Abstract

We describe an interferometric method that enables to measure the optical path delay between two consecutive femtosecond laser pulses by way of dispersive interferometry. This method allows a femtosecond laser to be utilized as a source of performing absolute distance measurements to unprecedented precision over extensive ranges. Our test result demonstrates a non-ambiguity range of ~1.46 mm with a resolution of 7 nm over a maximum distance reaching ~0.89 m.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]

2004

2003

J. Ye, H. Schnatz and L. W. Hollberg, "Optical frequency combs: from precision frequency metrology to optical phase control," IEEE J. Sel. Top. Quantum Electron. 9, 1041-1058 (2003).
[CrossRef]

S. T. Cundiff and J. Ye, "Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

2002

2000

K. Minoshima and H. Matsumoto, "High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser," Appl. Opt. 39, 5512-5517 (2000).
[CrossRef]

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

1995

1994

1993

1982

1972

Chériaux, G.

Cundiff, S. T.

S. T. Cundiff and J. Ye, "Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Fujimoto, J. G.

Hänsch, T. W.

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

Hee, M. R.

Hollberg, L. W.

J. Ye, H. Schnatz and L. W. Hollberg, "Optical frequency combs: from precision frequency metrology to optical phase control," IEEE J. Sel. Top. Quantum Electron. 9, 1041-1058 (2003).
[CrossRef]

Holzwarth, R.

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

Ina, H.

Izatt, J. A.

Jacobson, J. M.

Joffre, M.

Jones, J. D. C.

Knight, J. C.

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

Kobayashi, S.

Kowalczyk, A.

Lepetit, L.

MacPherson, W. N.

Maier, R. R. J.

Matsumoto, H.

Minoshima, K.

Reid, D. T.

Russell, P. St. J.

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

Sakai, K.

Schnatz, H.

J. Ye, H. Schnatz and L. W. Hollberg, "Optical frequency combs: from precision frequency metrology to optical phase control," IEEE J. Sel. Top. Quantum Electron. 9, 1041-1058 (2003).
[CrossRef]

Schwider, J.

Swanson, E.A.

Takeda, M.

Towers, C. E.

Towers, D. P.

Udem, T.

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

Wadsworth, W. J.

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

Wojtkowski, M.

Ye, J.

J. Ye, "Absolute measurement of a long, arbitrary distance to less than an optical fringe," Opt. Lett. 29, 1153-1155 (2004).
[CrossRef] [PubMed]

J. Ye, H. Schnatz and L. W. Hollberg, "Optical frequency combs: from precision frequency metrology to optical phase control," IEEE J. Sel. Top. Quantum Electron. 9, 1041-1058 (2003).
[CrossRef]

S. T. Cundiff and J. Ye, "Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

Zhou, L.

Appl. Opt.

IEEE J. Sel. Top. Quantum Electron.

J. Ye, H. Schnatz and L. W. Hollberg, "Optical frequency combs: from precision frequency metrology to optical phase control," IEEE J. Sel. Top. Quantum Electron. 9, 1041-1058 (2003).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. Lett.

R. Holzwarth, T. Udem, and T. W. Hänsch, J. C. Knight, W. J. Wadsworth, and P. St. J. Russell, "Optical frequency synthesizer for precision spectroscopy," Phys. Rev. Lett. 85, 2264-2267(2000).
[CrossRef] [PubMed]

Rev. Mod. Phys.

S. T. Cundiff and J. Ye, "Femtosecond optical frequency combs," Rev. Mod. Phys. 75, 325-342 (2003).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

Dispersive interferometer using femtosecond laser pulses. FS laser: femtosecond laser; OI: optical isolator; BS: beam splitter; CP: dispersion compensation plate; FPE: Fabry-Perot etalon; MR: reference mirror; MM: measurement mirror; CL: collimating lens. Inlets show the relative line density of the optical comb before and after filtering.

Fig. 2.
Fig. 2.

Data processing procedure for measurement of L; (a) dispersed interference intensity captured by the spectrometer, (b) band-pass filtering of the peak at α, (c) wrapped phase, and (d) unwrapped phase.

Fig. 3.
Fig. 3.

(a) Aliasing effect (envelop folding), (b) triangle-shaped variation of measured phase and (c) Test result with a repeated step motion of 500 µm over a distance range of 100 mm.

Fig. 4.
Fig. 4.

Optical layout for measuring the thickness of a glass plate. FS laser: femtosecond laser; OI: optical isolator; BS: beam splitter; FPE: Fabry-Perot etalon; S: glass sample.

Tables (2)

Tables Icon

Table 1 Performance of the dispersive interferometer with FPE filtering in comparison to the case of ideal sampling.

Tables Icon

Table 2 Two representative results of glass thickness measurement.

Equations (9)

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

g ( ν ) = a ( ν ) + b ( ν ) cos ϕ ( ν ) .
a ( ν ) = 1 2 s ( ν ) [ r r 2 ( ν ) + r m 2 ( ν ) ] and b ( ν ) = s ( ν ) r r ( ν ) r m ( ν )
g ( ν ) = s ( ν ) [ 1 + cos ϕ ( ν ) ]
ϕ ( ν ) = 2 π ν α
G ( τ ) = FT { g ( ν ) } = S ( τ ) [ 1 2 δ ( τ + α ) + δ ( τ ) + 1 2 δ ( τ α ) ]
g ( ν ) = FT 1 { S ( τ ) 1 2 δ ( τ Δ τ ) } = 1 2 s ( ν ) exp ( i ϕ ( ν ) )
ϕ ( ν ) = tan 1 ( Im { g ( ν ) } Re { g ( ν ) } )
d ϕ d ν = 4 π NL c
L = ( c 4 π N ) d ϕ d ν .

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