Fig. 12
Fig. 12

Curves showing two anomalous effects observed while measuring the intensity of the diffracted wave as a function of plate orientation, for emulsion of 42-μ thickness. (a) Curve is broader than predicted by theory, and the secondary maxima are absent. (b) Improvement by special developing methods, including presoaking plates to soften emulsion. (c) Result obtained by using an elaborate developing process involving low temperatures and extended development time. This curve conforms to the predicted result.

Equations (33)

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u s = a s e i k ( x cos θ s + y sin θ s ) .
u r = a r e i k ( x cos θ r + y sin θ r ) .
I = u s + u r 2 = 2 + 2 cos ϕ ,
T = T 0 + 2 B cos ϕ ,
u i = exp i k ( x cos θ i + y sin θ i ) .
u d v Q ( T 0 + 2 B cos ϕ ) exp ( i ϕ i + k s ) d v ,
u d ± = B v Q exp i ( ± ϕ + ϕ i + k s ) d v ,
x = x ^ cos ψ - y ^ sin ψ , y = x ^ sin ψ + y ^ cos ψ
u d ± = B Q 0 L / cos ψ e i [ ± ϕ + ϕ i + k ( d / cos ψ - x ^ ) ] d x ^ ,
u d ± = C F 0 L / cos ψ exp i { k x ^ [ ± p cos ( ψ - θ r ) p cos ( ψ - θ s ) + cos ( ψ - θ i ) - 1 ] + k d / cos ψ } d x ^ ,
u d ± = C F sec ψ sinc { ( k L / 2 cos ψ ) [ ± p cos ( ψ - θ r ) p cos ( ψ - θ s ) + cos ( ψ - θ i ) - 1 ] }
u d ± = C F sec ψ sinc { ( k L / 2 cos ψ ) [ ± cos ( ψ - θ r ) cos ( ψ - θ s ) + p cos ( ψ - θ i ) - p ] } ,
sin θ i - sin ψ = ± ( λ / Λ )
± e i θ r e i θ s + p e i θ i - p e i ψ = 2 K / k L
± k r k s + k i - k ψ = 2 K / L .
k L / 2 cos ψ [ ± cos ( θ r - ψ ) cos ( θ s - ψ ) + p cos ( θ i - ψ ) - p ] = K ,
θ b = tan - 1 ( cos θ r - cos θ i / sin θ r - sin θ s ) ,
θ i + ψ = θ s + θ r
sin ( θ r + Δ θ i ) - sin ( θ s + Δ ψ ) = - sin θ s + sin θ r
- cos ( θ s - θ r + Δ ψ ) + cos Δ ψ + cos ( θ s - θ r + Δ ψ - Δ θ i ) - 1 = ( λ / 2 L ) cos ( θ s + Δ ψ ) ,
sin θ r - sin ( θ s + Δ ψ ) = - ( 1 / p ) ( sin θ s - sin θ r )
- cos ( θ r - θ s - Δ ψ ) + cos Δ ψ + p cos ( θ r - θ s - Δ ψ ) - p = ( 2 K / k L ) cos ( θ s + Δ ψ ) .
u d ± = B Q 0 L / cos ψ W ( x ^ ) e i [ ± ϕ + ϕ i + k ( d / cos ψ - x ^ ) ] d x ^ ,
2 E 0 + k 1 2 E 0 = 0 ,
( 2 E z / x 2 ) + ( 2 E z / y 2 ) = - ( ω 2 / c 2 ) [ + i ( 4 π / ω ) ( σ 0 + σ 1 cos q x ) ] E z .
E z = l V l ( x ) e i [ ( k 1 sin θ l + l q ) y ] ,
F ± l ( x ) = - k 1 2 A ( 2 π σ 1 / ω ) sin [ ( α 0 ) 1 / 2 - ( α ± l ) 1 / 2 ] x ( α 0 - α ± l ) / 2 × exp i [ ( α ± l ) 1 / 2 - ( α 0 ) 1 / 2 ] x ,
V ± l ( L ) 2 = S { sin k L 2 ( cos θ i - cos ψ ) L k 2 ( cos 2 θ i - cos 2 ψ ) } 2
u d ± = C F 0 L / cos ψ e i k x ^ [ cos ψ cos θ i + sin ψ sin θ i ± ( q / k ) sin ψ - 1 ] d x ^ .
u d ± = C 1 0 L / cos ψ i i k x ^ [ cos ψ cos θ i + sin 2 ψ ( q / k ) sin ψ ± ( q / k ) sin ψ - 1 ] d x ^
u d ± = C 1 0 L / cos ψ e i k x ^ cos ψ ( cos θ i - cos ψ ) d x ^ .
I = S { sin ( k L / 2 ) ( cos θ i - cos ψ ) k / 2 ( cos θ i - cos ψ ) ( 2 cos ψ ) } 2 .
I = S { sin ( k L / 2 ) ( cos θ - cos ψ ) k / 2 ( cos 2 θ - cos 2 ψ ) } 2 ,

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