Abstract

Fringe analysis in the interferometry has been of long-standing interest to the academic community. However, the process of sparse fringe is always a headache in the measurement, especially when the specimen is very small. Through theoretical derivation and experimental measurements, our work demonstrates a new method for fringe multiplication. Theoretically, arbitrary integral-multiple fringe multiplication can be acquired by using the interferogram phase as the parameter. We simulate digital images accordingly and find that not only the skeleton lines of the multiplied fringe are very convenient to extract, but also the main frequency of which can be easily separated from the DC component. Meanwhile, the experimental results have a good agreement with the theoretic ones in a validation using the classical photoelasticity.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  7. T. H. Baek, M. S. Kim, and D. P. Hong, “Fringe Analysis for Photoelasticity Using Image Processing Techniques,” Int. J. Softw. Eng. Appl. 8, 91–102 (2014).
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2014 (2)

D. Misseroni, F. C. Dal, S. Shahzad, and D. Bigoni, “Stress concentration near stiff inclusions: validation of rigid inclusion model and boundary layers by means of photoelasticity,” Eng. Fract. Mech. 121-122, 87–97 (2014).
[Crossref]

T. H. Baek, M. S. Kim, and D. P. Hong, “Fringe Analysis for Photoelasticity Using Image Processing Techniques,” Int. J. Softw. Eng. Appl. 8, 91–102 (2014).

2011 (1)

2010 (1)

W. Wang and J. S. Hsu, “Investigation of vibration characteristics of bonded structures by time-averaged electronic speckle pattern interferometry,” Opt. Lasers Eng. 48(10), 958–965 (2010).
[Crossref]

2003 (1)

J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun. 224(4-6), 221–227 (2003).
[Crossref]

2001 (1)

J. A. Quiroga, J. A. Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
[Crossref]

1996 (1)

1993 (1)

1989 (1)

1986 (2)

1971 (1)

1966 (1)

D. Post, “Fringe multiplication in three-dimensional photoelasticity,” J. Strain Anal. Eng. Des. 1(5), 380–388 (1966).
[Crossref]

Andresen, K.

Bachor, H. A.

Baek, T. H.

T. H. Baek, M. S. Kim, and D. P. Hong, “Fringe Analysis for Photoelasticity Using Image Processing Techniques,” Int. J. Softw. Eng. Appl. 8, 91–102 (2014).

Bigoni, D.

D. Misseroni, F. C. Dal, S. Shahzad, and D. Bigoni, “Stress concentration near stiff inclusions: validation of rigid inclusion model and boundary layers by means of photoelasticity,” Eng. Fract. Mech. 121-122, 87–97 (2014).
[Crossref]

Bone, D. J.

Dal, F. C.

D. Misseroni, F. C. Dal, S. Shahzad, and D. Bigoni, “Stress concentration near stiff inclusions: validation of rigid inclusion model and boundary layers by means of photoelasticity,” Eng. Fract. Mech. 121-122, 87–97 (2014).
[Crossref]

Dong, X.

Feng, X.

García-Botella, Á.

J. A. Quiroga, J. A. Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
[Crossref]

Gómez-Pedrero, J. A.

J. A. Quiroga, J. A. Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
[Crossref]

Han, B.

Hong, D. P.

T. H. Baek, M. S. Kim, and D. P. Hong, “Fringe Analysis for Photoelasticity Using Image Processing Techniques,” Int. J. Softw. Eng. Appl. 8, 91–102 (2014).

Hsu, J. S.

W. Wang and J. S. Hsu, “Investigation of vibration characteristics of bonded structures by time-averaged electronic speckle pattern interferometry,” Opt. Lasers Eng. 48(10), 958–965 (2010).
[Crossref]

Hwang, K. C.

Jueptner, W.

Kim, M. S.

T. H. Baek, M. S. Kim, and D. P. Hong, “Fringe Analysis for Photoelasticity Using Image Processing Techniques,” Int. J. Softw. Eng. Appl. 8, 91–102 (2014).

Kreis, T.

Ma, Q.

Ma, S.

Misseroni, D.

D. Misseroni, F. C. Dal, S. Shahzad, and D. Bigoni, “Stress concentration near stiff inclusions: validation of rigid inclusion model and boundary layers by means of photoelasticity,” Eng. Fract. Mech. 121-122, 87–97 (2014).
[Crossref]

Osten, W.

Post, D.

D. Post, “Moiré fringe multiplication with a nonsymmetrical doubly blazed reference grating,” Appl. Opt. 10(4), 901–907 (1971).
[Crossref] [PubMed]

D. Post, “Fringe multiplication in three-dimensional photoelasticity,” J. Strain Anal. Eng. Des. 1(5), 380–388 (1966).
[Crossref]

Quiroga, J. A.

J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun. 224(4-6), 221–227 (2003).
[Crossref]

J. A. Quiroga, J. A. Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
[Crossref]

Sandeman, R. J.

Servin, M.

J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun. 224(4-6), 221–227 (2003).
[Crossref]

Shahzad, S.

D. Misseroni, F. C. Dal, S. Shahzad, and D. Bigoni, “Stress concentration near stiff inclusions: validation of rigid inclusion model and boundary layers by means of photoelasticity,” Eng. Fract. Mech. 121-122, 87–97 (2014).
[Crossref]

Wang, W.

W. Wang and J. S. Hsu, “Investigation of vibration characteristics of bonded structures by time-averaged electronic speckle pattern interferometry,” Opt. Lasers Eng. 48(10), 958–965 (2010).
[Crossref]

Yu, Q.

Appl. Opt. (5)

Eng. Fract. Mech. (1)

D. Misseroni, F. C. Dal, S. Shahzad, and D. Bigoni, “Stress concentration near stiff inclusions: validation of rigid inclusion model and boundary layers by means of photoelasticity,” Eng. Fract. Mech. 121-122, 87–97 (2014).
[Crossref]

Int. J. Softw. Eng. Appl. (1)

T. H. Baek, M. S. Kim, and D. P. Hong, “Fringe Analysis for Photoelasticity Using Image Processing Techniques,” Int. J. Softw. Eng. Appl. 8, 91–102 (2014).

J. Opt. Soc. Am. A (1)

J. Strain Anal. Eng. Des. (1)

D. Post, “Fringe multiplication in three-dimensional photoelasticity,” J. Strain Anal. Eng. Des. 1(5), 380–388 (1966).
[Crossref]

Opt. Commun. (2)

J. A. Quiroga, J. A. Gómez-Pedrero, and Á. García-Botella, “Algorithm for fringe pattern normalization,” Opt. Commun. 197(1-3), 43–51 (2001).
[Crossref]

J. A. Quiroga and M. Servin, “Isotropic n-dimensional fringe pattern normalization,” Opt. Commun. 224(4-6), 221–227 (2003).
[Crossref]

Opt. Express (1)

Opt. Lasers Eng. (1)

W. Wang and J. S. Hsu, “Investigation of vibration characteristics of bonded structures by time-averaged electronic speckle pattern interferometry,” Opt. Lasers Eng. 48(10), 958–965 (2010).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1

(a) The simulated digital image; (b) the 7-fold multiplied fringe pattern; (c) and (d) show the skeleton lines of the (a) and (b), respectively; (e) the intensity of centerline (seen the red line in the Figs. 1(a) and 1(b)).

Fig. 2
Fig. 2

(a) and (b) are the frequency domain of the original and the multiplied image respectively (To increase the contrast, the displayed intensity I=ln( 1+| I F | ) is used, where | I F | is the amplitude of frequency, however, the intensity in center of (b) appears lower than the two neighboring lobes, this optical illusion is mainly caused by picture zooming out in the text and the displaying function I=ln( 1+| I F | ) we used.); (c) and (d) are the frequency amplitude distribution along centerline of frequency map of the original and the multiplied image respectively.

Fig. 3
Fig. 3

(a) The wraped pase of multiplied fringes pattern; (b) The unwrapped phase ( ϕ N /N ) distribution of the simulated image; (c) The phase error distribution.

Fig. 4
Fig. 4

The arrangement of photoelasticity experiment.

Fig. 5
Fig. 5

The original photoelastic fringe obtained in this experiment.

Fig. 6
Fig. 6

The process of calibration (a) the experimental intensituy dependent on rotation degree of analyzer, (b) the fitting function of calibration.

Fig. 7
Fig. 7

The multiplication result of normalized fringe pattern with and without calibration, (a) the normalized fringe without calibration (only the area interested is shown with mask); (b) the 15-fold multiplication result of (a); (c) the 23-fold multiplication result of (a); (d) the normalized fringe with calibration; (e) the 15-fold multiplication result of (d); (f) the 23-fold multiplication result of (d).

Fig. 8
Fig. 8

Comparison the stress distributions along the white line in the Figs. 7(b), 7(c), 7(e) and 7(f) with theory result, in the Fig. the curve 15-MC stands for 15-fold multiplication of calibrated normalization, 15-MNC stands for 15-fold multiplication of non-calibrated normalization, so do the 23MC and 23-MNC.

Equations (13)

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I(r)=A[1+cos(ϕ(r))],
I N (r)=A[1+cos( ϕ N (r))],
ϕ N (r)=Nϕ(r)=Narccos( I(r) A 1).
I N (r)=A[1+cos(Narccos( I(r) A 1))].
I(r)= I 1 (r)( 1+cos[ ϕ(r) ] )+ I b (r)+ I random ,
I(r)= I 1 (r)( 1+cos[ ϕ(r) ] )+ I b (r).
I (r)= I 1 ·[ 1+cos( ϕ(r) ) ],
I (r)= C 0 +C(r)+ C (r),
ϕ(r)=arctan Im[ C(r) ] Re[ C(r) ] .
n( x 1 , y 1 )=0 n( x 1 , y i )={ n( x 1 , y i1 ) if| ϕ( x 1 , y i )ϕ( x 1 , y i1 ) |<π n( x 1 , y i1 )+1 ifϕ( x 1 , y i )ϕ( x 1 , y i1 )π n( x 1 , y i1 )1 ifϕ( x 1 , y i )ϕ( x 1 , y i1 )π i=2,3,..., n( x j , y i )={ n( x j1 , y i ) if| ϕ( x j , y i )ϕ( x j1 , y i ) |<π n( x j1 , y i )+1 ifϕ( x j , y i )ϕ( x j1 , y i )π n( x j1 , y i )1 ifϕ( x j , y i )ϕ( x j1 , y i )π . j=2,3,..., ϕ unwrep ( x j , y i )=ϕ( x j , y i )+2πn( x j , y i ), i,j=1,2,...
I(r)= I 1 [ 1+cos(ϕ(r)) ]+ I b + I random .
I=I(r)= I 1 [ 1+cos(2 θ rot +π) ]+ I b ,
( σ 1 σ 2 ) r = ϕ(r) f σ 2πh ,

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