Abstract

An asynchronous phase-shifting method based on principal component analysis (PCA) is presented. No restrictions about the background, modulation, and phase shifts are necessary. The presented method is very fast and needs very low computational requirements, so it can be used with very large images and/or very large image sets. The method is based on obtaining two quadrature signals by the PCA algorithm. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results.

© 2011 Optical Society of America

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References

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  1. D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).
  2. Z. Y. Wang and B. T. Han, Opt. Lett. 29, 1671 (2004).
    [CrossRef] [PubMed]
  3. I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
    [CrossRef]
  4. J. L. Marroquin, M. Servin, and R. R. Vera, Opt. Lett. 23, 238 (1998).
    [CrossRef]
  5. K. G. Larkin, Opt. Express 9, 236 (2001).
    [CrossRef] [PubMed]
  6. R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2007).
  7. http://goo.gl/80Kh6.

2004

2001

1998

1995

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2007).

Han, B. T.

Kim, S.-W.

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Kong, I.-B.

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Larkin, K. G.

Malacara, D.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

Malacara, Z.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

Marroquin, J. L.

Servin, M.

Servín, M.

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

Vera, R. R.

Wang, Z. Y.

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2007).

Opt. Eng.

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Other

D. Malacara, M. Servín, and Z. Malacara, Interferogram Analysis for Optical Testing (Dekker, 1998).

R. C. Gonzalez and R. E. Woods, Digital Image Processing, 3rd ed. (Prentice-Hall, 2007).

http://goo.gl/80Kh6.

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Figures (6)

Fig. 1
Fig. 1

Two of the 10 interferograms used in the simulation section.

Fig. 2
Fig. 2

Computed basis obtained by the PCA algorithm when 10 phase-shifted patterns with 10% signal-to-noise ratio are processed.

Fig. 3
Fig. 3

Obtained wrapped phases (a) when the proposed method is used and (b) actual phase map.

Fig. 4
Fig. 4

Two sample real interferograms used in the experimental results section.

Fig. 5
Fig. 5

Wrapped phases obtained by the (a) proposed and (b) SC methods.

Fig. 6
Fig. 6

Obtained wrapped phases when using the (a) proposed method and the (b) SC method to process four real interferograms.

Tables (2)

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Table 1 Results Obtained for Different Levels of Noise

Tables Icon

Table 2 Results Obtained for Different Patterns

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

I n ( x , y ) = a ( x , y ) + b ( x , y ) cos [ Φ ( x , y ) + δ n ] ,
I n = a + b [ cos ( Φ ) cos ( δ n ) sin ( Φ ) sin ( δ n ) ] .
I ˜ n = α n I c + β n I s ,
x = 1 N x y = 1 N y I c ( x , y ) I s ( x , y ) 0 ,
x = [ x 1 , x 2 , , x N ] T .
C = ( x m x ) ( x m x ) T .
D = A C A T ,
y = A ( x m x ) .
Φ = arctan ( I s / I c ) .

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