Abstract

An interference microscope is described, constructed in 1951–56, in which three-dimensional objects can be reconstructed, correctly incorporating amplitudes and phases, from two photographs simultaneously taken on one plate. These photographs are “holograms,” that is to say, records of the interference of the image-carrying wave, split in two, with a coherent background wave, also split in two. A phase difference of a quarter wave is produced, for the two otherwise identical photographs, between the image-carrying waves and their respective coherent backgrounds. The two photographs are in sine–cosine or “quadrature” relation; between them they contain the full optical information. If they are illuminated in such a way that there is a difference of a quarter wave in the phases at two corresponding points, and if the two beams are united, the original image-carrying wave is restored correctly in amplitude and in phase. An essential part of the instrument is a “quadrature prism”; a beam splitter with a three-layer sandwich, which establishes the quadrature relation in the taking of the holograms.

The microscope has the advantage that it need not be focused, as it gives a three-dimensional reconstruction. Moreover, photographs can be taken with 1/10 or even 1/100 of the light required for exposure going through the object; the rest of the energy is supplied by the background beam, which is 10–100 times stronger, and which goes around the object.

Many details of the instrument are now out of date owing to the invention of the laser. Alternative methods which have now become possible are discussed for realizing the principle of total reconstruction.

© 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, 475 (1949);Proc. Phys. Soc. (London) B64, 244 (1951).
    [Crossref]
  2. G. L. Rogers, Nature 166, 237 (1950);Proc. Roy. Soc. (Edinburgh) A63, III, 193 (1952).
    [Crossref]
  3. A. Lohmann, Opt. Acta 3, 97 (1956).
    [Crossref]
  4. W. L. Bragg and G. L. Rogers, Nature 167, 190 (1951).
    [Crossref] [PubMed]
  5. G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956).
  6. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963);J. Opt. Soc. Am. 54, 1295 (1964);J. Opt. Soc. Am. 55, 569 (1965).
    [Crossref]
  7. G. W. Stroke, Optics of Coherent and Non-Coherent Electromagnetic Radiations (University of Michigan, Ann Arbor, 1965), 2nd ed.;G. W. Stroke and D. G. Falconer, Phys. Letters 13, 306 (1964);Phys. Letters 15, 283 (1965).
    [Crossref]
  8. F. Zernike, Physica 5, 785 (1938);Proc. Phys. Soc. (London) 61, 158 (1948).
    [Crossref]
  9. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955and Optical Properties of Thin Solid FilmsDover Publications, Inc., New York, 1966), p. 58.
  10. W. P. Goss, “The Preparation of Thin Metallic Phase Changing Layers for Optical Purposes,” M.Sc. thesis, London, 1958.

1963 (1)

1956 (2)

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956).

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

1951 (1)

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

1950 (1)

G. L. Rogers, Nature 166, 237 (1950);Proc. Roy. Soc. (Edinburgh) A63, III, 193 (1952).
[Crossref]

1948 (1)

D. Gabor, Nature,  161, 777 (1948);Proc. Roy. Soc. (London) A197, 475 (1949);Proc. Phys. Soc. (London) B64, 244 (1951).
[Crossref]

1938 (1)

F. Zernike, Physica 5, 785 (1938);Proc. Phys. Soc. (London) 61, 158 (1948).
[Crossref]

Bragg, W. L.

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

Gabor, D.

D. Gabor, Nature,  161, 777 (1948);Proc. Roy. Soc. (London) A197, 475 (1949);Proc. Phys. Soc. (London) B64, 244 (1951).
[Crossref]

Goss, W. P.

W. P. Goss, “The Preparation of Thin Metallic Phase Changing Layers for Optical Purposes,” M.Sc. thesis, London, 1958.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955and Optical Properties of Thin Solid FilmsDover Publications, Inc., New York, 1966), p. 58.

Leith, E. N.

Lohmann, A.

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

Rogers, G. L.

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956).

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

G. L. Rogers, Nature 166, 237 (1950);Proc. Roy. Soc. (Edinburgh) A63, III, 193 (1952).
[Crossref]

Stroke, G. W.

G. W. Stroke, Optics of Coherent and Non-Coherent Electromagnetic Radiations (University of Michigan, Ann Arbor, 1965), 2nd ed.;G. W. Stroke and D. G. Falconer, Phys. Letters 13, 306 (1964);Phys. Letters 15, 283 (1965).
[Crossref]

Upatnieks, J.

Zernike, F.

F. Zernike, Physica 5, 785 (1938);Proc. Phys. Soc. (London) 61, 158 (1948).
[Crossref]

J. Opt. Soc. Am. (1)

Nature (3)

D. Gabor, Nature,  161, 777 (1948);Proc. Roy. Soc. (London) A197, 475 (1949);Proc. Phys. Soc. (London) B64, 244 (1951).
[Crossref]

G. L. Rogers, Nature 166, 237 (1950);Proc. Roy. Soc. (Edinburgh) A63, III, 193 (1952).
[Crossref]

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

Opt. Acta (1)

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

Physica (1)

F. Zernike, Physica 5, 785 (1938);Proc. Phys. Soc. (London) 61, 158 (1948).
[Crossref]

Proc. Roy. Soc. (Edinburgh) (1)

G. L. Rogers, Proc. Roy. Soc. (Edinburgh) A64, II, 209 (1956).

Other (3)

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworths, London, 1955and Optical Properties of Thin Solid FilmsDover Publications, Inc., New York, 1966), p. 58.

W. P. Goss, “The Preparation of Thin Metallic Phase Changing Layers for Optical Purposes,” M.Sc. thesis, London, 1958.

G. W. Stroke, Optics of Coherent and Non-Coherent Electromagnetic Radiations (University of Michigan, Ann Arbor, 1965), 2nd ed.;G. W. Stroke and D. G. Falconer, Phys. Letters 13, 306 (1964);Phys. Letters 15, 283 (1965).
[Crossref]

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Figures (9)

F. 1
F. 1

Varieties of holography: (a) Upper left: Straight illumination, reconstruction with original wavefront. Low coherence requirements but low contrast. (b) Upper right: Reconstructing wavefront O2 different from O1. (c) Lower left: Skew illumination and background. High coherence requirements but good contrast. Conjugate images separated by direction of light as well as by position. (d) Lower right: Illuminator separated from background. Same advantages as in (c) but in addition diffuse illuminator distributes information over the whole photographic plate.

F. 2
F. 2

Principle of complete wavefront reconstruction.

F. 3
F. 3

Interference microscope, 1951 design. Elements shown in interrupted lines are used in the reconstruction only.

F. 4
F. 4

Theory of the quadrature layer.

F. 5
F. 5

Complementary images for measuring the phase shift.

F. 6
F. 6

Quadrature prism evaporation schedule. First gold layer deposited in first 5 min. Aluminum layer deposited in second 5 min. Oxidation during 10 h. Second gold layer deposited in 2–3 min, after oxidation.

F. 7
F. 7

Modifications (1956) for avoiding and ensuring the parallelism and correct phase of the two wavefronts in the reconstruction.

F. 8
F. 8

Complementary images of a mica flake.

F. 9
F. 9

Top, image beam alone: left, unit exposure; right, tenfold exposure. Bottom, complementary images with coherent background. Unit exposure; background 9 times stronger than image beam. The object is a thin mica flake.

Equations (29)

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i ( x , y ) = ( a e i φ + A e i φ ) ( a * e i φ + A * e i φ ) = a a * + A A * + a A * e i ( φ ϕ ) + a * A e i ( φ ϕ ) .
t ( x , y ) A · e i ϕ = ( a a * + A A * ) A e i ϕ + a A A * e i φ + a * A 2 e i ( φ 2 ϕ ) .
A 1 2 + a 2 + 2 a A 1 cos ϕ .
A 2 2 + a 2 + 2 a A 2 sin ϕ .
( A 2 + a 2 ) A + 2 A 2 a ( cos ϕ + i sin ϕ ) .
A = R a + T A
A = T a + R A .
R = R = R .
R = T ,
R / T = e ± i π / 4 .
A = R ( a + e i π / 4 A )
A = R ( e i π / 4 a + A ) = R e i π / 4 ( a + e i π / 4 A ) .
| J R | = | a 11 a 12 a 21 a 22 | | F B | | 0 T | = | a 11 a 12 a 21 a 22 | | B F | .
J = 1 = a 11 F + a 12 B 0 = a 11 B + a 12 F R = a 21 F + a 22 B T = a 21 B + a 22 F .
R = a 11 a 21 a 22 a 12 a 11 2 a 12 2 , T = a 11 a 22 a 12 a 21 a 11 2 a 12 2 , R T = a 11 a 21 a 22 a 12 a 11 a 22 a 12 a 21 .
a 11 = 1 / t , a 21 = r / t .
a 12 = r / t , a 22 = ( 1 + a 12 a 21 ) a 11 = t r r / t ,
a 11 a 22 a 12 a 21 = 1 ,
ϕ = 2 π d / ( λ cos θ )
r = r = i r e i ϕ .
R = a 11 a 21 a 12 a 22 a 11 2 a 12 2 = r + t 2 r 1 r 2 = r + t 2 r ( 1 + r 2 + ) = i r e i ϕ ( 1 + t 2 / ( 1 + r 2 e 2 i ϕ )
T = a 11 a 22 a 12 a 21 a 11 2 a 12 2 = 1 a 11 2 a 12 2 = t 2 1 r 2 = t 2 ( 1 + r 2 + ) = t 2 / ( 1 + r 2 e 2 i ϕ ) .
R / T = ( i r e i ϕ / t 2 ) ( 1 + t 2 + r 2 e 2 i ϕ ) = e ± i π / 4 .
tan ϕ = ω ,
( 1 + t 2 ) ( 1 + ω 2 ) + r 2 ( 1 ω 2 ) = ± r 2 ω ( 1 ± ω ) / ( 1 ω )
( 1 + t 2 ) 2 + r 4 + 2 r 2 ( 1 + t 2 ) ( 1 + ω 2 ) 1 2 = t 4 / r 2 .
ω = ± 0.908 , r 2 = 0.178 , t 2 = 0.822 .
d = 0.117 λ cos θ
r 2 = [ ( n n 0 ) / ( n + n 0 ) ] 2 = 0.178 .