Abstract

A state space model for the determination of dual phase distributions in a holographic moiré in the presence of nonsinusoidal waveforms, random noise, and miscalibration of the piezoelectric (PZT) devices is proposed. The extraction of these phase terms requires incorporating two PZTs into the moiré setup. A Toeplitz approximation method (TAM) is applied for phase determination, and modification to the Toeplitz covariance matrix formed from the phase-shifted moiré fringes by application of a denoising step in the state-feedback matrix is proposed. This step ensures that the phase terms can even be estimated at a signal-to-noise ratio much lower than that of the original TAM or by our previously suggested polynomial based method.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. K. Rastogi, Appl. Opt. 31, 1680 (1992).
    [CrossRef] [PubMed]
  2. Y. Surrel, Appl. Opt. 35, 51 (1996).
    [CrossRef] [PubMed]
  3. S. Y. Kung, in Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems , Vol. 5–7 (1981), pp. 262–266.
  4. D. W. Tufts and R. Kumaresan, Proc. IEEE 70, 975 (1982).
    [CrossRef]
  5. C. Rathjen, J. Opt. Soc. Am. A 12, 1997 (1995).
    [CrossRef]
  6. A. Patil, P. Rastogi, and R. Langoju, Opt. Lett. 30, 391 (2005).
    [CrossRef] [PubMed]

2005

1996

1995

1992

1982

D. W. Tufts and R. Kumaresan, Proc. IEEE 70, 975 (1982).
[CrossRef]

Kumaresan, R.

D. W. Tufts and R. Kumaresan, Proc. IEEE 70, 975 (1982).
[CrossRef]

Kung, S. Y.

S. Y. Kung, in Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems , Vol. 5–7 (1981), pp. 262–266.

Langoju, R.

Patil, A.

Rastogi, P.

Rastogi, P. K.

Rathjen, C.

Surrel, Y.

Tufts, D. W.

D. W. Tufts and R. Kumaresan, Proc. IEEE 70, 975 (1982).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Lett.

Proc. IEEE

D. W. Tufts and R. Kumaresan, Proc. IEEE 70, 975 (1982).
[CrossRef]

Other

S. Y. Kung, in Proceedings of the International Symposium on the Mathematical Theory of Networks and Systems , Vol. 5–7 (1981), pp. 262–266.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Plots of (a) eigenvalues of matrix S for SNR = 10 dB and a noiseless signal, (b) standard deviation (SD) versus SNR.

Fig. 2
Fig. 2

Plots of phase steps α and β (in degrees) for the number of data frames: (a) 10, (b) 14, (c) 18 (modified approach), (d) 18 [original Toeplitz approximation method (TAM)] with respect to SNR for values of κ = 1 , α = 45 ° and β = 60 ° .

Fig. 3
Fig. 3

(a) Example of moiré fringes, (b) Plot of typical error in the computation of φ 1 , (c) wrapped phase distribution φ 1 + φ 2 , (d) wrapped phase distribution φ 1 φ 2 .

Equations (4)

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

I ( t ) = I d c + k = 1 κ l k u k t + k = 1 κ l k * ( u k * ) t + k = 1 κ k v k t + k = 1 κ k * ( v k * ) t + η ( t ) , for t = 0 , 1 , m , , N 1 ,
F = [ ρ 1 ρ 2 . ρ p 1 0 . 0 0 1 . 0 . . . . 0 0 0 0 ] , H = [ ρ 1 ρ 2 . ρ p ] .
R = [ r ( 0 ) r ( 1 ) . r ( L ) r ( 1 ) r ( 0 ) . r ( L + 1 ) . . . . r ( L ) r ( L 1 ) . r ( 0 ) ] .
[ exp ( j κ α 0 ) exp ( j κ α 0 ) exp ( j κ β 0 ) . 1 exp ( j κ α 1 ) exp ( j κ α 1 ) . . 1 . . . . . . . . . 1 exp ( j κ α ( N 1 ) ) . . . 1 ] [ l κ l κ * κ . I d c ] = [ I 0 I 1 . . I N 1 ] ,

Metrics