Abstract

Filtering off noise from fringe patterns is important for the processing and analysis of interferometric fringe patterns. Spin filters proposed by the author have been proven to be effective in filtering off noise without blurring and distortion to fringe patterns with small fringe curvature. But spin filters still have problems processing fringe patterns with large fringe curvature. We develop a new spin filtering with curve windows that is suitable for all kinds of fringe pattern regardless of fringe curvature. The experimental results show that the new spin filtering provides optimal results in filtering off noise without distortion of the fringe features, regardless of fringe curvature.

© 2002 Optical Society of America

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References

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  1. Q. Yu, X. Liu, K. Andresen, “New spin filters for interferometric fringe patterns and grating patterns,” Appl. Opt. 33, 3705–3711 (1994).
    [CrossRef] [PubMed]
  2. Q. Yu, “Calculation of strain from a single moire by filtering and normalizing an interferogram,” Ph.D. dissertation (Bremen University, Bremen, Germany, 1996).
  3. Q. Yu, X. Liu, X. Sun, “Generalized spin filtering and improved derivative-sign binary image method for extraction of fringe skeletons,” Appl. Opt. 37, 4504–4509 (1998).
    [CrossRef]
  4. Q. Yu, K. Andresen, “Fringe orientation maps and 2D derivative-sign binary image methods for extraction of fringe skeletons,” Appl. Opt. 33, 6873–6878 (1994).
    [CrossRef] [PubMed]
  5. Q. Yu, K. Andresen, W. Osten, W. Jueptner, “Noise-free normalized fringe patterns and local pixel transforms for strain extraction,” Appl. Opt. 35, 3783–3790 (1996).
    [CrossRef] [PubMed]

1998

1996

1994

Andresen, K.

Jueptner, W.

Liu, X.

Osten, W.

Sun, X.

Yu, Q.

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Figures (7)

Fig. 1
Fig. 1

Distributions of gray levels of a fringe in (a) a fringe-normal direction and (b) a fringe-tangential direction. (c) and (d) The corresponding frequencies of (a) and (b), respectively.

Fig. 2
Fig. 2

Simulated fringe pattern with Gaussian noise of σ = 10.

Fig. 3
Fig. 3

Standard deviations between the simulated ideal fringe pattern and the simulated fringe pattern in Fig. 2 filtered by the average filter, the median filter, and spin filters with line windows and with curve windows.

Fig. 4
Fig. 4

Practical hologram.

Fig. 5
Fig. 5

Resultant image of Fig. 4 filtered by spin filtering with curve windows.

Fig. 6
Fig. 6

Gray-level distributions of an intersection of Fig. 4 filtered by the average filter, the spin filter with straight-line windows, and the spin filter with curve windows.

Fig. 7
Fig. 7

Phase comparisons between the simulated ideal fringe pattern and the unfiltered pattern from Fig. 2 and between the simulated ideal fringe pattern and the filtered images (resulting from the pattern in Fig. 2) on a part of an intersection of the images.

Tables (1)

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Table 1 Standard Deviation between the Simulated Ideal and Filtered (or Unfiltered) Images

Equations (7)

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gi, j=ai+bj+c,
θ=arctanab=arctani,j fij ii,j fij j,
xi+1=xi+cos θi, yi+1=yi+sin θi,
x-i-1=x-i+cos θ-i, y-i-1=y-i+sin θ-i.
Ix, y=I0x, y+I1x, ycosϕx, y+Inx, y,
Ix, y=128 exp-r22562+60 exp-r22562cos1000r-r22500π+Inx, y,
ϕx, y=arccosIx, y-I0x, y/I1x, y,

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