Abstract

Phase-tilting interferometry for optical testing is proposed to retrieve the phase from interferograms with random phase tilts. The Radon transform is used to extract the tilted phase plane, and the phase distribution is retrieved by the least squares method. The proposed method has been applied to simulated and experimental interferograms, obtaining satisfactory results. The proposed method has high accuracy and good robustness, and it can be used for interferometric measurements in environmental vibrations. Additionally, it can be used for interferometers without a phase shifter to achieve high-precision analysis.

© 2013 Optical Society of America

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References

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  1. D. Malacara, Optical Shop Testing, 3rd ed. (CRC Press, 2007).
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    [CrossRef]
  13. http://en.wikipedia.org/wiki/Hough_transform .
  14. http://en.wikipedia.org/wiki/Radon_transform .

2011

2009

2006

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, Proc. SPIE 6292, 62920F (2006).
[CrossRef]

2004

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Z. Wang and B. Han, Opt. Lett. 29, 1671 (2004).
[CrossRef]

2002

2001

1995

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Álvarez-Herrero, A.

Apostol, D.

Belenguer, T.

Brock, N.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Broistedt, H.

Burge, J. H.

Chen, L.

Damian, V.

Deck, L. L.

Dobroiu, A.

Doloca, N. R.

Han, B.

Hayes, J.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, Proc. SPIE 6292, 62920F (2006).
[CrossRef]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Kim, S.-W.

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Kimbrough, B.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, Proc. SPIE 6292, 62920F (2006).
[CrossRef]

Kong, I.-B.

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Li, B.

Ma, S.

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (CRC Press, 2007).

Millerd, J.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, Proc. SPIE 6292, 62920F (2006).
[CrossRef]

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Nascov, V.

North-Morris, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Novak, M.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Quiroga, J. A.

Strube, S.

Tutsch, R.

Vargas, J.

Wang, Z.

Wulan, T.

Wyant, J.

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, Proc. SPIE 6292, 62920F (2006).
[CrossRef]

Wyant, J. C.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

Zhao, C.

Zhu, R.

Appl. Opt.

Opt. Eng.

I.-B. Kong and S.-W. Kim, Opt. Eng. 34, 183 (1995).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, Proc. SPIE 5531, 304 (2004).
[CrossRef]

B. Kimbrough, J. Millerd, J. Wyant, and J. Hayes, Proc. SPIE 6292, 62920F (2006).
[CrossRef]

Other

http://en.wikipedia.org/wiki/Hough_transform .

http://en.wikipedia.org/wiki/Radon_transform .

D. Malacara, Optical Shop Testing, 3rd ed. (CRC Press, 2007).

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Figures (7)

Fig. 1.
Fig. 1.

Radon transform of binary image. (a) Binary image of the difference between two interferograms. (b) Image obtained by Radon transform.

Fig. 2.
Fig. 2.

Interferograms in the simulation.

Fig. 3.
Fig. 3.

Φ600mm large-aperture phase-shifting interferometer.

Fig. 4.
Fig. 4.

Interferograms with random phase shifts and tilts for the proposed method.

Fig. 5.
Fig. 5.

Interferograms with π/2 phase shifts for PSI.

Fig. 6.
Fig. 6.

Wrapped phase. (a) Phase map obtained by PSI. (b) Phase obtained by the proposed method.

Fig. 7.
Fig. 7.

Retrieved phase. (a) Phase obtained by PSI. (b) Phase obtained by the proposed method.

Tables (1)

Tables Icon

Table 1. Comparison of the Plane Coefficients in the Simulation

Equations (17)

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I(x,y)=a(x,y)+b(x,y)cos(ϕ(x,y)),
In(x,y)=a(x,y)+b(x,y)cos(ϕ(x,y)+Pn(x,y)),
Pn(x,y)=αnx+βny+γn.
Dn(x,y)=In(x,y)I(x,y)=2b(x,y)sin((ϕ(x,y)+Pn(x,y))/2)sin(Pn(x,y)/2).
Dn(x,y)={1,Dn(x,y)=00,others.
R(ρ,θ)=ΩDn(x,y)δ(ρxcosθysinθ)dxdy,
αn=2π|cosθ|/d,
βn=sign(π/2θ)·2πsinθ/d,
γn=βnρsinθαnρcosθ,
In=c0+c1cosPn+c2sinPn.
S=n=1N(InIn)2,
S/c0=0,S/c1=0,S/c2=0.
C=A1B,
C=[c0c1c2]T,
B=[n=1NInn=1NIncosPnn=1NInsinPn]T,
A=[Nn=1NcosPnn=1NsinPnn=1NcosPnn=1Ncos2Pnn=1NcosPnsinPnn=1NsinPnn=1NsinPncosPnn=1Nsin2Pn].
ϕ(x,y)=tan1(c2/c1).

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