Abstract

Real-time holographic interferometry performed with two very thin, parallel, closely spaced object illumination beams can be used to produce a time-varying irradiance which, when incident on a photodetector, gives a signal whose analysis indicates both the normal displacement and tilt at a point on the object surface. The signal also contains information about in-plane translation which can be utilized in some cases.

© 1983 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), p. 115.
  2. K. A. Stetson, in Proceedings, SESA Spring Meeting (Society of Experimental Stress Analysis, Brookfield Center, Conn., 1981), pp. 236–241.

Stetson, K. A.

K. A. Stetson, in Proceedings, SESA Spring Meeting (Society of Experimental Stress Analysis, Brookfield Center, Conn., 1981), pp. 236–241.

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), p. 115.

Other (2)

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979), p. 115.

K. A. Stetson, in Proceedings, SESA Spring Meeting (Society of Experimental Stress Analysis, Brookfield Center, Conn., 1981), pp. 236–241.

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Figures (5)

Fig. 1
Fig. 1

Optical system and nomenclature. P and Q are points on the object surface. The imaging system is composed of lenses L1 and L2. The hologram is recorded in plane H, and the points P and Q are imaged onto detector D.

Fig. 2
Fig. 2

Typical plot of the output signal for the parameters Δx = 2.0 mm and α = 10°. A shift of one fringe in the fine structure corresponds to a normal displacement of 0.32 μm. Each pair of zero crossings of the modulation corresponds to a tilt of 0.16 mrad.

Fig. 3
Fig. 3

Output signal for the same motion and configuration as in Fig. 2, except the sensitivity to tilt has been decreased by changing Δx from 2.0 to 1.0 mm.

Fig. 4
Fig. 4

Output signal when the object is illuminated by only one beam. The surface motion is a nearly normal translation.

Fig. 5
Fig. 5

Output signal for single-beam illumination when there is a significant in-plane translation and tilt as well as normal displacement.

Equations (16)

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I = U P + U P 2 + U Q + U Q , 2
I P + I Q = I ( x , t ) + I ( x + Δ x , t ) ,
I ( x , t ) = I 0 { 1 + ν ( t ) cos [ 2 π λ ( k ^ 2 - k ^ 1 ) · L ( x , t ) ] } .
S ( x , t ) = - d s / 2 d s / 2 - d s / 2 d s / 2 I 0 { 1 + ν ( t ) cos [ 2 π λ ( k ^ 2 - k ^ 1 ) · L ( x , t ) ] } d x d y .
L ( x , t ) = i ^ L x ( t ) + j ^ L y ( t ) + k ^ × [ L z ( t ) + θ x ( t ) y - θ y ( t ) x ] ,
S ( x , t ) + S ( x + Δ x , t ) = S 0 { 1 + ν ( t ) μ ( t ) cos [ 2 π λ cos α θ y ( t ) Δ x ] × cos [ 4 π λ cos α L ¯ z ( t ) ] } ,
L ¯ z = λ N F 2 cos α ,
θ y = λ N 0 2 Δ x cos α ,
ν ( t ) = sinc ( D z 2 l 0 δ 0 x ) sinc ( D z 2 l 0 δ 0 y ) ,
δ 0 x = - 2 π λ { 1 z [ L x ( t ) ] + 2 θ y } ,
δ 0 y = - 2 π λ { 1 z [ L y ( t ) ] - 2 θ x } .
ν ( t ) = sinc [ π D λ l 0 L x ( t ) ] sinc [ π D λ l 0 L y ( t ) ] .
μ ( t ) = sinc [ 2 π λ d s θ x ( t ) ] sinc [ 2 π λ d s θ y ( t ) ] ,
S ( x , t ) + S ( x + Δ x , t ) = S 0 ( 1 + { sinc [ π D λ l 0 L x ( t ) ] sinc [ π D λ l 0 L y ( t ) ] } × { sinc [ 2 π d s λ θ x ( t ) ] sinc [ 2 π d s λ θ y ( t ) ] } × cos [ 2 π Δ x λ θ y ( t ) ] cos [ 4 π λ L ¯ z ( t ) ] ) .
S ( x , t ) + S ( x + Δ x , t ) = S 0 { 1 + sinc [ π D λ l 0 L T ( t ) ] sinc [ 2 π d s λ θ ( t ) ] × cos [ 2 π Δ x λ θ y ( t ) ] cos [ 4 π λ L ¯ z ( t ) ] } ,
L z / ( θ y Δ x ) = ( 2 L P z + θ y Δ x ) / ( 2 θ y Δ x ) = ½ + L P z / ( θ y Δ x ) .

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