Abstract

A spatial frequency domain method is presented to deal with tilt-shift errors and random phase shift in temporal phase-shift interferometry. The proposed method determines tilt shift and phase shift by analyzing positions and phase variances of sidebands in spatial frequency domain. The method is computationally fast for it is noniterative and needs only one 2D Fourier transform for each spatial carrier interferogram. No initial estimations are required and no ambiguous results are generated with the proposed method. Simulations indicate that the proposed method could detect tilt shift and piston phase shift with high accuracy. Results of experiments conducted in the presence of vibration demonstrate that the proposed method could alleviate fluctuations in the retrieved phase map. The method could be applied to interferometers that are uncalibrated or with an unbalanced piezoelectric transducer, besides interferometers in unsteady conditions.

© 2013 Optical Society of America

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References

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2011

2009

2008

J. Xu, Q. Xu, and L. Chai, “Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts,” Appl. Opt. 47, 480–485 (2008).
[CrossRef]

J. Xu, Q. Xu, and L. Chai, “Tilt-shift determination and compensation in phase-shifting interferometry,” J. Opt. A 10, 075011 (2008).

2006

2005

2004

2002

2001

2000

1982

Álvarez-Herrero, A.

Apostol, D.

Belenguer, T.

Bokor, J.

Bruno, L.

Chai, L.

J. Xu, Q. Xu, and L. Chai, “Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts,” Appl. Opt. 47, 480–485 (2008).
[CrossRef]

J. Xu, Q. Xu, and L. Chai, “Tilt-shift determination and compensation in phase-shifting interferometry,” J. Opt. A 10, 075011 (2008).

Chen, M.

Damian, V.

de Groot, P.

Dobroiu, A.

Goldberg, K. A.

Guo, H.

Han, B.

Hao, Q.

Hu, Y.

Ina, H.

Kobayashi, S.

Nascov, V.

Patorski, K.

Quiroga, J. A.

Soloviev, O.

Styk, A.

Szwaykowski, P.

Takeda, M.

Vargas, J.

Vdovin, G.

Wang, Z.

Wei, C.

Xu, J.

J. Xu, Q. Xu, and L. Chai, “Tilt-shift determination and compensation in phase-shifting interferometry,” J. Opt. A 10, 075011 (2008).

J. Xu, Q. Xu, and L. Chai, “Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts,” Appl. Opt. 47, 480–485 (2008).
[CrossRef]

Xu, Q.

J. Xu, Q. Xu, and L. Chai, “Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts,” Appl. Opt. 47, 480–485 (2008).
[CrossRef]

J. Xu, Q. Xu, and L. Chai, “Tilt-shift determination and compensation in phase-shifting interferometry,” J. Opt. A 10, 075011 (2008).

Zhu, Q.

Appl. Opt.

J. Opt. A

J. Xu, Q. Xu, and L. Chai, “Tilt-shift determination and compensation in phase-shifting interferometry,” J. Opt. A 10, 075011 (2008).

J. Opt. Soc. Am.

Opt. Express

Opt. Lett.

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Figures (6)

Fig. 1.
Fig. 1.

Retrieved phase from interferograms without vibration with 13-frame algorithm.

Fig. 2.
Fig. 2.

One of 13 interferograms recorded in the presence of vibration.

Fig. 3.
Fig. 3.

Phase map (a) retrieved from tilt-shift interferograms with 13-frame algorithm and its phase retrieval error map (b).

Fig. 4.
Fig. 4.

Phase map (a) retrieved from tilt-shift interferograms with Goldberg’s method and its phase retrieval error map (b).

Fig. 5.
Fig. 5.

Phase map (a) retrieved from tilt-shift interferograms with proposed method and its phase retrieval error map (b).

Fig. 6.
Fig. 6.

Comparison of phase retrieval error map (a) and determinant map of curvature matrix M (b).

Tables (1)

Tables Icon

Table 1. Detection Results of Tilt Shifts and Piston Phase Shifts

Equations (14)

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In(x,y)=A(x,y)+B(x,y)cos[φ(x,y)+2π(fxnx+fyny)+δn],
In(x,y)=A(x,y)+exp(jδn)C*(x,y)exp[j2π(fxnx+fyny)]+exp(jδn)C(x,y)exp[j2π(fxnx+fyny)],
C(x,y)=B(x,y)exp[jφ(x,y)]/2,
in(u,v)=a(u,v)+exp(jδn)c*(u+fxn,v+fyn)+exp(jδn)c(ufxn,vfyn),
{fxnfx1=(PxnPx1)/Lxfynfy1=(PynPy1)/Ly,
Δn=2π(fxnfx1)x+2π(fynfy1)y+δn.
Mα=β,
M=[NcosΔnsinΔncosΔncos2ΔncosΔnsinΔnsinΔncosΔnsinΔnsin2Δn],
α=[α1,α2,α3]T,
β=[In,IncosΔn,InsinΔn]T.
IWn(x,y)=In(x,y)W(x,y)=AW(x,y)+exp(jδn)CW*(x,y)exp[j2π(fxnx+fyny)]+exp(jδn)CW(x,y)exp[j2π(fxnx+fyny)],
AW(x,y)=A(x,y)W(x,y)
CW(x,y)=B(x,y)W(x,y)exp[jφ(x,y)]/2,
iWn(u,v)=aW(u,v)+exp(jδn)cW*(u+fxn,v+fyn)+exp(jδn)cW(ufxn,vfyn),

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