Abstract

A technique is presented for filtering and normalizing noisy fringe patterns, which may include closed fringes, so that single-frame demodulation schemes may be successfully applied. It is based on the construction of an adaptive filter as a linear combination of the responses of a set of isotropic bandpass filters. The space-varying coefficients are proportional to the envelope of the response of each filter, which in turn is computed by using the corresponding monogenic image [ Felsberg and Sommer, IEEE Trans. Signal Process. 49, 3136 (2001) ]. Some examples of demodulation of real Electronic Speckle Pattern Interferometry (ESPI) images patterns are presented.

© 2005 Optical Society of America

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References

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  1. M. Servin, J. L. Marroquin, and J. A. Quiroga, J. Opt. Soc. Am. A 21, 411 (2004).
    [CrossRef]
  2. K. G. Larkin, D. J. Bone, and M. A. Oldfield, J. Opt. Soc. Am. A 18, 1862 (2000).
    [CrossRef]
  3. J. Kozlowsky and G. Serra, Appl. Opt. 38, 2256 (1999).
    [CrossRef]
  4. M. Rivera, J. Opt. Soc. Am. A 22, 1170 (2005).
    [CrossRef]
  5. M. Felsberg and G. Sommer, IEEE Trans. Signal Process. 49, 3136 (2001).
    [CrossRef]

2005 (1)

2004 (1)

2001 (1)

M. Felsberg and G. Sommer, IEEE Trans. Signal Process. 49, 3136 (2001).
[CrossRef]

2000 (1)

1999 (1)

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Figures (4)

Fig. 1
Fig. 1

a, Frequency response of an isotropic bandpass filter; b, c, imaginary part of the frequency response of the companion odd components of the monogenic filter.

Fig. 2
Fig. 2

Magnitude of the response of the set of monogenic filters as a function of frequency magnitude.

Fig. 3
Fig. 3

First row, sequence of ESPI patterns. Second row, filtered and normalized images. Third row, output of a robust demodulation procedure (wrapped phase) applied to the second row.

Fig. 4
Fig. 4

Output (wrapped phase) of the same robust demodulation procedure applied to the first and last images of the first row of Fig. 3.

Equations (7)

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H 0 k ( ρ , θ ) = G ( ρ ρ k ) ,
H 1 k ( ρ , θ ) = i G ( ρ ρ k ) sin ( θ ) ,
H 2 k ( ρ , θ ) = i G ( ρ ρ k ) cos ( θ ) ,
F ( x ) = k = 1 K w k ( x ) F 0 k ( x ) k = 1 K w k ( x ) M k ( x ) .
w k ( x ) = ( M k ( x ) M max ( x ) ) p ,
I M ( x ) = max y W ( x ) I ( y ) ,
G ( ρ ) = 1 2 [ 1 + sin ( ( h + 2 ρ ) π 2 h ) ] for ρ [ h , h ] = 0 otherwise ,

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