We review Dennis Gabor’s early results in light of more than fifty years of technological achievements, including the advent of CCD cameras and fast computers. By applying digital reading to one of the first holograms, we demonstrate the continuity between the classical technique and the digital implementation. This experiment can be used as a demonstration without needing the instrumentation of an optics laboratory.
REFERENCES
1.
An exhaustive review of Gabor’s work can be found in D. Gabor, “Holography, 1948–1971,” in 〈http://www.nobel.se/physics/laureates/1971/gabor-lecture.html〉.
2.
D.
Gabor
, “A new microscopic principle
,” Nature (London)
161
, 777
–778
(1948
).3.
As Gabor reported in Ref. 5, the idea of dividing the imaging process into two steps was inspired by Sir W. L. Bragg’s x-ray microscope.
4.
In analogy to Ref. 3, the idea of using a coherent background to record phase-sensitive pictures of the electric field was drawn from F. Zernike’s investigations on lens aberrations. In this respect, we can say that Gabor’s work was also a wonderful synthesis of previous investigations, as often happens in science.
5.
D.
Gabor
, “Microscopy by reconstructed wavefronts
,” Proc. R. Soc. London, Ser. A
197
, 454
–487
(1949
).6.
W. Thomas Cathey, Optical Information Processing and Holography (Wiley, New York, 1974), pp. 314–363.
7.
For a review of digital techniques see
Ulf
Schnars
and Werner P. O.
Jüptner
, “Digital recording and numerical reconstruction of holograms
,” Meas. Sci. Technol.
13
, R85
–R101
(2002
).The specific case of in-line holograms is considered in detail in
S.
Grilli
, P.
Ferraro
, S. De
Nicola
, A.
Finizio
, G.
Pierattini
, and R.
Meucci
, “Whole optical wavefields reconstruction by digital holography
,” Opt. Express
9
, 294
–302
(2001
).8.
Joseph W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1968), pp. 21–25.
9.
This and the other pictures from Gabor’s experiment can be found in Ref. 5. They can also be found in Max Born and Emil Wolf, Principles of Optics (Pergamon, Oxford, 1991), 6th (corrected) ed., p. 456, but the caption is wrong.
10.
Emmett N.
Leith
, Juris
Upatnieks
, and Kenneth A.
Haines
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,” J. Opt. Soc. Am.
55
, 981
–986
(1965
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Emmett N.
Leith
and Juris
Upatnieks
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,” J. Opt. Soc. Am.
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(1962
);Emmett N.
Leith
and Juris
Upatnieks
, “Wavefront reconstruction with diffused illumination and three-dimensional objects
,” J. Opt. Soc. Am.
54
, 1295
–1301
(1964
).12.
A simple experimental proof of three-dimensional capability of holograms is reported in
Albert V.
Baez
and George
Castro
, “A laboratory demonstration of the three-dimensional nature of in-line holography
,” Am. J. Phys.
67
, 876
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(1999
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Reference 8, p. 10.
14.
The one-dimensional FFT function is included in most common commercial numerical software. The two-dimensional function can be obtained by applying the one-dimensional FFT first to all the rows and then to all the columns of the transformed matrix.
15.
On p. 486 of Ref. 5 Gabor reported that the reproduced part of the microphotograph is 350 times the theoretical resolution limit, which is estimated to be 3.5 μm.
16.
When repeating the experiment, it might be necessary to slightly modify Δ to obtain a well focused reconstruction. This modification is due to the fact that the captured area of the hologram can be different from our case.
17.
Maxime
Jacquot
, Patrick
Sandoz
, and Gilbert
Tribillon
, “High resolution digital holography
,” Opt. Commun.
190
, 87
–94
(2001
).18.
See Ref. 6, p. 128.
19.
P. Hariharan, Optical Holography (Cambridge U.P., Cambridge, 1984), p. 13.
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