Abstract

High quality holograms of flat objects are produced by developing an achromatic-fringe system that consists of a monochromatic but spatially incoherent source, a holographic beam splitting device, and a pair of Fourier transform lenses. The effects of using an incoherent extended source and the transfer characteristics of the holograms are discussed. Emphasis is also placed on the advantages of developing lens Fourier transform holography along with the practical lens systems. A further possible extension of the system to attain high storage density as well as high quality holograms is proposed by making use of a new type of pseudorandom phase sequence.

© 1975 Optical Society of America

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References

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  1. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964).
    [Crossref]
  2. H. J. Gerritsen, W. J. Hannan, E. G. Ramberg, Appl. Opt. 7, 2301 (1968).
    [Crossref] [PubMed]
  3. E. N. Leith, J. Upatnieks, Appl. Opt. 7, 2085 (1968).
    [Crossref] [PubMed]
  4. D. Gabor, IBM J. Res. Dev.509 (September1970).
    [Crossref]
  5. R. H. Katyl, Appl. Opt. 11, 198 (1972).
    [Crossref] [PubMed]
  6. W. J. Dallas, Appl. Opt. 12, 1179 (1973).
    [Crossref] [PubMed]
  7. Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
    [Crossref]
  8. Y. Tsunoda, Y. Takeda, Appl. Opt. 13, 2046 (1974).
    [Crossref] [PubMed]
  9. C. B. Burckhardt, Appl. Opt. 9, 695 (1970).
    [Crossref] [PubMed]
  10. R. E. Brooks, L. O. Heflinger, R. F. Wuerker, IEEE J. Quantum Electron. QE-2, 275 (1966).
    [Crossref]
  11. J. M. Burch, J. W. Gates, R. G. N. Hills, L. H. Tanner, Nature 212, 1347 (1966).
    [Crossref]
  12. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 57, 975 (1967).
    [Crossref]
  13. O. Bryngdahl, A. Lohmann, J. Opt. Soc. Am. 60, 281 (1970).
    [Crossref]
  14. M. Kato, T. Suzuki, J. Opt. Soc. Am. 59, 303 (1969).
    [Crossref]
  15. R. H. Katyl, Appl. Opt. 11, 1241, 1248, 1255 (1972).
    [Crossref] [PubMed]
  16. E. N. Leith, B. J. Chang, Appl. Opt. 12, 1957 (1973).
    [Crossref] [PubMed]
  17. M. Kato, J. Opt. Soc. Am. 64, 1507 (1974).
    [Crossref]
  18. M. Kato, Y. Okino, Appl. Opt. 12, 1199 (1973).
    [Crossref] [PubMed]
  19. K. von Bieren, Appl. Opt. 10, 2739 (1971).
    [Crossref] [PubMed]
  20. R. W. Meier, J. Opt. Soc. Am. 55, 987 (1965).
    [Crossref]
  21. E. N. Leith, J. Upatnieks, K. A. Haines, J. Opt. Soc. Am. 55, 981 (1965).
    [Crossref]

1974 (2)

1973 (4)

1972 (2)

R. H. Katyl, Appl. Opt. 11, 1241, 1248, 1255 (1972).
[Crossref] [PubMed]

R. H. Katyl, Appl. Opt. 11, 198 (1972).
[Crossref] [PubMed]

1971 (1)

1970 (3)

1969 (1)

1968 (2)

1967 (1)

1966 (2)

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, IEEE J. Quantum Electron. QE-2, 275 (1966).
[Crossref]

J. M. Burch, J. W. Gates, R. G. N. Hills, L. H. Tanner, Nature 212, 1347 (1966).
[Crossref]

1965 (2)

1964 (1)

Brooks, R. E.

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, IEEE J. Quantum Electron. QE-2, 275 (1966).
[Crossref]

Bryngdahl, O.

Burch, J. M.

J. M. Burch, J. W. Gates, R. G. N. Hills, L. H. Tanner, Nature 212, 1347 (1966).
[Crossref]

Burckhardt, C. B.

Chang, B. J.

Dallas, W. J.

Gabor, D.

D. Gabor, IBM J. Res. Dev.509 (September1970).
[Crossref]

Gates, J. W.

J. M. Burch, J. W. Gates, R. G. N. Hills, L. H. Tanner, Nature 212, 1347 (1966).
[Crossref]

Gerritsen, H. J.

Haines, K. A.

Hannan, W. J.

Heflinger, L. O.

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, IEEE J. Quantum Electron. QE-2, 275 (1966).
[Crossref]

Hills, R. G. N.

J. M. Burch, J. W. Gates, R. G. N. Hills, L. H. Tanner, Nature 212, 1347 (1966).
[Crossref]

Kato, M.

Katyl, R. H.

R. H. Katyl, Appl. Opt. 11, 1241, 1248, 1255 (1972).
[Crossref] [PubMed]

R. H. Katyl, Appl. Opt. 11, 198 (1972).
[Crossref] [PubMed]

Leith, E. N.

Lohmann, A.

Meier, R. W.

Okino, Y.

Ramberg, E. G.

Suzuki, T.

Takeda, Y.

Y. Tsunoda, Y. Takeda, Appl. Opt. 13, 2046 (1974).
[Crossref] [PubMed]

Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
[Crossref]

Tanner, L. H.

J. M. Burch, J. W. Gates, R. G. N. Hills, L. H. Tanner, Nature 212, 1347 (1966).
[Crossref]

Tsunoda, Y.

Y. Tsunoda, Y. Takeda, Appl. Opt. 13, 2046 (1974).
[Crossref] [PubMed]

Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
[Crossref]

Upatnieks, J.

von Bieren, K.

Wuerker, R. F.

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, IEEE J. Quantum Electron. QE-2, 275 (1966).
[Crossref]

Appl. Opt. (10)

IBM J. Res. Dev. (1)

D. Gabor, IBM J. Res. Dev.509 (September1970).
[Crossref]

IEEE J. Quantum Electron. (1)

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, IEEE J. Quantum Electron. QE-2, 275 (1966).
[Crossref]

J. Appl. Phys. (1)

Y. Tsunoda, Y. Takeda, J. Appl. Phys. 44, 2422 (1973).
[Crossref]

J. Opt. Soc. Am. (7)

Nature (1)

J. M. Burch, J. W. Gates, R. G. N. Hills, L. H. Tanner, Nature 212, 1347 (1966).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Achromatic-fringe interferometer arrangement with a holographic beam splitting device: (B.S.) Fourier hologram of random phase sampling pattern; (Hm) hologram plane.

Fig. 2
Fig. 2

Part of the reconstruction of the sample points obtained by illuminating the holographic beam splitter B.S. with a point source, as shown in Fig. 1. The phases 0 or π were distributed randomly to the sample spots.

Fig. 3
Fig. 3

Part of an object transparency backed by reconstruction shown in Fig. 2. Moiré is clearly evident.

Fig. 4
Fig. 4

Part of reconstruction of the same transparency as in Fig. 3. A spatially incoherent source of size 50 μm × 50 μm for lens fc = 70 mm was used in recording the hologram. The size of the original object transparency was 20 mm × 25 mm. The diameter of the hologram was 5 mm ϕ.

Fig. 5
Fig. 5

Reconstruction of an object transparency. The recording procedure was the same as in Fig. 4, but a spatially incoherent extended source was used in the reconstruction as well.

Fig. 6
Fig. 6

The same result as in Fig. 4, but with a 2-mm × 2-mm hologram.

Fig. 7
Fig. 7

Transfer function of the hologram recorded with a spatially incoherent source.

Fig. 8
Fig. 8

Illustrating the phases of plane wavefronts in the hologram plane: (LF−1) Fourier transform lens; (H) hologram plane.

Fig. 9
Fig. 9

Reconstructing the hologram.

Fig. 10
Fig. 10

An example of a 2-D pseudorandom phase sequence. Every phase step at the boundary is +π/2 or −π/2, and the probability of the occurrence of either step is equal.

Fig. 11
Fig. 11

A phase mask designed to add a regular phase shift of π/2 to the usual random phase mask.

Equations (13)

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u ( ξ m ) = C p = N N { [ T 0 ( l p Δ x s ) exp ( i 2 π λ f x s ξ m ) ] × exp [ i 2 π λ f ( p Δ l ) ξ m ] exp ( i ϕ p ) } + C 2 exp ( i 2 π λ f x s ξ m ) ,
x s
T 0 ( x ) = 1 + a sin ω x .
I ( ξ m ) = u ( ξ m ) u * ( ξ m ) d x s = C 3 p = N N { [ T 0 ( l p Δ x s ) d x s ] exp [ i 2 π λ f ( p Δ l ) ξ m ] exp ( i ϕ p ) } + ,
[ 1 + a sin ω ( l p Δ x s ) ] d x s = 2 [ 1 + a sin ω ω sin ω ( l p Δ ) ] .
0 ( ξ ) = δ ( x 1 X 0 ) exp ( i 2 π λ 1 f 1 x 1 ξ ) d x 1 = exp ( i 2 π λ 1 f 1 X 0 ξ ) ,
f 1 sin θ 0 = X 0
R ( ξ ) = exp ( i 2 π λ 1 f 1 X R ξ ) .
( 0 + R ) ( 0 + R ) * = | 0 | 2 + | R | 2 + 0 R * + 0 * R ,
0 R * = exp ( i 2 π λ 1 f 1 X 0 ξ ) exp ( i 2 π λ 1 f 1 X R ξ ) = exp [ i 2 π λ 1 f 1 ( sin θ 0 + sin θ R ) ξ ] , f 1 sin θ R = X R .
u ( x 2 ) = [ exp ( i 2 π λ 2 ξ sin θ C ) ] 0 R × exp ( i 2 π λ 1 f 2 x 2 ξ ) d ξ , = 2 π δ { 2 π [ f 2 sin θ C λ 1 f 2 λ 1 ( sin θ 0 + sin θ R ) x 2 ] } .
x 2 = f 2 sin θ C λ 2 f 2 λ 1 f 1 ( f 1 sin θ 0 + f 1 sin θ R ) = X C + M X 0 + M X R ,
X C = f 2 sin θ C , M = λ 2 f 2 λ 1 f 1 .

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