Abstract

Using the image waves from two similar objects as, respectively, object wave and reference wave in an electronic speckle pattern interferometer (ESPI) setup, it is possible to obtain interference patterns that indicate the amount of relative displacement between the two objects. Experimental results demonstrating direct interferometric subtraction and addition of vibration patterns are presented. Possible applications of the technique are also discussed.

© 1981 Optical Society of America

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References

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  1. O. J. Løkberg, Phys. Technol. 11, 16 (1980).
  2. G. Å. Slettemoen, Appl. Opt. 19, 616 (1980).
  3. C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).
  4. O. J. Løkberg, K. Høgmoen, Proc. Soc. Photo-Opt. Instrum. Eng. 136, 222 (1977).
  5. K. A. Stetson, J. Opt. Soc. Am. 60, 1378 (1970).
  6. N. E. Molin, K. A. Stetson, J. Phys. E: 2, 609 (1969).

1980 (2)

O. J. Løkberg, Phys. Technol. 11, 16 (1980).

G. Å. Slettemoen, Appl. Opt. 19, 616 (1980).

1977 (1)

O. J. Løkberg, K. Høgmoen, Proc. Soc. Photo-Opt. Instrum. Eng. 136, 222 (1977).

1970 (1)

1969 (2)

N. E. Molin, K. A. Stetson, J. Phys. E: 2, 609 (1969).

C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).

Aleksoff, C. C.

C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).

Høgmoen, K.

O. J. Løkberg, K. Høgmoen, Proc. Soc. Photo-Opt. Instrum. Eng. 136, 222 (1977).

Løkberg, O. J.

O. J. Løkberg, Phys. Technol. 11, 16 (1980).

O. J. Løkberg, K. Høgmoen, Proc. Soc. Photo-Opt. Instrum. Eng. 136, 222 (1977).

Molin, N. E.

N. E. Molin, K. A. Stetson, J. Phys. E: 2, 609 (1969).

Slettemoen, G. Å.

Stetson, K. A.

K. A. Stetson, J. Opt. Soc. Am. 60, 1378 (1970).

N. E. Molin, K. A. Stetson, J. Phys. E: 2, 609 (1969).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. C. Aleksoff, Appl. Phys. Lett. 14, 23 (1969).

J. Opt. Soc. Am. (1)

J. Phys. E: (1)

N. E. Molin, K. A. Stetson, J. Phys. E: 2, 609 (1969).

Phys. Technol. (1)

O. J. Løkberg, Phys. Technol. 11, 16 (1980).

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

O. J. Løkberg, K. Høgmoen, Proc. Soc. Photo-Opt. Instrum. Eng. 136, 222 (1977).

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Figures (5)

Fig. 1
Fig. 1

The optical part of a speckle reference ESPI. Upper part shows a head-on view (enlarged) of the beam combiner BC.

Fig. 2
Fig. 2

Schematic drawing of the speckle reference ESPI setup used to compare the vibrational displacement of object O1 with that of object O2.

Fig. 3
Fig. 3

Objects vibrating at 1575 Hz: (a)–(b) individual vibration patterns of objects O1 and O2; (c) subtraction pattern, objects O1 and O2 vibrating in phase; (d) sum pattern, O1 and O2 vibrating in antiphase.

Fig. 4
Fig. 4

Objects vibrating at 2069 Hz: (a)–(b) individual vibration patterns of objects O1 and O2; (c) optimized subtraction pattern; (d) sum pattern, relative phase changed 180° from (c).

Fig. 5
Fig. 5

Objects vibrating at 10,150 Hz: (a)–(b) individual vibration patterns of objects O1 and O2; (c) subtraction pattern; (d) sum pattern, relative phase changed 180° from (c).

Equations (10)

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A O ( r , t ) = A O ( r ) exp [ i k O r O ( t ) ] ,
A R ( r , t ) = A R ( r ) exp [ i k R r R ( t ) ] .
I T ( r , t ) = | A O ( r , t ) + A R ( r , t ) | 2 = | A O ( r ) A O * ( r ) | 2 + | A R ( r ) A R * ( r ) | 2
+ 2 Re { A O ( r ) A R * ( r ) exp [ i ( k O r O ( t ) k R r R ( t ) } .
I m ( r ) { 2 Re [ A O ( r ) A R * ( r ) f ( t ) exp { i k [ r O ( t ) r R ( t ) ] } dt ] } w = { 2 Re [ A O ( r ) A R * ( r ) M ( r ) ] } 2 ,
I m ( r ) 2 I O I R | M ( r ) | 2 ,
| M | 2 = cos 2 [ k ( r O r R ) ] .
| r O ( t ) | = a O ( x , y ) cos [ 2 π ft + ϕ O ( x , y ) ] ,
| r R ( t ) | = a R ( x , y ) cos [ 2 π ft + ϕ R ( x , y ) ] .
| M | 2 = J O 2 { 2 k { a O 2 ( x , y ) + a R 2 ( x , y ) 2 a O ( x , y ) a R ( x , y ) cos [ ϕ O ( x , y ) ϕ R ( x , y ) ] } 1 / 2 } .

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