Abstract

We study the characteristics of a dual-frequency laser Doppler velocimeter (DF-LDV) based on an optically injected semiconductor laser. The laser operated in a period-one (P1) dynamical state with two optical frequencies separated by 11.25 GHz is used as the dual-frequency light source. With a microwave beat signal carried by the light, the DF-LDV possesses both the advantages of good directionality, high intensity, and high spatial resolution from the light and low speckle noise and good coherence from the microwave, respectively. By phase-locking the two frequency components with a microwave signal, the coherence of the dual-frequency light source can be further improved and the detection range can be much extended. In this paper, velocity resolutions of the DF-LDV with different amounts of speckle noise and at different detection ranges are experimentally measured and analyzed. Compared with the conventional single-frequency LDV (SF-LDV), the velocity resolution of the DF-LDV is improved by 8×103 times from 2.5 m/s to 0.31 mm/s for a target with a longitudinal velocity vz = 4 cm/s, a transverse velocity vt = 5 m/s, and at a detection range of 108 m.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. Rajan, B. Varghese, T. G. Van Leeuwen, and W. Steenbergen, “Review of methodological developments in laser Doppler flowmetry,” Laser Med. Sci.24, 269–283 (2009).
    [CrossRef]
  2. R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
    [CrossRef]
  3. Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett.4, 176–178 (1964).
    [CrossRef]
  4. S. Rothberg, “Numerical simulation of speckle noise in laser vibrometry,” Appl. Opt.45, 4523–4533 (2006).
    [CrossRef] [PubMed]
  5. M. Denman, N. Halliwell, and S. Rothberg, “Speckle noise reduction in laser vibrometry experimental and numerical optimization,” Proc. SPIE2868, 12–21 (1996).
    [CrossRef]
  6. P. Martin and S. Rothberg, “Introducing speckle noise maps for laser vibrometry,” Opt. Lasers Eng.47, 431–442 (2009).
    [CrossRef]
  7. J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
    [CrossRef]
  8. H. W. Mocker and P. E. Bjork, “High accuracy laser Doppler velocimeter using stable long-wavelength semiconductor lasers,” Appl. Opt.28, 4914–4919 (1989).
    [CrossRef] [PubMed]
  9. U. Sharma, G. Chen, J. U. Kang, I. Ilev, and R. W. Waynant, “Fiber optic confocal laser Doppler velocimeter using an all-fiber laser source for high resolution measurements,” Opt. Express13, 6250–6258 (2005).
    [CrossRef] [PubMed]
  10. S. K. Hwang, J. M. Liu, and J. K. White, “Characteristics of period-one oscillations in semiconductor lasers subject to optical injection,” IEEE J. Sel. Top. Quantum Electron.10, 974–981 (2004).
    [CrossRef]
  11. F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor laser under repetitive optical pulse injection,” IEEE J. Sel. Top. Quantum Electron.15, 604–611 (2009).
    [CrossRef]
  12. Y. S. Juan and 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]
  13. F. Y. Lin and J. M. Liu, “Chaotic lidar,” IEEE J. Sel. Top. Quantum Electron.10, 991–997 (2004).
    [CrossRef]
  14. W. T. Wu, Y. H. Liao, and F. Y. Lin, “Noise suppressions in synchronized chaos lidar,” Opt. Express18, 26155–26162 (2010).
    [CrossRef] [PubMed]
  15. F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron.40, 815–820 (2004).
    [CrossRef]
  16. R. Diaz, S. C. Chan, and J. M. Liu, “Lidar detection using a dual-frequency source,” Opt. Lett.31, 3600–3602 (2006).
    [CrossRef] [PubMed]
  17. C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express20, 24577–24582 (2011).
  18. J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron.30, 957–965 (1994).
    [CrossRef]
  19. T. B. Simpson, “Phase-locked microwave-frequency modulations in optically-injected laser diodes,” Opt. Commun.170, 93–98 (1999).
    [CrossRef]
  20. Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express17, 18596–18605 (2009).
    [CrossRef]

2011

Y. S. Juan and 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]

C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express20, 24577–24582 (2011).

2010

R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
[CrossRef]

W. T. Wu, Y. H. Liao, and F. Y. Lin, “Noise suppressions in synchronized chaos lidar,” Opt. Express18, 26155–26162 (2010).
[CrossRef] [PubMed]

2009

Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express17, 18596–18605 (2009).
[CrossRef]

B. Rajan, B. Varghese, T. G. Van Leeuwen, and W. Steenbergen, “Review of methodological developments in laser Doppler flowmetry,” Laser Med. Sci.24, 269–283 (2009).
[CrossRef]

P. Martin and S. Rothberg, “Introducing speckle noise maps for laser vibrometry,” Opt. Lasers Eng.47, 431–442 (2009).
[CrossRef]

F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor laser under repetitive optical pulse injection,” IEEE J. Sel. Top. Quantum Electron.15, 604–611 (2009).
[CrossRef]

2008

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

2006

2005

2004

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron.40, 815–820 (2004).
[CrossRef]

S. K. Hwang, J. M. Liu, and J. K. White, “Characteristics of period-one oscillations in semiconductor lasers subject to optical injection,” IEEE J. Sel. Top. Quantum Electron.10, 974–981 (2004).
[CrossRef]

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

1999

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

1996

M. Denman, N. Halliwell, and S. Rothberg, “Speckle noise reduction in laser vibrometry experimental and numerical optimization,” Proc. SPIE2868, 12–21 (1996).
[CrossRef]

1994

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron.30, 957–965 (1994).
[CrossRef]

1989

1964

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett.4, 176–178 (1964).
[CrossRef]

Bagdahn, J.

R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
[CrossRef]

Bjork, P. E.

Brokmann, G.

R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
[CrossRef]

Chan, S. C.

Chang, S. M.

F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor laser under repetitive optical pulse injection,” IEEE J. Sel. Top. Quantum Electron.15, 604–611 (2009).
[CrossRef]

Chen, G.

Cristalli, C.

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

Cumming, H. Z.

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett.4, 176–178 (1964).
[CrossRef]

Denman, M.

M. Denman, N. Halliwell, and S. Rothberg, “Speckle noise reduction in laser vibrometry experimental and numerical optimization,” Proc. SPIE2868, 12–21 (1996).
[CrossRef]

Diaz, R.

Ebert, M.

R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
[CrossRef]

Gerbach, R.

R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
[CrossRef]

Halliwell, N.

M. Denman, N. Halliwell, and S. Rothberg, “Speckle noise reduction in laser vibrometry experimental and numerical optimization,” Proc. SPIE2868, 12–21 (1996).
[CrossRef]

Hein, T.

R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
[CrossRef]

Huang, C. C.

F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor laser under repetitive optical pulse injection,” IEEE J. Sel. Top. Quantum Electron.15, 604–611 (2009).
[CrossRef]

Hwang, S. K.

S. K. Hwang, J. M. Liu, and J. K. White, “Characteristics of period-one oscillations in semiconductor lasers subject to optical injection,” IEEE J. Sel. Top. Quantum Electron.10, 974–981 (2004).
[CrossRef]

Ilev, I.

Juan, Y. S.

Y. S. Juan and 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]

Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express17, 18596–18605 (2009).
[CrossRef]

Kang, J. U.

Liao, Y. H.

Lin, C. H.

C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express20, 24577–24582 (2011).

Lin, F. Y.

C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express20, 24577–24582 (2011).

Y. S. Juan and 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]

W. T. Wu, Y. H. Liao, and F. Y. Lin, “Noise suppressions in synchronized chaos lidar,” Opt. Express18, 26155–26162 (2010).
[CrossRef] [PubMed]

F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor laser under repetitive optical pulse injection,” IEEE J. Sel. Top. Quantum Electron.15, 604–611 (2009).
[CrossRef]

Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express17, 18596–18605 (2009).
[CrossRef]

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

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron.40, 815–820 (2004).
[CrossRef]

Lin, H. H.

C. H. Lin, H. H. Lin, and F. Y. Lin, “Four-wave mixing analysis of quantum dot semiconductor lasers for linewidth enhancement factor extraction,” Opt. Express20, 24577–24582 (2011).

Liu, J. M.

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

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron.40, 815–820 (2004).
[CrossRef]

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

S. K. Hwang, J. M. Liu, and J. K. White, “Characteristics of period-one oscillations in semiconductor lasers subject to optical injection,” IEEE J. Sel. Top. Quantum Electron.10, 974–981 (2004).
[CrossRef]

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron.30, 957–965 (1994).
[CrossRef]

Martin, P.

P. Martin and S. Rothberg, “Introducing speckle noise maps for laser vibrometry,” Opt. Lasers Eng.47, 431–442 (2009).
[CrossRef]

Mocker, H. W.

Rajan, B.

B. Rajan, B. Varghese, T. G. Van Leeuwen, and W. Steenbergen, “Review of methodological developments in laser Doppler flowmetry,” Laser Med. Sci.24, 269–283 (2009).
[CrossRef]

Randall, R. B.

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

Rothberg, S.

P. Martin and S. Rothberg, “Introducing speckle noise maps for laser vibrometry,” Opt. Lasers Eng.47, 431–442 (2009).
[CrossRef]

S. Rothberg, “Numerical simulation of speckle noise in laser vibrometry,” Appl. Opt.45, 4523–4533 (2006).
[CrossRef] [PubMed]

M. Denman, N. Halliwell, and S. Rothberg, “Speckle noise reduction in laser vibrometry experimental and numerical optimization,” Proc. SPIE2868, 12–21 (1996).
[CrossRef]

Sharma, U.

Simpson, T. B.

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

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron.30, 957–965 (1994).
[CrossRef]

Smid, R.

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

Sovka, P.

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

Steenbergen, W.

B. Rajan, B. Varghese, T. G. Van Leeuwen, and W. Steenbergen, “Review of methodological developments in laser Doppler flowmetry,” Laser Med. Sci.24, 269–283 (2009).
[CrossRef]

Torcianti, B.

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

Tu, S. Y.

F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor laser under repetitive optical pulse injection,” IEEE J. Sel. Top. Quantum Electron.15, 604–611 (2009).
[CrossRef]

Van Leeuwen, T. G.

B. Rajan, B. Varghese, T. G. Van Leeuwen, and W. Steenbergen, “Review of methodological developments in laser Doppler flowmetry,” Laser Med. Sci.24, 269–283 (2009).
[CrossRef]

Varghese, B.

B. Rajan, B. Varghese, T. G. Van Leeuwen, and W. Steenbergen, “Review of methodological developments in laser Doppler flowmetry,” Laser Med. Sci.24, 269–283 (2009).
[CrossRef]

Vass, J.

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

Waynant, R. W.

White, J. K.

S. K. Hwang, J. M. Liu, and J. K. White, “Characteristics of period-one oscillations in semiconductor lasers subject to optical injection,” IEEE J. Sel. Top. Quantum Electron.10, 974–981 (2004).
[CrossRef]

Wu, W. T.

Yeh, Y.

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett.4, 176–178 (1964).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. Yeh and H. Z. Cumming, “Localized fluid flow measurement with a He-Ne laser spectrometer,” Appl. Phys. Lett.4, 176–178 (1964).
[CrossRef]

IEEE J. Quantum Electron.

J. M. Liu and T. B. Simpson, “Four-wave mixing and optical modulation in a semiconductor laser,” IEEE J. Quantum Electron.30, 957–965 (1994).
[CrossRef]

F. Y. Lin and J. M. Liu, “Chaotic radar using nonlinear laser dynamics,” IEEE J. Quantum Electron.40, 815–820 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

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

S. K. Hwang, J. M. Liu, and J. K. White, “Characteristics of period-one oscillations in semiconductor lasers subject to optical injection,” IEEE J. Sel. Top. Quantum Electron.10, 974–981 (2004).
[CrossRef]

F. Y. Lin, S. Y. Tu, C. C. Huang, and S. M. Chang, “Nonlinear dynamics of semiconductor laser under repetitive optical pulse injection,” IEEE J. Sel. Top. Quantum Electron.15, 604–611 (2009).
[CrossRef]

IEEE Photonics J.

Y. S. Juan and 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]

Laser Med. Sci.

B. Rajan, B. Varghese, T. G. Van Leeuwen, and W. Steenbergen, “Review of methodological developments in laser Doppler flowmetry,” Laser Med. Sci.24, 269–283 (2009).
[CrossRef]

Mech. Syst. Sig. Process.

J. Vass, R. Smid, R. B. Randall, P. Sovka, C. Cristalli, and B. Torcianti, “Avoidance of speckle noise in laser vibrometry by the use of kurtosis ratio application to mechanical fault diagnostics,” Mech. Syst. Sig. Process.22, 647–671 (2008).
[CrossRef]

Microsyst. Technol.

R. Gerbach, M. Ebert, G. Brokmann, T. Hein, and J. Bagdahn, “Identification of mechanical defects in MEMS using dynamic measurements for application in production monitoring,” Microsyst. Technol.16, 1251–1257 (2010).
[CrossRef]

Opt. Commun.

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

Opt. Express

Opt. Lasers Eng.

P. Martin and S. Rothberg, “Introducing speckle noise maps for laser vibrometry,” Opt. Lasers Eng.47, 431–442 (2009).
[CrossRef]

Opt. Lett.

Proc. SPIE

M. Denman, N. Halliwell, and S. Rothberg, “Speckle noise reduction in laser vibrometry experimental and numerical optimization,” Proc. SPIE2868, 12–21 (1996).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Experimental setup of the DF-LDV based on an optically injected semiconductor laser. ML: master laser; SL: slave laser; SOA: semiconductor optical amplifier; PBS: polarizing beam splitter; ISO: isolator; FR: Faraday rotator; HWP: half-wave plate; QWP: quarter-wave plate; VA: variable attenuator; CL: coupling lens; FC: fiber coupler; L: lens; P: polarizer; M: mirror; APD: avalanche photodetector; MFS: microwave frequency synthesizer; OSA: optical spectrum analyzer; MSA: microwave spectrum analyzer; OSC: oscilloscope.

Fig. 2
Fig. 2

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

Fig. 3
Fig. 3

(a) Waveform, (b) its enlargement, and (c) power spectrum of the Doppler-shifted signal from the SF-LDV and (d) waveform, (e) its enlargement, and (f) power spectrum of the Doppler-shifted signal from the DF-LDV (with phase-locking), respectively. The target is moving away from the interferometer with vz = 4 cm/s while rotating with vt = 5 m/s.

Fig. 4
Fig. 4

(Velocity resolutions of the (a) SF-LDV and (b) DF-LDV without and with phase locking for different transverse velocities when the target is moving at vz = 4 cm/s. The averages and error bars obtained from several measurements are plotted.

Fig. 5
Fig. 5

Velocity resolutions of the (a) SF-LDV and (b) DF-LDV without and with phase-locking for different path differences.

Fig. 6
Fig. 6

Velocity resolutions of the (a) SF-LDV and (b) DF-LDV with phase-locking for different transverse velocities at different path differences, respectively.

Fig. 7
Fig. 7

Velocity resolutions of the (a) SF-LDV and (b) DF-LDV with phase-locking for different longitudinal velocities at different path differences, respectively.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

E r ( t ) = E 1 e j [ 2 π f 1 t + ϕ 1 ( t ) ] + E 2 e j [ 2 π f 2 t + ϕ 2 ( t ) ] ,
E t ( t ) = E 1 e j [ 2 π ( f 1 + f d , 1 ) t 2 π f 1 τ + ϕ 1 ( t τ ) + ϕ 1 , speckle ( t τ ) ] + E 2 e j [ 2 π ( f 2 + f d , 2 ) t 2 π f 2 τ + ϕ 2 ( t τ ) + ϕ 2 , speckle ( t τ ) ] ,
ϕ 1 , speckle ( t ) = 2 π × 2 γ ( p , t ) λ 1 d S
ϕ 2 , speckle ( t ) = 2 π × 2 γ ( p , t ) λ 2 d S ,
I 1 ( t ) = 2 E 1 2 cos [ 2 π f d , 1 t + [ ϕ 1 ( t τ ) ϕ 1 ( t ) ] + ϕ 1 , speckle ( t τ ) 2 π f 1 τ ]
I 2 ( t ) = 2 E 2 2 cos [ 2 π f d , 2 t + [ ϕ 2 ( t τ ) ϕ 2 ( t ) ] + ϕ 2 , speckle ( t τ ) 2 π f 2 τ ]
I mix ( t ) = 2 E 1 2 E 2 2 cos [ 2 π f d , P 1 t + [ ϕ P 1 ( t τ ) ϕ P 1 ( t ) ] + ϕ P 1 , speckle ( t τ ) 2 π ( f 1 f 2 ) τ ] ,

Metrics