Abstract

When a sawtooth voltage signal with the amplitude lower than its half-wave voltage is applied to drive an electro-optic modulator, the interference signals become a group of periodic sinusoidal segments. A new algorithm is proposed to modify these segments to an associated continuous sinusoidal wave, and then its initial phase can be determined. Subtracting the characteristic phase of the modulator from the initial phase, the absolute phase can be obtained. This technique is applied to all pixels, and full-field absolute phase measurements can be achieved. The validity of this method is demonstrated.

© 2008 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2007 (2)

Z. C. Jian, Y. L. Chen, H. C. Hsieh, P. J. Hsieh, and D. C. Su, “Optimal condition for full-field heterodyne interferometry,” Opt. Eng. 46, 115604 (2007).
[CrossRef]

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

2006 (1)

2004 (1)

2003 (2)

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391-2399 (2003).
[CrossRef]

M. Akiba, K. P. Chan, and N. Tanno, “Full-field optical coherence tomography by two-dimensional heterodyne detection with a pair of CCD cameras,” Opt. Lett. 28, 816-818 (2003).
[CrossRef] [PubMed]

1999 (1)

1997 (1)

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314-321(1997).
[CrossRef]

1996 (1)

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161-163 (1996).
[CrossRef]

1994 (1)

1988 (1)

1979 (1)

1928 (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617-644 (1928).
[CrossRef]

Akiba, M.

Briers, D.

D. Briers, “Interferometric optical testing,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech, 1997), pp. 101-103.

Cao, K.

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

Chan, K. P.

Chang, J. G.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314-321(1997).
[CrossRef]

Chang, M.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314-321(1997).
[CrossRef]

Chen, C. D.

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161-163 (1996).
[CrossRef]

Chen, Y. L.

Z. C. Jian, Y. L. Chen, H. C. Hsieh, P. J. Hsieh, and D. C. Su, “Optimal condition for full-field heterodyne interferometry,” Opt. Eng. 46, 115604 (2007).
[CrossRef]

Chen, Z.

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

Chiu, M. H.

Chou, C.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314-321(1997).
[CrossRef]

Connely, M. J.

Dandliker, R.

Docchio, F.

Dou, Q.

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

Egan, P.

Feng, C. M.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314-321(1997).
[CrossRef]

Gelmini, E.

Holly, S.

Hsieh, H. C.

Z. C. Jian, Y. L. Chen, H. C. Hsieh, P. J. Hsieh, and D. C. Su, “Optimal condition for full-field heterodyne interferometry,” Opt. Eng. 46, 115604 (2007).
[CrossRef]

Hsieh, P. J.

Z. C. Jian, Y. L. Chen, H. C. Hsieh, P. J. Hsieh, and D. C. Su, “Optimal condition for full-field heterodyne interferometry,” Opt. Eng. 46, 115604 (2007).
[CrossRef]

Huang, Y. C.

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314-321(1997).
[CrossRef]

Jia, G.

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

Jian, Z. C.

Z. C. Jian, Y. L. Chen, H. C. Hsieh, P. J. Hsieh, and D. C. Su, “Optimal condition for full-field heterodyne interferometry,” Opt. Eng. 46, 115604 (2007).
[CrossRef]

Jozwicki, R.

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391-2399 (2003).
[CrossRef]

Lakestani, F.

Lee, J. Y.

Ma, H.

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

Massie, N. A.

Minoni, U.

Nelson, R. D.

Nyquist, H.

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617-644 (1928).
[CrossRef]

Pitter, M. C.

Prongue, D.

See, C. W.

Somekh, M. G.

Su, D. C.

Z. C. Jian, Y. L. Chen, H. C. Hsieh, P. J. Hsieh, and D. C. Su, “Optimal condition for full-field heterodyne interferometry,” Opt. Eng. 46, 115604 (2007).
[CrossRef]

M. H. Chiu, J. Y. Lee, and D. C. Su, “Complex refractive-index measurement based on Fresnel's equations and uses of heterodyne interferometry,” Appl. Opt. 38, 4047-4052 (1999).
[CrossRef]

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161-163 (1996).
[CrossRef]

Tanno, N.

Thalmann, R.

Tkaczyk, T.

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391-2399 (2003).
[CrossRef]

Whelan, M. P.

Zhang, T.

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

Appl. Opt. (2)

Opt. Commun. (1)

C. M. Feng, Y. C. Huang, J. G. Chang, M. Chang, and C. Chou, “A true sensitive optical heterodyne polarimeter for glucose concentration measurement,” Opt. Commun. 141, 314-321(1997).
[CrossRef]

Opt. Eng. (2)

Z. C. Jian, Y. L. Chen, H. C. Hsieh, P. J. Hsieh, and D. C. Su, “Optimal condition for full-field heterodyne interferometry,” Opt. Eng. 46, 115604 (2007).
[CrossRef]

T. Tkaczyk and R. Jozwicki, “Full-field heterodyne interferometer for shape measurement: experimental characteristics of the system,” Opt. Eng. 42, 2391-2399 (2003).
[CrossRef]

Opt. Laser Technol. (1)

Q. Dou, H. Ma, G. Jia, Z. Chen, K. Cao, and T. Zhang, “Study on measurement of linear electro-optic coefficient of a minute irregular octahedron cBN wafer,” Opt. Laser Technol. 39, 647-651 (2007).
[CrossRef]

Opt. Lett. (5)

Precis. Eng. (1)

D. C. Su, M. H. Chiu, and C. D. Chen, “Simple two-frequency laser,” Precis. Eng. 18, 161-163 (1996).
[CrossRef]

Trans. Am. Inst. Electr. Eng. (1)

H. Nyquist, “Certain topics in telegraph transmission theory,” Trans. Am. Inst. Electr. Eng. 47, 617-644 (1928).
[CrossRef]

Other (2)

IEEE Standard 1241-2000, “Standard for terminology and test methods for analog to digital converters,” (IEEE, 2000), pp. 25-29.

D. Briers, “Interferometric optical testing,” in Optical Measurement Techniques and Applications, P. K. Rastogi, ed. (Artech, 1997), pp. 101-103.

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Figures (8)

Fig. 1
Fig. 1

Schematic diagram for the common-path heterodyne interferometer with an electro-optic modulator: LS, laser light source; EO, electro-optic modulator; FG, function generator; VLA, voltage linear amplifier; BS, beam splitter; AN, analyzer; D, photodetector.

Fig. 2
Fig. 2

Schematic diagram for the full-field common-path heterodyne interferometer: HLS, heterodyne light source; MO, microscopic objective; PH, pinhole; CL, collimating lens; AN, analyzer; IL, imaging lens; C, CMOS camera; PC, personal computer.

Fig. 3
Fig. 3

(a) Interference signals as V is changed from 80 V to 120 V with 20 V steps under the conditions V π = 148 V and ψ = 60 ° . (b) Corresponding modified interference signals with lengthened periods.

Fig. 4
Fig. 4

The conditions are applied to identify the optimum segment as (a)  P m + 1 > C m + T and (b)  P m + 1 C m + T .

Fig. 5
Fig. 5

Inserting Δ t into any two consecutive segments.

Fig. 6
Fig. 6

Flowchart for describing the whole process.

Fig. 7
Fig. 7

Intensities of the sampled signals at the pixel ( + 100 , + 100 ) .

Fig. 8
Fig. 8

Relation curves of phase error versus random noise level as ψ = 45 ° .

Equations (10)

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Γ = π V π V z = π V π [ 2 V T ( t m T ) V ] = 2 π V V π T ( t m T ) ϕ 0 ,
I ( t ) = 1 2 [ 1 + cos ( Γ + ϕ ) ] = 1 2 { 1 + cos [ 2 π V V π T ( t m T ) ϕ 0 + ϕ ] } = 1 2 { [ 1 + cos ( 2 π V V π T t + ψ ) ] · rect ( t T 1 2 ) } * i = 0 n 1 δ ( t i T ) ,
I ( t ) = 1 2 [ 1 + cos ( 2 π t T + ψ ) ] ,
I r ( t ) = 1 2 ( 1 + cos 2 π t T ) .
I c ( t ) = 1 2 { [ 1 + cos ( 2 π V V π T t + ψ ) ] · rect ( t T + Δ t 1 2 ) } * i = 0 n 1 δ [ t i ( T + Δ t ) ] ,
C m + 1 = C m + T , if     P m + 1 > C m + T ,
C m + 1 = P m + 1 , if     P m + 1 C m + T .
I i ( t ) = 1 2 { [ 1 + cos ( 2 π V V π T t + ψ ) ] · rect ( V V π T t 1 2 ) } * g = 0 h 1 δ ( t g f s ) ,
I c ( t ) = 1 2 [ 1 + cos ( 2 π V V π T t + ψ ) ] = A · cos ( 2 π V V π T t ) + B · sin ( 2 π V V π T t ) + C .
ψ = tan 1 ( B A ) .

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