Abstract

A new phase-shifting interferometric technique that uses an unknown phase step is described in which the phase step is determined by use of an algorithm called Probabilistic Global Search Lausanne (PGSL). One of the main sources of error in phase stepping is piezoelectric device (PZT) nonlinearity. The PGSL algorithm identifies the characteristics of the response of the PZT to the applied voltage through matching predicted and measured responses. The unknown phase step is also calculated with 0.097% error. This approach overcomes the limitations of existing techniques to determine unknown phase steps. Linear regression is subsequently applied for interference phase determination.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]

2003 (1)

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

2001 (1)

2000 (2)

X. Chen, M. Gramaglia, and J. A. Yeazell, Appl. Opt. 39, 585 (2000).
[CrossRef]

Q. Kemao, S. Fangjun, and W. Xiaoping, Meas. Sci. Technol. 11, 1220 (2000).
[CrossRef]

1994 (2)

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

G.-S. Han and S.-W. Kim, Appl. Opt. 33, 7321 (1994).
[CrossRef] [PubMed]

1993 (2)

Y. Surrel, Appl. Opt. 32, 3598 (1993).
[CrossRef] [PubMed]

J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibl, Opt. Eng. 32, 1883 (1993).
[CrossRef]

1991 (2)

1984 (1)

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).
[CrossRef]

1982 (1)

1966 (1)

P. Carré, Metrologia 2, 13 (1966).
[CrossRef]

Carré, P.

P. Carré, Metrologia 2, 13 (1966).
[CrossRef]

Chen, X.

Creath, K.

K. Creath, in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), Chap. 4.

Deason, V. A.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Falkenstorfer, O.

J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibl, Opt. Eng. 32, 1883 (1993).
[CrossRef]

Fangjun, S.

Q. Kemao, S. Fangjun, and W. Xiaoping, Meas. Sci. Technol. 11, 1220 (2000).
[CrossRef]

Frankena, J. J.

Gramaglia, M.

Greivenkamp, J. E.

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).
[CrossRef]

Han, G.-S.

Kemao, Q.

Q. Kemao, S. Fangjun, and W. Xiaoping, Meas. Sci. Technol. 11, 1220 (2000).
[CrossRef]

Kim, S.-W.

Lai, G.

Larkin, K. G.

Lassahn, G. D.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Lassahn, J. K.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Morgan, C. J.

Raphael, B.

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

Schreiber, H.

J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibl, Opt. Eng. 32, 1883 (1993).
[CrossRef]

Schwider, J.

J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibl, Opt. Eng. 32, 1883 (1993).
[CrossRef]

Smith, I. F. C.

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

Smorenburg, C.

Streibl, N.

J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibl, Opt. Eng. 32, 1883 (1993).
[CrossRef]

Surrel, Y.

Taylor, P. L.

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

van Wingerden, J.

Xiaoping, W.

Q. Kemao, S. Fangjun, and W. Xiaoping, Meas. Sci. Technol. 11, 1220 (2000).
[CrossRef]

Yatagai, T.

Yeazell, J. A.

Zoller, A.

J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibl, Opt. Eng. 32, 1883 (1993).
[CrossRef]

Appl. Math. Comput. (1)

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

Appl. Opt. (4)

J. Opt. Soc. Am. A (1)

Meas. Sci. Technol. (1)

Q. Kemao, S. Fangjun, and W. Xiaoping, Meas. Sci. Technol. 11, 1220 (2000).
[CrossRef]

Metrologia (1)

P. Carré, Metrologia 2, 13 (1966).
[CrossRef]

Opt. Eng. (3)

J. E. Greivenkamp, Opt. Eng. 23, 350 (1984).
[CrossRef]

J. Schwider, O. Falkenstorfer, H. Schreiber, A. Zoller, and N. Streibl, Opt. Eng. 32, 1883 (1993).
[CrossRef]

G. D. Lassahn, J. K. Lassahn, P. L. Taylor, and V. A. Deason, Opt. Eng. 33, 2039 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

K. Creath, in Holographic Interferometry, P. K. Rastogi, ed. (Springer-Verlag, Berlin, 1994), Chap. 4.

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Figures (2)

Fig. 1
Fig. 1

(a) Phase step (in degrees) versus number of frames. (b) Error coefficients (in percent) versus number of frames. Note that the number of frames is a discrete quantity, and the solid and dashed curves are added only to show the trend of convergence.

Fig. 2
Fig. 2

(a) Wrapped phase map (in radians) with (solid curve) and without (dashed curve) PZT nonlinearity compensation. Error in phase φ (b) with PGSL for the estimation of reference phase steps and (c) without PGSL (phase step 40° and error coefficients equal to zero).

Equations (8)

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

Inx,y=I0x,y1+γx,ycosφx,y+nα,n=0,1,2K-1,
αn*x,y=nαx,y+ε1nαx,y+ε2nαx,y22π+ε3nαx,y34π2+ε4nαx,y48π3,
Inx,y=I0x,y1+γx,ycosφx,y+αn*x,y,n=0,1,2K-1.
Πx,y=n=0K-1Inx,y-I0x,y1+γx,ycosφx,y+αn*x,y2.
0I0Imax-Imin2,    0γ1,0φ2π,    0απ,
Inx,y=n=0K-1I0x,y+x,ycos αnAVG*+ƛx,ysin αnAVG*,
Πx,y=n=0K-1I0x,y+x,ycos αnAVG*+ƛx,ysin αnAVG*-Inx,y2.
Kn=0K-1cos αnAVG*n=0K-1sin αnAVG*n=0K-1cos αnAVG*n=0K-1cos2 αnAVG*n=0K-1sin αnAVG* cos αnAVG*n=0K-1sin αnAVG*n=0K-1sin αnAVG* cos αnAVG*n=0K-1sin2 αnAVG*I0x,yx,yƛx,y=n=0K-1IKn=0K-1IK cos αnAVG*n=0K-1Ik sin αnAVG*.

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