Abstract

As the bandwidth and linearity of frequency modulated continuous wave chirp ladar increase, the resulting range resolution, precisions, and accuracy are improved correspondingly. An analysis of a very broadband (several THz) and linear (<1ppm) chirped ladar system based on active chirp linearization is presented. Residual chirp nonlinearity and material dispersion are analyzed as to their effect on the dynamic range, precision, and accuracy of the system. Measurement precision and accuracy approaching the part per billion level is predicted.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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2009

2008

2007

2006

2005

2004

2003

2001

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

T. H.Yoon, J. Ye, J. L.Hall, and J.-M. Chartier, “Absolute frequency measurement of the iodine-stabilized He-Ne laser at 633 nm,” Appl. Phys. B 72, 221-226 (2001).

2000

W.-C. Chuang, Y.-S. Tsai, J.-Y.Shieh, and C.-Y.Leung, Chin. J. Phys. 38, 437-442 (2000).

1999

L. Qiao, D. Sun, X. Zhang, and Y. Zhao, “Linearity requirements for a linear frequency modulation lidar,” Opt. Rev. 6, 160-162 (1999).
[CrossRef]

1998

1997

1996

K. Iiyama, L.-T. Wang, and K. ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for fmcw reflectometry,” J. Lightwave Technol. 14, 173-178 (1996).
[CrossRef]

1993

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

1992

1990

1979

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Ahn, T.-J.

Babbitt, W. R.

Baney, D. M.

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

Barber, Z. W.

Barwood, G. P.

Bava, E.

A. Pesatori, M. Norgia, V. Calabrese, G. Galzerano, E. Bava, and C. Svelto, “Optical frequency standard by high Doppler-broadened absorption and external-cavity laser diode at 1.541 m,” IEEE Trans. Instrum. Meas. 57, 1708-1712(2008).
[CrossRef]

Beck, S. M.

Berg, T.

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

Boggs, B.

Bretenaker, F.

Brezinski, M. E.

Buck, J. R.

Buell, W. F.

Cabral, A.

A. Cabral and J. Rebordão, “Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).
[CrossRef]

Calabrese, V.

A. Pesatori, M. Norgia, V. Calabrese, G. Galzerano, E. Bava, and C. Svelto, “Optical frequency standard by high Doppler-broadened absorption and external-cavity laser diode at 1.541 m,” IEEE Trans. Instrum. Meas. 57, 1708-1712(2008).
[CrossRef]

Chartier, J.-M.

T. H.Yoon, J. Ye, J. L.Hall, and J.-M. Chartier, “Absolute frequency measurement of the iodine-stabilized He-Ne laser at 633 nm,” Appl. Phys. B 72, 221-226 (2001).

Chinn, S. R.

Choma, M. A.

Chuang, W.-C.

W.-C. Chuang, Y.-S. Tsai, J.-Y.Shieh, and C.-Y.Leung, Chin. J. Phys. 38, 437-442 (2000).

Coddington, I.

Crozatier, V.

deGroot, P.

Dickinson, R. P.

Edwards, C. S.

Feder, K. S.

Fejer, M. M.

Fermann, M. E.

Fujimoto, J. G.

Galzerano, G.

A. Pesatori, M. Norgia, V. Calabrese, G. Galzerano, E. Bava, and C. Svelto, “Optical frequency standard by high Doppler-broadened absorption and external-cavity laser diode at 1.541 m,” IEEE Trans. Instrum. Meas. 57, 1708-1712(2008).
[CrossRef]

Gill, P.

Gorju, G.

Gout, J.-L. L.

Greiner, C.

Hall, J. L.

T. H.Yoon, J. Ye, J. L.Hall, and J.-M. Chartier, “Absolute frequency measurement of the iodine-stabilized He-Ne laser at 633 nm,” Appl. Phys. B 72, 221-226 (2001).

Hartl, I.

Hocker, G. B.

Huang, C.

Huang, G.

ichi Hayashi, K.

K. Iiyama, L.-T. Wang, and K. ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for fmcw reflectometry,” J. Lightwave Technol. 14, 173-178 (1996).
[CrossRef]

Iiyama, K.

K. Iiyama, L.-T. Wang, and K. ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for fmcw reflectometry,” J. Lightwave Technol. 14, 173-178 (1996).
[CrossRef]

Izatt, J. A.

Jain, A.

Jucha, A.

Kaylor, B.

Kim, D. Y.

Kozlowski, D. A.

Langrock, C.

Law, J. Y.

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

Lea, S. N.

Lee, A.

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

Lee, J. Y.

Leung, C.-Y.

W.-C. Chuang, Y.-S. Tsai, J.-Y.Shieh, and C.-Y.Leung, Chin. J. Phys. 38, 437-442 (2000).

Leyva, V.

Liu, B.

Lorgere, I.

Marechal, N. J.

Margolis, H. S.

McAlexander, W. I.

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

McFerran, J. J.

McLeod, R. R.

Moore, E. D.

Mossberg, T.

Newbury, N. R.

Nicholson, J. W.

Norgia, M.

A. Pesatori, M. Norgia, V. Calabrese, G. Galzerano, E. Bava, and C. Svelto, “Optical frequency standard by high Doppler-broadened absorption and external-cavity laser diode at 1.541 m,” IEEE Trans. Instrum. Meas. 57, 1708-1712(2008).
[CrossRef]

Pering, R. D.

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

Pesatori, A.

A. Pesatori, M. Norgia, V. Calabrese, G. Galzerano, E. Bava, and C. Svelto, “Optical frequency standard by high Doppler-broadened absorption and external-cavity laser diode at 1.541 m,” IEEE Trans. Instrum. Meas. 57, 1708-1712(2008).
[CrossRef]

Qiao, L.

L. Qiao, D. Sun, X. Zhang, and Y. Zhao, “Linearity requirements for a linear frequency modulation lidar,” Opt. Rev. 6, 160-162 (1999).
[CrossRef]

Rakuljic, G.

Rebordão, J.

A. Cabral and J. Rebordão, “Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).
[CrossRef]

Reibel, R. R.

Roos, P. A.

Rowley, W. R. C.

Sarunic, M. V.

Sasada, H.

Satyan, N.

Shieh, J.-Y.

W.-C. Chuang, Y.-S. Tsai, J.-Y.Shieh, and C.-Y.Leung, Chin. J. Phys. 38, 437-442 (2000).

Sun, D.

L. Qiao, D. Sun, X. Zhang, and Y. Zhao, “Linearity requirements for a linear frequency modulation lidar,” Opt. Rev. 6, 160-162 (1999).
[CrossRef]

Svelto, C.

A. Pesatori, M. Norgia, V. Calabrese, G. Galzerano, E. Bava, and C. Svelto, “Optical frequency standard by high Doppler-broadened absorption and external-cavity laser diode at 1.541 m,” IEEE Trans. Instrum. Meas. 57, 1708-1712(2008).
[CrossRef]

Swann, W. C.

Swanson, E. A.

Szafraniec, B.

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

Tan, T. S.

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

Tsai, Y.-S.

W.-C. Chuang, Y.-S. Tsai, J.-Y.Shieh, and C.-Y.Leung, Chin. J. Phys. 38, 437-442 (2000).

Vasilyev, A.

Wang, L.-T.

K. Iiyama, L.-T. Wang, and K. ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for fmcw reflectometry,” J. Lightwave Technol. 14, 173-178 (1996).
[CrossRef]

Wang, T.

Westbrook, P. S.

Wright, T. J.

Yamada, K.

Yang, C.

Yariv, A.

Ye, J.

T. H.Yoon, J. Ye, J. L.Hall, and J.-M. Chartier, “Absolute frequency measurement of the iodine-stabilized He-Ne laser at 633 nm,” Appl. Phys. B 72, 221-226 (2001).

Yoon, T. H.

T. H.Yoon, J. Ye, J. L.Hall, and J.-M. Chartier, “Absolute frequency measurement of the iodine-stabilized He-Ne laser at 633 nm,” Appl. Phys. B 72, 221-226 (2001).

Zhang, X.

L. Qiao, D. Sun, X. Zhang, and Y. Zhao, “Linearity requirements for a linear frequency modulation lidar,” Opt. Rev. 6, 160-162 (1999).
[CrossRef]

Zhao, Y.

L. Qiao, D. Sun, X. Zhang, and Y. Zhao, “Linearity requirements for a linear frequency modulation lidar,” Opt. Rev. 6, 160-162 (1999).
[CrossRef]

Zheng, J.

Zheng, K.

Appl. Opt.

Appl. Phys. B

T. H.Yoon, J. Ye, J. L.Hall, and J.-M. Chartier, “Absolute frequency measurement of the iodine-stabilized He-Ne laser at 633 nm,” Appl. Phys. B 72, 221-226 (2001).

Chin. J. Phys.

W.-C. Chuang, Y.-S. Tsai, J.-Y.Shieh, and C.-Y.Leung, Chin. J. Phys. 38, 437-442 (2000).

IEEE Trans. Instrum. Meas.

A. Pesatori, M. Norgia, V. Calabrese, G. Galzerano, E. Bava, and C. Svelto, “Optical frequency standard by high Doppler-broadened absorption and external-cavity laser diode at 1.541 m,” IEEE Trans. Instrum. Meas. 57, 1708-1712(2008).
[CrossRef]

B. Szafraniec, A. Lee, J. Y. Law, W. I. McAlexander, R. D. Pering, T. S. Tan, and D. M. Baney, “Swept coherent optical spectrum analysis,” IEEE Trans. Instrum. Meas. 53, 203-215 (2004).
[CrossRef]

J. Lightwave Technol.

K. Iiyama, L.-T. Wang, and K. ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for fmcw reflectometry,” J. Lightwave Technol. 14, 173-178 (1996).
[CrossRef]

Meas. Sci. Technol.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907-926 (1993).
[CrossRef]

Opt. Eng.

A. Cabral and J. Rebordão, “Accuracy of frequency-sweeping interferometry for absolute distance metrology,” Opt. Eng. 46, 073602 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

P. A. Roos, R. R. Reibel, T. Berg, B. Kaylor, Z. W. Barber, and W. R. Babbitt, “Ultrabroadband optical chirp linearization for precision metrological applications,” Opt. Lett. 34, 3692-3694(2009).
[CrossRef] [PubMed]

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, G. Huang, and W. R. C. Rowley, “Absolute frequency measurement of a 1.5 mm acetylene standard by use of a combined frequency chain and femtosecond comb,” Opt. Lett. 29, 566-568(2004).
[CrossRef] [PubMed]

S. R. Chinn, E. A. Swanson, and J. G. Fujimoto, “Optical coherence tomography using a frequency-tunable optical source,” Opt. Lett. 22, 340-343 (1997).
[CrossRef] [PubMed]

C. Greiner, B. Boggs, T. Wang, and T. Mossberg, “Laser frequency stabilization by means of optical self-heterodyne beat-frequency control,” Opt. Lett. 23, 1280-1282 (1998).
[CrossRef]

W. C. Swann, J. J. McFerran, I. Coddington, N. R. Newbury, I. Hartl, M. E. Fermann, P. S. Westbrook, J. W. Nicholson, K. S. Feder, C. Langrock, and M. M. Fejer, “Fiber-laser frequency combs with sub-hertz relative linewidths,” Opt. Lett. 31, 3046-3048 (2006).
[CrossRef] [PubMed]

G. Gorju, A. Jucha, A. Jain, V. Crozatier, I. Lorgere, J.-L. L. Gout, and F. Bretenaker, “Active stabilization of a rapidly chirped laser by an optoelectronic digital servo-loop control,” Opt. Lett. 32, 484-487 (2007).
[CrossRef] [PubMed]

P. deGroot, “Chromatic dipersion effects in coherent absolute ranging,” Opt. Lett. 17, 898-900 (1992).
[CrossRef]

Opt. Rev.

L. Qiao, D. Sun, X. Zhang, and Y. Zhao, “Linearity requirements for a linear frequency modulation lidar,” Opt. Rev. 6, 160-162 (1999).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

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Figures (3)

Fig. 1
Fig. 1

Setup of FMCW ladar system. The lower box shows setup of chirped linearization system that generates a very broadband ( > 5 THz ) and linear frequency sweep with chirp rate α. (See text for complete description.) The broadband laser chirp is used to perform ranging on a target at a distance L in air with index n t . The ladar signal ω b is analyzed using analog-to-digital conversion (A/D) and fast Fourier transforms (FFT) (upper box).

Fig. 2
Fig. 2

Carrier-to-noise ratio as a function of Ω rms τ , where Ω rms is the rms value of the time domain residual frequency error from a linear chirp. The curves were calculated using Eq. (5) for a single noise sideband (solid) and 10 noise sidebands. The points came from a numerical simulation that used 10 noise sidebands with normally distributed frequencies and modulation depths. The circles show the ratio of the carrier power to the mean sideband power near the carrier, and the triangles show the ratio of the carrier power to the peak sideband power.

Fig. 3
Fig. 3

Normalized range peak for different distances in air are shown in dB scale (top) and linear scale (bottom). The range peak broadens linearly with distance due to dispersion in the reference interferometer used to linearize the chirp laser. This broadening is unobserved for delay measurements made in fiber (see solid black, 3.8 m in fiber trace). The use of a Hanning window in the Fourier transform rounds the square shape of the chirped range peak (compare the blue dash-dot, 9 m Hanning, and solid magenta, 9 m square window traces).

Equations (17)

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E ( t ) exp ( - i [ ω 0 t + 1 2 α t 2 + n Ω n ω n cos ( ω n t ) ] ) ,
V s ( t ) cos ( ω 0 τ + α τ t - 1 2 α τ 2 + Ω n ω n [ cos ( ω n t ) - cos ( ω n ( t - τ ) ) ] ) ,
Ω n ω n ( - 2 sin ( ω n τ / 2 ) sin ( ω n t - ω n τ / 2 ) ) - Ω n τ sin ( ω n t - ω n τ / 2 ) ,
n J 0 2 ( Ω n τ ) J 0 2 ( τ n Ω n 2 ) , for     Ω n τ 1.
CNR J 0 2 ( Ω rms τ ) J 1 2 ¯ ( Ω n τ ) J 0 2 ( Ω rms τ ) J 1 2 ( Ω rms τ / N ) ,
E ( t ) = E 0 exp [ - i ( ω 0 t + 1 2 α t 2 ) ) ] E ˜ ( ω ) = E 0 1 - i 2 α exp [ i ( ( ω - ω 0 ) 2 2 α ) ] .
E ( z , t ) = E ˜ ( ω ) e i β 0 z e i β 1 ( ω - ω 0 ) z e i 1 2 β 2 ( ω - ω 0 ) 2 z e - i ω t d ω = E 0 α α exp [ - i ( ω 0 ( t - ( n / c ) z ) + 1 2 α ( t - β 1 z ) 2 ) ] ,
α = α 1 + α β 2 z = α ( 1 - α β 2 z + O ( α β 2 z ) 2 ) ,
ω b = α β 1 z ω b = α β 1 z ( 1 + α β 2 β 1 t ) .
ϕ E ( 0 , t ) = ω 0 t + 1 2 a t 2 + 1 6 b t 3 ,
ϕ ref = ω 0 ( n r / c ) L r + 1 2 ( a - a ) t 2 + a β 1 L r t - 1 2 a ( β 1 L r ) 2 + 1 2 b β 1 L r t 2 - 1 2 b ( β 1 L r ) 2 t ,
a β 1 L r - 1 2 b ( β 1 L r ) 2 = ω r , 1 2 ( a - a ) + 1 2 b β 1 L r = 0.
ϕ E ( 0 , t ) = ω 0 t + 1 2 α 0 t 2 1 6 α 0 2 β 2 β 1 t 3 .
V s ( t ) cos [ α 2 n air c R ( 1 + 1 2 α 0 β 2 β 1 2 n air c R - 1 2 α 0 β 2 β 1 t ) t + ϕ 0 ] ,
Δ R 2 π β 2 β 1 R B .
R = 1 2 n r L r ω b n t ω r ,
( δ R R ) 2 = ( δ n t n t ) 2 + ( δ ω b ω b ) 2 + ( δ ω r ω r ) 2 + ( δ τ r τ r ) 2 ,

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