Abstract

In two-wavelength interferometry, synthetic wavelengths are generated in order to reduce the sensitivity or to extend the range of unambiguity for interferometric measurements. Here a novel optoelectronic technique, called superheterodyne detection, is presented, which permits measurement of the phase difference of two optical frequencies that cannot be resolved by direct optoelectronic heterodyne detection. This technique offers the possibility for operation of two-wavelength interferometry in real time with arbitrary synthetic wavelengths from micrometers to meters in length. Preliminary experimental results are reported. An optical arrangement for absolute range-finding applications using tunable-laser sources (e.g., semiconductor lasers) is proposed.

© 1988 Optical Society of America

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References

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  1. See, e.g., J. C. Wyant, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 397–402.
  2. C. R. Tilford, Appl. Opt. 16, 1857 (1977).
    [CrossRef] [PubMed]
  3. J. C. Wyant, Appl. Opt. 10, 2113 (1971).
    [CrossRef] [PubMed]
  4. C. Polhemus, Appl. Opt. 12, 2071 (1973).
    [CrossRef] [PubMed]
  5. A. F. Fercher, H. Z. Hu, U. Vry, Appl. Opt. 24, 2181 (1985).
    [CrossRef] [PubMed]
  6. H. Kikuta, K. Iwata, R. Nagata, Appl. Opt. 25, 2976 (1986).
    [CrossRef] [PubMed]
  7. R. Dandliker, R. Thalmann, D. Prongué, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 9 (1987).
  8. U. Vry, A. F. Fercher, J. Opt. Soc. Am. A 3, 988 (1986).
    [CrossRef]
  9. T. Kubota, M. Nara, T. Yoshino, Opt. Lett. 12, 310 (1987).
    [CrossRef] [PubMed]

1987 (2)

R. Dandliker, R. Thalmann, D. Prongué, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 9 (1987).

T. Kubota, M. Nara, T. Yoshino, Opt. Lett. 12, 310 (1987).
[CrossRef] [PubMed]

1986 (2)

1985 (1)

1977 (1)

1973 (1)

1971 (1)

Dandliker, R.

R. Dandliker, R. Thalmann, D. Prongué, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 9 (1987).

Fercher, A. F.

Hu, H. Z.

Iwata, K.

Kikuta, H.

Kubota, T.

Nagata, R.

Nara, M.

Polhemus, C.

Prongué, D.

R. Dandliker, R. Thalmann, D. Prongué, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 9 (1987).

Thalmann, R.

R. Dandliker, R. Thalmann, D. Prongué, Proc. Soc. Photo-Opt. Instrum. Eng. 813, 9 (1987).

Tilford, C. R.

Vry, U.

Wyant, J. C.

J. C. Wyant, Appl. Opt. 10, 2113 (1971).
[CrossRef] [PubMed]

See, e.g., J. C. Wyant, in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), pp. 397–402.

Yoshino, T.

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Figures (4)

Fig. 1
Fig. 1

Optical setup for two-wavelength superheterodyne interferometry. P’s, polarizers; BS’s, beam splitters (nonpolarizing); PBS’s, polarizing beam splitters; QWP, quarter-wave plate; AOM’s, acousto-optical modulators.

Fig. 2
Fig. 2

Electronic signals from two-wavelength superheterodyne interferometry. Upper trace: optical detector signal I(t); lower trace: amplitude-demodulated and bandpass-filtered signal Idem(t)

Fig. 3
Fig. 3

Displacement measurement of a mirror translated in 1-mm increments.

Fig. 4
Fig. 4

Schematic arrangement for absolute range finding using two-wavelength superheterodyne interferometry, tunable sources, and a calibration optical path length.

Equations (4)

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I ( t ) = a 0 + a 1 cos ( 2 π f 1 t + ϕ 1 ) + a 2 cos ( 2 π f 2 t + ϕ 2 ) ,
ϕ 1 = 4 π L / λ 1 = 4 π ν 1 L / c , ϕ 2 = 4 π L / λ 2 = 4 π ν 2 L / c .
I dem ( t ) = a 12 cos [ 2 π ( f 1 f 2 ) t + ( ϕ 1 ϕ 2 ) ] .
ϕ = ϕ 1 ϕ 2 = 4 π ( ν 1 ν 2 ) L / c = 4 π L / Λ ,

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