Abstract

The carrier squeezing interferometry algorithm is proposed to retrieve the phase from interferograms with phase shift errors. A linear carrier is introduced in the interferograms, and the image data is rearranged by the squeezing interferometry technology. In the spectrum of the rearranged image, the error lobe and the phase lobe are separated so the error-free phase can be retrieved by filtering. The simulated interferograms with phase shift errors are computed, and the precisions are better than 8.4×104λ. Its validation is verified by experiments, where a mean precision of 0.0040λ is obtained.

© 2011 Optical Society of America

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References

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2010 (1)

Q. Kemao, H. Wang, W. Gao, L. Feng, and S. HockSoon, Opt. Laser Eng. 48, 684 (2010).
[Crossref]

2009 (1)

2008 (1)

2004 (1)

1998 (1)

1995 (1)

1983 (1)

Burow, R.

Cywiak, M.

de Groot, P.

Deck, L. L.

Elssner, K.-E.

Estrada, J. C.

Feng, L.

Q. Kemao, H. Wang, W. Gao, L. Feng, and S. HockSoon, Opt. Laser Eng. 48, 684 (2010).
[Crossref]

Gao, W.

Q. Kemao, H. Wang, W. Gao, L. Feng, and S. HockSoon, Opt. Laser Eng. 48, 684 (2010).
[Crossref]

Grzanna, J.

Han, B.

HockSoon, S.

Q. Kemao, H. Wang, W. Gao, L. Feng, and S. HockSoon, Opt. Laser Eng. 48, 684 (2010).
[Crossref]

Huntley, J. M.

Kemao, Q.

Q. Kemao, H. Wang, W. Gao, L. Feng, and S. HockSoon, Opt. Laser Eng. 48, 684 (2010).
[Crossref]

Malacara, D.

D. Malacara, Optical Shop Testing, 3rd ed. (CRC Press, Taylor & Francis, 2007).
[Crossref]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (CRC Press, Taylor & Francis, 2005).
[Crossref]

Malacara, Z.

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (CRC Press, Taylor & Francis, 2005).
[Crossref]

Malacara-Hernandez, D.

Merkel, K.

Quiroga, J. A.

Schwider, J.

Servin, M.

M. Servin, M. Cywiak, D. Malacara-Hernandez, J. C. Estrada, and J. A. Quiroga, Opt. Express 16, 9276 (2008).
[Crossref] [PubMed]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (CRC Press, Taylor & Francis, 2005).
[Crossref]

Spolaczyk, R.

Wang, H.

Q. Kemao, H. Wang, W. Gao, L. Feng, and S. HockSoon, Opt. Laser Eng. 48, 684 (2010).
[Crossref]

Wang, Z.

Appl. Opt. (3)

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

Opt. Express (1)

Opt. Laser Eng. (1)

Q. Kemao, H. Wang, W. Gao, L. Feng, and S. HockSoon, Opt. Laser Eng. 48, 684 (2010).
[Crossref]

Opt. Lett. (1)

Other (2)

D. Malacara, Optical Shop Testing, 3rd ed. (CRC Press, Taylor & Francis, 2007).
[Crossref]

D. Malacara, M. Servin, and Z. Malacara, Interferogram Analysis for Optical Testing, 2nd ed. (CRC Press, Taylor & Francis, 2005).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Squeezing interferometry. (a) A PS interferograms sequence ( f 0 = 1 / 4 ). (b) The rearranged interferogram.

Fig. 2
Fig. 2

Distribution schematic of the rearranged interferogram spectrum. (a) Background spectrum and phase spectrum. (b)  + 1 order error spectrum. (c)  1 order error spectrum.

Fig. 3
Fig. 3

Demodulated result of CSI. (a) Demodulated phase. (b) Demodulated error ( RMS = 7.6 × 10 4 λ ).

Fig. 4
Fig. 4

A frame of the experiment interferograms (a) and the retrieved phase map by four-step algorithm (b), seven-step algorithm (c) and CSI algorithm (d) (Unit: λ).

Fig. 5
Fig. 5

Demodulated error RMS values of experiment interferograms by three algorithms.

Tables (1)

Tables Icon

Table 1 Demodulation Error RMS of a Phase Shift Sequence (unit: λ)

Equations (15)

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s m ( x , y ) = I 0 { 1 + V cos [ 2 π f 0 m + φ 0 ( x , y ) + r m ] } ,
s ( M x + m , y ) = s m ( x , y ) .
s ( x , y ) = I 0 { 1 + V cos [ 2 π f 0 x + φ + p ( x , y ) ] } ,
φ ( int [ x / M ] , y ) = φ 0 ( x , y ) ,
S ( f x , f y ) = S 0 + S + 1 + S 1 + E + 1 + E 1 ,
S 0 = I 0 V · δ ( 0 , 0 ) ,
S ± 1 = I 0 V 2 Φ ± 1 ( f x f 0 , f y ) ,
E ± 1 = 1 i M m = 0 M 1 r m n = exp ( i 2 π m n f 0 ) S ± 1 ( f x n f 0 , f y ) .
Φ ± 1 ( f x , f y ) = FT [ exp ( ± i φ ) ] ,
S ( f 0 , 0 ) = I 0 V 2 [ ( 1 + R 1 ) Φ + 1 ( f x f 0 , 0 ) + R 2 Φ 1 ( f x f 0 , 0 ) ] ,
Φ ± 1 = FT [ exp ( ± i φ + 2 π f c x ) ] = Φ ± 1 ( f x f c , f y ) .
S ( f 0 + f c , 0 ) = I 0 V 2 ( 1 + R 1 ) Φ + 1 ( f x f 0 f c , f y ) ,
S ( f 0 f c , 0 ) = I 0 V 2 R 2 Φ 1 ( f x f 0 + f c , f y ) .
1 2 π | φ x | max f c f 0 3 .
φ e w ( x , y ) = tan 1 Im { FT 1 [ S ( f x , f y ) g ( f x , f y ) ] } Re { FT 1 [ S ( f x , f y ) g ( f x , f y ) ] } ,

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