Abstract

A new self-mixing interferometry based on sinusoidal phase modulating technique is presented. Self-mixing interference occurs in the laser cavity by reflecting the light from a mirror-like target in front of the laser. Sinusoidal phase modulation of the beam is obtained by an electro-optic modulator (EOM) in the external cavity. The phase of the interference signal is calculated by Fourier analysis method. The interferometer is applied to measure the displacement of a high-precision commercial PZT with an accuracy of <10nm. The measurement range of the system mainly depends on the maximum operating frequency of EOM and the maximum sampling rate of A/D converter.

© 2005 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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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]

Am. J. Phys. (1)

Th. H. Peek, P. T. Bolwjin, and C. Th. Alkemade, �??Axial mode number of gas lasers from moving-mirror experiments,�?? Am. J. Phys. 35, 820-831 (1967).
[CrossRef]

Appl Opt. (2)

T. Yoshino, M. Nara, S. Mnatzakanian , �??Laser diode feedback interferometer for stabilization and displacement measurements,�?? Appl Opt. 26, 872-877 (1987).
[CrossRef]

S. Shinohara, A. Mochizuki, H. Yoshida et al. �??Laser Doppler velocimeter using the self-mixing effect of a semiconductor laser diode,�?? Appl Opt. 25, 1417-1419 (1986).
[CrossRef] [PubMed]

IEEE Trans Instrum. Meas. (1)

S. Shinohara, H. Yoshida, H. Ikeda, K. Nishide, and M. Sumi, �??Compact and high-precision range finder with wide dynamic range and its application,�?? IEEE Trans Instrum. Meas. 41, 40-44 (1992).
[CrossRef]

Meas. Sci. Technol. (1)

Kato J, Kikuchi N, Yamaguchi I, Ozono S. �??Optical feedback displacement sensor using a laser diode and its performance improvement,�?? Meas. Sci. Technol. 6, 45-52 (1995).
[CrossRef]

Opt. Commun. (1)

G. Liu, S. L. Zhang et al, �??Theoretical and experimental study of intensity branch phenomena in self-mixing interference in a He-Ne laser,�?? Opt. Commun. 221, 387-393 (2003).
[CrossRef]

Opt. Eng. (1)

T. Suzuki, S. Hirabayashi, O. Sasaki et al �??Self-mixing type of phase-locked laser diode interferometry,�?? Opt. Eng. 38, 543-548 (1999).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

M. Wang, Guangming Lai, �??Displacement measurement based on Fourier transform method with external cavity modulation,�?? Rev. Sci. Instrum. 72, 3440-3445 (2001).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

(a) Simulated phase change due to the motion of the external target. (b) Simulated modulated interference signal. (c) Fourier spectra of the interference signal. (d) Calculated phase (wrapping). (e) Retrieved phase (unwrapped). (f) Phase retrieved error.

Fig. 3.
Fig. 3.

Phase retrieved error due to the second feedback.

Fig. 4.
Fig. 4.

Error caused by second feedback with respect to m.

Fig. 5.
Fig. 5.

Standard deviation caused by second feedback versus the modulation depth a.

Fig. 6.
Fig. 6.

(a) The obtained SMI signal. (b) Fourier spectra of the SMI signal. (c) Extracted phase (wrapping). (d) Displacement reconstruction result.

Fig. 7.
Fig. 7.

Displacement reconstruction result of PZT with frequency 40HZ and amplitude of 4µ m (peak to peak).

Tables (1)

Tables Icon

Table 1. Values of a which null J1(2a) or J2(2a) (represented by X)

Equations (15)

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I = I 0 [ 1 + m cos ( ϕ ) j = 0 ( η ) j cos ( j ϕ ) ]
I = I 0 [ 1 + m cos ( ϕ ) ]
I ( t ) = I 0 { 1 + m cos [ ϕ ( t ) + 2 a sin ( 2 π f m t + β ) ] }
I ( f m , t ) = 2 m I 0 sin ϕ ( t ) J 1 ( 2 a ) sin ( 2 π f m t + β )
= A 1 ( t ) sin ( 2 π f m t + β )
I ( 2 f m , t ) = 2 m I 0 cos ϕ ( t ) J 2 ( 2 a ) cos ( 4 π f m t + 2 β )
= A 2 ( t ) cos ( 4 π f m t + 2 β )
ϕ ( t ) = arc tan [ A 1 ( t ) A 2 ( t ) · J 2 ( 2 a ) J 1 ( 2 a ) ]
A 1 ( t ) = imag { I f m ( t ) e j ( 2 π f m t + β ) }
A 2 ( t ) = real { I 2 f m ( t ) e j ( 4 π f m t + 2 β ) }
F f m 2
F = d ϕ ( t ) ( 2 π d t ) = 4 π f d 0 cos ( 2 π f t ) λ
F max = 4 π f d 0 λ f m 2 f m 8 π f d 0 λ
I ( t ) = I 0 { 1 + m cos [ ϕ ( t ) + 2 a sin ( 2 π f m t + β ) ] m η cos 2 [ ϕ ( t ) + 2 a sin ( 2 π f m t + β ) ] }
tan ( ϕ ( t ) j = 0 , 1 ) = A 1 ( t ) A 2 ( t ) · J 2 ( 2 a ) J 1 ( 2 a ) = 1 η cos ϕ ( t ) J 1 ( 4 a ) J 1 ( 2 a ) 1 η cos ϕ ( t ) J 2 ( 4 a ) J 2 ( 2 a ) + η 2 cos ϕ ( t ) J 2 ( 4 a ) J 2 ( 2 a ) tan ϕ ( t )

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