Abstract

We propose a distance meter that utilizes an intermode beat of terahertz frequency in an optical frequency comb to perform high resolution and high dynamic range absolute distance measurements. The proposed system is based on a novel method, called multiheterodyne cross-correlation detection, in which intermode beat frequencies are scaled down to radio frequencies by optical mixing of two detuned optical frequency combs with a nonlinear optical crystal. Using this method, we obtained a 1.056 THz intermode beat and achieved a distance resolution of 0.820 μm from its phase measurement. Absolute distance measurement using 1.056 THz and 8.187 GHz intermode beats was also demonstrated in the range of 10 mm, resulting in a precision of 0.688 μm.

© 2009 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. K. Minoshima, Y. Sakai, H. Takahashi, H. Inaba, and S. Kawato, “Direct comparison of absolute distance meter using an optical comb and integrated optical interferometer with an optical sub-wavelength accuracy”, in CLEO 2009, Technical Digest(CD)(Optical Society of America, 2009), paper CTuS6.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  16. D. C. Williams, Optical methods in engineering metrology (Chaoman & Hall,1993), Chap.5.
  17. A. Yariv, Optical Electronics in modern communications 5th edition(Oxford University Press,1997),Chap.8.
  18. CASIX, Crystal guide ’99
  19. D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986).
    [CrossRef]

2009 (1)

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

2008 (2)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008).
[CrossRef] [PubMed]

Y. Salvadé, N. Schuhler, S. Lévêque, and S. Le Floch, “High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source,” Appl. Opt. 47(14), 2715–2720 (2008).
[CrossRef] [PubMed]

2006 (3)

2005 (1)

2004 (1)

2003 (2)

2000 (1)

1999 (1)

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

1998 (1)

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[CrossRef]

1988 (1)

1986 (1)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986).
[CrossRef]

Ahn, S. W.

Araki, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88(24), 241104 (2006).
[CrossRef]

Brehm, M.

Burger, J. P.

Chang, Y.

Coddington, I.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008).
[CrossRef] [PubMed]

Cundiff, S. T.

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[CrossRef]

Dandliker, R.

Dändliker, R.

Dubovitsky, S.

Fetterman, H. R.

Fujima, I.

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[CrossRef]

Holzwarth, R.

Iwasaki, S.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[CrossRef]

Joo, K. N.

Kabetani, Y.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88(24), 241104 (2006).
[CrossRef]

Keilmann, F.

Kim, S. W.

Lay, O. P.

Le Floch, S.

Leveque, S.

Lévêque, S.

Matsumoto, H.

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(30), 5512–5517 (2000).
[CrossRef]

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

Minoshima, K.

Nenadovic, L.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

Newbury, N. R.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008).
[CrossRef] [PubMed]

Ohnishi, J.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

Peters, R. D.

Prongue, D.

Salvade, Y.

Salvadé, Y.

Saneyoshi, E.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88(24), 241104 (2006).
[CrossRef]

Schliesser, A.

Schuhler, N.

Seta, K.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[CrossRef]

Steier, W. H.

Suzuki, N.

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

Swann, W. C.

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008).
[CrossRef] [PubMed]

Thalmann, R.

van der Weide, D.

von der Linde, D.

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986).
[CrossRef]

Yasui, T.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88(24), 241104 (2006).
[CrossRef]

Ye, J.

J. Ye, “Absolute measurement of a long, arbitrary distance to less than an optical fringe,” Opt. Lett. 29(10), 1153–1155 (2004).
[CrossRef] [PubMed]

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[CrossRef]

Yokoyama, S.

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88(24), 241104 (2006).
[CrossRef]

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

D. von der Linde, “Characterization of the noise in continuously operating mode-locked lasers,” Appl. Phys. B 39(4), 201–217 (1986).
[CrossRef]

Appl. Phys. Lett. (1)

T. Yasui, Y. Kabetani, E. Saneyoshi, S. Yokoyama, and T. Araki, “Terahertz frequency comb by multifrequency-heterodyning photoconductive detection for high-accuracy, high-resolution terahertz spectroscopy,” Appl. Phys. Lett. 88(24), 241104 (2006).
[CrossRef]

Meas. Sci. Technol. (2)

S. Yokoyama, J. Ohnishi, S. Iwasaki, K. Seta, H. Matsumoto, and N. Suzuki, “Real-time and high-resolution absolute-distance measurement using an two-wavelength superheterodyne interferometer,” Meas. Sci. Technol. 10(12), 1233–1239 (1999).
[CrossRef]

I. Fujima, S. Iwasaki, and K. Seta, “High-resolution distance meter using optical intensity modulation at 28GHz,” Meas. Sci. Technol. 9(7), 1049–1052 (1998).
[CrossRef]

Nat. Photonics (1)

I. Coddington, W. C. Swann, L. Nenadovic, and N. R. Newbury, “Rapid and precise absolute distance measurements at long range,” Nat. Photonics 3(6), 351–356 (2009).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

I. Coddington, W. C. Swann, and N. R. Newbury, “Coherent multiheterodyne spectroscopy using stabilized optical frequency combs,” Phys. Rev. Lett. 100(1), 013902 (2008).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

S. T. Cundiff and J. Ye, “Colloquium: Femtosecond optical frequency combs,” Rev. Mod. Phys. 75(1), 325–342 (2003).
[CrossRef]

Other (4)

K. Minoshima, Y. Sakai, H. Takahashi, H. Inaba, and S. Kawato, “Direct comparison of absolute distance meter using an optical comb and integrated optical interferometer with an optical sub-wavelength accuracy”, in CLEO 2009, Technical Digest(CD)(Optical Society of America, 2009), paper CTuS6.

D. C. Williams, Optical methods in engineering metrology (Chaoman & Hall,1993), Chap.5.

A. Yariv, Optical Electronics in modern communications 5th edition(Oxford University Press,1997),Chap.8.

CASIX, Crystal guide ’99

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Figures (9)

Fig. 1
Fig. 1

(A) Optical system and (B) spectral behavior of multiheterodyne cross-correlation detection. FSML: femtosecond mode-locked laser, CC: cross correlator, NLO: nonlinear optical crystal, SHG: second-harmonic generation light and SFG light: sum-frequency generation light.

Fig. 2
Fig. 2

Experimental setup. PZT: piezoelectric transducer, CC-T and CC-R: cross correlators for target measurement and phase drift compensation, M: parabolic mirror (f = 50 mm), BBO: BBO crystal (type I, 500 μm thick), BPF: blue-pass filter (350−600 nm), AP: aperture, PM: photomultiplier, PD: photodetector and P and I: electrical circuits for proportional and integral control of mode spacing.

Fig. 3
Fig. 3

Instabilities of f1, f2, Δ, and the rubidium frequency standard evaluated by the standard deviation with respect to the gate time.

Fig. 4
Fig. 4

Typical optical beat comb modes in different frequency regions observed by the SFG beat comb modes (red: comb modes, gray: background noise). Spectrum analyzer settings: resolution bandwidth = 1 Hz, sweep time = 4.6 s, span = 1.4 kHz.

Fig. 5
Fig. 5

Power of signal and noise calculated from the optical beat spectrum in Fig. 4. The signal indicates the comb mode level and the noise is the average level of the continuous spectrum between comb modes. The background noise, which includes detector and instrument noise, was subtracted. The upper scale indicates the observed frequency of the SFG beat comb when Δ is 650 Hz and the lower scale indicates the optical beat comb frequency.

Fig. 6
Fig. 6

(a) Power of signal and noise and (b) phase fluctuation and signal-to-noise ratio (SNR) of 1.056 THz with respect to Δ. Phase fluctuation was the standard deviation over a 125 s measurement with a time constant of 300 ms and the SNR was calculated from (a).

Fig. 7
Fig. 7

Phase fluctuation and signal-to-noise ratio (SNR) of optical beat comb. The upper scale indicates the observed frequency of SFG beat comb when Δ is 650 Hz and the lower scale indicates the frequency of the optical beat comb. The phase fluctuation is the standard deviation over a 125 s measurement with a time constant of 300 ms and the SNR is calculated from Fig. 5.

Fig. 8
Fig. 8

Distance measurement using the 1.056 THz mode. (a) Measured distance with respect to the stage scale and linear approximation. (b) Deviations from the linear approximation.

Fig. 9
Fig. 9

Absolute distance measurement using the 1.056 THz mode (λ = 284 μm, N = 12,900) and the 8.187 GHz mode (λ = 36,720 μm, N = 100). (a) Measured distance with respect to the stage scale and linear approximation. (b) Deviations from the linear approximation.

Equations (13)

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ET=nE1,ncos[2π(nf1+f1o)t+ϕ1,n],
ϕ1,n=2π(nf1+f1o)npcl,
EL=mE2,mcos[2π(mf2+f2o)t+ϕ2,m],
ϕ2,m=2π(mf2+f2o)npcl0,
ESFGnmE1,nE2,mcos[2π((n+m)f2+nΔ+f1o+f2o)t+ϕ1,n+ϕ2,m+θn,m+ϕn,mSFG]       nmESFGn,m
ϕn,mSFG=2π((n+m)f2+nΔ+f1o+f2o)n2ωpclSFG,
iGN=1{nm(ESFGn,m   +   ESFGn+N,mN)2}=D.C.+N=1{nmE1,nE2,mE1,n+NE2,mN*cos[2πNΔt2πNf1ngcl+2πNf2ngcl02πNΔn2ωgclSFG+θn,mθn+N,mN]}
ΦN=2πNf1ngcl+ΦctN,
D=c2Nf1ng(IN+ΦN2π),
INH=[12π(ΦNLNHNLΦNH)],
ΦN=ΦT,NΦR,N.
θn,m=   tan1(sin(Δkn,mL)cos(Δkn,mL)   1)        θ0θ0=0(Δkn,mL>0),θ0=180(Δkn,mL<0),
Δkn,m=kn+km-kn,m,

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