Abstract

A maximum-likelihood (ML) method based on spectral estimation theory for the extraction of dual phase distributions in holographic moire in the presence of nonsinusoidal waveforms, noise, and the miscalibration of piezoelectric (PZT) devices is proposed. The extraction of these phases requires incorporating two PZTs into the moire setup. ML estimators are asymptotically efficient for sufficient data samples. The approach presented uses a direct stochastic algorithm called probabilistic global search Lausanne for minimizing the ML function.

© 2005 Optical Society of America

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References

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    [CrossRef]
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2003

B. Raphael and I. F.C. Smith, Appl. Math. Comput. 146, 729 (2003).
[CrossRef]

1992

1989

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

K. C. Sharman and G. D. McClurkin, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. ICASSP-89, 2716 (1989).
[CrossRef]

1988

K. C. Sharman, Proc. IEEE Int. Conf. Acoust. Speech Signal Process ICASSP-88, 2741 (1988).

1984

McClurkin, G. D.

K. C. Sharman and G. D. McClurkin, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. ICASSP-89, 2716 (1989).
[CrossRef]

Nehorai, A.

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

Raphael, B.

B. Raphael and I. F.C. Smith, Appl. Math. Comput. 146, 729 (2003).
[CrossRef]

Rastogi, P. K.

Sharman, K. C.

K. C. Sharman and G. D. McClurkin, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. ICASSP-89, 2716 (1989).
[CrossRef]

K. C. Sharman, Proc. IEEE Int. Conf. Acoust. Speech Signal Process ICASSP-88, 2741 (1988).

Smith, I. F.C.

B. Raphael and I. F.C. Smith, Appl. Math. Comput. 146, 729 (2003).
[CrossRef]

Stoica, P.

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

Appl. Math. Comput.

B. Raphael and I. F.C. Smith, Appl. Math. Comput. 146, 729 (2003).
[CrossRef]

Appl. Opt.

IEEE Trans. Acoust. Speech Signal Process.

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

Proc. IEEE Int. Conf. Acoust. Speech Signal Process

K. C. Sharman, Proc. IEEE Int. Conf. Acoust. Speech Signal Process ICASSP-88, 2741 (1988).

Proc. IEEE Int. Conf. Acoust. Speech Signal Process.

K. C. Sharman and G. D. McClurkin, Proc. IEEE Int. Conf. Acoust. Speech Signal Process. ICASSP-89, 2716 (1989).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Phase steps α and β (in degrees) versus SNR for (a) 10, (b) 13, (c) 15, and (d) 20 data frames. We have assumed that κ = 2 , α = π 4 , and β = π 3 .

Fig. 2
Fig. 2

Plots of (a) a typical error in phase φ 1 and (b) wrapped phases φ 1 and φ 2 (in radians) for a SNR of 30 dB.

Equations (9)

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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 ) , t = 0 , 1 , . , m , . . , N 1 ,
I ( t ) = A ( ω ) Ψ ( t ) + η ( t ) .
l ( I , ξ ) p [ I ( 0 ) , ξ ] p [ I ( 1 ) , ξ ] p [ I ( N 1 ) , ξ ] .
l = 1 ( 2 π σ ) N 2 exp { 1 2 σ t = 1 N [ I ( t ) A ( ω ) ψ ( t ) ] * [ I ( t ) A ( ω ) ψ ( t ) ] } .
L = const N 2 ln σ { 1 2 σ t = 1 N [ I ( t ) A ( ω ) ψ ( t ) ] * [ I ( t ) A ( ω ) ψ ( t ) ] } .
ψ ( t ) = [ A * A ] 1 [ A * I ( t ) ] , t = 0 , 1 , 2 , , N ,
σ = 1 N t = 1 N [ I ( t ) A ψ ( t ) ] * [ I ( t ) A ψ ( t ) ] .
[ 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 exp [ j κ α N 1 ] 1 ]
× [ l κ l κ * I d c ] = [ I 0 I 1 I N 1 ] ,

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