Abstract

A phase-shifting piezo device commonly employed in phase-shifting interferometry exhibits a nonlinear response to applied voltage. Hence, a method for estimation of phase distribution in the presence of nonlinear phase steps is presented. The proposed method compensates for the harmonics present in the intensity fringe, allows the use of arbitrary phase-step values between 0 and πrad, and does not impose constraints on the selection of particular phase-step values for minimizing nonlinearity and compensating for the harmonics. The comparison of the proposed method with other well-known benchmarking algorithms shows that our method is highly efficient and also works well in the presence of noise.

© 2006 Optical Society of America

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References

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2005

2003

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

1997

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

1995

1982

Creath, K.

de Groot, P.

Farrant, D. I.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Hibino, K.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Langoju, R.

Larkin, K. G.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Morgan, C. J.

Oreb, B. F.

K. Hibino, B. F. Oreb, D. I. Farrant, and K. G. Larkin, J. Opt. Soc. Am. A 4, 918 (1997).
[CrossRef]

Patil, A.

Raphael, B.

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

Rastogi, P.

Schmit, J.

Smith, I. F. C.

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

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Figures (2)

Fig. 1
Fig. 1

Plots of mean square error (in rad 2 ) versus SNR for different values of nonlinearity coefficient ϵ 2 : (a) 0.01, (b) 0.1, (c) 0.2, and (d) 0.4.

Fig. 2
Fig. 2

Plots of the estimated phase (in radians) versus SNR for different values of nonlinearity coefficient ϵ 2 and κ = 2 in Eq. (1).

Tables (1)

Tables Icon

Table 1 Phase Error (in Radians) in Computation of Phase φ

Equations (6)

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

I n = I dc { 1 + k = 1 κ γ k cos [ k ( φ + α n ) ] } + η n ,
I ¯ = I + η = S ( ξ ) C + η ,
p ( I ¯ ; ξ ) = 1 π N σ N exp [ 1 σ 2 ( I ¯ S C ) H ( I ¯ S C ) ] ,
Υ C = C [ I ¯ H I ¯ I ¯ H S C C H S H I ¯ + C H S H S C ] = 2 S H [ I ¯ S C ] .
Υ = I ¯ H I ¯ I ¯ H S ( S H S ) 1 S H I ¯ .
ξ = max I ¯ H [ S ( S H S ) 1 S H ] I ¯ .

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