Abstract

A new fiber-optic interferometer fringe projection with the integrating bucket method is presented. This method is based on the sinusoidal phase-modulating technique and makes use of Mach–Zehnder interferometer structure and Young’s double pinhole interference principle to achieve interference fringe projection. Here, we consider the modulated signal with the modulation intensity of laser (companion amplitude modulation) m in the calculation directly, adjust the optimal value of z to accommodate different m, and calculate the initial phase with phase generated carrier technology at the same time. Preliminary results from the optimum phase modulation z and initial phase φ0 are discussed.

© 2012 Optical Society of America

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References

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2012

2010

D. Guo and M. Wang, “Self-mixing interferometry based on sinusoidal phase modulation and integrating-bucket method,” Opt. Commun. 283, 2186–2192 (2010).
[CrossRef]

2007

2006

2003

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

2002

2001

1999

1987

1986

Chao, Z.

D. Fajie, Z. Cong, Z. Chao, and X. Hai, “Fourier transform profilometry based on fiber-optic interferometric projection,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (CISP) (2009), Vol. 9, pp. 1–5.

Chih, H.-W.

Cong, Z.

D. Fajie, Z. Cong, Z. Chao, and X. Hai, “Fourier transform profilometry based on fiber-optic interferometric projection,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (CISP) (2009), Vol. 9, pp. 1–5.

Dubois, A.

Fajie, D.

D. Fajie, Z. Cong, Z. Chao, and X. Hai, “Fourier transform profilometry based on fiber-optic interferometric projection,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (CISP) (2009), Vol. 9, pp. 1–5.

Guo, D.

D. Guo and M. Wang, “Self-mixing interferometry based on sinusoidal phase modulation and integrating-bucket method,” Opt. Commun. 283, 2186–2192 (2010).
[CrossRef]

Hai, X.

D. Fajie, Z. Cong, Z. Chao, and X. Hai, “Fourier transform profilometry based on fiber-optic interferometric projection,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (CISP) (2009), Vol. 9, pp. 1–5.

He, G.

Izatt, J. A.

Li, Z.

Liu, Y.

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Lo, Y.-L.

Maruyama, T.

Matsuda, M.

Okazaki, H.

Sakai, M.

Sasaki, O.

Sasaki, S.

Suzuki, T.

Tang, F.

Tao, Y. K.

Wang, B.

Wang, M.

D. Guo and M. Wang, “Self-mixing interferometry based on sinusoidal phase modulation and integrating-bucket method,” Opt. Commun. 283, 2186–2192 (2010).
[CrossRef]

Wang, X.

B. Wang, X. Wang, O. Sasaki, and Z. Li, “Sinusoidal phase-modulating interferometer insensitive to intensity modulation of a laser diode for displacement measurement,” Appl. Opt. 51, 1939–1944 (2012).
[CrossRef]

G. He, X. Wang, A. Zeng, and F. Tang, “Sinusoidal phase-modulating laser diode interferometer for real-time surface profile measurement,” Chin. Opt. Lett. 5, 164–166 (2007).

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Yazawa, T.

Yeh, C.-Y.

Yu, D.

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Yu, T.-C.

Zeng, A.

Zhang, C.

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Zhao, M.

Appl. Opt.

Chin. Opt. Lett.

J. Opt. Soc. Am. A

Opt. Commun.

D. Guo and M. Wang, “Self-mixing interferometry based on sinusoidal phase modulation and integrating-bucket method,” Opt. Commun. 283, 2186–2192 (2010).
[CrossRef]

Opt. Laser Technol.

X. Wang, X. Wang, Y. Liu, C. Zhang, and D. Yu, “A sinusoidal phase-modulating fiber-optic interferometer insensitive to the intensity change of the light source,” Opt. Laser Technol. 35, 219–222 (2003).
[CrossRef]

Opt. Lett.

Other

D. Fajie, Z. Cong, Z. Chao, and X. Hai, “Fourier transform profilometry based on fiber-optic interferometric projection,” in Proceedings of the 2009 2nd International Congress on Image and Signal Processing (CISP) (2009), Vol. 9, pp. 1–5.

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Figures (8)

Fig. 1.
Fig. 1.

Schematics diagram of optical setup. OI, optic isolator; OC, optical coupler; PD, photodetector; SFCS, servo feedback control system.

Fig. 2.
Fig. 2.

Fringe projection measurement system.

Fig. 3.
Fig. 3.

CCD exposure signal and the phase-modulated signal synchronous control.

Fig. 4.
Fig. 4.

Simulation results of F(m,z).

Fig. 5.
Fig. 5.

Relationship between F(m,z) and z.

Fig. 6.
Fig. 6.

Relative ratio of error ΔF/F.

Fig. 7.
Fig. 7.

Schematic representationof the initial phase measurement. LMS, laser modulated signal; AD, analog-to-digital conversion; SP, signal processor; FRM, Faraday rotator mirror.

Fig. 8.
Fig. 8.

Two orthogonal signals constitute a Lissajous Graphics.

Tables (1)

Tables Icon

Table 1. Values of z, F(m,z) and dF(m,z)/dz for Different m

Equations (22)

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s(x,y,t)=[1+mcos(ωt+θ)]{A+Bcos[zcos(ωt+θ)+φ(x,y)]},
xsinβ+zcosβ=Lsinβ.
xm=yn=zd,
{x=mLmd·cotβy=nLmd·cotβz=dLmd·cotβ,
φ(x,y)=2πλatan(ββ0)+φ0,
φ(x,y)=2πλa(ββ0)+φ0.
s(x,y,t)=[1+mcosϕ]A+Bcos[φ(x,y)](1+mcosϕ)J0(z)+Bcos[φ(x,y)]·n=1(1)nJ2n(z)[2cos2nϕ+mcos(2n+1)ϕ+mcos(2n1)ϕ]Bsin[φ(x,y)]·n=0(1)nJ2n+1(z)[2cos(2n+1)ϕ+mcos(2n+2)ϕ+mcos2nϕ],
Ep=4Tp14Tp4Ts(x,y,t)dt,p=1,2,3,4.
Up=4Tp14Tp4Tn=1(1)nJ2n(z)[2cos2nϕ+mcos(2n+1)ϕ+mcos(2n1)ϕ]dt,
Vp=4Tp14Tp4Tn=0(1)nJ2n+1(z)[2cos(2n+1)ϕ+mcos(2n+2)ϕ+mcos2nϕ]dt,
Ep=[A+BJ0(z)cos(φ(x,y))]+2πm[A+BJ0(z)cos(φ(x,y))][sin(pπ2+θ)+cos(pπ2+θ)]+Bcos(φ(x,y))UpBsin(φ(x,y))VP.
M=U1U2+U3U4,N=(2tanθ+1)U1+(12tanθ)U2U3U4,P=V1V2+V3V4,Q=(2tanθ+1)V1+(12tanθ)V2V3V4,
Σs=E1E2+E3E4=MBcos(φ(x,y))+PBsin(φ(x,y)),
Σc=(2tanθ+1)E1+(12tanθ)E2E3E4=NBcos(φ(x,y))+QBsin(φ(x,y)).
φ(x,y)=arctan(NΣsMΣc)/(PΣcQΣs).
S(t)=[1+mcos(ωt+θ)]{C+Dcos[zcos(ωt+θ)+α]},
V1=G1[mDJ0(z)cosαmDJ2(z)cosα2DJ1(z)sinα].
V2=G2[2DJ2(z)cosα+mDJ1(z)sinαmDJ3(z)sinα],
tanα=2J2(z)V1G1+[mJ0(z)mJ2(z)]V2G2[mJ1(z)mJ3(z)]V2G2+2J1(z)V1G1.
V1G1G2V2=[mJ0(z)mJ2(z)]2J1(z)tanα[mJ1(z)mJ3(z)]tanα2J2(z)=2J1(z)mJ1(z)mJ3(z)1F(m,z)[tanα2J2(z)mJ1(z)mJ3(z)].
F(m,z)=m2[J1(z)J3(z)]24J1(z)J2(z)m2[J0(z)J2(z)][J1(z)J3(z)].
dF(m,z)dz0.

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