## Resolving range ambiguity in a photon counting depth imager operating at kilometer distances

Optics Express, Vol. 18, Issue 9, pp. 9192-9206 (2010)

http://dx.doi.org/10.1364/OE.18.009192

Acrobat PDF (3501 KB)

### Abstract

Time-correlated single-photon counting techniques have recently been used in ranging and depth imaging systems that are based on time-of-flight measurements. These systems transmit low average power pulsed laser signals and measure the scattered return photons. The use of periodic laser pulses means that absolute ranges can only be measured unambiguously at low repetition rates (typically <100 kHz for > 1 km) to ensure that only one pulse is in transit at any instant. We demonstrate the application of a pseudo-random pattern matching technique to a scanning rangefinder system using GHz base clock rates, permitting the acquisition of unambiguous, three-dimensional images at average pulse rates equivalent to >10 MHz. Depth images with centimeter distance uncertainty at ranges between 50 m and 4.4 km are presented.

© 2010 OSA

## 1. Introduction

9. C. Ho, K. L. Albright, A. W. Bird, J. Bradley, D. E. Casperson, M. Hindman, W. C. Priedhorsky, W. R. Scarlett, R. C. Smith, J. Theiler, and S. K. Wilson, “Demonstration of literal three-dimensional imaging,” Appl. Opt. **38**(9), 1833–1840 (1999). [CrossRef]

11. J. Massa, G. Buller, A. Walker, G. Smith, S. Cova, M. Umasuthan, and A. Wallace, “Optical design and evaluation of a three-dimensional imaging and ranging system based on time-correlated single-photon counting,” Appl. Opt. **41**(6), 1063–1070 (2002). [CrossRef] [PubMed]

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. **48**(32), 6241–6251 (2009). [CrossRef] [PubMed]

*d*, is simply that range which permits only one optical pulse in transit at one time. For a repetition rate

_{Rep}*f*, this corresponds to [Eq. (1)]:where

_{Rep}*c*is the speed of light in vacuum. In the measurements described in [12

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. **48**(32), 6241–6251 (2009). [CrossRef] [PubMed]

*π*phase shifts to the output wave (phase-coding pulse compression). Implementation of random pattern approaches has also been demonstrated in lidar systems and usually comprises direct on/off-modulation of the outgoing light beam according to a digital random bit stream. Takeuchi et al. investigated this method, using a continuous wave laser with external optical modulator [16

16. N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. **22**(9), 1382–1386 (1983). [CrossRef] [PubMed]

17. N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. **25**(1), 63–67 (1986). [CrossRef] [PubMed]

*b*bits, sampled with a clock rate

*f*, is

_{Sample}*b/f*. To allow for unambiguous range resolution, target return photons must complete their target round-trip within this time, resulting in an unambiguous range

_{Sample}*d*[Eq. (2)]:

_{Nonrep}*b*, the length of the repeated pattern, rather than decreasing the average repetition rate of the source, as necessary in the periodic case. Without additional processing, correlations between single target return histogram peaks and every 1-bit throughout the bit stream impose a base correlation level against which an actual, wanted correlation between all target return photon events of an object with a lower return intensity and the bit stream has to stand out. Given the large variation in return intensities of different target materials, typically varying by several orders of magnitude, this effect would severely limit a system's capability to resolve low-return targets in the presence of other high-intensity returns.

## 2. System description

12. A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. **48**(32), 6241–6251 (2009). [CrossRef] [PubMed]

*f*/2.8 camera objective was used as the system objective.

**48**(32), 6241–6251 (2009). [CrossRef] [PubMed]

19. R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express **13**(26), 10846–10853 (2005). [CrossRef] [PubMed]

20. R. E. Warburton, A. McCarthy, A. M. Wallace, S. Hernandez-Marin, R. H. Hadfield, S. W. Nam, and G. S. Buller, “Subcentimeter depth resolution using a single-photon counting time-of-flight laser ranging system at 1550 nm wavelength,” Opt. Lett. **32**(15), 2266–2268 (2007). [CrossRef] [PubMed]

^{7}s

^{−1}.

## 3. Experiment

### 3.1. Pseudo-random modulation setup

18. P. A. Hiskett, C. S. Parry, A. McCarthy, and G. S. Buller, “A photon-counting time-of-flight ranging technique developed for the avoidance of range ambiguity at gigahertz clock rates,” Opt. Express **16**(18), 13685–13698 (2008). [CrossRef] [PubMed]

*d*of 7372.8 m) before being re-synchronized by a trigger pulse, and did not cause any noticeable temporal broadening effects. Future experiments may require temporal synchronization of the source and detection hardware.

_{Nonrep}### 3.2. Data acquisition and evaluation

*d*. Processing software reads in the bit stream and constructs a reference histogram with the selected binning size, replacing each 1-bit with a pre-recorded instrumental temporal response shape dictated by the combined timing jitter of the photon detector and all other system components. Using this prepared histogram as a correlation reference significantly improves the system’s target resolution capability and depth uncertainty for registered target surfaces. Target returns in the recorded histogram will contain a shape of the same temporal characteristics, resulting in a symmetrical correlation shape with reduced relative sideband noise.

_{Nonrep}*n*, of both the synthesized reference histogram and the target return histograms, at a channel width

*t*(typically 16 ps in this setup), is given by Eq. (3):

_{Bin}*C*,

_{p}(i)*p*. Based on the reference histogram

*R(i)*and the target return

*H*, it is determined by element-wise multiplication of the DFT of

_{p}(i)*R*with the complex conjugate of the DFT of

*H*, according to the cross-correlation theorem [Eq. (4)]:

_{p}*F(R)*only needs to be calculated once at the beginning of the analysis routine and can be re-used for each pixel. The algorithm identifies the highest target correlation

*C*for every pixel, as shown in Fig. 3(b). The position of this maximum,

_{max,p}*i*, corresponds to the timing offset between reference and return, and therefore denotes the photon round-trip time. Additional target returns at other points in the correlation function now would still have to stand out against an elevated correlation noise level, caused by cross-correlation of the highest returns (in this case caused by optical back-reflections in the sensor) at wrong timing offsets, as illustrated in Fig. 3(b). The lower limit of this noise is

_{max,p}*C*, where

_{max,p}/L*L*is the number of laser trigger pulses in each bit stream: this limit is reached when triggers are distributed sparsely enough so that only one pulse contributes to the correlation noise at any given wrong time offset.

*R*in the time domain which correspond to expected back-reflections Fig. 3(c). The cross-correlation subsequently is re-calculated, so that both

*C*and its correlation noise are removed and additional, smaller returns are revealed Fig. 3(d). This process is repeated until the defined maximum number of target returns per pixel or a minimum correlation threshold is reached. Application of this technique is particularly beneficial for our scanning depth profiler, as the additional relay optics required for spatial steering of the transmit- and receive-channel cause a level of internal optical back-reflection which is far greater than that encountered in previous, less complex, photon counting time-of-flight ranging systems [21

_{max,p}21. G. S. Buller, R. D. Harkins, A. McCarthy, P. A. Hiskett, G. R. MacKinnon, G. R. Smith, R. Sung, A. M. Wallace, R. A. Lamb, K. A. Ridley, and J. G. Rarity, “A multiple wavelength time-of-flight sensor based on time-correlated single-photon counting,” Rev. Sci. Instrum. **76**(8), 083112 (2005). [CrossRef]

22. J. S. Massa, A. M. Wallace, G. S. Buller, S. J. Fancey, and A. C. Walker, “Laser depth measurement based on time-correlated single-photon counting,” Opt. Lett. **22**(8), 543–545 (1997). [CrossRef] [PubMed]

## 4. Modeling predictions

### 4.1 Numerical simulation

^{4}s

^{−1}at 575 m and 6.10 × 10

^{4}s

^{−1}at 325 m for outgoing pulse rates of 7 × 10

^{6}s

^{−1}. The simulated base clock rate was 2 GHz, with a histogram binning size of 16 ps and pseudo-random bit stream lengths of 16 kbit and 64 kbit (corresponding to 1228.8 m and 4915.2 m maximum unambiguous distance, respectively). Ambiguous, periodic ranging at the same laser pulse rate was simulated with a 286 bit stream containing a single 1-bit. It must be noted that the current iteration of the system would not be able to process periodic illumination ranging information at this rate, as the number of trigger pulses to be processed by the TCSPC hardware would be in excess of its maximum data throughput of 5 × 10

^{6}s

^{−1}.

23. W. P. Cole, M. A. Marciniak, and M. B. Haeri, “Atmospheric-turbulence-effects correction factors for the laser range equation,” Opt. Eng. **47**(12), 126001 (2008). [CrossRef]

### 4.2 Atmospheric modeling

**48**(32), 6241–6251 (2009). [CrossRef] [PubMed]

*n*, and the average number of background noise photons per channel,

_{p}*n*[Eq. (5)]:

_{b}*n*for a given acquisition time

_{b}*t*is determined based on the average background count rate,

_{Acq}*r*, [Eq. (6)]

_{BG}*d*[Eq. (7)]:

*P*is the average output power of the depth profiler at the illumination wavelength λ and

_{Out}*h*is Planck’s constant. The atmospheric attenuation coefficient

*α*was determined with the MODTRAN software package [24]. Transmission factors

_{Mod}*T*,

_{Lens}*T*and

_{Trans}*T*take into account the loss in photons caused by the system objective and the remaining transceiver components in both directions of travel, and the back scattering properties of the target material, respectively. The detector response coefficient DRC converts the number of returned photons into the number of photons in the highest bin of the detector response and is based on the temporal detector output shape and the employed binning width.

_{Mat}*a priori*-knowledge about the output signal shape, the required SNR of each individual peak is drastically decreased and will vary for each employed bit stream. The application of the peak removal technique described in section 3.2 furthermore alters the return signal shape during the analysis process.

**48**(32), 6241–6251 (2009). [CrossRef] [PubMed]

## 5. Results

### 5.1. Distance determination

*d*dependency [compare Eq. (7)]. These effects, combined with the increased susceptibility to atmospheric turbulence and other non-homogenous distortion effects in turbid environments pose a challenge to all optical depth profiling systems in terms of both spatial and depth resolution at extended target distances, particularly at kilometer ranges. Figure 8 shows a scan of the upper half of a target board covered with retro-reflective material at a distance of 4.4 km. A thick-junction SPAD was used to measure target returns based on a 96 kbit pattern at a base clock rate of 2 GHz (

^{−2}*d*= 7372.8 m). The chosen angle between adjacent depth pixels of approximately 37.8 µrad horizontally and 138.2 µrad vertically correspond to spatial translations at the target of 166.8 mm and 610.0 mm, respectively. Scans were performed with per-pixel dwell times of 0.5 s and 1 s, and a depth uncertainty estimate was calculated based on the matrix norm of the depth residuals of a plane fitted to the range information of the two front surfaces of the target. Pixel-to-pixel depth errors of 25.1 mm (0.5 s dwell time) and 15.1 mm (1 s dwell time) were determined with this method.

_{Nonrep}### 5.2. Segmented target separation

*d*or

_{Nonrep}*d*, their relative positioning is unclear, as the surface which is further away from the observer might be assigned to the next time-of-flight period and consequently be displayed in front of the closer surface. The ability to reliably resolve much higher target separations for example becomes critical in cluttered scenes, as commonly encountered in urban scenarios.

_{Rep}*d*of 1228.8 m. Scans of the same scene with pattern lengths of 64 kbit (

_{Nonrep}*d*= 4915.2 m) were also successfully acquired, but required reduction of the TCSPC timing resolution from 16 ps to 128 ps bin width to maintain the same total number of pixels, due to memory restrictions. The applied 20 × 20 pixel pattern within a scanned field angle of 0.82 × 0.89 mrad corresponds to a horizontal pixel-to-pixel stepping of 41 µrad or 23.9 mm at the furthest target distance.

_{Nonrep}## 6. Conclusions

## Acknowledgments

## References and links

1. | W. Becker, |

2. | N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. |

3. | E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature |

4. | A. Cleary, A. Glidle, P. J. R. Laybourn, S. García-Blanco, S. Pellegrini, C. Helfter, G. S. Buller, J. S. Aitchison, and J. M. Cooper, “Integrating optics and microfluidics for time-correlated single-photon counting in lab-on-a-chip devices,” Appl. Phys. Lett. |

5. | J. J. Degnan, “Satellite Laser Ranging: Current Status and Future Prospects,” IEEE Trans. Geosci. Rem. Sens. |

6. | J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. |

7. | G. S. Buller and A. M. Wallace, “Ranging and Three-Dimensional Imaging Using Time-Correlated Single-Photon Counting and Point-by-Point Acquisition,” IEEE J. Sel. Top. Quantum Electron. |

8. | W. C. Priedhorsky, R. C. Smith, and C. Ho, “Laser ranging and mapping with a photon-counting detector,” Appl. Opt. |

9. | C. Ho, K. L. Albright, A. W. Bird, J. Bradley, D. E. Casperson, M. Hindman, W. C. Priedhorsky, W. R. Scarlett, R. C. Smith, J. Theiler, and S. K. Wilson, “Demonstration of literal three-dimensional imaging,” Appl. Opt. |

10. | R. M. Marino and W. R. Davis Jr., “Jigsaw: A Foliage-Penetrating 3D Imaging Laser Radar System,” Lincoln Lab. J. |

11. | J. Massa, G. Buller, A. Walker, G. Smith, S. Cova, M. Umasuthan, and A. Wallace, “Optical design and evaluation of a three-dimensional imaging and ranging system based on time-correlated single-photon counting,” Appl. Opt. |

12. | A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. |

13. | W. H. Long, D. H. Mooney, and W. A. Skillman, “Pulse Doppler Radar,” in |

14. | G. Trunk, and S. Brockett, “Range and velocity ambiguity resolution,” in |

15. | E. C. Farnett, and G. H. Stevens, “Pulse Compression Radar,” in |

16. | N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. |

17. | N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. |

18. | P. A. Hiskett, C. S. Parry, A. McCarthy, and G. S. Buller, “A photon-counting time-of-flight ranging technique developed for the avoidance of range ambiguity at gigahertz clock rates,” Opt. Express |

19. | R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express |

20. | R. E. Warburton, A. McCarthy, A. M. Wallace, S. Hernandez-Marin, R. H. Hadfield, S. W. Nam, and G. S. Buller, “Subcentimeter depth resolution using a single-photon counting time-of-flight laser ranging system at 1550 nm wavelength,” Opt. Lett. |

21. | G. S. Buller, R. D. Harkins, A. McCarthy, P. A. Hiskett, G. R. MacKinnon, G. R. Smith, R. Sung, A. M. Wallace, R. A. Lamb, K. A. Ridley, and J. G. Rarity, “A multiple wavelength time-of-flight sensor based on time-correlated single-photon counting,” Rev. Sci. Instrum. |

22. | J. S. Massa, A. M. Wallace, G. S. Buller, S. J. Fancey, and A. C. Walker, “Laser depth measurement based on time-correlated single-photon counting,” Opt. Lett. |

23. | W. P. Cole, M. A. Marciniak, and M. B. Haeri, “Atmospheric-turbulence-effects correction factors for the laser range equation,” Opt. Eng. |

24. | A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN 7,” Technical Note GL-TR-89–0122, available from Geophysics Laboratory/OPE, Air Force Systems Command, Hanscom AFB, Mass. (1989). |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(030.5290) Coherence and statistical optics : Photon statistics

(040.3780) Detectors : Low light level

(110.6880) Imaging systems : Three-dimensional image acquisition

(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation

(280.3400) Remote sensing and sensors : Laser range finder

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: February 23, 2010

Revised Manuscript: April 8, 2010

Manuscript Accepted: April 12, 2010

Published: April 16, 2010

**Citation**

Nils J. Krichel, Aongus McCarthy, and Gerald S. Buller, "Resolving range ambiguity in a photon counting depth imager operating at kilometer distances," Opt. Express **18**, 9192-9206 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-9-9192

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### References

- W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, Berlin, 2005).
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74(1), 145–195 (2002). [CrossRef]
- E. Knill, R. Laflamme, and G. J. Milburn, “A scheme for efficient quantum computation with linear optics,” Nature 409(6816), 46–52 (2001). [CrossRef] [PubMed]
- A. Cleary, A. Glidle, P. J. R. Laybourn, S. García-Blanco, S. Pellegrini, C. Helfter, G. S. Buller, J. S. Aitchison, and J. M. Cooper, “Integrating optics and microfluidics for time-correlated single-photon counting in lab-on-a-chip devices,” Appl. Phys. Lett. 91(7), 071123 (2007). [CrossRef]
- J. J. Degnan, “Satellite Laser Ranging: Current Status and Future Prospects,” IEEE Trans. Geosci. Rem. Sens. GE-23(4), 398–413 (1985). [CrossRef]
- J. J. Degnan, “Photon-counting multikilohertz microlaser altimeters for airborne and spaceborne topographic measurements,” J. Geodyn. 34(3-4), 503–549 (2002). [CrossRef]
- G. S. Buller and A. M. Wallace, “Ranging and Three-Dimensional Imaging Using Time-Correlated Single-Photon Counting and Point-by-Point Acquisition,” IEEE J. Sel. Top. Quantum Electron. 13(4), 1006–1015 (2007). [CrossRef]
- W. C. Priedhorsky, R. C. Smith, and C. Ho, “Laser ranging and mapping with a photon-counting detector,” Appl. Opt. 35(3), 441–452 (1996). [CrossRef] [PubMed]
- C. Ho, K. L. Albright, A. W. Bird, J. Bradley, D. E. Casperson, M. Hindman, W. C. Priedhorsky, W. R. Scarlett, R. C. Smith, J. Theiler, and S. K. Wilson, “Demonstration of literal three-dimensional imaging,” Appl. Opt. 38(9), 1833–1840 (1999). [CrossRef]
- R. M. Marino and W. R. Davis., “Jigsaw: A Foliage-Penetrating 3D Imaging Laser Radar System,” Lincoln Lab. J. 15, 23–36 (2005).
- J. Massa, G. Buller, A. Walker, G. Smith, S. Cova, M. Umasuthan, and A. Wallace, “Optical design and evaluation of a three-dimensional imaging and ranging system based on time-correlated single-photon counting,” Appl. Opt. 41(6), 1063–1070 (2002). [CrossRef] [PubMed]
- A. McCarthy, R. J. Collins, N. J. Krichel, V. Fernández, A. M. Wallace, and G. S. Buller, “Long-range time-of-flight scanning sensor based on high-speed time-correlated single-photon counting,” Appl. Opt. 48(32), 6241–6251 (2009). [CrossRef] [PubMed]
- W. H. Long, D. H. Mooney, and W. A. Skillman, “Pulse Doppler Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).
- G. Trunk, and S. Brockett, “Range and velocity ambiguity resolution,” in Proceedings of IEEE National Radar Conference (Institute of Electrical and Electronics Engineers, New York, 1993), pp. 146–149.
- E. C. Farnett, and G. H. Stevens, “Pulse Compression Radar,” in Radar Handbook, M. I. Skolnik, ed. (McGraw-Hill, New York, 1990).
- N. Takeuchi, N. Sugimoto, H. Baba, and K. Sakurai, “Random modulation cw lidar,” Appl. Opt. 22(9), 1382–1386 (1983). [CrossRef] [PubMed]
- N. Takeuchi, H. Baba, K. Sakurai, and T. Ueno, “Diode-laser random-modulation cw lidar,” Appl. Opt. 25(1), 63–67 (1986). [CrossRef] [PubMed]
- P. A. Hiskett, C. S. Parry, A. McCarthy, and G. S. Buller, “A photon-counting time-of-flight ranging technique developed for the avoidance of range ambiguity at gigahertz clock rates,” Opt. Express 16(18), 13685–13698 (2008). [CrossRef] [PubMed]
- R. H. Hadfield, M. J. Stevens, S. S. Gruber, A. J. Miller, R. E. Schwall, R. P. Mirin, and S. W. Nam, “Single photon source characterization with a superconducting single photon detector,” Opt. Express 13(26), 10846–10853 (2005). [CrossRef] [PubMed]
- R. E. Warburton, A. McCarthy, A. M. Wallace, S. Hernandez-Marin, R. H. Hadfield, S. W. Nam, and G. S. Buller, “Subcentimeter depth resolution using a single-photon counting time-of-flight laser ranging system at 1550 nm wavelength,” Opt. Lett. 32(15), 2266–2268 (2007). [CrossRef] [PubMed]
- G. S. Buller, R. D. Harkins, A. McCarthy, P. A. Hiskett, G. R. MacKinnon, G. R. Smith, R. Sung, A. M. Wallace, R. A. Lamb, K. A. Ridley, and J. G. Rarity, “A multiple wavelength time-of-flight sensor based on time-correlated single-photon counting,” Rev. Sci. Instrum. 76(8), 083112 (2005). [CrossRef]
- J. S. Massa, A. M. Wallace, G. S. Buller, S. J. Fancey, and A. C. Walker, “Laser depth measurement based on time-correlated single-photon counting,” Opt. Lett. 22(8), 543–545 (1997). [CrossRef] [PubMed]
- W. P. Cole, M. A. Marciniak, and M. B. Haeri, “Atmospheric-turbulence-effects correction factors for the laser range equation,” Opt. Eng. 47(12), 126001 (2008). [CrossRef]
- A. Berk, L. S. Bernstein, and D. C. Robertson, “MODTRAN: A moderate resolution model for LOWTRAN 7,” Technical Note GL-TR-89–0122, available from Geophysics Laboratory/OPE, Air Force Systems Command, Hanscom AFB, Mass. (1989).

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