Abstract

A generalized technique of two-wavelength, nondiffuse holographic interferometry is developed for use with transparent experimental media. It is shown that a single pair of nondiffuse transmission holograms recorded simultaneously at different wavelengths can be reconstructed so as to produce a large number of interferograms with widely varying sensitivities. For ease in interpretation, these interferograms can have either an infinite-fringe background or a multiple-fringe background with any desired fringe orientation and spacing.

© 1971 Optical Society of America

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References

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  1. O. Bryngdahl, J. Opt. Soc. Amer. 59, 142 (1969).
    [CrossRef]
  2. F. Weigl, O. M. Friedrich, A. A. Dougal, IEEE J. Quantum Electron. QE-6, 41 (1970).
    [CrossRef]
  3. M. De, L. Sevigny, Appl. Opt. 6, 1665 (1967).
    [CrossRef] [PubMed]
  4. F. Weigl, O. M. Friedrich, A. A. Dougal, 1969 SWIEEECO Record-IEEE Cat. No. 69C16-SWIECO, 7E1 (1969); Space Age News 12, 21 (1969).
  5. F. Weigl, “Variable Sensitivity Optical Mach-Zehnder and Holographic Interferometry for Plasma Diagnostics,” Ph.D. Dissertation, The University of Texas at Austin (1969).
  6. G. V. Ostrovskaya, Yu. I. Ostrovsky, Rep. No. 214, A. F. Ioffe Physico-Technical Inst., Leningrad, U.S.S.R. (1969).
  7. B. P. Hildebrand, K. A. Haines, J. Opt. Soc. Amer. 57, 155 (1967).
    [CrossRef]
  8. L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1965).
    [CrossRef]
  9. G. S. Ballard, J. Appl. Phys. 39, 4846 (1968).
    [CrossRef]
  10. G. B. Brandt, Appl. Opt. 8, 1421 (1969).
    [CrossRef] [PubMed]

1970 (1)

F. Weigl, O. M. Friedrich, A. A. Dougal, IEEE J. Quantum Electron. QE-6, 41 (1970).
[CrossRef]

1969 (2)

G. B. Brandt, Appl. Opt. 8, 1421 (1969).
[CrossRef] [PubMed]

O. Bryngdahl, J. Opt. Soc. Amer. 59, 142 (1969).
[CrossRef]

1968 (1)

G. S. Ballard, J. Appl. Phys. 39, 4846 (1968).
[CrossRef]

1967 (2)

B. P. Hildebrand, K. A. Haines, J. Opt. Soc. Amer. 57, 155 (1967).
[CrossRef]

M. De, L. Sevigny, Appl. Opt. 6, 1665 (1967).
[CrossRef] [PubMed]

1965 (1)

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1965).
[CrossRef]

Ballard, G. S.

G. S. Ballard, J. Appl. Phys. 39, 4846 (1968).
[CrossRef]

Brandt, G. B.

Brooks, R. E.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1965).
[CrossRef]

Bryngdahl, O.

O. Bryngdahl, J. Opt. Soc. Amer. 59, 142 (1969).
[CrossRef]

De, M.

Dougal, A. A.

F. Weigl, O. M. Friedrich, A. A. Dougal, IEEE J. Quantum Electron. QE-6, 41 (1970).
[CrossRef]

F. Weigl, O. M. Friedrich, A. A. Dougal, 1969 SWIEEECO Record-IEEE Cat. No. 69C16-SWIECO, 7E1 (1969); Space Age News 12, 21 (1969).

Friedrich, O. M.

F. Weigl, O. M. Friedrich, A. A. Dougal, IEEE J. Quantum Electron. QE-6, 41 (1970).
[CrossRef]

F. Weigl, O. M. Friedrich, A. A. Dougal, 1969 SWIEEECO Record-IEEE Cat. No. 69C16-SWIECO, 7E1 (1969); Space Age News 12, 21 (1969).

Haines, K. A.

B. P. Hildebrand, K. A. Haines, J. Opt. Soc. Amer. 57, 155 (1967).
[CrossRef]

Heflinger, L. O.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1965).
[CrossRef]

Hildebrand, B. P.

B. P. Hildebrand, K. A. Haines, J. Opt. Soc. Amer. 57, 155 (1967).
[CrossRef]

Ostrovskaya, G. V.

G. V. Ostrovskaya, Yu. I. Ostrovsky, Rep. No. 214, A. F. Ioffe Physico-Technical Inst., Leningrad, U.S.S.R. (1969).

Ostrovsky, Yu. I.

G. V. Ostrovskaya, Yu. I. Ostrovsky, Rep. No. 214, A. F. Ioffe Physico-Technical Inst., Leningrad, U.S.S.R. (1969).

Sevigny, L.

Weigl, F.

F. Weigl, O. M. Friedrich, A. A. Dougal, IEEE J. Quantum Electron. QE-6, 41 (1970).
[CrossRef]

F. Weigl, O. M. Friedrich, A. A. Dougal, 1969 SWIEEECO Record-IEEE Cat. No. 69C16-SWIECO, 7E1 (1969); Space Age News 12, 21 (1969).

F. Weigl, “Variable Sensitivity Optical Mach-Zehnder and Holographic Interferometry for Plasma Diagnostics,” Ph.D. Dissertation, The University of Texas at Austin (1969).

Wuerker, R. F.

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1965).
[CrossRef]

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

F. Weigl, O. M. Friedrich, A. A. Dougal, IEEE J. Quantum Electron. QE-6, 41 (1970).
[CrossRef]

J. Appl. Phys. (2)

L. O. Heflinger, R. F. Wuerker, R. E. Brooks, J. Appl. Phys. 37, 642 (1965).
[CrossRef]

G. S. Ballard, J. Appl. Phys. 39, 4846 (1968).
[CrossRef]

J. Opt. Soc. Amer. (2)

O. Bryngdahl, J. Opt. Soc. Amer. 59, 142 (1969).
[CrossRef]

B. P. Hildebrand, K. A. Haines, J. Opt. Soc. Amer. 57, 155 (1967).
[CrossRef]

Other (3)

F. Weigl, O. M. Friedrich, A. A. Dougal, 1969 SWIEEECO Record-IEEE Cat. No. 69C16-SWIECO, 7E1 (1969); Space Age News 12, 21 (1969).

F. Weigl, “Variable Sensitivity Optical Mach-Zehnder and Holographic Interferometry for Plasma Diagnostics,” Ph.D. Dissertation, The University of Texas at Austin (1969).

G. V. Ostrovskaya, Yu. I. Ostrovsky, Rep. No. 214, A. F. Ioffe Physico-Technical Inst., Leningrad, U.S.S.R. (1969).

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Figures (6)

Fig. 1
Fig. 1

Recording arrangement for two-wavelength holographic interferometry.

Fig. 2
Fig. 2

Reconstruction arrangement for two-wavelength holographic interferometry.

Fig. 3
Fig. 3

Experimental arrangement to verify two-wavelength holographic interferometry—recording.

Fig. 4
Fig. 4

Experimental arrangement to verify two-wavelength holographic interferometry—reconstruction.

Fig. 5
Fig. 5

Comparison of six infinite-fringe interference patterns obtained from the same hologram pair.

Fig. 6
Fig. 6

Set of four interferograms obtained by combining a single pair of reconstructed images.

Equations (19)

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U ( x , y ) = A t 1 exp [ j ϕ 1 ( x , y ) ] exp ( - j ω 1 t ) + A t 2 exp [ j ϕ 2 ( x , y ) ] exp ( - j ω 2 t ) + A r 1 exp [ j ( 2 π x sin α 1 / λ 1 ) ] × exp ( - j ω 1 t ) + A r 2 exp [ j ( 2 π x sin α 1 / λ 2 ) ] exp ( - j ω 2 t ) ,
ϕ 1 , 2 ( x , y ) = 2 π λ 1 , 2 z = - Z z = 0 μ 1 , 2 ( x , y , z ) d z ,
I = U 2 .
exp [ ± j ( ω 1 - ω 2 ) t ] ,
I = 4 + exp [ j ( ϕ 1 - δ 1 x ) ] + exp [ - j ( ϕ 1 - δ 1 x ) ] + exp [ j ( ϕ 2 - δ 2 x ) ] + exp [ - j ( ϕ 2 - δ 2 x ) ] ,
δ 1 , 2 = 2 π sin α 1 / λ 1 , 2 .
T ( x , y ) = K I ( x , y ) ,
U i = exp ( j δ 3 x ) exp ( - j ω 3 t ) + exp ( j δ 4 x ) exp ( - j ω 3 t ) ,
δ 3 , 4 = 2 π sin α 3 , 4 / λ 3 .
U t = T ( x , y ) U i .
U t = { 4 exp ( j δ 3 x ) + 4 exp ( j δ 4 x ) + exp [ j ϕ 1 + j ( δ 3 - δ 1 ) x ] + exp [ j ϕ 1 + j ( δ 4 - δ 1 ) x ] + exp [ - j ϕ 1 + j ( δ 3 + δ 1 ) x ] + exp [ - j ϕ 1 + j ( δ 4 + δ 1 ) x ] + exp [ j ϕ 2 + j ( δ 3 - δ 2 ) x ] + exp [ j ϕ 2 + j ( δ 4 - δ 2 ) x ] + exp [ - j ϕ 2 + j ( δ 3 + δ 2 ) x ] + exp [ - j ϕ 2 + j ( δ 4 + δ 2 ) x ] + exp ( - j ω 3 t ) .
I 1 = 2 + 2 cos [ ϕ 1 - ϕ 2 + ( δ 3 - δ 1 - δ 4 + δ 2 ) x ] .
I 1 = 2 + 2 cos [ ϕ 1 - ϕ 2 + ( δ 3 - δ 1 - δ 4 + δ 2 ) x + δ 5 y ] .
δ 4 - δ 1 δ 3 - δ 2 , δ 3 + δ 1 δ 4 + δ 2 , or δ 4 + δ 1 δ 3 + δ 2 .
I 2 = 2 + 2 cos [ ϕ 1 + ϕ 2 + ( δ 3 - δ 1 - δ 4 - δ 2 ) x ] .
I 3 = 2 + 2 cos [ 2 ϕ 1 + ( δ 3 - 2 δ 1 - δ 4 ) x ] .
I 4 = 2 + 2 cos [ 2 ϕ 2 + ( δ 3 - 2 δ 2 - δ 4 ) x ] ,
I 5 = 17 + 2 cos [ ϕ 1 + ( δ 4 - δ 1 - δ 3 ) x ] ,
I 6 = 17 + 2 cos [ ϕ 2 + ( δ 3 - δ 4 + δ 2 ) x ] .

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