Abstract

An ultrafast and Doppler-free optical ranging system based on dispersive frequency-modulated interferometry is demonstrated. The principle is similar to the conventional frequency-modulated continuous-wave interferometry where the range information is derived from the beat frequency between the object signal and the reference signal. However, a passive and static frequency scanning is performed based on the chromatic dispersion of a transform-limited femtosecond pulse in the time domain. We point out that the unbalanced dispersion introduced in the Mach-Zehnder interferometer can be optimized to eliminate the frequency chirp in the temporal interferograms pertaining to the third order dispersion of the all-fiber system, if the dynamic range being considered is small. Some negative factors, such as the polarization instability of the femtosecond pulse, the power fluctuation of the optical signal and the nonuniform gain spectrum of the erbium-doped fiber amplifier lead to an obvious envelope deformation of the temporal interferograms from the Gaussian shape. Thus a new data processing method is proposed to guarantee the range resolution. In the experiment, the vibration of a speaker is measured. A range resolution of 1.59 μm is achieved with an exposure time of 394 fs at a sampling rate of 48.6 MHz.

© 2010 OSA

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2009 (3)

2008 (4)

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett. 92(11), 1111021–1111023 (2008).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength–time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[CrossRef]

T.-J. Ahn, Y. Park, and J. Azaña, “Improved Optical Pulse Characterization Based on Feedback-Controlled Hilbert Transformation Temporal Interferometry,” IEEE Photon. Technol. Lett. 20(7), 475–477 (2008).
[CrossRef]

K. Goda, D. R. Solli, and B. Jalali, “Real-time optical reflectometry enabled by amplified dispersive Fourier transformation,” Appl. Phys. Lett. 93(3), 0311061–0311063 (2008).
[CrossRef]

2007 (3)

2006 (5)

2005 (1)

2004 (5)

2002 (2)

H. Yoon and P. Tsiotras, “Spacecraft adaptive attitude and power tracking with variable speed control moment gyroscopes,” J. Guid. Control Dyn. 25(6), 1081–1090 (2002).
[CrossRef]

M. Amemiya, “Pulse broadening due to higher order dispersion and its transmission limit,” J. Lightwave Technol. 20(4), 591–597 (2002).
[CrossRef]

2001 (2)

F. Hakimi and H. Hakimi, “Measurement of optical fiber dispersion and dispersion slope using a pair of short optical pulses and Fourier transform property of dispersive medium,” Opt. Eng. 40(6), 1053–1056 (2001).
[CrossRef]

A. Pf Rtner and J. Schwider, “Dispersion error in white-light linnik interferometers and its implications for evaluation procedures,” Appl. Opt. 40(34), 6223–6228 (2001).
[CrossRef]

2000 (3)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

K. Minoshima and H. Matsumoto, “High-accuracy measurement of 240 m distance in an optical tunnel by using of a compact femtosecond laser,” Appl. Opt. 39(30), 5512–5517 (2000).
[CrossRef]

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000).
[CrossRef]

1997 (2)

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “fiber dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997).
[CrossRef]

J. Zhang, X. Zhao, X. Hu, and J. Sun, “Sinewave fit algorithm based on total least-squares method with application to ADC effective bits measurement,” IEEE Trans. Instrum. Meas. 46(4), 1026–1030 (1997).
[CrossRef]

1996 (1)

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[CrossRef]

1995 (1)

R. Dandliker, K. Hug, J. Politch, and E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34(8), 2407 (1995).
[CrossRef]

1994 (1)

1992 (2)

A. G. Stove, “Linear FMCW radar techniques,” Radar and Signal Processing, IEE Proceedings F 139, 343–350 (1992).
[CrossRef]

J. M. Payne, D. Parker, and R. F. Bradley, “Range finder with fast multiple range capability,” Rev. Sci. Instrum. 63(6), 3311–3316 (1992).
[CrossRef]

1990 (1)

E. C. Burrows and K.-Y. Liou, “High-resolution laser LIDAR utilizing two-section distributed feedback semiconductor laser as a coherent source,” Electron. Lett. 26(9), 577–579 (1990).
[CrossRef]

1988 (1)

1983 (1)

1979 (1)

Ahn, T.-J.

T.-J. Ahn, Y. Park, and J. Azaña, “Improved Optical Pulse Characterization Based on Feedback-Controlled Hilbert Transformation Temporal Interferometry,” IEEE Photon. Technol. Lett. 20(7), 475–477 (2008).
[CrossRef]

Y. Park, T.-J. Ahn, J.-C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15(8), 4597–4616 (2007), http://www.opticsinfobase.org/abstract.cfm?id=131858 .
[CrossRef] [PubMed]

Akiba, M.

Alic, N.

Amemiya, M.

Azaña, J.

T.-J. Ahn, Y. Park, and J. Azaña, “Improved Optical Pulse Characterization Based on Feedback-Controlled Hilbert Transformation Temporal Interferometry,” IEEE Photon. Technol. Lett. 20(7), 475–477 (2008).
[CrossRef]

Y. Park, T.-J. Ahn, J.-C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15(8), 4597–4616 (2007), http://www.opticsinfobase.org/abstract.cfm?id=131858 .
[CrossRef] [PubMed]

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000).
[CrossRef]

Bartels, A.

Berger, N. K.

Bradley, R. F.

J. M. Payne, D. Parker, and R. F. Bradley, “Range finder with fast multiple range capability,” Rev. Sci. Instrum. 63(6), 3311–3316 (1992).
[CrossRef]

Burrows, E. C.

E. C. Burrows and K.-Y. Liou, “High-resolution laser LIDAR utilizing two-section distributed feedback semiconductor laser as a coherent source,” Electron. Lett. 26(9), 577–579 (1990).
[CrossRef]

Calatroni, J.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[CrossRef]

Chan, L. Y.

Y. C. Tong, L. Y. Chan, and H. K. Tsang, “fiber dispersion or pulse spectrum measurement using a sampling oscilloscope,” Electron. Lett. 33(11), 983–985 (1997).
[CrossRef]

Chen, Y.

Chou, J.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength–time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett. 92(11), 1111021–1111023 (2008).
[CrossRef]

Coddington, I.

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Dandliker, R.

R. Dandliker, K. Hug, J. Politch, and E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34(8), 2407 (1995).
[CrossRef]

Dändliker, R.

Diddams, S. A.

A. Bartels, C. W. Oates, L. Hollberg, and S. A. Diddams, “Stabilization of femtosecond laser frequency combs with subhertz residual linewidths,” Opt. Lett. 29(10), 1081–1083 (2004).
[CrossRef] [PubMed]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Dorrer, C.

Duker, J.

Escalona, R.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[CrossRef]

Fainman, Y.

Feder, K. S.

Fejer, M. M.

Fermann, M. E.

Fischer, B.

Fujimoto, J.

Fujimoto, J. G.

Goda, K.

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[CrossRef] [PubMed]

K. Goda, D. R. Solli, and B. Jalali, “Real-time optical reflectometry enabled by amplified dispersive Fourier transformation,” Appl. Phys. Lett. 93(3), 0311061–0311063 (2008).
[CrossRef]

Guerrero, A. L.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[CrossRef]

Hakimi, F.

F. Hakimi and H. Hakimi, “Measurement of optical fiber dispersion and dispersion slope using a pair of short optical pulses and Fourier transform property of dispersive medium,” Opt. Eng. 40(6), 1053–1056 (2001).
[CrossRef]

Hakimi, H.

F. Hakimi and H. Hakimi, “Measurement of optical fiber dispersion and dispersion slope using a pair of short optical pulses and Fourier transform property of dispersive medium,” Opt. Eng. 40(6), 1053–1056 (2001).
[CrossRef]

Hall, J. L.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Hartl, I.

Hollberg, L.

Hong, Y.

Hsiung, P.

Hu, X.

J. Zhang, X. Zhao, X. Hu, and J. Sun, “Sinewave fit algorithm based on total least-squares method with application to ADC effective bits measurement,” IEEE Trans. Instrum. Meas. 46(4), 1026–1030 (1997).
[CrossRef]

Hug, K.

R. Dandliker, K. Hug, J. Politch, and E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34(8), 2407 (1995).
[CrossRef]

Ikeda, K.

Ippen, E. P.

Jalali, B.

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458(7242), 1145–1149 (2009).
[CrossRef] [PubMed]

K. Goda, D. R. Solli, and B. Jalali, “Real-time optical reflectometry enabled by amplified dispersive Fourier transformation,” Appl. Phys. Lett. 93(3), 0311061–0311063 (2008).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett. 92(11), 1111021–1111023 (2008).
[CrossRef]

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength–time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[CrossRef]

Jannson, T.

Jones, D. J.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Joo, K.-N.

Kieffer, J.-C.

Kim, D. Y.

Kim, S.-W.

Ko, T.

Kowalczyk, A.

Langrock, C.

Levit, B.

Liou, K.-Y.

E. C. Burrows and K.-Y. Liou, “High-resolution laser LIDAR utilizing two-section distributed feedback semiconductor laser as a coherent source,” Electron. Lett. 26(9), 577–579 (1990).
[CrossRef]

Makita, S.

Matsumoto, H.

McFerran, J. J.

Minoshima, K.

Miura, M.

Miyagi, M.

Moon, S.

Muriel, M. A.

J. Azaña and M. A. Muriel, “Real-time optical spectrum analysis based on the time-space duality in chirped fiber gratings,” IEEE J. Quantum Electron. 36(5), 517–526 (2000).
[CrossRef]

Newbury, N. R.

Nicholson, J. W.

Nishida, S.

Nishizawa, N.

Oates, C. W.

Park, Y.

T.-J. Ahn, Y. Park, and J. Azaña, “Improved Optical Pulse Characterization Based on Feedback-Controlled Hilbert Transformation Temporal Interferometry,” IEEE Photon. Technol. Lett. 20(7), 475–477 (2008).
[CrossRef]

Y. Park, T.-J. Ahn, J.-C. Kieffer, and J. Azaña, “Optical frequency domain reflectometry based on real-time Fourier transformation,” Opt. Express 15(8), 4597–4616 (2007), http://www.opticsinfobase.org/abstract.cfm?id=131858 .
[CrossRef] [PubMed]

Parker, D.

J. M. Payne, D. Parker, and R. F. Bradley, “Range finder with fast multiple range capability,” Rev. Sci. Instrum. 63(6), 3311–3316 (1992).
[CrossRef]

Payne, J. M.

J. M. Payne, D. Parker, and R. F. Bradley, “Range finder with fast multiple range capability,” Rev. Sci. Instrum. 63(6), 3311–3316 (1992).
[CrossRef]

Pf Rtner, A.

Politch, J.

R. Dandliker, K. Hug, J. Politch, and E. Zimmermann, “High-accuracy distance measurements with multiple-wavelength interferometry,” Opt. Eng. 34(8), 2407 (1995).
[CrossRef]

Prongué, D.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Sainz, C.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, “Spectrally resolved white-light interferometry as a profilometry tool,” Opt. Laser Technol. 28(7), 485–489 (1996).
[CrossRef]

Saperstein, R. E.

Schwider, J.

Slutsky, B.

Smulakovsky, V.

Solli, D. R.

D. R. Solli, J. Chou, and B. Jalali, “Amplified wavelength–time transformation for real-time spectroscopy,” Nat. Photonics 2(1), 48–51 (2008).
[CrossRef]

J. Chou, D. R. Solli, and B. Jalali, “Real-time spectroscopy with subgigahertz resolution using amplified dispersive Fourier transformation,” Appl. Phys. Lett. 92(11), 1111021–1111023 (2008).
[CrossRef]

K. Goda, D. R. Solli, and B. Jalali, “Real-time optical reflectometry enabled by amplified dispersive Fourier transformation,” Appl. Phys. Lett. 93(3), 0311061–0311063 (2008).
[CrossRef]

Srinivasan, V.

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, “Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis,” Science 288(5466), 635–639 (2000).
[CrossRef] [PubMed]

Stove, A. G.

A. G. Stove, “Linear FMCW radar techniques,” Radar and Signal Processing, IEE Proceedings F 139, 343–350 (1992).
[CrossRef]

Sun, J.

J. Zhang, X. Zhao, X. Hu, and J. Sun, “Sinewave fit algorithm based on total least-squares method with application to ADC effective bits measurement,” IEEE Trans. Instrum. Meas. 46(4), 1026–1030 (1997).
[CrossRef]

Swann, W. C.

Thalmann, R.

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Figures (5)

Fig. 1
Fig. 1

(a) Schematic of the ultrafast ranging system. FSFL, femtosecond fiber laser; C, fused fiber coupler; AWG, arbitrary waveform generator; PC, polarization controller; DCF, dispersion compensating fiber; EDFA, erbium doped fiber amplifier; PD, photodetector; OSC, oscilloscope; OSA, optical spectrum analyzer. (b) Picture of the spectral interferogram recorded on the OSA (Ando Model AQ6317B). (c) Picture of the temporal interferogram recorded on the OSC (Agilent Model 86116A).

Fig. 2
Fig. 2

Visualization of the instantaneous frequency on the frequency-time plane. (a) Time-to-frequency conversion function derived from the temporal and the spectral interferograms. (b) Femtosecond pulses before the dispersion. (c) Femtosecond pulses after the dispersion. To avoid pulse overlap, an offset perpendicular to the time-to-frequency conversion function is introduced between the Dopper-shifted pulse and the static pulse. One should also note that, generally, Doppler shift is very small relative to the optical bandwidth. For clarity, the Doppler shift is magnified in (b) and (c).

Fig. 3
Fig. 3

Linear frequency chirp due to the unbalanced dispersion. (a) Interferogram observed on the OSA when a 6 m length DCF is incorporated in the object arm of the MZI ( τ 10 p s ). (b) Interferogram observed on the OSA when a 6 m length DCF is incorporated in the object arm of the MZI ( τ 8 p s ).

Fig. 4
Fig. 4

(a) A typical temporal interferogram (for clarity, τ 0 = 9.65 p s is used). (b) Temporal interferogram passing through a band-pass filter. (c) Spectral interferogram transferred from the time domain. (d) Intensity normalized spectral interferogram (dots) and the sine fit result (line).

Fig. 5
Fig. 5

(a) Picture of the temporal interferograms recorded on the OSC (Tektronix Model TDS7704B, 7 GHz bandwidth, 20 Gs/s sampling speed). (b) Vibration measurement results. Single-shot measurements based on the new data processing method (blue dots). Averaged results (yellow dots). Sine fit result (red line). Single-shot measurements based on the FFT algorithm (light gray region).

Equations (21)

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H ^ ( ω ) = H a ( ω ) exp ( j n = 0 β n L n ! ω n ) ,
A ^ 1 ( ω ) = A 1 ( ω ) exp [ j φ 1 ( ω ) ] = A ^ 0 ( ω ) H ^ ( ω ) .
φ 1 ( ω ) = φ 0 ( ω ) n = 0 β n L n ! ω n .
t ( ω ) = φ 0 ( ω ) / ω + n = 2 β n L ( n 1 ) ! ω n 1 .
ω ( t ) = [ 1 + 1 + X ( t ) ] β 2 / β 3 ,
| X ( t ) | | 2 β 3 L Δ T / ( β 2 L ) 2 | = | 4 π c β 3 Δ λ / β 2 λ 2 | = 0.063.
ω ( t ) = { X ( t ) / 2 X 2 ( t ) / 8 + O [ X 3 ( t ) ] } β 2 / β 3 c 1 t + c 2 t 2 ,
Ω ( t ) = | d ω ( t ) / d t | τ = c 1 τ + 2 c 2 t τ .
i ( t ) | a ( t ) 1 | 2 + | a ( t + τ ) 1 | 2 + 2 | a ( t ) 1 | | a ( t + τ ) 1 | cos [ Ω ( t ) t ] .
i ( t ) i ( t ) 1 { 1 + V T cos [ Ω ( t ) t ] } ,
I ( ω ) I ( ω ) 0 [ 1 + V S cos ( ω τ ) ] ,
ω T ( t ) = t / β 2 ( L + Δ L ) β 3 ( L + Δ L ) t 2 / 2 [ β 2 ( L + Δ L ) ] 3 .
ω R ( t ) = ( t τ ) / β 2 L β 3 L ( t τ ) 2 / 2 [ β 2 L ] 3 .
Ω ( t ) = τ / β 2 L + [ Δ L / β 2 L 2 β 3 τ ( L + 2 Δ L ) / ( β 2 L ) 3 ] t + β 3 Δ L t 2 / ( β 2 L ) 3 ,
Ω ( t ) τ / β 2 L + [ Δ L / β 2 L 2 β 3 τ L / ( β 2 L ) 3 ] t .
f = α 1 t + α 2 t 2 ,
f D ( t ) = f T ( t Δ t ) + Δ f ,
f T ( t Δ t ) = f T ( t ) + d f T ( t ) d t ( Δ t ) + d 2 f T ( t ) 2 d t 2 ( Δ t ) 2 = f T ( t ) Δ f + α 2 ( Δ f α 2 + 2 α 2 t ) 2 .
f D ( t ) = f T ( t ) + f E ( v ) ,
Ω ( t ) = f D ( t ) f R ( t ) = ( α 1 + 2 α 2 t ) τ + f E ( v ) .
Ω ( t ) = ( α 1 + 2 α 2 t ) τ .

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