Abstract

The photon counting detection of Geiger mode avalanche photodiode is discrete due to its dead time, therefore the intermediate frequency (IF) spectrum is also discrete after the mixing and fast Fourier transform processing. When the peak of the IF spectrum is in the interval of the discrete IF spectrum, it limits the range accuracy without obtaining the exact position of the desired target in the interval. In this paper, the phase postprocessing method is proposed, which extracts not only the frequency of the IF signal, but also the phase of the IF signal that was not exploited before. The theoretical analysis demonstrates significant improvements in the range accuracy of the ladar and the simulation verifies the validity of the method.

© 2013 Optical Society of America

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References

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  1. B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
    [CrossRef]
  2. B. L. Stann, W. C. Ruff, and Z. G. Sztankay, “Intensity-modulated diode laser radar using frequency modulation/continuous wave ranging techniques,” Opt. Eng. 35, 3270–3278 (1996).
    [CrossRef]
  3. W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
    [CrossRef]
  4. M. Ren, X. R. Gu, Y. Liang, W. B. Kong, E. Wu, G. Wu, and H. P. Zeng, “Laser ranging at 1550 nm with 1 GHz sine-wave gated InGaAs/InP APD single-photon detector,” Opt. Express 19, 13497–13502 (2011).
    [CrossRef]
  5. P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
    [CrossRef]
  6. G. A. Shaw, A. M. Siegel, J. Model, and A. Geboff, “Deep UV photon-counting detectors and applications,” Proc. SPIE 7320, 73200J (2009).
    [CrossRef]
  7. H. J. Kong, T. H. Kim, S. E. Jo, and M. S. Oh, “Smart three-dimensional imaging ladar using two Geiger-mode avalanche photodiodes,” Opt. Express 19, 19323–19329 (2011).
    [CrossRef]
  8. A. Stern, D. Alonia, and B. Javidib, “An overview of 3D visualization with integral imaging in photon starved conditions,” Proc. SPIE 8384, 83840K (2012).
    [CrossRef]
  9. B. Redman, W. Ruff, and M. Giza, “Photon counting chirped AM Ladar: concept, simulation, and initial experimental results,” Proc. SPIE 6214, 62140P (2006).
    [CrossRef]
  10. F. Yang, Y. He, J. H. Shang, and W. B. Chen, “Experimental study on the 1550 nm all fiber heterodyne laser range finder,” Appl. Opt. 48, 6575–6582 (2009).
    [CrossRef]
  11. Z. W. Barber, W. R. Babbitt, B. Kaylor, R. R. Reibel, and P. A. Roos, “Accuracy of active chirp linearization for broadband frequency modulated continuous wave ladar,” Appl. Opt. 49, 213–219 (2010).
    [CrossRef]
  12. B. G. Quinn, “Estimating frequency by interpolation using Fourier coefficients,” IEEE Trans. Signal Process. 42, 1264–1268 (1994).
    [CrossRef]
  13. A. Choi, “Real-time fundamental frequency estimation by least-square fitting,” IEEE Trans. Speech Audio Process. 5, 201–205 (1997).
    [CrossRef]
  14. T. J. Abatzoglou, “A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton’s method,” IEEE Trans. Acoust. Speech Signal Process. 33, 77–89 (1985).
    [CrossRef]
  15. C. J. Karlsson and F. Å. A. Olsson, “Linearization of the frequency sweep of a frequency-modulated continuous-wave semiconductor laser radar and the resulting ranging performance,” Appl. Opt. 38, 3376–3385 (1999).
    [CrossRef]
  16. L. E. Drain, The Laser Doppler Technique (Wiley, 1980), p. 146.

2012 (1)

A. Stern, D. Alonia, and B. Javidib, “An overview of 3D visualization with integral imaging in photon starved conditions,” Proc. SPIE 8384, 83840K (2012).
[CrossRef]

2011 (3)

2010 (1)

2009 (2)

F. Yang, Y. He, J. H. Shang, and W. B. Chen, “Experimental study on the 1550 nm all fiber heterodyne laser range finder,” Appl. Opt. 48, 6575–6582 (2009).
[CrossRef]

G. A. Shaw, A. M. Siegel, J. Model, and A. Geboff, “Deep UV photon-counting detectors and applications,” Proc. SPIE 7320, 73200J (2009).
[CrossRef]

2006 (1)

B. Redman, W. Ruff, and M. Giza, “Photon counting chirped AM Ladar: concept, simulation, and initial experimental results,” Proc. SPIE 6214, 62140P (2006).
[CrossRef]

2004 (1)

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

2003 (1)

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

1999 (1)

1997 (1)

A. Choi, “Real-time fundamental frequency estimation by least-square fitting,” IEEE Trans. Speech Audio Process. 5, 201–205 (1997).
[CrossRef]

1996 (1)

B. L. Stann, W. C. Ruff, and Z. G. Sztankay, “Intensity-modulated diode laser radar using frequency modulation/continuous wave ranging techniques,” Opt. Eng. 35, 3270–3278 (1996).
[CrossRef]

1994 (1)

B. G. Quinn, “Estimating frequency by interpolation using Fourier coefficients,” IEEE Trans. Signal Process. 42, 1264–1268 (1994).
[CrossRef]

1985 (1)

T. J. Abatzoglou, “A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton’s method,” IEEE Trans. Acoust. Speech Signal Process. 33, 77–89 (1985).
[CrossRef]

Abatzoglou, T. J.

T. J. Abatzoglou, “A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton’s method,” IEEE Trans. Acoust. Speech Signal Process. 33, 77–89 (1985).
[CrossRef]

Abou-Auf, A.

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Aliberti, K.

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Alonia, D.

A. Stern, D. Alonia, and B. Javidib, “An overview of 3D visualization with integral imaging in photon starved conditions,” Proc. SPIE 8384, 83840K (2012).
[CrossRef]

Babbitt, W. R.

Bai, X. G.

P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
[CrossRef]

Barber, Z. W.

Boisvert, J.

P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
[CrossRef]

Chen, W. B.

Choi, A.

A. Choi, “Real-time fundamental frequency estimation by least-square fitting,” IEEE Trans. Speech Audio Process. 5, 201–205 (1997).
[CrossRef]

Dammann, J.

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Dang, G.

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Drain, L. E.

L. E. Drain, The Laser Doppler Technique (Wiley, 1980), p. 146.

Geboff, A.

G. A. Shaw, A. M. Siegel, J. Model, and A. Geboff, “Deep UV photon-counting detectors and applications,” Proc. SPIE 7320, 73200J (2009).
[CrossRef]

Giza, M.

B. Redman, W. Ruff, and M. Giza, “Photon counting chirped AM Ladar: concept, simulation, and initial experimental results,” Proc. SPIE 6214, 62140P (2006).
[CrossRef]

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Gu, X. R.

He, Y.

Javidib, B.

A. Stern, D. Alonia, and B. Javidib, “An overview of 3D visualization with integral imaging in photon starved conditions,” Proc. SPIE 8384, 83840K (2012).
[CrossRef]

Jo, S. E.

Karlsson, C. J.

Kaylor, B.

Kim, T. H.

Kong, H. J.

Kong, W. B.

Labios, E.

P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
[CrossRef]

Liang, Y.

McDonald, P.

P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
[CrossRef]

Model, J.

G. A. Shaw, A. M. Siegel, J. Model, and A. Geboff, “Deep UV photon-counting detectors and applications,” Proc. SPIE 7320, 73200J (2009).
[CrossRef]

Oh, M. S.

Olsson, F. Å. A.

Ovrebo, G.

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Potter, W.

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

Quinn, B. G.

B. G. Quinn, “Estimating frequency by interpolation using Fourier coefficients,” IEEE Trans. Signal Process. 42, 1264–1268 (1994).
[CrossRef]

Redman, B.

B. Redman, W. Ruff, and M. Giza, “Photon counting chirped AM Ladar: concept, simulation, and initial experimental results,” Proc. SPIE 6214, 62140P (2006).
[CrossRef]

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Reibel, R. R.

Ren, M.

Roos, P. A.

Ruff, W.

B. Redman, W. Ruff, and M. Giza, “Photon counting chirped AM Ladar: concept, simulation, and initial experimental results,” Proc. SPIE 6214, 62140P (2006).
[CrossRef]

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Ruff, W. C.

B. L. Stann, W. C. Ruff, and Z. G. Sztankay, “Intensity-modulated diode laser radar using frequency modulation/continuous wave ranging techniques,” Opt. Eng. 35, 3270–3278 (1996).
[CrossRef]

Shang, J. H.

Shaw, G. A.

G. A. Shaw, A. M. Siegel, J. Model, and A. Geboff, “Deep UV photon-counting detectors and applications,” Proc. SPIE 7320, 73200J (2009).
[CrossRef]

Siegel, A. M.

G. A. Shaw, A. M. Siegel, J. Model, and A. Geboff, “Deep UV photon-counting detectors and applications,” Proc. SPIE 7320, 73200J (2009).
[CrossRef]

Simon, D.

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Stann, B.

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

Stann, B. L.

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

B. L. Stann, W. C. Ruff, and Z. G. Sztankay, “Intensity-modulated diode laser radar using frequency modulation/continuous wave ranging techniques,” Opt. Eng. 35, 3270–3278 (1996).
[CrossRef]

Stern, A.

A. Stern, D. Alonia, and B. Javidib, “An overview of 3D visualization with integral imaging in photon starved conditions,” Proc. SPIE 8384, 83840K (2012).
[CrossRef]

Sudharsanan, R.

P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
[CrossRef]

Sztankay, Z. G.

B. L. Stann, W. C. Ruff, and Z. G. Sztankay, “Intensity-modulated diode laser radar using frequency modulation/continuous wave ranging techniques,” Opt. Eng. 35, 3270–3278 (1996).
[CrossRef]

Wu, E.

Wu, G.

Yang, F.

Yuan, P.

P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
[CrossRef]

Zeng, H. P.

Appl. Opt. (3)

IEEE Trans. Acoust. Speech Signal Process. (1)

T. J. Abatzoglou, “A fast maximum likelihood algorithm for frequency estimation of a sinusoid based on Newton’s method,” IEEE Trans. Acoust. Speech Signal Process. 33, 77–89 (1985).
[CrossRef]

IEEE Trans. Signal Process. (1)

B. G. Quinn, “Estimating frequency by interpolation using Fourier coefficients,” IEEE Trans. Signal Process. 42, 1264–1268 (1994).
[CrossRef]

IEEE Trans. Speech Audio Process. (1)

A. Choi, “Real-time fundamental frequency estimation by least-square fitting,” IEEE Trans. Speech Audio Process. 5, 201–205 (1997).
[CrossRef]

Microw. Opt. Technol. Lett. (1)

W. Ruff, K. Aliberti, M. Giza, W. Potter, B. Redman, and B. Stann, “Translational Doppler detection using a direct-detection chirp amplitude modulated laser radar,” Microw. Opt. Technol. Lett. 43, 358–363 (2004).
[CrossRef]

Opt. Eng. (1)

B. L. Stann, W. C. Ruff, and Z. G. Sztankay, “Intensity-modulated diode laser radar using frequency modulation/continuous wave ranging techniques,” Opt. Eng. 35, 3270–3278 (1996).
[CrossRef]

Opt. Express (2)

Proc. SPIE (5)

P. Yuan, R. Sudharsanan, X. G. Bai, J. Boisvert, P. McDonald, and E. Labios, “Geiger-mode LADAR cameras,” Proc. SPIE 8037, 803712 (2011).
[CrossRef]

G. A. Shaw, A. M. Siegel, J. Model, and A. Geboff, “Deep UV photon-counting detectors and applications,” Proc. SPIE 7320, 73200J (2009).
[CrossRef]

A. Stern, D. Alonia, and B. Javidib, “An overview of 3D visualization with integral imaging in photon starved conditions,” Proc. SPIE 8384, 83840K (2012).
[CrossRef]

B. Redman, W. Ruff, and M. Giza, “Photon counting chirped AM Ladar: concept, simulation, and initial experimental results,” Proc. SPIE 6214, 62140P (2006).
[CrossRef]

B. L. Stann, A. Abou-Auf, K. Aliberti, J. Dammann, M. Giza, G. Dang, G. Ovrebo, B. Redman, W. Ruff, and D. Simon, “Research progress on a focal plane array ladar system using chirped amplitude modulation,” Proc. SPIE 5086, 47–57 (2003).
[CrossRef]

Other (1)

L. E. Drain, The Laser Doppler Technique (Wiley, 1980), p. 146.

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Figures (6)

Fig. 1.
Fig. 1.

Operational principle diagram. The solid line is the electrical signal and the dashed line is the computer processing flow. All computer processing steps are shown in the dashed (blue) box (LPF, low pass filter; LO-I, the local oscillator signal-I; LO-II, the local oscillator signal-II; FFT, fast Fourier transform).

Fig. 2.
Fig. 2.

Schematic diagram of the echo signal in the IF spectrum. X is the true peak of the IF signal, and A, B, C, D, and E are the discrete measurement data of the IF signal, whose frequency interval δω corresponds to the range interval δR. The (blue) dashed line is the envelope of the whole IF signal.

Fig. 3.
Fig. 3.

Fine range value obtained by the phase method. The discrete measurement data of the IF spectrum A, B, C, D, and E can tell the true peak X in which interval by WCLA, but cannot tell the exact position of X in this interval. The exact position X can be obtained by the phase ranging method.

Fig. 4.
Fig. 4.

Simulation results. 30003030m is a whole range interval in the IF spectrum for the modulation bandwidth B=5MHz. The initial frequency f0=B=5MHz is for ΔR=δR. (a) WCLA results. (b) PPPM results. (c) Comparison of the range error for WCLA and PPPM.

Fig. 5.
Fig. 5.

Schematic diagram of the fine range value selection. RX is the position of the target, the range interval δR produced by the IF spectrum equals the period ΔR of the PPPM. The (blue) dashed line is the probability distribution of the coarse range value, and the (red) solid line is the probability distribution of the fine range value that is of periodic repetition. When the coarse range value is in the A region, the true fine range value is selected out, or the false value will be produced.

Fig. 6.
Fig. 6.

Range accuracy and false detection probability of the system.

Equations (21)

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S(t)=rect(tT)cos[f0t+12kt2+ϕ0],
SIF(t)=SR(t)·SL(t)=MI0rect(tτ/2Tτ)cos[f0t+12kt2+ϕ0]cos[f0(tτ)+12k(tτ)2+ϕ0]=MI0rect(tτ/2Tτ)×12×{cos[f0τ+ktτ12kτ2]+cos[f0(2tτ)+kt2ktτ+12kτ2+2ϕ0]}.
SIF(ω)=F{SIF(t)}=A1F{rect(tτ/2Tτ)}*F{cos[ktτ+ϕ(τ)]}sinc(ω)*δ(ωkτ)sinc(ωkτ).
fIF|WCLA=m=lm=lPmωmm=lm=lPm.
Rcoarse=(fIF|WCLA/k)·c/2,
τcoarse=(fIF|WCLA/k)/2.
SIF(t)=MI0rect(tτ/2Tτ)×12×cos(f0τ+ktτ12kτ2)+ε(t),
SQ(t)=cos(kτcoarset),
SI(t)=cos(kτcoarset+π/2).
SIF(t)SQ(t)=1T0T[MI0rect(tτ/2Tτ)×12×cos(f0τ+ktτ12kτ2)+ε(t)]cos(kτcoarset)dt=1T0T12MI0cos[f0τ12kτ2+kt(ττcoarse)]dt+1T0T12MI0rect(tτ/2Tτ){cos[k(τ+τcoarse)t+f0τ12kτ2]}dt+1T0Tε(t)cos(kτcoarset)dt.
Q=12MI0cos(f0τ12kτ2).
I=12MI0sin(f0τ12kτ2).
tan(f0τ12kτ2)=I/Q.
Rfine=(f0τ)/π·ΔR+nΔR=(Δφ+12kτ2)/π·ΔR+nΔR(n=0,1,2,3,).
R={Rfine|n=0,1,2,}(RcoarseΔR/2,Rcoarse+ΔR/2).
δ2(Δφ1)=((Δφ1)IdI)2+((Δφ1)QdQ)2=(I/Q)2[1+(I/Q)2]2[(dII)2+(dQQ)2]={1π0πtan2(Δφ1)[1+tan2(Δφ1)]2d(Δφ1)}[(dII)2+(dQQ)2]=18[(1SNRI)2+(1SNRQ)2]=14·SNR2.
δ2(Δφ2)=[0Tkt(ττcoarse)dt]2=(0TktΔτdt)2=12kΔτT2.
δ2(12kτ2)=(d(12kτ2)dτ)2=(kτdτ)2.
δRfine=δ[Δφ+12kτ2k(ττ0)t]/π·δR=δ2(Δφ)+δ2(12kτ2)+δ2[ktΔτ]/π·δR=14·SNR2+(kτdτ)2+12kΔτT2/π·δR.
P(x)=12πδRcoarsee(xRx)22δRcoarse2.
Pfalse=12ΔR/212πδRcoarseex22δRcoarse2=erfc(ΔR22δRcoarse).

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