Abstract

The optical path difference (OPD) and amplitude of a sinusoidal wavelength scanning (SWS) are controlled with a double feedback control system in an interferometer, so that a ruler marking every wavelength and a ruler with scales smaller than a wavelength are generated. These two rulers enable us to measure an OPD longer than a wavelength. A liquid-crystal Fabry–Perot interferometer (LC-FPI) is adopted as a wavelength-scanning device, and double sinusoidal phase modulation is incorporated in the SWS interferometer. Because of a high resolution of the LC-FPI, the upper limit of the measurement range can be extended to 280μm by the use of the phase lock where the amplitude of the SWS is doubled in the feedback control. The ruler marking every wavelength is generated between 80μm and 280μm, and distances are measured with a high accuracy of the order of a nanometer in real time.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. P. de Groot and S. Kishner, "Synthetic wavelength stabilization for two-color laser-diode interferometry," Appl. Opt. 30, 4026-4033 (1991).
    [CrossRef] [PubMed]
  2. R. Onodera and Y. Ishii, "Two-wavelength laser-diode interferometer with fractional fringe techniques," Appl. Opt. 34, 4740-4746 (1995).
    [CrossRef] [PubMed]
  3. T. Suzuki, K. Kobayashi, and O. Sasaki, "Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode," Appl. Opt. 39, 2646-2652 (2000).
    [CrossRef]
  4. S. Kuwamura and I. Yamaguchi, "Wavelength scanning profilometry for real-time surface shape measurement," Appl. Opt. 36, 4473-4482 (1997).
    [CrossRef] [PubMed]
  5. F. Lexer, C. K. Hitzenberger, A. F. Fercher, and M. Kulhavy, "Wavelength-tuning interferometry of intraocular distances," Appl. Opt. 36, 6548-6553 (1997).
    [CrossRef]
  6. T. Li, R. G. May, A. Wang, and R. O. Claus, "Optical scanning extrinsic Fabry-Perot interferometer for absolute microdisplacement measurement," Appl. Opt. 36, 8859-8861 (1997).
    [CrossRef]
  7. X. Dai and K. Seta, "High-accuracy absolute disatnace measurement by means of wavelength scanning heterodyne interferometry," Meas. Sci. Technol. 9, 1013-1035 (1998).
  8. O. Sasaki, N. Murata, and T. Suzuki, "Sinusoidal wavelength-scanning interferometer with a superluminescent diode for step-profile measurement," Appl. Opt. 39, 4589-4592 (2000).
    [CrossRef]
  9. T. Suzuki, O. Sasaki, and T. Maruyama, "Phase-locked laser diode interferometry for surface profile measurement," Appl. Opt. 28, 4407-4410 (1989).
    [CrossRef] [PubMed]
  10. O. Sasaki, K. Akiyama, and T. Suzuki, "Sinusoidal-wavelength-scanning interferometer with double feedback control for real-time distance measurement," Appl. Opt. 41, 3906-3910 (2002).
    [CrossRef] [PubMed]
  11. M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, and T. Kurokawa, "Optical frequency-domain microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device," Appl. Opt. 38, 7063-7068 (1999).
    [CrossRef]
  12. O. Sasaki, T. Yoshida, and T. Suzuki, "Double sinusoidal phase-modulating laser diode interferometer for distance measurement," Appl. Opt. 30, 3617-3621 (1991).
    [CrossRef] [PubMed]

2002 (1)

2000 (2)

1999 (1)

1998 (1)

X. Dai and K. Seta, "High-accuracy absolute disatnace measurement by means of wavelength scanning heterodyne interferometry," Meas. Sci. Technol. 9, 1013-1035 (1998).

1997 (3)

1995 (1)

1991 (2)

1989 (1)

Appl. Opt. (11)

P. de Groot and S. Kishner, "Synthetic wavelength stabilization for two-color laser-diode interferometry," Appl. Opt. 30, 4026-4033 (1991).
[CrossRef] [PubMed]

R. Onodera and Y. Ishii, "Two-wavelength laser-diode interferometer with fractional fringe techniques," Appl. Opt. 34, 4740-4746 (1995).
[CrossRef] [PubMed]

T. Suzuki, K. Kobayashi, and O. Sasaki, "Real-time displacement measurement with a two-wavelength sinusoidal phase-modulating laser diode," Appl. Opt. 39, 2646-2652 (2000).
[CrossRef]

S. Kuwamura and I. Yamaguchi, "Wavelength scanning profilometry for real-time surface shape measurement," Appl. Opt. 36, 4473-4482 (1997).
[CrossRef] [PubMed]

F. Lexer, C. K. Hitzenberger, A. F. Fercher, and M. Kulhavy, "Wavelength-tuning interferometry of intraocular distances," Appl. Opt. 36, 6548-6553 (1997).
[CrossRef]

T. Li, R. G. May, A. Wang, and R. O. Claus, "Optical scanning extrinsic Fabry-Perot interferometer for absolute microdisplacement measurement," Appl. Opt. 36, 8859-8861 (1997).
[CrossRef]

O. Sasaki, N. Murata, and T. Suzuki, "Sinusoidal wavelength-scanning interferometer with a superluminescent diode for step-profile measurement," Appl. Opt. 39, 4589-4592 (2000).
[CrossRef]

T. Suzuki, O. Sasaki, and T. Maruyama, "Phase-locked laser diode interferometry for surface profile measurement," Appl. Opt. 28, 4407-4410 (1989).
[CrossRef] [PubMed]

O. Sasaki, K. Akiyama, and T. Suzuki, "Sinusoidal-wavelength-scanning interferometer with double feedback control for real-time distance measurement," Appl. Opt. 41, 3906-3910 (2002).
[CrossRef] [PubMed]

M. Kinoshita, M. Takeda, H. Yago, Y. Watanabe, and T. Kurokawa, "Optical frequency-domain microprofilometry with a frequency-tunable liquid-crystal Fabry-Perot etalon device," Appl. Opt. 38, 7063-7068 (1999).
[CrossRef]

O. Sasaki, T. Yoshida, and T. Suzuki, "Double sinusoidal phase-modulating laser diode interferometer for distance measurement," Appl. Opt. 30, 3617-3621 (1991).
[CrossRef] [PubMed]

Meas. Sci. Technol. (1)

X. Dai and K. Seta, "High-accuracy absolute disatnace measurement by means of wavelength scanning heterodyne interferometry," Meas. Sci. Technol. 9, 1013-1035 (1998).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Schematic diagram of sinusoidal wavelength-scanning interferometer with double feedback control for real-time distance measurement.

Fig. 2
Fig. 2

Change in the OPD by feedback control, which keeps phase α at 2 m π .

Fig. 3
Fig. 3

Regions of Z b where the phase lock of Z b = p π occurs when the feedback signal is (a) A 2 = 2 B   sin   Z b and (b) A 2 = 2 B   sin   Z b .

Fig. 4
Fig. 4

Schematic illustration of the sinusoidal wavelength-scanning light source (SWS-LS) using a liquid-crystal Fabry–Perot interferometer (LC-FPI).

Fig. 5
Fig. 5

Stable points of V b obtained at the phase lock of Z b = π . N is the number of the stable points. The stable point is assigned to the number m in which L z = m λ 0 .

Tables (3)

Tables Icon

Table 1 Measured Values at the Phase Lock of Z b = π

Tables Icon

Table 2 Measured Values at the Phase Lock of Z b = 2π

Tables Icon

Table 3 Results of Distance Measurement

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

λ ( t ) = λ 0 + b   cos ( ω b t ) .
S D ( t ) = A + B   cos [ Z c   cos ( ω c t ) + Z b   cos ( ω b t ) + α ] ,
Z c = 4 π a / λ 0 ,
Z b = ( 2 π b / λ 0 2 ) L ,
α = ( 2 π / λ 0 ) L .
S D ( t ) = A + B   cos   ϕ ( t ) [ J 0 ( Z c ) 2 J 2 ( Z c ) cos   2 ω c t + ] B   sin   ϕ ( t ) [ 2 J 1 ( Z c ) cos   ω c t + 2 J 3 ( Z c ) cos   3 ω c t + ] ,
S ( t ) = C   sin [ Z b   cos ( ω b t ) + α ] ,
A 1 = C   sin   α ,
L z = L L α = m λ 0 .
S ( t ) = C   sin [ Z b   cos ( ω b t ) ] ,
Z b = ( 2 π b / λ 0 2 ) L z .
A 2 = S 1 S 1 = 2 B   sin   Z b
b = p λ 0 2 / 2 L z = p λ 0 / 2 m .
m c = L z / λ 0 .
L = m λ 0 + L α .
Δ b = ( p λ 0 3 / 2 L z 2 ) .

Metrics