Abstract

Vibration is one of the confused problems in many fields. To give a comprehensive analysis of vibration, an electro-optical heterodyne interferometry with temporal intensity analysis method that can track the trajectory of the vibration dynamically has been built in this paper. The carrier frequency is introduced by the electrically controlled electro-optical frequency shifter. The trajectory is obtained by using temporal evolution of the light intensity in heterodyne interferometry. The instantaneous displacement of the vibration is extracted with spectral analysis technique. No target mirror and moving parts are required in our self-developed system. The principle and system configuration are described. The simulations and the preliminary experiments have been performed and the results show that this trajectory tracking system is high-efficiency, low-cost, jamproof, robust, precise and simple.

© 2014 Optical Society of America

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References

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2011 (2)

R. Sato, K. Nagaoka, “Motion trajectory measurement of NC machine tools using accelerometers,” Int. J. Automation Technol. 5(3), 387–394 (2011).

Y. Park, K. Cho, “Heterodyne interferometer scheme using a double pass in an acousto-optic modulator,” Opt. Lett. 36(3), 331–333 (2011).
[CrossRef] [PubMed]

2005 (1)

C. H. Liu, W. Y. Jywe, C. C. Hsu, T. H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[CrossRef]

1996 (1)

1991 (1)

1990 (1)

1988 (1)

1982 (2)

1981 (1)

1975 (1)

1966 (1)

1965 (1)

1963 (1)

1962 (1)

C. F. Buhrer, D. Baird, E. M. Conwell, “Optical frequency shifting by electro-optics effect,” Appl. Phys. Lett. 1(2), 46–49 (1962).

Apostol, I.

Baird, D.

C. F. Buhrer, D. Baird, E. M. Conwell, “Optical frequency shifting by electro-optics effect,” Appl. Phys. Lett. 1(2), 46–49 (1962).

Baird, D. H.

Bloom, L. R.

Brohinsky, W. R.

Buhrer, C. F.

C. F. Buhrer, L. R. Bloom, D. H. Baird, “Electro-optic light modulation with cubic crystals,” Appl. Opt. 2(8), 839–846 (1963).
[CrossRef]

C. F. Buhrer, D. Baird, E. M. Conwell, “Optical frequency shifting by electro-optics effect,” Appl. Phys. Lett. 1(2), 46–49 (1962).

Cho, K.

Conwell, E. M.

C. F. Buhrer, D. Baird, E. M. Conwell, “Optical frequency shifting by electro-optics effect,” Appl. Phys. Lett. 1(2), 46–49 (1962).

Hamanaka, K.

Hsu, C. C.

C. H. Liu, W. Y. Jywe, C. C. Hsu, T. H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[CrossRef]

Hsu, T. H.

C. H. Liu, W. Y. Jywe, C. C. Hsu, T. H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[CrossRef]

Hwang, C. H.

Ina, H.

Jywe, W. Y.

C. H. Liu, W. Y. Jywe, C. C. Hsu, T. H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[CrossRef]

Kaminow, I. P.

Kobayashi, S.

Kyuma, K.

Lin, S. Y.

Liu, C. H.

C. H. Liu, W. Y. Jywe, C. C. Hsu, T. H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[CrossRef]

Nagaoka, K.

R. Sato, K. Nagaoka, “Motion trajectory measurement of NC machine tools using accelerometers,” Int. J. Automation Technol. 5(3), 387–394 (2011).

Nunoshita, M.

Park, Y.

Popa, D.

Powell, R. L.

Sato, R.

R. Sato, K. Nagaoka, “Motion trajectory measurement of NC machine tools using accelerometers,” Int. J. Automation Technol. 5(3), 387–394 (2011).

Sokolov, I. A.

Sommargren, G. E.

Stepanov, S. I.

Stetson, K. A.

Tai, S.

Takeda, M.

Trofimov, G. S.

Turner, E. H.

Vlad, V. I.

Wang, W. C.

Wright, O. B.

Appl. Opt. (4)

Appl. Phys. Lett. (1)

C. F. Buhrer, D. Baird, E. M. Conwell, “Optical frequency shifting by electro-optics effect,” Appl. Phys. Lett. 1(2), 46–49 (1962).

Int. J. Automation Technol. (1)

R. Sato, K. Nagaoka, “Motion trajectory measurement of NC machine tools using accelerometers,” Int. J. Automation Technol. 5(3), 387–394 (2011).

J. Opt. Soc. Am. (3)

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

Opt. Lett. (4)

Rev. Sci. Instrum. (1)

C. H. Liu, W. Y. Jywe, C. C. Hsu, T. H. Hsu, “Development of a laser-based high-precision six-degrees-of-freedom motion errors measuring system for linear stage,” Rev. Sci. Instrum. 76(5), 055110 (2005).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

The indicatrix of LiNbO3 in the absence of electric field. (a) is a three-dimensional plot, (b) is a profile along z-axis at z = 0, and (c) is a profile along x-axis at x = 0.

Fig. 2
Fig. 2

The three-fold axis is rotated with an angle θ under the action of the two transversely electric fields represented by Eq. (1).

Fig. 3
Fig. 3

Frequency shifter.

Fig. 4
Fig. 4

System configuration.

Fig. 5
Fig. 5

Signal processing flowchart.

Fig. 6
Fig. 6

(a), (b), and (c) are the normalized frequency spectrums of the simulations; (d), (e), and (f) are the normalized filtered spectrums; (g), (h), and (i) are the instantaneous displacements of the simulated vibrations; (j), (k), and (l) are the errors in each simulation.

Fig. 7
Fig. 7

System arrangement.

Fig. 8
Fig. 8

(a) is the plot of the original frequency spectrum, at the central of the spectrum, 0 Hz is removed to show the spectrum more clearly. (b) is the plot of the filtered spectrum, the frequency remained is the spectrum around the carrier frequency which is represented by C in Eq. (18).

Fig. 9
Fig. 9

Red line is the vibration trajectory of the mechanical vibrator. Blue line is the output of the signal generator.

Tables (1)

Tables Icon

Table 1 System simulation parameters.

Equations (22)

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{ E x = E m cos ω m t E y = E m sin ω m t ,
{ r 12 = r 61 = r 22 r 21 = r 62 = r 11 .
[ 1 n 0 2 + ( r 11 2 + r 22 2 ) 1/2 E ]x ' 2 +[ 1 n 0 2 ( r 11 2 + r 22 2 ) 1/2 E ]y ' 2 =1,
θ= 1 2 [ ω m t+arcsin r 22 r 11 2 + r 22 2 ].
Γ( E m )=2πd n 0 3 E m /λ,
V input =[ 1 0 ] e iwt ,
T NWP =[ cos Γ 2 +isin Γ 2 cos ω m t isin Γ 2 sin ω m t isin Γ 2 sin ω m t cos Γ 2 isin Γ 2 cos ω m t ],
V'= T NWP V input =cos Γ 2 [ 1 0 ] e iωt + isin Γ 2 2 ( [ 1 i ] e i(ω+ ω m )t +[ 1 i ] e i(ω ω m )t ).
T QWP = 1 2 [ 1 i i 1 ].
V''= T QWP V'= cos Γ 2 2 [ 1 i ] e iωt + sin Γ 2 2 ( i[ 1 0 ] e i(ω+ ω m )t +[ 0 1 ] e i(ω ω m )t ).
I( t )= I 1 + I 2 + I 3 +2 I 1 I 2 cos( Φ 12 +2 ω m t )+2 I 1 I 3 cos( Φ 13 ω m t )+2 I 2 I 3 cos( Φ 23 + ω m t ),
I( t )= I 0 + I c cos[ Φ 12 +2 ω m t ],
φ( t )=4πΔz( t )/λ,
I( t )= I 0 + I c cos[ Φ 12 +2π f 0 t±φ( t ) ],
I( t )= I 0 +cexp( j2π f 0 t )+ c * exp( j2π f 0 t ),
c= 1 2 I c exp[ jΦ( t ) ],
Φ( t )= Φ 12 +2π f 0 t+φ( t ).
F( ΔI )=A+C+ C * ,
log[ c( t ) ]=log[ ( 1/2 ) I c ]+iΦ( t ),
S1: Δz( t )=200sin( 200Hz2πt ),
S2: Δz( t )=0.8sin( 200Hz2πt ),
S3: Δz( t )=200sin( 5Hz2πt ),

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