Abstract

This Letter presents an efficient, fast, and straightforward two-step demodulating method based on a Gram–Schmidt (GS) orthonormalization approach. The phase-shift value has not to be known and can take any value inside the range (0,2π), excluding the singular case, where it corresponds to π. The proposed method is based on determining an orthonormalized interferogram basis from the two supplied interferograms using the GS method. We have applied the proposed method to simulated and experimental interferograms, obtaining satisfactory results. A complete MATLAB software package is provided at http://goo.gl/IZKF3.

© 2012 Optical Society of America

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References

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  1. T. M. Kreis, and W. P. O. Jueptner, Proc. SPIE 1553, 263 (1992).
    [CrossRef]
  2. J. Vargas, J. A. Quiroga, T. Belenguer, M. Servín, and J. C. Estrada, Opt. Express 19, 638 (2011).
    [CrossRef]
  3. J. Vargas, J. A. Quiroga, C. O. S. Sorzano, J. C. Estrada, and J. M. Carazo, Opt. Lett. 36, 3485 (2011).
    [CrossRef]
  4. J. Vargas, J. A. Quiroga, and T. Berenguer, Opt. Lett. 36, 1326 (2011).
    [CrossRef]
  5. J. Vargas, J. A. Quiroga, and T. Berenguer, Opt. Lett. 36, 2215 (2011).
    [CrossRef]
  6. G. Strang, Introduction to Linear Algebra (Wellesley Cambridge, 2009).
  7. Z. Y. Wang and B. T. Han, Opt. Lett. 29, 1671(2004).
    [CrossRef]
  8. http://goo.gl/IZKF3 .

2011

2004

1992

T. M. Kreis, and W. P. O. Jueptner, Proc. SPIE 1553, 263 (1992).
[CrossRef]

Belenguer, T.

Berenguer, T.

Carazo, J. M.

Estrada, J. C.

Han, B. T.

Jueptner, W. P. O.

T. M. Kreis, and W. P. O. Jueptner, Proc. SPIE 1553, 263 (1992).
[CrossRef]

Kreis, T. M.

T. M. Kreis, and W. P. O. Jueptner, Proc. SPIE 1553, 263 (1992).
[CrossRef]

Quiroga, J. A.

Servín, M.

Sorzano, C. O. S.

Strang, G.

G. Strang, Introduction to Linear Algebra (Wellesley Cambridge, 2009).

Vargas, J.

Wang, Z. Y.

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Figures (6)

Fig. 1.
Fig. 1.

Two fringe patterns used in the first simulation.

Fig. 2.
Fig. 2.

Theoretical phase map of the simulated fringe patterns.

Fig. 3.
Fig. 3.

Reconstructed wrapped phases by (a) the proposed GS method and the (b) ST, (c) Kreis, and (d) OF methods.

Fig. 4.
Fig. 4.

Two sample real interferograms used.

Fig. 5.
Fig. 5.

Reference wrapped phase.

Fig. 6.
Fig. 6.

Reconstructed wrapped phases by (a) the proposed GS method and the (b) ST, (c) Kreis, and (d) OF methods using real interferograms.

Tables (2)

Tables Icon

Table 1. Root-Mean-Square Errors and Processing Times Obtained by the GS, Kreis, ST, and OF Methods in the Simulation

Tables Icon

Table 2. Root-Mean-Square Errors and Processing Times Obtained by the GS, Kreis, ST, and OF Methods with Real Patterns

Equations (12)

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

In(x,y)=a(x,y)+b(x,y)cos[Φ(x,y)+δn],
In=a+b(cos[Φ]cos[δn]sin[Φ]sin[δn]).
In=a+αnIc+βnIs,
u˜1=u1/u1,u1=u1/u1.
u^2=u2u2,u˜1·u˜1.
u˜2=u^2/u^2,u^2=u^2/u^2.
I1(x,y),I2(x,y)=x=1Nxy=1NyI1(x,y)I2(x,y),
I˜1=bcos(Φ)/κ1=bcos(Φ)/x=1Nxy=1Ny(bcos(Φ))2.
I^2=bcos(Φ+δ)(x=1Nxy=1Nyb2cos(Φ+δ)cos(Φ))bcos(Φ)/κ12.
I^2bsin(Φ)sin(δ).
I˜2=bsin(Φ)/κ2=bsin(Φ)/x=1Nxy=1Ny(bsin(Φ))2.
Φarctan(I˜1/I˜2).

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