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Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser

Ki-Nam Joo and Seung-Woo Kim

Open Access Open Access

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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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.

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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.

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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.

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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.

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Tables (2)

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

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Table 2 Two representative results of glass thickness measurement.

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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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