Abstract

Through modeling we explored the possibility of utilizing a sparse frequency linear frequency modulation (LFM) signal for laser radar (ladar) applications. We propose a potential transmit and receive experiment utilizing the superposition of two LFM laser sources with a known difference frequency to provide the necessary segmented bandwidth. Finally we analyzed the signal performance of the proposed system showing that the range resolution of the signal can be improved by two to three times while utilizing the same modulator bandwidth as that of a continuous LFM signal.

©2009 Optical Society of America

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References

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  1. N. Levenon and E. Mozeson, Radar Signals, (Wiley-Interscience, NY, 2004).
    [Crossref]
  2. J. M. Senior, Optical Fiber Communications Principles and Practice 2nd ed., (Prentice Hall, NJ, 1992).
    [PubMed]
  3. D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” J. Lightwave Technol.  24, 12–21 (2006). http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-1-12.
    [Crossref]
  4. M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3×3 fiber-optic couplers,” Opt. Lett.  28, 2162–2164 (2003). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-22-2162.
    [Crossref] [PubMed]
  5. C. Weidong, X. Shanjia, W. Dongjin, and L. Falin, “Range Performance Analysis in Linear FMCW Radar,” in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, 654–657 (2000).
  6. A. G. Stove, “Linear FMCW Radar Techniques,” in IEE Proceedings F (Radar and Signal Processing) 139, 343–350 (1992).
  7. 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, 3376–3386 (1999).
    [Crossref]
  8. D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng.  44, 74202–74205 (2005).
    [Crossref]
  9. N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.  46, 5933–5943 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-23-5933
    [Crossref] [PubMed]
  10. R. L. Lucke, “Fundamentals of Wide-Field Sparse-Aperture Imaging,” in 2001 IEEE Aerospace Conference Proceedings  3, 1401–1419 (2001).
  11. P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett.  17, 1626–1628 (1992). http://www.opticsinfobase.org/abstract.cfm?URI=ol-17-22-1626
    [Crossref] [PubMed]
  12. W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett.  43, 1387–1389 (2007).
    [Crossref]
  13. M. J. Lindenfeld, “Sparse Frequency Transmit and Receive Waveform Design,” IEEE Trans. Aerosp. Electron. Syst.  40, 851–860 (2004).
    [Crossref]
  14. P. M. Woodward, Probability and Information Theory, with Applications to Radar, (Pergamon Press, Oxford1953).
  15. J. W. Goodman, Statistical Optics 1st ed., (Wiley-Interscience, 1985).
    [PubMed]
  16. A. Freedman and N. Levanon, “Properties of the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  30, 938–941 (1994).
    [Crossref]
  17. B. Getz and N. Levanon, “Weight effects on the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  31, 182–193 (1995).
    [Crossref]
  18. J. W. Goodman, Introduction to Fourier Optics 3rd ed., (Roberts & Company, NY, 2005).

2007 (2)

N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.  46, 5933–5943 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-23-5933
[Crossref] [PubMed]

W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett.  43, 1387–1389 (2007).
[Crossref]

2006 (1)

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” J. Lightwave Technol.  24, 12–21 (2006). http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-1-12.
[Crossref]

2005 (2)

D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng.  44, 74202–74205 (2005).
[Crossref]

J. W. Goodman, Introduction to Fourier Optics 3rd ed., (Roberts & Company, NY, 2005).

2004 (1)

M. J. Lindenfeld, “Sparse Frequency Transmit and Receive Waveform Design,” IEEE Trans. Aerosp. Electron. Syst.  40, 851–860 (2004).
[Crossref]

2003 (1)

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3×3 fiber-optic couplers,” Opt. Lett.  28, 2162–2164 (2003). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-22-2162.
[Crossref] [PubMed]

2001 (1)

R. L. Lucke, “Fundamentals of Wide-Field Sparse-Aperture Imaging,” in 2001 IEEE Aerospace Conference Proceedings  3, 1401–1419 (2001).

2000 (1)

C. Weidong, X. Shanjia, W. Dongjin, and L. Falin, “Range Performance Analysis in Linear FMCW Radar,” in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, 654–657 (2000).

1999 (1)

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, 3376–3386 (1999).
[Crossref]

1995 (1)

B. Getz and N. Levanon, “Weight effects on the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  31, 182–193 (1995).
[Crossref]

1994 (1)

A. Freedman and N. Levanon, “Properties of the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  30, 938–941 (1994).
[Crossref]

1992 (1)

P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett.  17, 1626–1628 (1992). http://www.opticsinfobase.org/abstract.cfm?URI=ol-17-22-1626
[Crossref] [PubMed]

Choma, M. A.

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3×3 fiber-optic couplers,” Opt. Lett.  28, 2162–2164 (2003). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-22-2162.
[Crossref] [PubMed]

de Groot, P.

P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett.  17, 1626–1628 (1992). http://www.opticsinfobase.org/abstract.cfm?URI=ol-17-22-1626
[Crossref] [PubMed]

Dierking, M. P.

N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.  46, 5933–5943 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-23-5933
[Crossref] [PubMed]

Dongjin, W.

C. Weidong, X. Shanjia, W. Dongjin, and L. Falin, “Range Performance Analysis in Linear FMCW Radar,” in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, 654–657 (2000).

Duncan, B. D.

N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.  46, 5933–5943 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-23-5933
[Crossref] [PubMed]

Falin, L.

C. Weidong, X. Shanjia, W. Dongjin, and L. Falin, “Range Performance Analysis in Linear FMCW Radar,” in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, 654–657 (2000).

Freedman, A.

A. Freedman and N. Levanon, “Properties of the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  30, 938–941 (1994).
[Crossref]

Getz, B.

B. Getz and N. Levanon, “Weight effects on the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  31, 182–193 (1995).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics 3rd ed., (Roberts & Company, NY, 2005).

J. W. Goodman, Statistical Optics 1st ed., (Wiley-Interscience, 1985).
[PubMed]

Hyyppa, K.

D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng.  44, 74202–74205 (2005).
[Crossref]

Izatt, J. A.

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3×3 fiber-optic couplers,” Opt. Lett.  28, 2162–2164 (2003). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-22-2162.
[Crossref] [PubMed]

Karlsson, C. J.

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, 3376–3386 (1999).
[Crossref]

Katoh, K.

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” J. Lightwave Technol.  24, 12–21 (2006). http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-1-12.
[Crossref]

Kikuchi, K.

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” J. Lightwave Technol.  24, 12–21 (2006). http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-1-12.
[Crossref]

Lesturgie, M.

W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett.  43, 1387–1389 (2007).
[Crossref]

Levanon, N.

B. Getz and N. Levanon, “Weight effects on the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  31, 182–193 (1995).
[Crossref]

A. Freedman and N. Levanon, “Properties of the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  30, 938–941 (1994).
[Crossref]

Levenon, N.

N. Levenon and E. Mozeson, Radar Signals, (Wiley-Interscience, NY, 2004).
[Crossref]

Lindenfeld, M. J.

M. J. Lindenfeld, “Sparse Frequency Transmit and Receive Waveform Design,” IEEE Trans. Aerosp. Electron. Syst.  40, 851–860 (2004).
[Crossref]

Liu, W. X.

W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett.  43, 1387–1389 (2007).
[Crossref]

Lu, Y. L.

W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett.  43, 1387–1389 (2007).
[Crossref]

Lucke, R. L.

R. L. Lucke, “Fundamentals of Wide-Field Sparse-Aperture Imaging,” in 2001 IEEE Aerospace Conference Proceedings  3, 1401–1419 (2001).

Ly-Gagnon, D. S.

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” J. Lightwave Technol.  24, 12–21 (2006). http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-1-12.
[Crossref]

McGarvey, J.

P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett.  17, 1626–1628 (1992). http://www.opticsinfobase.org/abstract.cfm?URI=ol-17-22-1626
[Crossref] [PubMed]

Miller, N. J.

N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.  46, 5933–5943 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-23-5933
[Crossref] [PubMed]

Mozeson, E.

N. Levenon and E. Mozeson, Radar Signals, (Wiley-Interscience, NY, 2004).
[Crossref]

Nordin, D.

D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng.  44, 74202–74205 (2005).
[Crossref]

Olsson, F. Å. A.

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, 3376–3386 (1999).
[Crossref]

Senior, J. M.

J. M. Senior, Optical Fiber Communications Principles and Practice 2nd ed., (Prentice Hall, NJ, 1992).
[PubMed]

Shanjia, X.

C. Weidong, X. Shanjia, W. Dongjin, and L. Falin, “Range Performance Analysis in Linear FMCW Radar,” in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, 654–657 (2000).

Stove, A. G.

A. G. Stove, “Linear FMCW Radar Techniques,” in IEE Proceedings F (Radar and Signal Processing) 139, 343–350 (1992).

Tsukamoto, S.

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” J. Lightwave Technol.  24, 12–21 (2006). http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-1-12.
[Crossref]

Weidong, C.

C. Weidong, X. Shanjia, W. Dongjin, and L. Falin, “Range Performance Analysis in Linear FMCW Radar,” in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, 654–657 (2000).

Woodward, P. M.

P. M. Woodward, Probability and Information Theory, with Applications to Radar, (Pergamon Press, Oxford1953).

Yang, C.

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3×3 fiber-optic couplers,” Opt. Lett.  28, 2162–2164 (2003). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-22-2162.
[Crossref] [PubMed]

Appl. Opt (2)

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, 3376–3386 (1999).
[Crossref]

N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt.  46, 5933–5943 (2007). http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-23-5933
[Crossref] [PubMed]

Electron. Lett (1)

W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett.  43, 1387–1389 (2007).
[Crossref]

IEEE Trans. Aerosp. Electron. Syst (3)

M. J. Lindenfeld, “Sparse Frequency Transmit and Receive Waveform Design,” IEEE Trans. Aerosp. Electron. Syst.  40, 851–860 (2004).
[Crossref]

A. Freedman and N. Levanon, “Properties of the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  30, 938–941 (1994).
[Crossref]

B. Getz and N. Levanon, “Weight effects on the periodic ambiguity function,” IEEE Trans. Aerosp. Electron. Syst.  31, 182–193 (1995).
[Crossref]

J. Lightwave Technol (1)

D. S. Ly-Gagnon, S. Tsukamoto, K. Katoh, and K. Kikuchi, “Coherent Detection of Optical Quadrature Phase-Shift Keying Signals With Carrier Phase Estimation,” J. Lightwave Technol.  24, 12–21 (2006). http://www.opticsinfobase.org/JLT/abstract.cfm?URI=JLT-24-1-12.
[Crossref]

Opt. Eng (1)

D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng.  44, 74202–74205 (2005).
[Crossref]

Opt. Lett (2)

M. A. Choma, C. Yang, and J. A. Izatt, “Instantaneous quadrature low-coherence interferometry with 3×3 fiber-optic couplers,” Opt. Lett.  28, 2162–2164 (2003). http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-28-22-2162.
[Crossref] [PubMed]

P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett.  17, 1626–1628 (1992). http://www.opticsinfobase.org/abstract.cfm?URI=ol-17-22-1626
[Crossref] [PubMed]

Other (8)

C. Weidong, X. Shanjia, W. Dongjin, and L. Falin, “Range Performance Analysis in Linear FMCW Radar,” in 2nd International Conference on Microwave and Millimeter Wave Technology Proceedings, 654–657 (2000).

A. G. Stove, “Linear FMCW Radar Techniques,” in IEE Proceedings F (Radar and Signal Processing) 139, 343–350 (1992).

N. Levenon and E. Mozeson, Radar Signals, (Wiley-Interscience, NY, 2004).
[Crossref]

J. M. Senior, Optical Fiber Communications Principles and Practice 2nd ed., (Prentice Hall, NJ, 1992).
[PubMed]

J. W. Goodman, Introduction to Fourier Optics 3rd ed., (Roberts & Company, NY, 2005).

R. L. Lucke, “Fundamentals of Wide-Field Sparse-Aperture Imaging,” in 2001 IEEE Aerospace Conference Proceedings  3, 1401–1419 (2001).

P. M. Woodward, Probability and Information Theory, with Applications to Radar, (Pergamon Press, Oxford1953).

J. W. Goodman, Statistical Optics 1st ed., (Wiley-Interscience, 1985).
[PubMed]

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Figures (5)

Fig. 1.
Fig. 1. Normalized power spectral density (PSD) of sparse frequency LFM signal.
Fig. 2.
Fig. 2. Schematic setup for sparse frequency LFM chirped signal generation, detection and processing.
Fig. 3.
Fig. 3. Comparison of numeric and analytic representation of the ambiguity function. (a) Full range, (b) Left peak, (c) Center peak, (d) Right peak.
Fig. 4.
Fig. 4. (a) PSLR of sparse frequency LFM chirped signal, (b) PSLR of standard LFM chirp signal, (c) Range resolution of the sparse frequency LFM chirped signal, (d) Range resolution of a standard LFM chirp signal.
Fig. 5.
Fig. 5. Autocorrelation function (dB) plotted verses difference frequency.

Equations (14)

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s(t)0T=A˜1ei(2π(f+fo)t+12βt2)+A˜2ei(2π(f+fo+df)t+12βt2)+A˜LOei2πft2,
s(t)0TILO +[A˜A˜LO*ei(2πfot+12βt2)+A˜A˜LO*ei(2π(fo+df)t+12βt2)+c.c.],
u(t)0TA˜ A˜LO* [ei(2πfot+12βt2)+ei(2π(fo+df)t+12βt2)] .
χ(τ,υ)=u(t)u*(t+τ)ei2πυtdt,
U(f)=A˜A˜LO* {πβ ei2π2β(ffo)2 πβ(ffo)πβ(Tπβ(ffo)) eiπ2u2 du
+πβ ei2π2β(ffodf)2 πβ(fo+dff)πβ(Tπβ(ffodf)) eiπ2u2 du } .
U(f)A˜A˜LO*{i2πβei2π2β(ffo)2rect(f(fo+B2)B)+i2πβei2π2β(ffodf)2rect(f(fo+df+B2)B)} .
PSDU(f)=I×ILOB[rect(f(fo+B2)B)+rect(f(fo+df+B2)B)
+2cos(2πTdfBfπTdfB(2fo+df))
×{rect(f(fo+Bdf2)B)0,ifdf>B,ifdfB
χ(τ)=I×ILOsinc() ei2π(fo+B2)τ (1+ei2πdfτ) +
BdfB [δ(τ+TdfB)+δ(τTdfB)]ei2π2dfB(df+2fo)τ
{sinc((Bdf)τ)ei2πi(fo+B+df2)τ0,ifdf>B , if df B .
δR=δτ×c2 .

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