Abstract

Absolute distance measurements can be performed with an interferometric method that uses only a single tunable laser. This method has one major drawback, because a small target movement of the order of one wavelength during a measurement will be interpreted as a movement of one synthetic wavelength. This effect is usually mitigated by adding a second (nonscanning) laser. We show that absolute distance measurements can be performed with only one laser if the movements encountered are smooth, on the time scale of one measurement. In this case the movement errors can be compensated with a simple algorithm that combines several subsequent measurements. First experimental results show good agreement with theory.

© 2005 Optical Society of America

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References

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2004 (1)

B. L. Swinkels, T. J. Wendrich, N. Bhattacharya, A. A. Wielders, and J. J.M. Braat, Proc. SPIE 5495, 314 (2004).
[CrossRef]

2003 (1)

2002 (1)

Th. Kinder and K.-D. Salewski, J. Opt. Soc. 4, S364 (2002).

2001 (1)

1998 (2)

D. Xiaoli and S. Katuo, Meas. Sci. Technol. 9, 1031 (1998).
[CrossRef]

K. H. Bechstein and W. Fuchs, J. Opt. (Paris) 29, 179 (1998).
[CrossRef]

1995 (1)

J. Thiel, T. Pfeifer, and M. Hartmann, Measurement 16, 1 (1995).
[CrossRef]

1992 (1)

J. M. Payne, D. Parker, and R. F. Bradley, Rev. Sci. Instrum. 63, 3311 (1992).
[CrossRef]

Bechstein, K. H.

K. H. Bechstein and W. Fuchs, J. Opt. (Paris) 29, 179 (1998).
[CrossRef]

Bhattacharya, N.

B. L. Swinkels, T. J. Wendrich, N. Bhattacharya, A. A. Wielders, and J. J.M. Braat, Proc. SPIE 5495, 314 (2004).
[CrossRef]

Braat, J. J.M.

B. L. Swinkels, T. J. Wendrich, N. Bhattacharya, A. A. Wielders, and J. J.M. Braat, Proc. SPIE 5495, 314 (2004).
[CrossRef]

Bradley, R. F.

J. M. Payne, D. Parker, and R. F. Bradley, Rev. Sci. Instrum. 63, 3311 (1992).
[CrossRef]

Burger, J. P.

Cabeza, I.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Cabral, A.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Calvel, B.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Dubovitsky, S.

Fuchs, W.

K. H. Bechstein and W. Fuchs, J. Opt. (Paris) 29, 179 (1998).
[CrossRef]

Grünert, J.

Hartmann, M.

J. Thiel, T. Pfeifer, and M. Hartmann, Measurement 16, 1 (1995).
[CrossRef]

Hemmerich, A.

Katuo, S.

D. Xiaoli and S. Katuo, Meas. Sci. Technol. 9, 1031 (1998).
[CrossRef]

Kinder, Th.

Th. Kinder and K.-D. Salewski, J. Opt. Soc. 4, S364 (2002).

Lay, O. P.

Manske, E.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Parker, D.

J. M. Payne, D. Parker, and R. F. Bradley, Rev. Sci. Instrum. 63, 3311 (1992).
[CrossRef]

Payne, J. M.

J. M. Payne, D. Parker, and R. F. Bradley, Rev. Sci. Instrum. 63, 3311 (1992).
[CrossRef]

Peters, R. D.

Pfeifer, T.

J. Thiel, T. Pfeifer, and M. Hartmann, Measurement 16, 1 (1995).
[CrossRef]

Rebordao, J.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Ritter, S.

Salewski, K.-D.

Th. Kinder and K.-D. Salewski, J. Opt. Soc. 4, S364 (2002).

Schoof, A.

Sesselmann, R.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Sodnik, Z.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Swinkels, B. L.

B. L. Swinkels, T. J. Wendrich, N. Bhattacharya, A. A. Wielders, and J. J.M. Braat, Proc. SPIE 5495, 314 (2004).
[CrossRef]

Thiel, J.

J. Thiel, T. Pfeifer, and M. Hartmann, Measurement 16, 1 (1995).
[CrossRef]

Verlaan, A.

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

Wendrich, T. J.

B. L. Swinkels, T. J. Wendrich, N. Bhattacharya, A. A. Wielders, and J. J.M. Braat, Proc. SPIE 5495, 314 (2004).
[CrossRef]

Wielders, A. A.

B. L. Swinkels, T. J. Wendrich, N. Bhattacharya, A. A. Wielders, and J. J.M. Braat, Proc. SPIE 5495, 314 (2004).
[CrossRef]

Xiaoli, D.

D. Xiaoli and S. Katuo, Meas. Sci. Technol. 9, 1031 (1998).
[CrossRef]

J. Opt. (Paris) (1)

K. H. Bechstein and W. Fuchs, J. Opt. (Paris) 29, 179 (1998).
[CrossRef]

J. Opt. Soc. (1)

Th. Kinder and K.-D. Salewski, J. Opt. Soc. 4, S364 (2002).

Meas. Sci. Technol. (1)

D. Xiaoli and S. Katuo, Meas. Sci. Technol. 9, 1031 (1998).
[CrossRef]

Measurement (1)

J. Thiel, T. Pfeifer, and M. Hartmann, Measurement 16, 1 (1995).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (1)

B. L. Swinkels, T. J. Wendrich, N. Bhattacharya, A. A. Wielders, and J. J.M. Braat, Proc. SPIE 5495, 314 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

J. M. Payne, D. Parker, and R. F. Bradley, Rev. Sci. Instrum. 63, 3311 (1992).
[CrossRef]

Other (1)

B. Calvel, I. Cabeza, A. Cabral, E. Manske, J. Rebordao, R. Sesselmann, Z. Sodnik, and A. Verlaan, in Proceedings of the 5th International Conference on Space Optics, B. Warmbein, ed. (ESA Publications Division, 2004), p. 501.

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Figures (2)

Fig. 1
Fig. 1

Raw signals: (a) interferometric phase, (b) transmission of the Fabry–Perot cavity. The dashed line is the threshold value. (c) Unwrapped phase of (a). The dashed lines and the arrow describe the four-point algorithm.

Fig. 2
Fig. 2

Calculated distance as a function of speed for the different methods.

Equations (13)

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ϕ 2 ϕ 1 = 2 π ν 2 L c 2 π ν 1 L c = 2 π Δ ν c L = 2 π L Λ ,
Λ = c Δ ν .
L = ϕ 2 ϕ 1 2 π Λ = Δ ϕ 2 π Λ .
δ L = [ ( Λ δ Δ ϕ 2 π ) 2 + ( L δ Λ Λ ) 2 ] 1 2 [ 2 ( Λ δ ϕ 2 π ) 2 + 2 ( L ν Δ ν δ ν ν ) 2 ] 1 2 .
L ( t ) = L 0 + L 1 t + L 2 t 2 2 + L 3 t 3 6 + .
ϕ 1 = 2 π ν 1 L ( τ 2 ) c , ϕ 2 = 2 π ν 2 L ( τ 2 ) c ,
L calc = ϕ 2 ϕ 1 2 π Λ = L 0 + ν Δ ν L 1 τ + τ 2 8 L 2 + ,
ϕ 1 = 2 π ν 2 L ( τ ) c , ϕ 2 = 2 π ν 1 L ( 0 ) c ,
ϕ 3 = 2 π ν 2 L ( τ ) c .
L calc = ϕ 1 2 ϕ 2 + ϕ 3 4 π Λ = L 0 + ν τ 2 2 Δ ν L 2 + τ 2 4 L 2 + .
ϕ 1 = 2 π ν 2 L ( 3 τ 2 ) c , ϕ 2 = 2 π ν 1 L ( τ 2 ) c ,
ϕ 3 = 2 π ν 2 L ( τ 2 ) c , ϕ 4 = 2 π ν 1 L ( 3 τ 2 ) c ,
L calc = ϕ 1 3 ϕ 2 + 3 ϕ 3 ϕ 4 8 π Λ = L 0 + 3 τ 2 8 L 2 ν τ 3 4 Δ ν L 3 + .

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