## Experimental verification of sparse frequency linearly frequency modulated ladar signals modeling |

Optics Express, Vol. 18, Issue 15, pp. 15400-15407 (2010)

http://dx.doi.org/10.1364/OE.18.015400

Acrobat PDF (1312 KB)

### Abstract

We present the results of an experiment designed to verify the results of a previously published theoretical model that predicts the range resolution and peak-to-side lobe ratio of sparse frequency linearly frequency modulated (SF-LFM) ladar signals. We use two ultra stable diode lasers which are frequency locked and can be current tuned in order to adjust the difference frequency between the two lasers. The results of the experiment verify the previously developed model proving that SF-LFM ladar signals have the ability to increase the range resolution of a ladar system without the need for larger bandwidth modulators. Finally we simulate a target at a range of approximately 150 meters through the use of a fiber optic delay line, and demonstrate the ability of SF-LFM ladar signals to detect a target at range.

© 2010 OSA

## 1. Introduction

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**(15), 3376–3386 (1999), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-15-3376. [CrossRef]

3. C. J. Karlsson, F. Å. A. Olsson, D. Letalick, and M. Harris, “All-Fiber Multifunction Continuous-Wave Coherent Laser Radar at 1.55 num for Range, Speed, Vibration, and Wind Measurements,” Appl. Opt. **39**(21), 3716–3726 (2000), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-21-3716. [CrossRef]

4. D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng. **44**(7), 74202–74205 (2005). [CrossRef]

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

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

8. W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett. **43**(24), 1387–1389 (2007). [CrossRef]

9. M. J. Lindenfeld, “Sparse Frequency Transmit and Receive Waveform Design,” IEEE Trans. Aerosp. Electron. Syst. **40**(3), 851–861 (2004). [CrossRef]

10. R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Sparse frequency LFM ladar signals,” Opt. Express **17**(10), 8302–8309 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8302. [CrossRef] [PubMed]

10. R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Sparse frequency LFM ladar signals,” Opt. Express **17**(10), 8302–8309 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8302. [CrossRef] [PubMed]

*I*is the intensity of each of the superimposed chirped lasers, which were assumed to be equal in the model,

*I*is the intensity of the local oscillator which is assumed to be much greater than

_{LO}*I*,

*B*is the chirp bandwidth of the modulator,

*T*is the pulse duration,

*f*is the optical carrier frequency,

_{o}*df*is the difference frequency between the laser lines, and

*τ*is the signal time delay [10

10. R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Sparse frequency LFM ladar signals,” Opt. Express **17**(10), 8302–8309 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8302. [CrossRef] [PubMed]

**17**(10), 8302–8309 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8302. [CrossRef] [PubMed]

11. R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Multiple chirp sparse frequency LFM ladar signals,” Proc. SPIE **7323**, 73230N (2009). [CrossRef]

*δτ*) which was measured at the −3dB point. The numerical model also calculates the PSRL of the matched filter output, determined by the ratio of the value of the largest side lobe divided by the central peak value. The range resolution δR, determined by the relationship,was calculated as the model steps through difference frequencies in 1MHz increments [10

**17**(10), 8302–8309 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8302. [CrossRef] [PubMed]

## 2. Experimental setup

*df*) to be monitored in real time. One of the outputs from the bottom splitter (the stationary laser line) is split again so one leg can be used as the local oscillator (LO). This leaves one fiber with each laser line propagating in it; these fibers are then coupled together and sent through the AOM, which has a linear frequency ramp applied to it, producing the desired dual chirp SF-LFM signal. The signal is then coupled with the LO allowing for the heterodyne mixing to occur, and then the heterodyned signal is coupled to the other photodiode. Just as with the other photodiode the output is coupled to the digitizer. The output of the digitizer is recorded and processed to determine the range resolution and the PSLR.

## 3. Verification of range resolution and PSLR modeling

*df*> 23MHz, but there are significant discrepancies in the region where

*df*< 23MHz. Unlike in Fig. 2a, Fig. 2b shows that the data matches the theory extremely well regardless of the difference frequency.

*df*< 23MHz) that the PSLR has a large oscillatory component, See Fig. 3a . The reason for the oscillation is that the symmetric delta-functions are the dominant side lobe peaks and they have amplitudes that rapidly change in this region. When the chirped bandwidths do not overlap (

*df*> 23MHz) the symmetric delta function amplitudes decrease below the amplitudes of the second peak of the central sinc function, which is a smoothly varying function of difference frequency. Since the symmetric delta functions in Eq. (1) have no effect on the FWHM of the central sinc function, it is no surprise that the range resolution shown in Fig. 3b was unchanged by the modifications to the model.

## 4. Target Simulation (~1µs Delay)

## 5. Conclusion and Outlook

11. R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Multiple chirp sparse frequency LFM ladar signals,” Proc. SPIE **7323**, 73230N (2009). [CrossRef]

## Acknowledgments

## References and links

1. | N. Levenon, and E. Mozeson, |

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. |

3. | C. J. Karlsson, F. Å. A. Olsson, D. Letalick, and M. Harris, “All-Fiber Multifunction Continuous-Wave Coherent Laser Radar at 1.55 num for Range, Speed, Vibration, and Wind Measurements,” Appl. Opt. |

4. | D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng. |

5. | N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt. |

6. | R. L. Lucke, “Fundamentals of Wide-Field Sparse-Aperture Imaging,” in 2001 IEEE Aerospace Conference Proceedings (Institute of Electrical and Electronics Engineers, Big Sky,” Montana (March): 10–17 (2001). |

7. | P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett. |

8. | W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett. |

9. | M. J. Lindenfeld, “Sparse Frequency Transmit and Receive Waveform Design,” IEEE Trans. Aerosp. Electron. Syst. |

10. | R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Sparse frequency LFM ladar signals,” Opt. Express |

11. | R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Multiple chirp sparse frequency LFM ladar signals,” Proc. SPIE |

12. | R. V. Chimenti, E. S. Bailey, R. V. Dierking, M. P. Powers, P. E. Haus, and J. W. Haus, “A review of sparse frequency linearly frequency modulated (SF-LFM) laser radar signal modeling with preliminary experimental results,” 15th Coherent Laser Radar Conference (2009). |

13. | R. V. Chimenti, “Sparse Frequency Linear Frequency Modulated Laser Radar Signal Generation, Detection, and Processing,” M. S. Thesis (University of Dayton, Dayton, OH, 2009). |

**OCIS Codes**

(040.2840) Detectors : Heterodyne

(280.3400) Remote sensing and sensors : Laser range finder

**ToC Category:**

Remote Sensing

**History**

Original Manuscript: February 8, 2010

Revised Manuscript: June 17, 2010

Manuscript Accepted: June 23, 2010

Published: July 6, 2010

**Citation**

Robert V. Chimenti, Matthew P. Dierking, Peter E. Powers, Joseph W. Haus, and Eric S. Bailey, "Experimental verification of sparse frequency linearly frequency modulated ladar signals modeling," Opt. Express **18**, 15400-15407 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-15-15400

Sort: Year | Journal | Reset

### References

- N. Levenon and E. Mozeson, Radar Signals, (Wiley-Interscience, 2004).
- 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(15), 3376–3386 (1999), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-15-3376 . [CrossRef]
- C. J. Karlsson, F. Å. A. Olsson, D. Letalick, and M. Harris, “All-Fiber Multifunction Continuous-Wave Coherent Laser Radar at 1.55 num for Range, Speed, Vibration, and Wind Measurements,” Appl. Opt. 39(21), 3716–3726 (2000), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-21-3716 . [CrossRef]
- D. Nordin and K. Hyyppa, “Using a discrete thermal model to obtain a linear frequency ramping in a FMCW system,” Opt. Eng. 44(7), 74202–74205 (2005). [CrossRef]
- N. J. Miller, M. P. Dierking, and B. D. Duncan, “Optical sparse aperture imaging,” Appl. Opt. 46(23), 5933–5943 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ao-46-23-5933 . [CrossRef] [PubMed]
- R. L. Lucke, “Fundamentals of Wide-Field Sparse-Aperture Imaging,” in 2001 IEEE Aerospace Conference Proceedings (Institute of Electrical and Electronics Engineers, Big Sky,” Montana (March): 10–17 (2001).
- P. de Groot and J. McGarvey, “Chirped synthetic-wavelength interferometry,” Opt. Lett. 17(22), 1626–1628 (1992), http://www.opticsinfobase.org/abstract.cfm?URI=ol-17-22-1626 . [CrossRef] [PubMed]
- W. X. Liu, M. Lesturgie, and Y. L. Lu, “Real-time sparse frequency waveform design for HFSWR system,” Electron. Lett. 43(24), 1387–1389 (2007). [CrossRef]
- M. J. Lindenfeld, “Sparse Frequency Transmit and Receive Waveform Design,” IEEE Trans. Aerosp. Electron. Syst. 40(3), 851–861 (2004). [CrossRef]
- R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Sparse frequency LFM ladar signals,” Opt. Express 17(10), 8302–8309 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-10-8302 . [CrossRef] [PubMed]
- R. V. Chimenti, M. P. Dierking, P. E. Powers, and J. W. Haus, “Multiple chirp sparse frequency LFM ladar signals,” Proc. SPIE 7323, 73230N (2009). [CrossRef]
- R. V. Chimenti, E. S. Bailey, R. V. Dierking, M. P. Powers, P. E. Haus, and J. W. Haus, “A review of sparse frequency linearly frequency modulated (SF-LFM) laser radar signal modeling with preliminary experimental results,” 15th Coherent Laser Radar Conference (2009).
- R. V. Chimenti, “Sparse Frequency Linear Frequency Modulated Laser Radar Signal Generation, Detection, and Processing,” M. S. Thesis (University of Dayton, Dayton, OH, 2009).

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.