Abstract

A two-wavelength interferometer with a fractional fringe technique (the method of coincidence) has been constructed by using dual frequency-ramped laser diodes. The respective wavelengths of two optical phases were measured by the heterodyne technique. The detected two phases are employed with real-time electronic processing to produce two signals that correspond to the integer and the fractional fringe numbers at a single wavelength. These summed signals can yield a synthetic phase having a single-wavelength resolution. The upper limits for the measurement accuracy are theoretically analyzed.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. P. de Groot, “Three-color laser-diode interferometer,” Appl. Opt. 30, 3612–3616 (1991).
    [CrossRef] [PubMed]
  2. P. de Groot, S. Kishner, “Synthetic wavelength stabilization for two-color laser-diode interferometry,” Appl. Opt. 30, 4026–4033 (1991).
    [CrossRef] [PubMed]
  3. O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
    [CrossRef] [PubMed]
  4. A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  5. C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
    [CrossRef] [PubMed]
  6. C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
    [CrossRef]
  7. R. Dändliker, R. Thalmann, D. Prongué, “Two-wavelength laser interferometry using superheterodyne detection,” Opt. Lett. 13, 339–341 (1988).
    [CrossRef] [PubMed]
  8. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [CrossRef]
  9. L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
    [CrossRef]
  10. Y. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef] [PubMed]
  11. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef] [PubMed]
  12. Y. Ishii, R. Onodera, “Two-wavelength laser-diode interferometry that uses phase-shifting techniques,” Opt. Lett. 16, 1523–1525 (1991).
    [CrossRef] [PubMed]
  13. R. Onodera, Y. Ishii, “Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes,” Appl. Opt. 33, 5052–5061 (1994).
    [CrossRef] [PubMed]
  14. C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977).
    [CrossRef] [PubMed]
  15. R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” IEEE J. Lightwave Technol. 13, 675–681 (1995).
    [CrossRef]

1995

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” IEEE J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

1994

1991

1990

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

1988

1987

1986

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

1985

1984

1977

1973

Bartolini, L.

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

Cheng, Y. Y.

Collibus, De

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

Creath, K.

Dändliker, R.

de Groot, P.

den Boef, A. J.

Fercher, A. F.

Ferri, M.

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

Fornetti, G.

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

Hu, H. Z.

Ishii, Y.

Kishner, S.

Occhionero, G.

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

Ohde, N.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” IEEE J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

Onodera, R.

Papetti, F.

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

Polhemus, C.

Prongué, D.

Sasaki, O.

Sasazaki, H.

Suzuki, T.

Takahashi, Y.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” IEEE J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

Thalmann, R.

Tilford, C. R.

Vry, U.

Wickramasinghe, H. K.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Williams, C. C.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Wyant, J. C.

Yoshino, T.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” IEEE J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

Appl. Opt.

P. de Groot, “Three-color laser-diode interferometer,” Appl. Opt. 30, 3612–3616 (1991).
[CrossRef] [PubMed]

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

O. Sasaki, H. Sasazaki, T. Suzuki, “Two-wavelength sinusoidal phase/modulating laser-diode interferometer insensitive to external disturbances,” Appl. Opt. 30, 4040–4045 (1991).
[CrossRef] [PubMed]

A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
[CrossRef] [PubMed]

C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071–2074 (1973).
[CrossRef] [PubMed]

A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
[CrossRef]

Y. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
[CrossRef] [PubMed]

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

R. Onodera, Y. Ishii, “Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes,” Appl. Opt. 33, 5052–5061 (1994).
[CrossRef] [PubMed]

C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977).
[CrossRef] [PubMed]

IEEE J. Lightwave Technol.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” IEEE J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

J. Appl. Phys.

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

L. Bartolini, G. Fornetti, M. Ferri, De Collibus, G. Occhionero, F. Papetti, “Two-wavelength infrared heterodyne transceiver with a continuous phase tracking system,” Rev. Sci. Instrum. 61, 1177–1181 (1990).
[CrossRef]

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 (10)

Fig. 1
Fig. 1

Variations of the optical frequency in laser diodes as a function of time. The beat frequencies ωb1 and ωb2 are generated between two arms of the interferometer.

Fig. 2
Fig. 2

Experimental setup for a two-wavelength laser-diode interferometer with a phase demodulator by using fractional fringe techniques.

Fig. 3
Fig. 3

Schematic explanation of the measurement principle based on the fractional fringe technique. The fractional fringe numbers [m1]frac and [M]frac change from 0 to 1 with respect to the optical path length 2w, where 2w ranges from 0 to Λ. The integer part [m1]int of the fringe number was obtained by assigning the sampled values [M]frac into Λ/λ1 levels.

Fig. 4
Fig. 4

Block diagram of the electric phase demodulator for determining the integer fringe number [m1]int.

Fig. 5
Fig. 5

Operation of the phase-measurement system for the change of the optical path length 2w. ϕ1 and ϕ2 are the phases at wavelengths λ1 and λ2, respectively. [M]frac is the fractional fringe number at the synthetic wavelength. [m1]int is the integer part of the fringe number. The fringe number m1 represents the desired results.

Fig. 6
Fig. 6

Schematic of the phase-unwrapping circuit. Voltage V corresponds to that of a 2π phase.

Fig. 7
Fig. 7

Experimental results of displacement moving with a PZT mirror longer than the optical wavelength. The result of fringe number m1 demonstrates single-wavelength resolution.

Fig. 8
Fig. 8

Experimental setup of the profilometry measurement of the step object having a height longer than λ1. Two beat signals are detected by a photodiode attached to an XY motorized stage.

Fig. 9
Fig. 9

Phase map of a step object. The measurement result shows the actual height that cannot be tested by a conventional one-color interferometer.

Fig. 10
Fig. 10

Upper limit of the measurement accuracy of the heterodyne method in two-wavelength interferometry with the fractional fringe technique. The lower area of each curve satisfies inequality (12), which means that the detection of the integer fringe number is without error.

Equations (14)

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

ω b k = Δ ω k τ T k ,
s k ( t ) = I M k [ 1 + γ k cos ( ω b k t + ϕ k ) ] ,
ϕ k = 2 π 2 w ( x , y ) λ k ,
m k = ϕ k 2 π = [ m k ] int + [ m k ] frac ,
[ M ] frac = 2 w Λ = m 1 - m 2 .
2 w = Λ [ M ] frac .
[ m 1 ] int = int [ 2 w λ 1 ] ,
[ m 1 ] int = int [ Λ λ 1 [ M ] frac ] .
[ M ] frac = [ m 1 ] frac - [ m 2 ] frac + [ m 1 ] int - [ m 2 ] int .
| δ ( Λ λ 1 [ M ] frac ) | < 1 2 ,
| δ [ Λ λ 1 ϕ 1 - ϕ 2 2 π ] | < 1 2 .
Δ m < 1 4 G - 2 w Λ ( Δ G 2 G + G Δ λ λ ) .
Δ m = Δ ϕ 2 π ,
Δ ϕ = ρ π γ cos ϕ ,

Metrics