Abstract

By using two phase conjugate reflectors a dynamic interferometric system has been constructed which can sequentially measure differential changes in an object at short intervals. Holograms are recorded in two BSO crystals; one of them is used as an optical storage medium for a 2-D optical field to obtain a delayed phase conjugated wavefront and the other is used for the current wavefront. The phase conjugated wavefronts are generated sequentially, so that only interferograms of changes in optical phase shift with time are extracted. From the detected interferogram the amount of change of the desired parameter is derived and it is displayed in 3-D. The construction of the device and some measurement results are given.

© 1988 Optical Society of America

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References

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  1. D. Z. Anderson, D. M. Lininger, J. Feinberg, “Optical Tracking Novelty Filter,” Opt. Lett. 12, 123 (1987).
    [CrossRef] [PubMed]
  2. G. S. Ballard, “Double-Exposure Holographic Interferometry with Separate Reference Beams,” J. Appl. Phys. 39, 4846 (1968).
    [CrossRef]
  3. J. P. Huignard, J. P. Herriau, “Real-Time Double-Exposure Interferometry with Bi12SiO2O Crystals in Transverse Electrooptic Configuration,” Appl. Opt. 16, 1807 (1977).
    [CrossRef] [PubMed]
  4. T. Sato, T. Hatsuzawa, O. Ikeda, “Dynamic Interferometric Observation of Differential Movement,” Appl. Opt. 22, 3895 (1983).
    [CrossRef] [PubMed]

1987 (1)

1983 (1)

1977 (1)

1968 (1)

G. S. Ballard, “Double-Exposure Holographic Interferometry with Separate Reference Beams,” J. Appl. Phys. 39, 4846 (1968).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Principle of dynamic interferometry using two phase conjugate waves. The interferometry is divided into two steps: the first is for storing the object field in phase conjugator 1 (dashed line); the second stage simultaneously reads out the stored field from phase conjugator 2 after the desired delay time (solid line).

Fig. 2
Fig. 2

Schematic of the constructed experimental system: M1M4, mirrors; BS1–BS6, beam splitters; S1–S3, shutters.

Fig. 3
Fig. 3

Typical basic interferogram constructed by slightly inclining one of the two returned fields. The basic pattern consists of sixteen almost parallel fringes.

Fig. 4
Fig. 4

Experimental results for movement of a tapered water tank: (a) basic fringe pattern of the system obtained when no object is in place; (b) observed dynamic interferogram when the object is in place; (c) corresponding 2-D distribution of the change in density related to the thickness of the object.

Fig. 5
Fig. 5

Experimental results for diffusion of a saltwater lump in the water tank: (a) basic fringe pattern obtained when constant temperature water is in place; (b)–(d) sequentially observed dynamic interferograms; (e)–(g) corresponding 2-D distributions of the change in density over 2.5 s.

Fig. 6
Fig. 6

Experimental results for convection in the water tank due to heating: (a) basic fringe pattern; (b)–(d) sequentially observed dynamic interferograms; (e)–(g) corresponding 2-D distributions of the change in temperature over 2.5 s.

Equations (12)

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h 1 ( x , y ; t 1 ) = g ( x , y ) · f ( x , y ; t 1 ) .
g j ( x , y ; t j ) = h j * ( x , y ; t j ) = f * ( x , y ; t j ) g * ( x , y )             ( j = 1 , 2 ) ,
f ( x , y ; t j ) = exp [ i k n ( x , y , z ; t j ) d z ] ,             ( j = 1 , 2 ) ,
g ( x , y ; t j ) = exp [ - i k n ( x , y , z ; t j ) d z ] g * ( x , y )             ( j = 1 , 2 ) .
I ( x , y ) = A + B cos { k [ n ( x , y , z ; t 2 ) - n ( x , y , z ; t 1 ) ] d z } ,
n ( x , y , z ; t 2 ) - n ( x , y , z ; t 1 ) = n ( x , y , z ; t ) t · Δ t ;
n ( x , y , z ; t 2 ) - n ( x , y , z ; t 1 ) = n ( x + Δ x , y + Δ y , z ) - n ( x , y , z ) = n ( x , y , z ) x Δ x + n ( x , y , z ) y Δ y .
h ( x , y ; t ) ( d / λ ) Δ n ( x , y ; t ) h 0 ,
Δ n ( x , y ; t ) = A · Δ ρ ( x , y ; t ) ,
Δ ρ ( x , y ; t ) = ( λ / A d ) [ h ( x , y ; t ) / h 0 ] .
Δ n ( x , y ; t ) = B · Δ T ( x , y ; t ) ,
Δ T ( x , y ; t ) = ( λ / B d ) [ h ( x , y ; t ) / h 0 ] .

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