Abstract

A phase shifting method based on high-resolution frequency estimation and Fourier transform technique is introduced. This method, also referred to as the eigenvector method, draws on the complementary strengths of both these methods. The salient feature of the method lies in its ability to handle nonsinusoidal waveforms, multiple piezoelectric transducers, and arbitrary phase steps in an optical configuration. The method does not need the addition of carrier fringes to separate the spectral contents in the intensity fringes. The proposed concept thus overcomes the limitations of methods based on Fourier transform techniques. The robustness of the proposed method is studied in the presence of noise.

© 2005 Optical Society of America

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References

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  1. T. Kreis, Holographic Interferometry Principles and Methods (Akademie, 1996), pp. 101–170.
  2. K. A. Goldberg and J. Bokor, Appl. Opt. 40, 2886 (2001).
    [CrossRef]
  3. K. G. Larkin, Opt. Express 9, 236 (2001).
    [CrossRef] [PubMed]
  4. P. K. Rastogi, Appl. Opt. 32, 3669 (1993).
    [CrossRef] [PubMed]
  5. P. Stoica and R. Moses, Introduction to Spectral Analysis (Prentice-Hall, 1997).
  6. Parametric Methods, The MathWorks, Inc., http://www.mathworks.com/access/helpdesk/help/toolbox/signal/spectra8.html.
  7. P. Stoica and A. Nehorai, IEEE Trans. Acoust. Speech Signal Process. 37, 720 (1989).
    [CrossRef]

2001 (2)

1993 (1)

1989 (1)

P. Stoica and A. Nehorai, IEEE Trans. Acoust. Speech Signal Process. 37, 720 (1989).
[CrossRef]

Bokor, J.

Goldberg, K. A.

Kreis, T.

T. Kreis, Holographic Interferometry Principles and Methods (Akademie, 1996), pp. 101–170.

Larkin, K. G.

Moses, R.

P. Stoica and R. Moses, Introduction to Spectral Analysis (Prentice-Hall, 1997).

Nehorai, A.

P. Stoica and A. Nehorai, IEEE Trans. Acoust. Speech Signal Process. 37, 720 (1989).
[CrossRef]

Rastogi, P. K.

Stoica, P.

P. Stoica and A. Nehorai, IEEE Trans. Acoust. Speech Signal Process. 37, 720 (1989).
[CrossRef]

P. Stoica and R. Moses, Introduction to Spectral Analysis (Prentice-Hall, 1997).

Appl. Opt. (2)

IEEE Trans. Acoust. Speech Signal Process. (1)

P. Stoica and A. Nehorai, IEEE Trans. Acoust. Speech Signal Process. 37, 720 (1989).
[CrossRef]

Opt. Express (1)

Other (3)

P. Stoica and R. Moses, Introduction to Spectral Analysis (Prentice-Hall, 1997).

Parametric Methods, The MathWorks, Inc., http://www.mathworks.com/access/helpdesk/help/toolbox/signal/spectra8.html.

T. Kreis, Holographic Interferometry Principles and Methods (Akademie, 1996), pp. 101–170.

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Figures (3)

Fig. 1
Fig. 1

Plot for frequency spectrum obtained using (a) Fourier transform and (b) enhanced Fourier transform for determining phase steps α and β. The dc component is not considered during the simulation.

Fig. 2
Fig. 2

Plot for phase steps α and β (in degrees) for data frames (a) 7, (b) 9, (c) 11, and (d) 13 with respect to the SNR for κ = 1 , α = π 5 , and β = π 3 .

Fig. 3
Fig. 3

(a) Moiré; fringes corresponding to (b) ϕ 1 + ϕ 2 and (c) ϕ 1 ϕ 2 ; (d) plot of typical error (in radians) for computation of phase φ 1 .

Equations (7)

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I ( t ) = k = κ κ exp [ j k ( ϕ 1 + t α ) ] + k = κ κ exp [ j k ( ϕ 2 + t β ) ] + η ( t ) ,
I = S ψ + η .
R I = E ( I I H ) = E [ ( S ψ + η ) ( S ψ + η ) H ] ,
V i [ exp ( j ω ) ] = t = 0 N 1 ν i ( t ) exp ( j ω t )
P i [ exp ( j ω ) ] = 1 s H , v i 2 .
P [ exp ( j ω ) ] = 1 i = 4 κ + 1 N 1 1 λ i s H , v i 2 .
[ exp ( j κ α 0 ) exp ( j κ α 0 ) exp ( j κ β 0 ) exp ( j κ α 1 ) exp ( j κ α 1 ) exp ( j κ β 1 ) exp ( j κ α N 1 ) ] [ C κ C κ * D κ ] = [ I 0 I 1 I N 1 ] ,

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