Abstract

A self-mixing (SM) dual-frequency (DF) laser Doppler velocimeter (LDV) (SM DF-LDV) is proposed and studied, which integrates the advantages of both the SM-LDV and the DF-LDV. An optically injected semiconductor laser operated in a dual-frequency period-one (P1) dynamical state is used as the light source. By probing the target with the light-carried microwave generated from the beat of the two optical frequency components, the spectral broadening in the Doppler signal due to the speckle noise can be significantly reduced. Together with an SM configuration, the SM DF-LDV has the advantages of direction discriminability, self-alignment, high sensitivity, and compact setup. In this study, speckle noise reduction and direction discriminability with an SM DF-LDV are demonstrated. The signal-to-noise ratios (SNRs) at different feedback powers are investigated. Benefiting from the high sensitivity of the SM configuration, an SNR of 23 dB is achieved without employing an avalanched photodetector or photomultiplier tube. The velocity resolution and the SNR under different speckle noise conditions are studied. Average velocity resolution of 0.42 mm/s and SNR of 22.1 dB are achieved when a piece of paper is rotating at a transverse velocity of 5 m/s. Compared with a conventional single-frequency LDV (SF-LDV), the SM DF-LDV shows improvements of 20-fold in the velocity resolution and 8 dB in the SNR.

© 2014 Optical Society of America

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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]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]

2013

R. Atashkhooei, S. Royo, F. J. Azcona, “Dealing with speckle effects in self-mixing interferometry measurements,” IEEE Sens. J. 13, 1641–1647 (2013).
[CrossRef]

Y. H. Liao, J. M. Liu, F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[CrossRef]

Y. H. Liao, F. Y. Lin, “Dynamical characteristics and their applications of semiconductor lasers subject to both optical injection and optical feedback,” Opt. Express 21, 23568–23578 (2013).
[CrossRef] [PubMed]

2012

2011

Y. S. Juan, F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. 3, 644–650 (2011).
[CrossRef]

L. Rovati, S. Cattini, N. Palanisamy, “Measurement of the fluid-velocity profile using a self-mixing superluminescent diode,” Meas. Sci. Technol. 22, 025402 (2011).
[CrossRef]

2010

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

2008

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

S. K. Ozdemir, I. Ohno, S. Shinohara, “A comparative study for the assessment on blood flow measurement using self-mixing laser speckle interferometer,” IEEE Trans. Instrum. Meas. 57, 355–363 (2008).
[CrossRef]

2006

2005

2004

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

S. C. Chan, J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
[CrossRef]

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

2003

M. Norgia, S. Donati, “A displacement-measuring instrument utilizing self-mixing interferometry,” IEEE Trans. Instrum. Meas. 52, 1765–1770 (2003).
[CrossRef]

2002

G. Giuliani, M. Norgia, S. Donati, T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

2001

M. Norgia, S. Donati, D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37, 800–806 (2001).
[CrossRef]

2000

G. Giuliani, M. Norgia, “Laser diode linewidth measurement by means of self-mixing interferometry,” IEEE Photonics Technol. Lett. 12, 1028–1030 (2000).
[CrossRef]

1999

T. B. Simpson, “Phase-locked microwave-frequency modulations in optically-injected laser diodes,” Opt. Commun. 170, 93–98 (1999).
[CrossRef]

Atashkhooei, R.

R. Atashkhooei, S. Royo, F. J. Azcona, “Dealing with speckle effects in self-mixing interferometry measurements,” IEEE Sens. J. 13, 1641–1647 (2013).
[CrossRef]

Azcona, F. J.

R. Atashkhooei, S. Royo, F. J. Azcona, “Dealing with speckle effects in self-mixing interferometry measurements,” IEEE Sens. J. 13, 1641–1647 (2013).
[CrossRef]

Bes, C.

G. Plantier, C. Bes, T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

Bosch, T.

G. Plantier, C. Bes, T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

Cao, Z.

Cattini, S.

L. Rovati, S. Cattini, N. Palanisamy, “Measurement of the fluid-velocity profile using a self-mixing superluminescent diode,” Meas. Sci. Technol. 22, 025402 (2011).
[CrossRef]

Chan, S. C.

Chen, G.

Cheng, C. H.

D’Alessandro, D.

M. Norgia, S. Donati, D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37, 800–806 (2001).
[CrossRef]

Dai, J.

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

Diaz, R.

Donati, S.

M. Norgia, S. Donati, “A displacement-measuring instrument utilizing self-mixing interferometry,” IEEE Trans. Instrum. Meas. 52, 1765–1770 (2003).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

M. Norgia, S. Donati, D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37, 800–806 (2001).
[CrossRef]

Giuliani, G.

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

G. Giuliani, M. Norgia, “Laser diode linewidth measurement by means of self-mixing interferometry,” IEEE Photonics Technol. Lett. 12, 1028–1030 (2000).
[CrossRef]

Gui, H.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

He, D.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

Huang, W.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

Ilev, I.

Juan, Y. S.

Y. S. Juan, F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. 3, 644–650 (2011).
[CrossRef]

Kang, J. U.

Kliese, R.

Lee, C. W.

Li, X. Z.

Liao, Y. H.

Y. H. Liao, F. Y. Lin, “Dynamical characteristics and their applications of semiconductor lasers subject to both optical injection and optical feedback,” Opt. Express 21, 23568–23578 (2013).
[CrossRef] [PubMed]

Y. H. Liao, J. M. Liu, F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[CrossRef]

Lin, F. Y.

Y. H. Liao, J. M. Liu, F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[CrossRef]

Y. H. Liao, F. Y. Lin, “Dynamical characteristics and their applications of semiconductor lasers subject to both optical injection and optical feedback,” Opt. Express 21, 23568–23578 (2013).
[CrossRef] [PubMed]

C. H. Cheng, C. W. Lee, T. W. Lin, F. Y. Lin, “Dual-frequency laser Doppler velocimeter for speckle noise reduction and coherence enhancement,” Opt. Express 20, 20255–20265 (2012).
[CrossRef] [PubMed]

Y. S. Juan, F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. 3, 644–650 (2011).
[CrossRef]

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

Lin, T. W.

Liu, J. M.

Y. H. Liao, J. M. Liu, F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[CrossRef]

R. Diaz, S. C. Chan, J. M. Liu, “Lidar detection using a dual-frequency source,” Opt. Lett. 31, 3600–3602 (2006).
[CrossRef] [PubMed]

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

S. C. Chan, J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
[CrossRef]

Lu, L.

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, B. Yu, “Self-mixing interference measurement system of a fiber ring laser with ultra-narrow linewidth,” Opt. Express 20, 8598–8607 (2012).
[CrossRef] [PubMed]

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

Ming, H.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

Norgia, M.

M. Norgia, S. Donati, “A displacement-measuring instrument utilizing self-mixing interferometry,” IEEE Trans. Instrum. Meas. 52, 1765–1770 (2003).
[CrossRef]

G. Giuliani, M. Norgia, S. Donati, T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

M. Norgia, S. Donati, D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37, 800–806 (2001).
[CrossRef]

G. Giuliani, M. Norgia, “Laser diode linewidth measurement by means of self-mixing interferometry,” IEEE Photonics Technol. Lett. 12, 1028–1030 (2000).
[CrossRef]

Ohno, I.

S. K. Ozdemir, I. Ohno, S. Shinohara, “A comparative study for the assessment on blood flow measurement using self-mixing laser speckle interferometer,” IEEE Trans. Instrum. Meas. 57, 355–363 (2008).
[CrossRef]

Ozdemir, S. K.

S. K. Ozdemir, I. Ohno, S. Shinohara, “A comparative study for the assessment on blood flow measurement using self-mixing laser speckle interferometer,” IEEE Trans. Instrum. Meas. 57, 355–363 (2008).
[CrossRef]

Palanisamy, N.

L. Rovati, S. Cattini, N. Palanisamy, “Measurement of the fluid-velocity profile using a self-mixing superluminescent diode,” Meas. Sci. Technol. 22, 025402 (2011).
[CrossRef]

Plantier, G.

G. Plantier, C. Bes, T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

Raki, A. D.

Rothberg, S.

Rovati, L.

L. Rovati, S. Cattini, N. Palanisamy, “Measurement of the fluid-velocity profile using a self-mixing superluminescent diode,” Meas. Sci. Technol. 22, 025402 (2011).
[CrossRef]

Royo, S.

R. Atashkhooei, S. Royo, F. J. Azcona, “Dealing with speckle effects in self-mixing interferometry measurements,” IEEE Sens. J. 13, 1641–1647 (2013).
[CrossRef]

Scalise, L.

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

Sharma, U.

Shinohara, S.

S. K. Ozdemir, I. Ohno, S. Shinohara, “A comparative study for the assessment on blood flow measurement using self-mixing laser speckle interferometer,” IEEE Trans. Instrum. Meas. 57, 355–363 (2008).
[CrossRef]

Simpson, T. B.

T. B. Simpson, “Phase-locked microwave-frequency modulations in optically-injected laser diodes,” Opt. Commun. 170, 93–98 (1999).
[CrossRef]

Wang, H.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

Wang, R.

Waynant, R. W.

Xie, J.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

Yang, J.

Yu, B.

L. Lu, J. Yang, L. Zhai, R. Wang, Z. Cao, B. Yu, “Self-mixing interference measurement system of a fiber ring laser with ultra-narrow linewidth,” Opt. Express 20, 8598–8607 (2012).
[CrossRef] [PubMed]

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

Yu, Y.

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

Zhai, L.

Zhang, K.

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

Zhao, T.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

Zhen, S.

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

Zhu, J.

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

G. Plantier, C. Bes, T. Bosch, “Behavioral model of a self-mixing laser diode sensor,” IEEE J. Quantum Electron. 41, 1157–1167 (2005).
[CrossRef]

M. Norgia, S. Donati, D. D’Alessandro, “Interferometric measurements of displacement on a diffusing target by a speckle tracking technique,” IEEE J. Quantum Electron. 37, 800–806 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

F. Y. Lin, J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron. 10, 991–997 (2004).
[CrossRef]

Y. H. Liao, J. M. Liu, F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. Sel. Top. Quantum Electron. 19, 1500606 (2013).
[CrossRef]

S. C. Chan, J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
[CrossRef]

IEEE Photonics J.

Y. S. Juan, F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor laser,” IEEE Photonics J. 3, 644–650 (2011).
[CrossRef]

IEEE Photonics Technol. Lett.

G. Giuliani, M. Norgia, “Laser diode linewidth measurement by means of self-mixing interferometry,” IEEE Photonics Technol. Lett. 12, 1028–1030 (2000).
[CrossRef]

IEEE Sens. J.

R. Atashkhooei, S. Royo, F. J. Azcona, “Dealing with speckle effects in self-mixing interferometry measurements,” IEEE Sens. J. 13, 1641–1647 (2013).
[CrossRef]

IEEE Trans. Instrum. Meas.

M. Norgia, S. Donati, “A displacement-measuring instrument utilizing self-mixing interferometry,” IEEE Trans. Instrum. Meas. 52, 1765–1770 (2003).
[CrossRef]

L. Scalise, Y. Yu, G. Giuliani, G. Plantier, T. Bosch, “Self-mixing laser diode velocimetry: application to vibration and velocity measurement,” IEEE Trans. Instrum. Meas. 53, 223–232 (2004).
[CrossRef]

S. K. Ozdemir, I. Ohno, S. Shinohara, “A comparative study for the assessment on blood flow measurement using self-mixing laser speckle interferometer,” IEEE Trans. Instrum. Meas. 57, 355–363 (2008).
[CrossRef]

J. Opt. A: Pure Appl. Opt.

G. Giuliani, M. Norgia, S. Donati, T. Bosch, “Laser diode self-mixing technique for sensing applications,” J. Opt. A: Pure Appl. Opt. 4, S283–S294 (2002).
[CrossRef]

Meas. Sci. Technol.

L. Rovati, S. Cattini, N. Palanisamy, “Measurement of the fluid-velocity profile using a self-mixing superluminescent diode,” Meas. Sci. Technol. 22, 025402 (2011).
[CrossRef]

Opt. Commun.

W. Huang, H. Gui, L. Lu, J. Xie, H. Ming, D. He, H. Wang, T. Zhao, “Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system,” Opt. Commun. 281, 1662–1667 (2008).
[CrossRef]

T. B. Simpson, “Phase-locked microwave-frequency modulations in optically-injected laser diodes,” Opt. Commun. 170, 93–98 (1999).
[CrossRef]

Opt. Eng.

L. Lu, K. Zhang, J. Dai, J. Zhu, S. Zhen, B. Yu, “Study of speckle pattern effect for self-mixing laser diodes in vertical-cavity surface-emitting lasers,” Opt. Eng. 49, 094301 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (7)

Fig. 1
Fig. 1

Experimental setup of the SM DF-LDV. ML: master laser; SL: slave laser; ISO: isolator; PBS: polarizing beamsplitter; HWP: half-wave plate; FR: Faraday rotator; M: mirror; BS: beamsplitter; PC: polarization controller; VA: variable attenuator; L: lens; FC: fiber coupler; C: circulator; SOA: semiconductor optical amplifier; MSG: microwave signal generator; OSA: optical spectrum analyzer; PD: photodetector; MSA: microwave spectrum analyzer; OSC: oscilloscope; TR: target.

Fig. 2
Fig. 2

(a) Optical spectrum, (b) power spectrum without phase-locking, and (c) power spectrum with phase-locking of the P1 state obtained from the optically-injected SL.

Fig. 3
Fig. 3

(a)–(b) The Doppler signals ISM,DF (t), (c)–(d) the mixed Doppler signals ISM,DF (t)2, and (e)–(f) their corresponding spectra for a target moving with vz = −2 cm/s and vz = +2 cm/s toward and away from the SL, respectively. The red dashed curves shown in (c) and (d) are the mixed Doppler signals after low pass filtering.

Fig. 4
Fig. 4

(a) Doppler spectra measured with the target at different vz. (b) The measured Doppler frequencies and the corresponding velocities obtained with different vz.

Fig. 5
Fig. 5

(a) Signal amplitudes, (b) noise levels, and (c) signal-to-noise ratios under different feedback power. (d)–(f) Power spectra of the SL obtained with feedback power of 2.5, 32.5, 102.5 μW, respectively.

Fig. 6
Fig. 6

(a)–(b) Velocity resolutions and (c)–(d) SNRs of the SF-LDV (red) and the SM DF-LDV (black) obtained at different transverse velocities, respectively. The blue dashed lines are the average velocity resolution and SNR of the SM DF-LDV.

Fig. 7
Fig. 7

The filtered mixed Doppler signals obtained with the SM DF-LDV when the target is moving (a) toward (vz = −2 cm/s) and (b) away (vz = +2 cm/s) from the SL with a transverse velocity of vt = 5 m/s.

Equations (12)

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I SM ( t ) = F ( Φ ) = F ( 2 π f d , 1 t ) ,
I S M ( t ) = A speckle , 1 ( t ) × F [ 2 π f d , 1 t + ϕ speckle , 1 ( t ) + ϕ 1 ( t ) ] ,
A speckle , 1 ( t ) = | e j [ 2 π × 2 γ ( p , t ) / λ 1 ] d S |
ϕ speckle , 1 ( t ) = arctan { Im [ e j [ 2 π × 2 γ ( p , t ) / λ 1 ] d S ] Re [ e j [ 2 π × 2 γ ( p , t ) / λ 1 ] d S ] } ,
I S M , D F ( t ) = A speckle , 1 ( t ) × F [ 2 π f d , 1 t + ϕ speckle , 1 ( t ) + ϕ 1 ( t ) ] + A speckle , 2 ( t ) × F [ 2 π f d , 2 t + ϕ speckle , 2 ( t ) + ϕ 2 ( t ) ] .
I S M , D F mixed ( t ) = LDF [ I S M , D F ( t ) 2 ] = A speckle , P 1 ( t ) × F [ 2 π f d , P 1 t + ϕ speckle , P 1 ( t ) + ϕ P 1 ( t ) ] ,
f d , P 1 = 2 v z ( f 1 f 2 ) / c = 2 v z f P 1 / c ,
A speckle , P 1 ( t ) = | e j [ 2 π × 2 γ ( p , t ) / ( c / f P 1 ) ] d S + [ e j [ 2 π × 2 γ ( p , t ) / λ 1 2 π × 2 γ ( p , t ) / λ 2 ] d S + c . c . ] | ,
ϕ s peckle , P 1 ( t ) = arctan { Im [ e j [ 2 π × 2 γ ( p , t ) / ( c / f P 1 ) ] d S + [ e j [ 2 π × 2 γ ( p , t ) / λ 1 2 π × 2 γ ( p , t ) / λ 2 ] d S + c . c . ] ] Re [ e j [ 2 π × 2 γ ( p , t ) / ( c / f P 1 ) ] d S + [ e j [ 2 π × 2 γ ( p , t ) / λ 1 2 π × 2 γ ( p , t ) / λ 2 ] d S + c . c . ] ] } ,
ϕ P 1 ( t ) = ϕ 1 ( t ) ϕ 2 ( t ) .
A speckle , P 1 ( t ) | e j [ 2 π × 2 γ ( p , t ) / ( c / f P 1 ) ] d S | ,
ϕ speckle , P 1 ( t ) arctan { Im [ e j [ 2 π × 2 γ ( p , t ) / ( c / f P 1 ) ] d S ] Re [ e j [ 2 π × 2 γ ( p , t ) / ( c / f P 1 ) ] d S ] } .

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