Abstract

The technique of wavefront reconstruction has made possible several basic extensions of interferometry. In the hologram interferometer it is not necessary that either beam be analytically expressible, nor is it necessary that the perturbances of the optical path be small. Moreover, it becomes possible to generate interferograms between wave disturbances which exist at different times, have different wavelengths, and/or have quadrature polarizations. We present a set of experiments which indicates the performance of the hologram recording system as an interferometer. The discussion of these extensions of classical interferometry with their applications is aided by reference to several independent developments of the hologram interferometry technique.

© 1966 Optical Society of America

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References

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  1. E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1300 (1964).
    [Crossref]
  2. R. Powell and K. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).
    [Crossref]
  3. M. H. Horman, Appl. Opt. 4, 333 (1965).
    [Crossref]
  4. K. Stetson and R. Powell, J. Opt. Soc. Am. 55, 1694 (1965).
    [Crossref]
  5. K. Stetson and R. Powell, J. Opt. Soc. Am. 55, 1570A (1965).
    [Crossref]
  6. B. P. Hildebrand and K. A. Haines, Appl. Opt. 5, 172 (1966).
    [Crossref] [PubMed]
  7. K. A. Haines and B. P. Hildebrand, Appl. Opt. 5, 595 (1966).
    [Crossref] [PubMed]
  8. K. A. Haines and B. P. Hildebrand, Phys. Letters 19, 10 (1965).
    [Crossref]
  9. R. J. Collier, E. I. Doherty, and K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
    [Crossref]
  10. R. E. Brooks, L. O. Heflinger, R. F. Wuerker, and R. A. Briones, Appl. Phys. Letters 7, 92 (1965);Appl. Phys. Letters 7, 248 (1965).
    [Crossref]
  11. L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
    [Crossref]
  12. J. M. Burch, “The 1965 Viscount Nuffield Memorial Paper,” in Prodt. Engr. 36, 431 (1965).
    [Crossref]
  13. F. T. Arecchi and A. Sona, in Quasi-Optics Symposium Proceedings, Ed. by Jerome Fox (Polytechnic Press, Brooklyn, N. Y., 1964), p. 623.

1966 (3)

1965 (8)

J. M. Burch, “The 1965 Viscount Nuffield Memorial Paper,” in Prodt. Engr. 36, 431 (1965).
[Crossref]

K. A. Haines and B. P. Hildebrand, Phys. Letters 19, 10 (1965).
[Crossref]

R. J. Collier, E. I. Doherty, and K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[Crossref]

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, and R. A. Briones, Appl. Phys. Letters 7, 92 (1965);Appl. Phys. Letters 7, 248 (1965).
[Crossref]

R. Powell and K. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).
[Crossref]

M. H. Horman, Appl. Opt. 4, 333 (1965).
[Crossref]

K. Stetson and R. Powell, J. Opt. Soc. Am. 55, 1694 (1965).
[Crossref]

K. Stetson and R. Powell, J. Opt. Soc. Am. 55, 1570A (1965).
[Crossref]

1964 (1)

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1300 (1964).
[Crossref]

Arecchi, F. T.

F. T. Arecchi and A. Sona, in Quasi-Optics Symposium Proceedings, Ed. by Jerome Fox (Polytechnic Press, Brooklyn, N. Y., 1964), p. 623.

Briones, R. A.

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, and R. A. Briones, Appl. Phys. Letters 7, 92 (1965);Appl. Phys. Letters 7, 248 (1965).
[Crossref]

Brooks, R. E.

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[Crossref]

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, and R. A. Briones, Appl. Phys. Letters 7, 92 (1965);Appl. Phys. Letters 7, 248 (1965).
[Crossref]

Burch, J. M.

J. M. Burch, “The 1965 Viscount Nuffield Memorial Paper,” in Prodt. Engr. 36, 431 (1965).
[Crossref]

Collier, R. J.

R. J. Collier, E. I. Doherty, and K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[Crossref]

Doherty, E. I.

R. J. Collier, E. I. Doherty, and K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[Crossref]

Haines, K. A.

Heflinger, L. O.

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[Crossref]

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, and R. A. Briones, Appl. Phys. Letters 7, 92 (1965);Appl. Phys. Letters 7, 248 (1965).
[Crossref]

Hildebrand, B. P.

Horman, M. H.

Leith, E.

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1300 (1964).
[Crossref]

Pennington, K. S.

R. J. Collier, E. I. Doherty, and K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[Crossref]

Powell, R.

Sona, A.

F. T. Arecchi and A. Sona, in Quasi-Optics Symposium Proceedings, Ed. by Jerome Fox (Polytechnic Press, Brooklyn, N. Y., 1964), p. 623.

Stetson, K.

Upatnieks, J.

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1300 (1964).
[Crossref]

Wuerker, R. F.

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[Crossref]

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, and R. A. Briones, Appl. Phys. Letters 7, 92 (1965);Appl. Phys. Letters 7, 248 (1965).
[Crossref]

Appl. Opt. (3)

Appl. Phys. Letters (2)

R. J. Collier, E. I. Doherty, and K. S. Pennington, Appl. Phys. Letters 7, 223 (1965).
[Crossref]

R. E. Brooks, L. O. Heflinger, R. F. Wuerker, and R. A. Briones, Appl. Phys. Letters 7, 92 (1965);Appl. Phys. Letters 7, 248 (1965).
[Crossref]

J. Appl. Phys. (1)

L. O. Heflinger, R. F. Wuerker, and R. E. Brooks, J. Appl. Phys. 37, 642 (1966).
[Crossref]

J. Opt. Soc. Am. (4)

K. Stetson and R. Powell, J. Opt. Soc. Am. 55, 1694 (1965).
[Crossref]

K. Stetson and R. Powell, J. Opt. Soc. Am. 55, 1570A (1965).
[Crossref]

E. Leith and J. Upatnieks, J. Opt. Soc. Am. 54, 1300 (1964).
[Crossref]

R. Powell and K. Stetson, J. Opt. Soc. Am. 55, 1593 (1965).
[Crossref]

Phys. Letters (1)

K. A. Haines and B. P. Hildebrand, Phys. Letters 19, 10 (1965).
[Crossref]

Prodt. Engr. (1)

J. M. Burch, “The 1965 Viscount Nuffield Memorial Paper,” in Prodt. Engr. 36, 431 (1965).
[Crossref]

Other (1)

F. T. Arecchi and A. Sona, in Quasi-Optics Symposium Proceedings, Ed. by Jerome Fox (Polytechnic Press, Brooklyn, N. Y., 1964), p. 623.

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Figures (5)

F. 1
F. 1

An experimental setup to compare hologram interferometry with classical interferometry. The object (A) of the hologram (B) is a broad-source Michelson interferometer; the setup also includes mirror (C), lens with pin hole (D), back-surface mirror (E), and laser beam (F).

F. 2
F. 2

Reconstructions of two holograms made in Fig. 1. One of interferometer output was made with both beams present (a), the other is a sequential recording of each beam separately (b).

F. 3
F. 3

Three reconstructions from holograms made with slight motions half-way-through the exposure, (a) Reference mirror moved; (b) object moved; (c) hologram plate moved.

F. 4
F. 4

Reconstruction of an extended series of objects spaced 10 cm apart illustrating periodic coherence of the laser.

F. 5
F. 5

Three views of a reconstruction of a laser beam with simultaneous 2,0 and 0,0 modes.

Equations (14)

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I ( x 1 , y 1 ) = [ 1 / t r 0 t r e i ϕ ( z ) d t ] I s t ( x 1 , y 1 ) ,
1 t r 0 t r e i ϕ ( z ) d t M ,
ϕ = zero , for 0 t < t r / 2 , ϕ = f ( x 1 , y 1 ) for t r / 2 < t t r .
M = 1 + e i f ( x 1 , y 1 ) .
f ( x 1 , y 1 ) = ( 2 π / λ ) ( cos ϕ 1 + cos ϕ 2 ) a x 1 ,
M = 2 + 2 cos { ( 2 π / λ ) ( cos θ 1 + cos θ 2 ) a x 1 } .
a x 1 = z d ,
M = J 0 [ ( 2 π / λ ) ( cos θ 1 + cos θ 2 ) m ( x 1 , y 1 ) ] ,
M = 2 + 2 cos { ( 2 π / λ ) ( cos θ 1 + cos θ 2 ) × [ a x 1 + m ( x 1 , y 1 ) cos ω t ] } .
M = 2 + 2 cos [ ( 2 π / λ ) ( cos θ 1 + cos θ 2 ) a x 1 ] × J 0 [ ( 2 π / λ ) ( cos θ 1 + cos θ 2 ) m ( x 1 , y 1 ) ] .
n = 1 N e i ( 2 π / λ n ) z Δ ,
λ n = 2 L / ( m + n ) ,
n = 1 N e i ( 2 π / λ n ) z Δ = e i m π z Δ / L n = 1 N e i n π z Δ / L .
N + 2 ( n 1 ) cos π z Δ / L + 2 ( N 2 ) cos 2 π z Δ / L + 2 cos ( N 2 ) π z Δ / L .