Abstract

In making in-line holograms of amplitude objects with a strong background, the single-sideband technique can be used to improve the quality of the reconstruction. The main advantage of this method is the suppression of the twin image. Modifications of the same technique are also presented for making holograms of complex objects and objects with a weak background.

© 1968 Optical Society of America

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References

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  1. D. Gabor, Nature 161, 777 (1948).
    [CrossRef]
  2. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
    [CrossRef]
  3. A. Lohmann, Opt. Acta 3, 97 (1956).
    [CrossRef]
  4. W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951); G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956); D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
    [CrossRef] [PubMed]
  5. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 56, 523 (1966).
    [CrossRef]
  6. H. Wolter, Ann. Physik (6) 7, 341 (1950); A. Kastler, Rev. Opt. 29, 307 (1950); S. Lowenthal and Y. Belvaux, Appl. Phys. Letters 11, 49 (1967).
    [CrossRef]

1966 (1)

1962 (1)

1956 (1)

A. Lohmann, Opt. Acta 3, 97 (1956).
[CrossRef]

1951 (1)

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951); G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956); D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
[CrossRef] [PubMed]

1950 (1)

H. Wolter, Ann. Physik (6) 7, 341 (1950); A. Kastler, Rev. Opt. 29, 307 (1950); S. Lowenthal and Y. Belvaux, Appl. Phys. Letters 11, 49 (1967).
[CrossRef]

1948 (1)

D. Gabor, Nature 161, 777 (1948).
[CrossRef]

Bragg, W. L.

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951); G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956); D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
[CrossRef] [PubMed]

Gabor, D.

D. Gabor, Nature 161, 777 (1948).
[CrossRef]

Leith, E. N.

Lohmann, A.

A. Lohmann, Opt. Acta 3, 97 (1956).
[CrossRef]

Rogers, G. L.

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951); G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956); D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
[CrossRef] [PubMed]

Upatnieks, J.

Wolter, H.

H. Wolter, Ann. Physik (6) 7, 341 (1950); A. Kastler, Rev. Opt. 29, 307 (1950); S. Lowenthal and Y. Belvaux, Appl. Phys. Letters 11, 49 (1967).
[CrossRef]

Ann. Physik (6) (1)

H. Wolter, Ann. Physik (6) 7, 341 (1950); A. Kastler, Rev. Opt. 29, 307 (1950); S. Lowenthal and Y. Belvaux, Appl. Phys. Letters 11, 49 (1967).
[CrossRef]

J. Opt. Soc. Am. (2)

Nature (2)

D. Gabor, Nature 161, 777 (1948).
[CrossRef]

W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951); G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956); D. Gabor and W. P. Goss, J. Opt. Soc. Am. 56, 849 (1966).
[CrossRef] [PubMed]

Opt. Acta (1)

A. Lohmann, Opt. Acta 3, 97 (1956).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Optical setup used for recording and reconstructing single-sideband holograms. For notation see text.

Fig. 2
Fig. 2

Holograms and reconstructions of an object with a strong background. Diameter of circle in object 7 mm; (a) shows a single-sideband hologram and (b) its reconstruction; (c) and (d) show the corresponding conventional ones.

Fig. 3
Fig. 3

Hologram and reconstruction of an object without background with single-sideband technique. Height of letters 1.2 mm.

Fig. 4
Fig. 4

Optical setup for recording and reconstruction of holograms of complex objects using a single-sideband technique. For notation see text.

Fig. 5
Fig. 5

Holograms of a fly’s wing using (a) left and (b) right sideband, respectively, in recording.

Fig. 6
Fig. 6

Reconstructions of the holograms in Fig. 5. (a) reconstruction of the fly’s wing using left sideband and (b) using right sideband. (c) shows the interferometric superposition of (a) and (b).

Equations (14)

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u 0 ( x 0 , y 0 ) = u 0 * ( x 0 , y 0 ) ; u ˜ 0 ( ν , μ ) = u ˜ 0 * ( ν , μ ) .
u 0 ( x 0 , y 0 ) = 1 + Δ u 0 ( x 0 , y 0 ) ; Δ u 0 2 1 ; u ˜ 0 ( ν , μ ) = δ ( ν , μ ) + Δ u ˜ 0 ( ν , μ ) .
u 1 ( x , y ) = 0 + A d ν A + A u ˜ 0 ( ν , μ ) exp [ 2 π i ( x ν + y μ ) ] d μ = 1 2 + 0 + A A + A Δ u ˜ 0 ( ν , μ ) exp [ 2 π i ( x ν + y μ ) ] d ν d μ ,
| u I | 2 1 4 + 1 2 0 + A A + A Δ u ˜ 0 exp ( ) d ν d μ + 1 2 { Δ u ˜ 0 exp ( ) d ν d μ } * .
{ } * = 0 + A A + A Δ u ˜ 0 * ( ν , μ ) exp [ 2 π i ( x ν + y μ ) ] d ν d μ = 0 + A A + A Δ u ˜ 0 ( ν , μ ) × exp [ 2 π i ( x ν + y μ ) ] d ν d μ = A 0 A + A Δ u ˜ 0 ( ν , μ ) × exp [ + 2 π i ( x ν + y μ ) ] d ν d μ .
| u I ( x , y ) | 2 1 4 u 0 2 ( x 0 , y 0 ) .
u H ( x , y ) = 0 + A A + A u ˜ 0 ( ν , μ ) × exp 2 π i ( x ν + y μ + [ 1 λ 2 ( ν 2 + μ 2 ) ] 1 2 z / λ ) } d ν d μ .
| u H | 2 = | 1 2 exp ( 2 π i z / λ ) + Δ u ˜ 0 exp ( ) d ν d μ | 2 1 4 + 1 2 exp ( 2 π i z / λ ) d ν d μ + 1 2 exp ( + 2 π i z / λ ) { d ν d μ } * .
1 4 exp ( 2 π i z / λ ) + 1 2 0 + A A + A Δ u ˜ 0 ( ν , μ ) × exp { 2 π i ( x ν + y μ + [ 1 λ 2 ( ν 2 + μ 2 ) ] 1 2 z / λ ) } d ν d μ .
1 4 + 1 2 0 + A A + A Δ u ˜ 0 ( ν , μ ) × exp [ 2 π i ( x ν + y μ ) ] d ν d μ = 1 2 u I ( x , y ) .
F ( ν , μ ) = 0 ( if ν < 0 ) ; = 1 ( if ν = μ = 0 ) ; = 1 / 10 ( if ν > 0 ) .
| u I I R | 2 = | 1 2 exp ( 2 π i z / λ ) + 0 + A A + A Δ u ˜ 0 exp ( ) d ν d μ | 2 1 4 + 1 2 exp ( 2 π i z / λ ) d ν d μ + 1 2 exp ( + 2 π i z / λ ) { d ν d μ } * .
{ d ν d μ } * = 0 + A A + A Δ u ˜ 0 * ( ν , μ ) × exp { 2 π i ( x ν + y μ + [ 1 λ 2 ( ν 2 + μ 2 ) ] 1 2 z / λ ) } d ν d μ = A 0 A + A Δ u ˜ 0 * ( ν , μ ) exp { + 2 π i ( x ν + y μ [ 1 λ 2 ( ν 2 + μ 2 ) ] 1 2 z / λ ) } d ν d μ .
1 2 + 1 2 A + A A + A Δ u ˜ 0 ( ν , μ ) × exp [ 2 π i ( x ν + y μ ) ] d ν d μ = 1 2 μ 0 ( x , y ) .