Abstract

The process of image formation by reconstructed wave fronts, brought to notice and placed upon a broad theoretical foundation through the writings of D. Gabor, is here discussed from a less abstract standpoint in an attempt to establish a satisfying conceptual explanation of the phenomena. The imperfections which the photographically recorded images ordinarily exhibit are accounted for and classified, and means for their removal are described. Sample reconstructions are presented.

© 1956 Optical Society of America

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References

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  1. W. L. Bragg, Nature 143, 678 (1939).
    [Crossref]
  2. M. J. Buerger, J. Appl. Phys. 21, 909 (1950).
    [Crossref]
  3. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).
  4. G. L. Rogers, Proc. Roy. Soc. Edinburgh A63, 193 (1952).
  5. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951); M. E. Haine and T. Mulvey, J. Opt. Soc. Am. 42, 763 (1952); A. V. Baez, J. Opt. Soc. Am. 42, 756 (1953).
    [Crossref]
  6. D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).
  7. G. L. Rogers and W. L. Bragg, Nature 167, 190 (1951).
    [Crossref]

1952 (1)

G. L. Rogers, Proc. Roy. Soc. Edinburgh A63, 193 (1952).

1951 (1)

G. L. Rogers and W. L. Bragg, Nature 167, 190 (1951).
[Crossref]

1950 (1)

M. J. Buerger, J. Appl. Phys. 21, 909 (1950).
[Crossref]

1949 (3)

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951); M. E. Haine and T. Mulvey, J. Opt. Soc. Am. 42, 763 (1952); A. V. Baez, J. Opt. Soc. Am. 42, 756 (1953).
[Crossref]

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).

1939 (1)

W. L. Bragg, Nature 143, 678 (1939).
[Crossref]

Bragg, W. L.

G. L. Rogers and W. L. Bragg, Nature 167, 190 (1951).
[Crossref]

W. L. Bragg, Nature 143, 678 (1939).
[Crossref]

Buerger, M. J.

M. J. Buerger, J. Appl. Phys. 21, 909 (1950).
[Crossref]

Gabor, D.

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951); M. E. Haine and T. Mulvey, J. Opt. Soc. Am. 42, 763 (1952); A. V. Baez, J. Opt. Soc. Am. 42, 756 (1953).
[Crossref]

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).

Rogers, G. L.

G. L. Rogers, Proc. Roy. Soc. Edinburgh A63, 193 (1952).

G. L. Rogers and W. L. Bragg, Nature 167, 190 (1951).
[Crossref]

J. Appl. Phys. (1)

M. J. Buerger, J. Appl. Phys. 21, 909 (1950).
[Crossref]

Nature (2)

W. L. Bragg, Nature 143, 678 (1939).
[Crossref]

G. L. Rogers and W. L. Bragg, Nature 167, 190 (1951).
[Crossref]

Proc. Roy. Soc. (London) (3)

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951); M. E. Haine and T. Mulvey, J. Opt. Soc. Am. 42, 763 (1952); A. V. Baez, J. Opt. Soc. Am. 42, 756 (1953).
[Crossref]

D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949); Proc. Roy. Soc. (London) B64, 449 (1951).

Proc. Roy. Soc. Edinburgh (1)

G. L. Rogers, Proc. Roy. Soc. Edinburgh A63, 193 (1952).

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Figures (11)

Fig. 1
Fig. 1

(a) Light from the point source S and the point scatterer O may produce a diffraction pattern (hologram) on the photographic surface WW. Alternatively, with WW absent and the lens LL in place, the same light produces, among other effects, a real image of O at I. (b) The image at I also appears with the object O removed and the finished hologram replaced.

Fig. 2
Fig. 2

System of three light sources which would jointly produce at the spherical locus WW a wave pattern equivalent to that transmitted by the hologram of Fig. 1(b).

Fig. 3
Fig. 3

Above, amplitude vectors representing illumination from the three sources as received at a point on WW of Fig. 2 where the resultant intensity is maximum. Below, amplitudes at a general point.

Fig. 4
Fig. 4

Hologram WP illuminated by a point source S not located at the center of curvature of WP. Virtual sources O and O′ still appear, but at new positions.

Fig. 5
Fig. 5

Light source S and positive hologram HH, aided by lens LL, produce at I a real image of the absent object virtually located at O. The clarity of the image is impaired however by light associated with the conjugate virtual source at O′ (broken rays).

Fig. 6
Fig. 6

(a) Hologram of an irregular wire, showing noisy background effects. (b) Reconstruction from (a), showing a mottled background resulting from the hologram noise.

Fig. 7
Fig. 7

(a) Clean hologram of the wire object used in Fig. 6. (b) Clean reconstruction, to be compared with Fig. 6(b).

Fig. 8
Fig. 8

(a) Reconstruction from a clean hologram, showing streaky exposure caused by thickness variations of the film base. (b) Nearly clean reconstruction from the same hologram, obtained by immersing the film in a liquid with equal refractive index.

Fig. 9
Fig. 9

(a) Hologram of a microscope reticle with 5-mm scale. (b) Reconstruction from the hologram.

Fig. 10
Fig. 10

System illustrating removal of effects of the unfocused conjugate image by use of a negative hologram and real object.

Fig. 11
Fig. 11

(a) Hologram of a straight wire. (b) Reconstruction from the hologram, showing not only the wire but also parallel fringes associated with the conjugate source. (c) Intensity pattern recorded on a film placed in the position occupied by the film in case (b) but illuminated by light from the source and the scattering object. No hologram present. (d) Reconstruction from the hologram shown in (a) but with object restored to its original position. Light scattered from the object has filled in the fringe pattern shown in (b) and removed visible effects of the conjugate source.

Equations (2)

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1 u - 1 v = 1 u 0 - 1 v 0
1 w - 1 v = - 1 u 0 + 1 v 0 .