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

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