Abstract

Noise reduction is one of the most exciting problems in automatic fringe processing. We propose a two-dimensional (2-D) envelope transform for normalization of fringe patterns, coupled with spin filtering, to construct so-called noise-free normalized fringe patterns. The 2-D envelope transform uses correct fringe intensity envelopes for normalization of fringe patterns, i.e., for making the fringe background and amplitude constant over the whole field. Spin filtering is applied to fringe patterns for removal of random noise taking into account fringe flow. With spin filtering and the 2-D envelope transform, a noise-free normalized fringe pattern is constructed for postprocessing. Based on this improved fringe pattern, two local pixel transforms for strain extraction from a single moiré pattern are developed, in which the digital pure secondary moiré method is improved and the strain-field image method with division is developed.

© 1996 Optical Society of America

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References

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  1. H. E. Cline, W. E. Lorensen, A. S. Holik, “Automatic moiré contouring,” Appl. Opt. 23, 1454–1459 (1984).
    [CrossRef] [PubMed]
  2. N. Eichhorn, W. Osten, “An algorithm for the fast derivation of line structures from interferograms,” J. Mod. Opt. 35, 1717–1725 (1988).
    [CrossRef]
  3. Q. Yu, K. Andresen, “Fringe-orientation maps and fringe skeleton extraction by the two-dimensional derivative-sign binary-fringe method,” Appl. Opt. 33, 6873–6878 (1994).
    [CrossRef] [PubMed]
  4. A. S. Voloshin, C. P. Burger, “Half-fringe photoelasticity: a new approach to whole-field stress analysis,” Exp. Mech. 23, 304–313 (1983).
    [CrossRef]
  5. M. Takeda, H. Ina, S. Kobayashi, “Fourier transform method of fringe pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  6. D. J. Bone, H. A. Bachor, R. J. Sandeman, “Fringepattern analysis using a 2-D Fourier transform,” Appl. Opt. 25, 1653–1660 (1986).
    [CrossRef] [PubMed]
  7. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 24, pp. 351–393.
  8. G. Lai, T. Yatagai, “Generalized phase-shifting interferometry,” J. Opt. Soc. Am. A 8, 822–827 (1991).
    [CrossRef]
  9. Q. F. Yu, K. Andresen, W. Osten, W. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
    [CrossRef]
  10. Q. F. Yu, X. L. Liu, K. Andresen, “New spin filters for interferometric fringe patterns and grating patterns,” Appl. Opt. 33, 3705–3711 (1994).
    [CrossRef] [PubMed]
  11. Q. F. Yu, “Constructing pure digital secondary moire patterns,” Exp. Mech. 30, 247–252 (1990).
    [CrossRef]
  12. Q. F. Yu, K. Andresen, D. S. Zhang, “Digital pure shear-strain moiré patterns,” Appl. Opt. 31, 1813–1817 (1992).
    [CrossRef] [PubMed]
  13. H. A. Vrooman, A. A. M. Maas, “Interferogram analysis using image processing techniques,” in Interferometry '89, Z. Jaroszewicz, M. Pluta, eds., Proc. SPIE1121, 655–659 (1990).
  14. K. Andresen, Q. F. Yu, “Robust phase unwrapping by spin filtering combined with a phase direction map,” Optik (Stutt-gart) 94, 145–149 (1993).

1994 (3)

1993 (1)

K. Andresen, Q. F. Yu, “Robust phase unwrapping by spin filtering combined with a phase direction map,” Optik (Stutt-gart) 94, 145–149 (1993).

1992 (1)

1991 (1)

1990 (1)

Q. F. Yu, “Constructing pure digital secondary moire patterns,” Exp. Mech. 30, 247–252 (1990).
[CrossRef]

1988 (1)

N. Eichhorn, W. Osten, “An algorithm for the fast derivation of line structures from interferograms,” J. Mod. Opt. 35, 1717–1725 (1988).
[CrossRef]

1986 (1)

1984 (1)

1983 (1)

A. S. Voloshin, C. P. Burger, “Half-fringe photoelasticity: a new approach to whole-field stress analysis,” Exp. Mech. 23, 304–313 (1983).
[CrossRef]

1982 (1)

Andresen, K.

Bachor, H. A.

Bone, D. J.

Burger, C. P.

A. S. Voloshin, C. P. Burger, “Half-fringe photoelasticity: a new approach to whole-field stress analysis,” Exp. Mech. 23, 304–313 (1983).
[CrossRef]

Cline, H. E.

Creath, K.

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 24, pp. 351–393.

Eichhorn, N.

N. Eichhorn, W. Osten, “An algorithm for the fast derivation of line structures from interferograms,” J. Mod. Opt. 35, 1717–1725 (1988).
[CrossRef]

Holik, A. S.

Ina, H.

Jueptner, W.

Q. F. Yu, K. Andresen, W. Osten, W. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

Kobayashi, S.

Lai, G.

Liu, X. L.

Lorensen, W. E.

Maas, A. A. M.

H. A. Vrooman, A. A. M. Maas, “Interferogram analysis using image processing techniques,” in Interferometry '89, Z. Jaroszewicz, M. Pluta, eds., Proc. SPIE1121, 655–659 (1990).

Osten, W.

Q. F. Yu, K. Andresen, W. Osten, W. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

N. Eichhorn, W. Osten, “An algorithm for the fast derivation of line structures from interferograms,” J. Mod. Opt. 35, 1717–1725 (1988).
[CrossRef]

Sandeman, R. J.

Takeda, M.

Voloshin, A. S.

A. S. Voloshin, C. P. Burger, “Half-fringe photoelasticity: a new approach to whole-field stress analysis,” Exp. Mech. 23, 304–313 (1983).
[CrossRef]

Vrooman, H. A.

H. A. Vrooman, A. A. M. Maas, “Interferogram analysis using image processing techniques,” in Interferometry '89, Z. Jaroszewicz, M. Pluta, eds., Proc. SPIE1121, 655–659 (1990).

Yatagai, T.

Yu, Q.

Yu, Q. F.

Q. F. Yu, X. L. Liu, K. Andresen, “New spin filters for interferometric fringe patterns and grating patterns,” Appl. Opt. 33, 3705–3711 (1994).
[CrossRef] [PubMed]

Q. F. Yu, K. Andresen, W. Osten, W. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

K. Andresen, Q. F. Yu, “Robust phase unwrapping by spin filtering combined with a phase direction map,” Optik (Stutt-gart) 94, 145–149 (1993).

Q. F. Yu, K. Andresen, D. S. Zhang, “Digital pure shear-strain moiré patterns,” Appl. Opt. 31, 1813–1817 (1992).
[CrossRef] [PubMed]

Q. F. Yu, “Constructing pure digital secondary moire patterns,” Exp. Mech. 30, 247–252 (1990).
[CrossRef]

Zhang, D. S.

Appl. Opt. (5)

Exp. Mech. (2)

Q. F. Yu, “Constructing pure digital secondary moire patterns,” Exp. Mech. 30, 247–252 (1990).
[CrossRef]

A. S. Voloshin, C. P. Burger, “Half-fringe photoelasticity: a new approach to whole-field stress analysis,” Exp. Mech. 23, 304–313 (1983).
[CrossRef]

J. Mod. Opt. (1)

N. Eichhorn, W. Osten, “An algorithm for the fast derivation of line structures from interferograms,” J. Mod. Opt. 35, 1717–1725 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

Q. F. Yu, K. Andresen, W. Osten, W. Jueptner, “Analysis and removal of the systematic phase error in interferograms,” Opt. Eng. 33, 1630–1637 (1994).
[CrossRef]

Optik (Stutt-gart) (1)

K. Andresen, Q. F. Yu, “Robust phase unwrapping by spin filtering combined with a phase direction map,” Optik (Stutt-gart) 94, 145–149 (1993).

Other (2)

H. A. Vrooman, A. A. M. Maas, “Interferogram analysis using image processing techniques,” in Interferometry '89, Z. Jaroszewicz, M. Pluta, eds., Proc. SPIE1121, 655–659 (1990).

K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1988), Vol. 24, pp. 351–393.

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Figures (16)

Fig. 1
Fig. 1

2-D envelope transform.

Fig. 2
Fig. 2

Simulated fringe pattern with five circular fringes plus Gaussian random noise with an amplitude of 60.

Fig. 3
Fig. 3

Intensity distribution of a cross section of Fig. 2.

Fig. 4
Fig. 4

Intensity distribution of a cross section of Fig. 2 after spin filtering.

Fig. 5
Fig. 5

Resultant image of Fig. 2 after spin filtering and a 2-D envelope transform.

Fig. 6
Fig. 6

Intensity distribution of Fig. 5 on the same cross section shown in Fig. 4.

Fig. 7
Fig. 7

Practical hologram of a valve specimen loaded by internal pressure.

Fig. 8
Fig. 8

Intensity distribution of Fig. 7 on the cross section of line 333 for (a) the original pattern of Fig. 7(b), the pattern after spin filtering, (c) the resultant pattern of Fig. 9.

Fig. 9
Fig. 9

Resultant noise-free normalized fringe pattern of Fig. 7 after spin filtering and a 2-D envelope transform.

Fig. 10
Fig. 10

Simulation fringe pattern after spin filtering and a 2-D envelope transform.

Fig. 11
Fig. 11

Pure secondary moiré pattern of Fig. 10.

Fig. 12
Fig. 12

Wrapped phase pattern of Fig. 11.

Fig. 13
Fig. 13

Unwrapped phase pattern of Fig. 12.

Fig. 14
Fig. 14

Fringe orientation map of Fig. 10.

Fig. 15
Fig. 15

Strain sign map of the fringe pattern of Fig. 10.

Fig. 16
Fig. 16

Strain-field image of Fig. 10 after median filtering.

Equations (21)

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Ī ( x , y ) = I 0 ( x , y ) + I 1 ( x , y ) cos [ ϕ ( x , y ) ] + I n ( x , y ) ,
I max ( x , y ) = I 0 ( x , y ) + I 1 ( x , y ) ,
I min ( x , y ) = I 0 ( x , y ) I 1 ( x , y ) .
I ( x , y ) = A [ Ī ( x , y ) I min ( x , y ) ] [ I max ( x , y ) I min ( x , y ) ] + B = A { I 0 ( x , y ) + I 1 ( x , y ) cos [ ϕ ( x , y ) ] I 0 ( x , y ) + I 1 ( x , y ) } [ I 0 ( x , y ) + I 1 ( x , y ) I 0 ( x , y ) + I 1 ( x , y ) ] + B
= A 2 + B + A 2 cos [ ϕ ( x , y ) ] = I 0 c + I 1 c cos [ ϕ ( x , y ) ] ,
Ī u ( x , y ) = I 0 ( x , y ) + I 1 ( x , y ) cos [ 2 π U ( x , y ) / P ] ,
I u ( x , y ) = I 0 c + I 1 c cos [ 2 π U ( x , y ) / P ] ,
J u ( x , y ) = I 0 c + I 1 c sin [ 2 π U ( x , y ) / P ] .
I u ( x + Δ x , y ) = I 0 c + I 1 c cos { 2 π [ U ( x , y ) + Δ U ] / P } ,
J u ( x + Δ x , y ) = I 0 c + I 1 c sin { 2 π [ U ( x , y ) + Δ U ] / P } .
M 1 = [ I u ( x , y ) I 0 c ] [ I u ( x + Δ x , y ) I 0 c ] = I 1 c 2 ( cos ( 2 π Δ U / P ) + cos { 2 π [ 2 U ( x , y ) + Δ U ] / P } ) / 2 ,
M 2 = [ J u ( x , y ) I 0 c ] [ J u ( x + Δ x , y ) I 0 c ] = I 1 c 2 ( cos ( 2 π Δ U / P ) ] cos { 2 π [ 2 U ( x , y ) + Δ U ] / P } ) / 2 ,
M ( x , y ) = [ M 1 ( x , y ) + M 2 ( x , y ) ] / I 1 c + I 0 c = I 0 c + I 1 c cos ( 2 π Δ U / P ) = I 0 c + I 1 c cos [ 2 π x ( x , y ) / 0 ] ,
M 1 s = [ I u ( x , y ) I 0 c ] [ J u ( x + Δ x , y ) I 0 c ] = I 1 c 2 ( sin ( 2 π Δ U / P ) + sin { 2 π [ 2 U ( x , y ) + Δ U ] / P } ) / 2 ,
M 2 s = [ J u ( x , y ) I 0 c ] [ I u ( x + Δ x , y ) I 0 c ] = I 1 c 2 { sin [ 2 π ( Δ U / P ] sin [ 2 π ( 2 U ( x , y ) + Δ U / P ] } / 2 ,
M s ( x , y ) = [ M 1 s ( x , y ) + M 2 s ( x , y ) ] / I 1 c + I 0 c = I 0 c + I 1 c sin ( 2 π Δ U / P ) = I 0 c + I 1 c sin [ 2 π x ( x , y ) / 0 ] .
x ( x , y ) = 0 2 π arctan [ M s ( x , y ) I 0 c M ( x , y ) I 0 c ] + k 0 = 0 2 π arctan { sin [ 2 π x ( x , y ) / 0 ] cos [ 2 π x ( x , y ) / 0 ] } + k 0 ,
| I ( x , y ) x | = 2 π P | U ( x , y ) x | | sin [ 2 π U ( x , y ) / P ] | .
cos 2 ϕ + sin 2 ϕ = 1 ,
{ I 1 c 2 [ I ( x , y ) I 0 c ] 2 } 1 / 2 = I 1 c | sin [ 2 π U ( x , y ) / P ] | .
| x ( x , y ) | = | U ( x , y ) x | = | I ( x , y ) x | P 2 π { I 1 c 2 [ I ( x , y ) I 0 c ] 2 } 1 / 2 .

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