Abstract

Compressive sampling has been previously proposed as a technique for sampling radar returns and determining sparse range profiles with a reduced number of measurements compared to conventional techniques. By employing modulation on both transmission and reception, compressive sensing in ranging is extended to the direct measurement of range profiles without intermediate measurement of the return waveform. This compressive ranging approach enables the use of pseudorandom binary transmit waveforms and return modulation, along with low-bandwidth optical detectors to yield high-resolution ranging information. A proof-of-concept experiment is presented. With currently available compact, off-the-shelf electronics and photonics, such as high data rate binary pattern generators and high-bandwidth digital optical modulators, compressive laser ranging can readily achieve subcentimeter resolution in a compact, lightweight package.

© 2011 Optical Society of America

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References

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2010 (5)

M. Tello Alonso, P. Lopez-Dekker, and J. J. Mallorqui, IEEE Trans. Geosci. Remote Sens. 48, 4285 (2010).
[CrossRef]

M. Mishali and Y. Eldar, IEEE J. Sel. Top. Signal Process. 4, 375 (2010).
[CrossRef]

C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, IEEE J. Sel. Top. Signal Process. 4, 226 (2010).
[CrossRef]

Y. Yu, A. P. Petropulu, and H. V. Poor, IEEE J. Sel. Top. Signal Process. 4, 146 (2010).
[CrossRef]

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

2009 (1)

M. Herman and T. Strohmer, IEEE Trans. Signal Process. 57, 2275 (2009).
[CrossRef]

2007 (2)

R. G. Baraniuk, IEEE Signal Process. Mag. 24, 118 (2007).
[CrossRef]

G. C. Valley, Opt. Express 15, 1955 (2007).
[CrossRef]

2003 (1)

Alonso, M. Tello

M. Tello Alonso, P. Lopez-Dekker, and J. J. Mallorqui, IEEE Trans. Geosci. Remote Sens. 48, 4285 (2010).
[CrossRef]

Baraniuk, R.

R. Baraniuk and P. Steeghs, in Proceedings of IEEE Radar Conference (IEEE, 2007), p. 128.

Baraniuk, R. G.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

R. G. Baraniuk, IEEE Signal Process. Mag. 24, 118 (2007).
[CrossRef]

Berger, C. R.

C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, IEEE J. Sel. Top. Signal Process. 4, 226 (2010).
[CrossRef]

Candes, E. J.

E. J. Candes, in Proceedings of International Congress of Mathematicians (European Mathematical Society, 2006), p. 1433.

Demissie, B.

C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, IEEE J. Sel. Top. Signal Process. 4, 226 (2010).
[CrossRef]

Duarte, M. F.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Eldar, Y.

M. Mishali and Y. Eldar, IEEE J. Sel. Top. Signal Process. 4, 375 (2010).
[CrossRef]

Heckenbach, J.

C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, IEEE J. Sel. Top. Signal Process. 4, 226 (2010).
[CrossRef]

Herman, M.

M. Herman and T. Strohmer, IEEE Trans. Signal Process. 57, 2275 (2009).
[CrossRef]

Laska, J. N.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Lopez-Dekker, P.

M. Tello Alonso, P. Lopez-Dekker, and J. J. Mallorqui, IEEE Trans. Geosci. Remote Sens. 48, 4285 (2010).
[CrossRef]

Mallorqui, J. J.

M. Tello Alonso, P. Lopez-Dekker, and J. J. Mallorqui, IEEE Trans. Geosci. Remote Sens. 48, 4285 (2010).
[CrossRef]

Mishali, M.

M. Mishali and Y. Eldar, IEEE J. Sel. Top. Signal Process. 4, 375 (2010).
[CrossRef]

Neifeld, M. A.

Petropulu, A. P.

Y. Yu, A. P. Petropulu, and H. V. Poor, IEEE J. Sel. Top. Signal Process. 4, 146 (2010).
[CrossRef]

Poor, H. V.

Y. Yu, A. P. Petropulu, and H. V. Poor, IEEE J. Sel. Top. Signal Process. 4, 146 (2010).
[CrossRef]

Romberg, J. K.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Shankar, P.

Steeghs, P.

R. Baraniuk and P. Steeghs, in Proceedings of IEEE Radar Conference (IEEE, 2007), p. 128.

Strohmer, T.

M. Herman and T. Strohmer, IEEE Trans. Signal Process. 57, 2275 (2009).
[CrossRef]

Tropp, J. A.

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

Valley, G. C.

Willett, P.

C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, IEEE J. Sel. Top. Signal Process. 4, 226 (2010).
[CrossRef]

Yu, Y.

Y. Yu, A. P. Petropulu, and H. V. Poor, IEEE J. Sel. Top. Signal Process. 4, 146 (2010).
[CrossRef]

Zhou, S.

C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, IEEE J. Sel. Top. Signal Process. 4, 226 (2010).
[CrossRef]

Appl. Opt. (1)

IEEE J. Sel. Top. Signal Process. (3)

Y. Yu, A. P. Petropulu, and H. V. Poor, IEEE J. Sel. Top. Signal Process. 4, 146 (2010).
[CrossRef]

M. Mishali and Y. Eldar, IEEE J. Sel. Top. Signal Process. 4, 375 (2010).
[CrossRef]

C. R. Berger, B. Demissie, J. Heckenbach, P. Willett, and S. Zhou, IEEE J. Sel. Top. Signal Process. 4, 226 (2010).
[CrossRef]

IEEE Signal Process. Mag. (1)

R. G. Baraniuk, IEEE Signal Process. Mag. 24, 118 (2007).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

M. Tello Alonso, P. Lopez-Dekker, and J. J. Mallorqui, IEEE Trans. Geosci. Remote Sens. 48, 4285 (2010).
[CrossRef]

IEEE Trans. Inf. Theory (1)

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, IEEE Trans. Inf. Theory 56, 520 (2010).
[CrossRef]

IEEE Trans. Signal Process. (1)

M. Herman and T. Strohmer, IEEE Trans. Signal Process. 57, 2275 (2009).
[CrossRef]

Opt. Express (1)

Other (2)

R. Baraniuk and P. Steeghs, in Proceedings of IEEE Radar Conference (IEEE, 2007), p. 128.

E. J. Candes, in Proceedings of International Congress of Mathematicians (European Mathematical Society, 2006), p. 1433.

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Figures (2)

Fig. 1.
Fig. 1.

The CR demonstrator. The transmit and return light are separately modulated (with null biased Mach–Zehnder modulators MZ Tx and MZ Rx, respectively) with distinct synchronized binary waveforms from the arbitrary waveform generator (AWG). The AWG also produces an IF signal to the mixer for lock-in detection. The system is all-fiber, except for free space to the targets. The modulated return light is detected, mixed with lock-in IF signal, low pass filtered (LPF), digitized (ADC), and postprocessed by the computer (PC).

Fig. 2.
Fig. 2.

(a) The CR measurements made of the closest target position (at 1.3 m) with the 24 pairs of transmit and return modulation waveforms. (b) The determined range profiles for three target positions (1.3 m (red solid), 2.2 m (green dotted), and 3.1 m (blue dashed)) over the full range window (80 m). The inset shows the same range profiles from 0 m to 4 m.

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