Tom O. H. Charrett, Daniel Francis, and Ralph P. Tatam, "Quantitative shearography: error reduction by using more than three measurement channels," Appl. Opt. 50, 134-146 (2011)

Shearography is a noncontact optical technique used to measure surface displacement derivatives. Full surface strain characterization can be achieved using shearography configurations employing at least three measurement channels. Each measurement channel is sensitive to a single displacement gradient component defined by its sensitivity vector. A matrix transformation is then required to convert the measured components to the orthogonal displacement gradients required for quantitative strain measurement. This transformation, conventionally performed using three measurement channels, amplifies any errors present in the measurement. This paper investigates the use of additional measurement channels using the results of a computer model and an experimental shearography system. Results are presented showing that the addition of a fourth channel can reduce the errors in the computed orthogonal components by up to 33% and that, by using 10 channels, reductions of around 45% should be possible.

Shengjia Wang, Jie Dong, Franziska Pöller, Xingchen Dong, Min Lu, Laura M. Bilgeri, Martin Jakobi, Félix Salazar-Bloise, and Alexander W. Koch Appl. Opt. 58(3) 593-603 (2019)

Jie Dong, Shengjia Wang, Min Lu, Martin Jakobi, Zhanwei Liu, Xingchen Dong, Franziska Pöller, Laura Maria Bilgeri, Félix Salazar Bloise, Ali K. Yetisen, and Alexander Walter Koch Opt. Express 27(3) 3276-3283 (2019)

References

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Determined by radius of circular low-pass filter applied in the Fourier domain [17].
Value determined from camera specifications and experimental characterization.
Level determined by comparison with experimental data and represents noise sources other than camera noise.

Table 2

Results of the Zero Deformation Test for the Three-Channel and Four-Channel Methods

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

$\partial u/\partial y$

$\partial v/\partial y$

$\partial w/\partial y$

Experimental data

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

3.71

5.20

1.24

3.32

3.26

1.02

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

3.03

3.59

0.81

2.22

2.44

0.70

% Reduction

18.2%

31.0%

34.7%

33.0%

25.1%

31.8%

Modeled data (mean of 20 runs)

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

4.57

5.17

1.22

4.57

5.17

1.22

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

3.03

3.45

0.82

3.02

3.45

0.82

% Reduction

33.6%

33.2%

32.4%

33.8%

33.2%

32.5%

Table 3

Results of the Out-of-Plane Deformation Test for Experimental Data for the Three-Channel and Four-Channel Methods^{
a
}

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

8.99

14.75

3.26

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

7.46

8.20

2.06

% Reduction

17.1%

44.4%

36.8%

These are the standard deviations of the estimated error calculated by subtracting the local mean.

Table 4

Results of the Out-of-Plane Deformation Test for Modeled Data (Mean of 20 Runs) for the Three-Channel and Four-Channel Methods

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

$\partial u/\partial y$

$\partial v/\partial y$

$\partial w/\partial y$

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

6.38

7.18

1.70

6.36

7.22

1.74

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

4.19

4.84

1.20

4.22

4.80

1.21

% Reduction

34.3%

32.5%

29.2%

33.7%

33.5%

30.7%

Table 5

Results of the In-Plane Deformation Test for Experimental Data, for the Three-channel and Four-Channel Methods^{
a
}

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

$\partial u/\partial y$

$\partial v/\partial y$

$\partial w/\partial y$

Experimental data

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

27.14

27.94

11.88

28.09

20.91

9.88

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

15.84

21.84

11.39

21.49

17.77

7.85

% Reduction

41.6%

21.8%

4.14%

23.5%

15.0%

20.6%

These are the standard deviations of the estimated error calculated by subtracting the local mean.

Tables (5)

Table 1

Settings Used in Multichannel Shearography Model, Chosen to Match Values Used in the Experimental System

Determined by radius of circular low-pass filter applied in the Fourier domain [17].
Value determined from camera specifications and experimental characterization.
Level determined by comparison with experimental data and represents noise sources other than camera noise.

Table 2

Results of the Zero Deformation Test for the Three-Channel and Four-Channel Methods

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

$\partial u/\partial y$

$\partial v/\partial y$

$\partial w/\partial y$

Experimental data

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

3.71

5.20

1.24

3.32

3.26

1.02

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

3.03

3.59

0.81

2.22

2.44

0.70

% Reduction

18.2%

31.0%

34.7%

33.0%

25.1%

31.8%

Modeled data (mean of 20 runs)

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

4.57

5.17

1.22

4.57

5.17

1.22

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

3.03

3.45

0.82

3.02

3.45

0.82

% Reduction

33.6%

33.2%

32.4%

33.8%

33.2%

32.5%

Table 3

Results of the Out-of-Plane Deformation Test for Experimental Data for the Three-Channel and Four-Channel Methods^{
a
}

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

8.99

14.75

3.26

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

7.46

8.20

2.06

% Reduction

17.1%

44.4%

36.8%

These are the standard deviations of the estimated error calculated by subtracting the local mean.

Table 4

Results of the Out-of-Plane Deformation Test for Modeled Data (Mean of 20 Runs) for the Three-Channel and Four-Channel Methods

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

$\partial u/\partial y$

$\partial v/\partial y$

$\partial w/\partial y$

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

6.38

7.18

1.70

6.36

7.22

1.74

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

4.19

4.84

1.20

4.22

4.80

1.21

% Reduction

34.3%

32.5%

29.2%

33.7%

33.5%

30.7%

Table 5

Results of the In-Plane Deformation Test for Experimental Data, for the Three-channel and Four-Channel Methods^{
a
}

$\partial u/\partial x$

$\partial v/\partial x$

$\partial w/\partial x$

$\partial u/\partial y$

$\partial v/\partial y$

$\partial w/\partial y$

Experimental data

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—3 channels

27.14

27.94

11.88

28.09

20.91

9.88

Standard deviation in error ($\mathrm{\mu m}/\mathrm{m}$)—4 channels

15.84

21.84

11.39

21.49

17.77

7.85

% Reduction

41.6%

21.8%

4.14%

23.5%

15.0%

20.6%

These are the standard deviations of the estimated error calculated by subtracting the local mean.