## Single-photon pulsed-light indirect time-of-flight 3D ranging |

Optics Express, Vol. 21, Issue 4, pp. 5086-5098 (2013)

http://dx.doi.org/10.1364/OE.21.005086

Acrobat PDF (1693 KB)

### Abstract

“Indirect” time-of-flight is one technique to obtain depth-resolved images through active illumination that is becoming more popular in the recent years. Several methods and light timing patterns are used nowadays, aimed at improving measurement precision with smarter algorithms, while using less and less light power. Purpose of this work is to present an indirect time-of-flight imaging camera based on pulsed-light active illumination and a 32 × 32 single-photon avalanche diode array with an improved illumination timing pattern, able to increase depth resolution and to reach single-photon level sensitivity.

© 2013 OSA

## 1. Introduction

1. A. Leone, G. Diraco, and P. Siciliano, “Detecting falls with 3D range camera in ambient assisted living applications: A preliminary study,” Med. Eng. Phys. **33**(6), 770–781 (2011). [CrossRef] [PubMed]

7. F. Rinaudo, F. Chiabrando, F. Nex, and D. Piatti, “New instruments and technologies for cultural heritage survey: full integration between point clouds and digital photogrammetry,” Lect. Notes Comput. Sci. **6436**, 56–70 (2010). [CrossRef]

12. M. Crotti, I. Rech, and M. Ghioni, “Four channel, 40 ps resolution, fully integrated time-to-amplitude converter for time-resolved photon counting,” IEEE J. Solid-state Circuits **47**(3), 699–708 (2012). [CrossRef]

2. N. J. Krichel, A. McCarthy, A. M. Wallace, J. Ye, and G. S. Buller, “Long-range depth imaging using time-correlated single-photon counting,” Proc. SPIE **7780**, 77801I, 77801I-12 (2010). [CrossRef]

13. J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, and A. M. Wallace, “Time-of-flight optical ranging system based on time-correlated single-photon counting,” Appl. Opt. **37**(31), 7298–7304 (1998). [CrossRef] [PubMed]

14. R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. **37**(3), 390–397 (2001). [CrossRef]

14. R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. **37**(3), 390–397 (2001). [CrossRef]

15. M. L. Hafiane, W. Wagner, Z. Dibi, and O. Manck, “Analysis and estimation of NEP and DR in CMOS TOF-3D image sensor based on MDSI,” Sens. Actuators A Phys. **169**(1), 66–73 (2011). [CrossRef]

## 2. Pulsed-light indirect time-of-flight

15. M. L. Hafiane, W. Wagner, Z. Dibi, and O. Manck, “Analysis and estimation of NEP and DR in CMOS TOF-3D image sensor based on MDSI,” Sens. Actuators A Phys. **169**(1), 66–73 (2011). [CrossRef]

_{max}is set equal to the maximum expected one-way trip, i.e. the time took by a photon to reach the furthest object in the scene at the distance D and being reflected back to the sensor. A first integration window W

_{0}is synchronously enabled, with a duration of 2·Δt

_{max}. While the light pulse travels towards the scene and backward to the detector, the detector collects the signal Q

_{0}, given by background light (during the first duration Δt

_{TOF}shown in Fig. 1) and then also the reflected light signal.

_{1}(Fig. 1, center) is enabled in advance by Δt

_{MAX}with respect to the light pulse. In this way the corresponding sample Q

_{1}(Fig. 1, bottom) provides a “useful” information about the object distance, since it contains just a portion of the (and not the whole) reflected signal. Since the amount of back reflected light depends on the distance of the object in the scene, but also on its reflectivity, it is compulsory to normalize the signal Q

_{1}over the signal Q

_{0}. However, during W

_{0}and W

_{1}the sensor acquires also a background signal from the scene (e.g. ambient light, stray light, and also detector dark-counting). Therefore a third integration window W

_{b}is required to accumulate just the background intensity (Q

_{b}), with no light signal therein. Such a quantity must be subtracted from both Q

_{0}and Q

_{1}, before the normalization, in order to compute the distance aswhere D is the maximum distance under investigation, given by D = c·Δt

_{max}, proportional to the speed of light, c, and the pulse duration Δt

_{max}.

_{0}, Q

_{1}and Q

_{b}could be either charge, current or voltage levels. Hence one single pulse excitation could be enough to compute the distance, if electronic noise (and background fluctuations) were negligible. Instead, because of the “digital” nature of photon-counting sensors, only one single photon per integration window can be counted. Therefore for accumulating enough photons to improve statistics, the number of frames, i.e. the excitation pulses and the integration windows, must be repeated for a sufficient number of cycles. An example of the repetitive excitation and acquisition is shown in Fig. 2, where photons are added in subsequent time windows W

_{0}, W

_{1}and W

_{b}, which are time-multiplexed in three consecutive frames. As another example Fig. 2 shows a different timing of the time windows W

_{0}, W

_{1}and W

_{b}, which are cyclical multiplexed within every frame (with the repetitive excitation and acquisition shown in Fig. 3).

_{0}, Q

_{1}and Q

_{b}. Therefore the variance of the distance measurements d(Q

_{0}, Q

_{1}, Q

_{b}) due to the photon statistics, i.e. the uncertainty in the depth assessment, is given by

_{0}) but in two different time windows (Q

_{2}and Q

_{3}) that slice the overall reflected signal. This method, known as Double Sampling Technique (DST), is shown in Fig. 4 and employs time-windows with duration equal to the excitation pulse and to the maximum one-way trip Δ

_{tMAX}of the photon, but with different synchronizations compared to the emitted pulse. The whole reflected pulse (equivalent to Q

_{0}Fig. 1) can be obtained as the sum of Q

_{2}and Q

_{3}, which are the number of photons acquired in the time-windows W

_{2}and W

_{3}, respectively, each with half the duration of the previous W

_{0}and W

_{1}of Fig. 1 and with different synchronization timings with respect to light pulses. The first window W

_{2}is delayed in respect to the light excitation (it starts at the falling-edge of the light pulse), hence it acquires just the last portion of the reflected signal, which comes after a delay Δt

_{TOF}, i.e. the return trip of the light pulse; instead the second integration window W

_{3}overlaps the excitation pulse and it acquires only the first portion of the reflected signal. Eventually, the background alone is acquired in a third integration window W

_{b}.

_{2}and Q

_{3}provide useful information about the distance, as compared to the sample Q

_{0}of the previous approach, which provided just information on the total detected signal intensity and none on the distance. Since the new Q

_{3}sample provides the same information as the previous Q

_{1}and Eq. (1) computes Q

_{0}-Q

_{1}, now the distance information will be proportional to the ratio between Q

_{2}and Q

_{2}+ Q

_{3}, that is,The uncertainty in the computation of the distance now is reduced, thanks to the partial correlation between numerator and denominator, since both depend on the same actual measured quantity Q

_{2}. The measurement precision can be computed again starting from Eq. (4):Taking background into consideration and after its subtraction from every window we get and the corresponding variance is

## 3. Simulations

_{0}or Q

_{2}+ Q

_{3}) and background photons Q

_{b}: more background photons lead to worse precision. Moreover, this is particularly evident near the boundaries of the measurement range, where the contribution of the signal photons to at least one of the signal samples (Q

_{0}, Q

_{2}or Q

_{3}) tends to be negligible compared to the background ones. This is the reason of the dramatic change between the situations depicted in Fig. 5 and in Fig. 6. Consider for instance the DST technique.

## 4. Measurements

17. See SPC2 module data-sheet by MPD srl, http://www.micro-photon-devices.com/products_spc2.asp.

18. F. Guerrieri, S. Tisa, A. Tosi, and F. Zappa, “Two-dimensional SPAD imaging camera for photon counting,” IEEE Photonics J. **2**(5), 759–774 (2010). [CrossRef]

20. S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, “Avalanche photodiodes and quenching circuits for single-photon detection,” Appl. Opt. **35**(12), 1956–1976 (1996). [CrossRef] [PubMed]

_{TOF}delays), both time windows W

_{1}(see Fig. 1) and W

_{3}(see Fig. 4) collect lower and lower signal due to the slow rising-edge of the emitted light (see the initial part of the excitation pulse in Fig. 11).

^{2}at 15 m). This result is well in agreement with the previous Monte Carlo simulations, when an average reflectivity of the objects in the scene is set equal to 70% and taking into account the geometrical attenuation over the field-of-view of the scene.

## 5. Conclusions

## Acknowledgments

## References and links

1. | A. Leone, G. Diraco, and P. Siciliano, “Detecting falls with 3D range camera in ambient assisted living applications: A preliminary study,” Med. Eng. Phys. |

2. | N. J. Krichel, A. McCarthy, A. M. Wallace, J. Ye, and G. S. Buller, “Long-range depth imaging using time-correlated single-photon counting,” Proc. SPIE |

3. | J. R. Bruzzi, K. Strohbehn, B. G. Boone, S. Kerem, R. S. Layman, and M. W. Noble, “A compact laser altimeter for spacecraft landing applications,” Johns Hopkins APL Tech. Dig. |

4. | P. Mengel, L. Listl, B. König, C. Toepfer, M. Pellkofer, W. Brockherde, B. Hosticka, O. Elkhalili, O. Schrey, and W. Ulfig, “Three-dimensional CMOS image sensor for pedestrian protection and collision mitigation,” Adv. Microsyst. Automotive Appl. |

5. | S. May, B. Werner, H. Surmann, and K. Pervölz, “3D time-of-flight cameras for mobile robotics,” in |

6. | F. Chiabrando, R. Chiabrando, D. Piatti, and F. Rinaudo, “Sensors for 3D Imaging: Metric Evaluation and Calibration of a CCD/CMOS Time-of-Flight Camera,” Sensors (Basel) |

7. | F. Rinaudo, F. Chiabrando, F. Nex, and D. Piatti, “New instruments and technologies for cultural heritage survey: full integration between point clouds and digital photogrammetry,” Lect. Notes Comput. Sci. |

8. | N. Cottini, M. De Nicola, M. Gottardi, and R. Manduchi, “A low-power stereo vision system based on a custom CMOS imager with positional data coding,” |

9. | Y. Sooyeong, S. Jinho, H. Youngjin, and D. Hwang, “Active ranging system based on structured laser light image,” |

10. | D. Stoppa and A. Simoni, “Single-photon detectors for time-of-flight range imaging,” in |

11. | B. Markovic, S. Tisa, F.A. Villa, A. Tosi, and F. Zappa, “A high-linearity, 17 ps precision time-to-digital coverter based on a single-stage delay Vernier loop fine interpolation,” IEEE Trans. Circuits . Syst. I. Reg. Pap. |

12. | M. Crotti, I. Rech, and M. Ghioni, “Four channel, 40 ps resolution, fully integrated time-to-amplitude converter for time-resolved photon counting,” IEEE J. Solid-state Circuits |

13. | J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, and A. M. Wallace, “Time-of-flight optical ranging system based on time-correlated single-photon counting,” Appl. Opt. |

14. | R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. |

15. | M. L. Hafiane, W. Wagner, Z. Dibi, and O. Manck, “Analysis and estimation of NEP and DR in CMOS TOF-3D image sensor based on MDSI,” Sens. Actuators A Phys. |

16. | S. Bellisai, F. Guerrieri, S. Tisa, and F. Zappa, “3D ranging with a single-photon imaging array,” |

17. | See SPC2 module data-sheet by MPD srl, http://www.micro-photon-devices.com/products_spc2.asp. |

18. | F. Guerrieri, S. Tisa, A. Tosi, and F. Zappa, “Two-dimensional SPAD imaging camera for photon counting,” IEEE Photonics J. |

19. | S. Tisa, F. Guerrieri, A. Tosi, and F. Zappa, “100 kframe/s 8 bit monolithic single-photon imagers,” |

20. | S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, “Avalanche photodiodes and quenching circuits for single-photon detection,” Appl. Opt. |

**OCIS Codes**

(030.5260) Coherence and statistical optics : Photon counting

(040.1240) Detectors : Arrays

(040.1490) Detectors : Cameras

(110.2970) Imaging systems : Image detection systems

(110.6880) Imaging systems : Three-dimensional image acquisition

(040.1345) Detectors : Avalanche photodiodes (APDs)

**ToC Category:**

Detectors

**History**

Original Manuscript: November 6, 2012

Revised Manuscript: January 18, 2013

Manuscript Accepted: January 25, 2013

Published: February 22, 2013

**Citation**

S. Bellisai, D. Bronzi, F. A. Villa, S. Tisa, A. Tosi, and F. Zappa, "Single-photon pulsed-light indirect time-of-flight 3D ranging," Opt. Express **21**, 5086-5098 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-5086

Sort: Year | Journal | Reset

### References

- A. Leone, G. Diraco, and P. Siciliano, “Detecting falls with 3D range camera in ambient assisted living applications: A preliminary study,” Med. Eng. Phys.33(6), 770–781 (2011). [CrossRef] [PubMed]
- N. J. Krichel, A. McCarthy, A. M. Wallace, J. Ye, and G. S. Buller, “Long-range depth imaging using time-correlated single-photon counting,” Proc. SPIE7780, 77801I, 77801I-12 (2010). [CrossRef]
- J. R. Bruzzi, K. Strohbehn, B. G. Boone, S. Kerem, R. S. Layman, and M. W. Noble, “A compact laser altimeter for spacecraft landing applications,” Johns Hopkins APL Tech. Dig.30, 331–345 (2012).
- P. Mengel, L. Listl, B. König, C. Toepfer, M. Pellkofer, W. Brockherde, B. Hosticka, O. Elkhalili, O. Schrey, and W. Ulfig, “Three-dimensional CMOS image sensor for pedestrian protection and collision mitigation,” Adv. Microsyst. Automotive Appl.2, 23–39 (2006).
- S. May, B. Werner, H. Surmann, and K. Pervölz, “3D time-of-flight cameras for mobile robotics,” in 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems (IEEE/RSJ, 2006), pp. 790–795.
- F. Chiabrando, R. Chiabrando, D. Piatti, and F. Rinaudo, “Sensors for 3D Imaging: Metric Evaluation and Calibration of a CCD/CMOS Time-of-Flight Camera,” Sensors (Basel)9(12), 10080–10096 (2009). [CrossRef] [PubMed]
- F. Rinaudo, F. Chiabrando, F. Nex, and D. Piatti, “New instruments and technologies for cultural heritage survey: full integration between point clouds and digital photogrammetry,” Lect. Notes Comput. Sci.6436, 56–70 (2010). [CrossRef]
- N. Cottini, M. De Nicola, M. Gottardi, and R. Manduchi, “A low-power stereo vision system based on a custom CMOS imager with positional data coding,” 2011 7th Conference on Ph.D. Research in Microelectronics and Electronics (PRIME) (2011), pp. 161–164.
- Y. Sooyeong, S. Jinho, H. Youngjin, and D. Hwang, “Active ranging system based on structured laser light image,” Proceedings of SICE Annual Conference 2010 (2010), pp. 747–752.
- D. Stoppa and A. Simoni, “Single-photon detectors for time-of-flight range imaging,” in Single-Photon Imaging, 1st ed, P. Seitz and A. J. P. Theuwissen, eds. (Springer, Berlin, 2011), pp. 275–300.
- B. Markovic, S. Tisa, F.A. Villa, A. Tosi, and F. Zappa, “A high-linearity, 17 ps precision time-to-digital coverter based on a single-stage delay Vernier loop fine interpolation,” IEEE Trans. Circuits . Syst. I. Reg. Pap.99, 1-13 (2013).
- M. Crotti, I. Rech, and M. Ghioni, “Four channel, 40 ps resolution, fully integrated time-to-amplitude converter for time-resolved photon counting,” IEEE J. Solid-state Circuits47(3), 699–708 (2012). [CrossRef]
- J. S. Massa, G. S. Buller, A. C. Walker, S. Cova, M. Umasuthan, and A. M. Wallace, “Time-of-flight optical ranging system based on time-correlated single-photon counting,” Appl. Opt.37(31), 7298–7304 (1998). [CrossRef] [PubMed]
- R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron.37(3), 390–397 (2001). [CrossRef]
- M. L. Hafiane, W. Wagner, Z. Dibi, and O. Manck, “Analysis and estimation of NEP and DR in CMOS TOF-3D image sensor based on MDSI,” Sens. Actuators A Phys.169(1), 66–73 (2011). [CrossRef]
- S. Bellisai, F. Guerrieri, S. Tisa, and F. Zappa, “3D ranging with a single-photon imaging array,” Proc. of SPIE Conference on Sensors, Cameras, and Systems XII, 78750M (2011).
- See SPC2 module data-sheet by MPD srl, http://www.micro-photon-devices.com/products_spc2.asp .
- F. Guerrieri, S. Tisa, A. Tosi, and F. Zappa, “Two-dimensional SPAD imaging camera for photon counting,” IEEE Photonics J.2(5), 759–774 (2010). [CrossRef]
- S. Tisa, F. Guerrieri, A. Tosi, and F. Zappa, “100 kframe/s 8 bit monolithic single-photon imagers,” Proceedings of the 38th European Solid-State Device Research Conference, 274–277 (2008).
- S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, “Avalanche photodiodes and quenching circuits for single-photon detection,” Appl. Opt.35(12), 1956–1976 (1996). [CrossRef] [PubMed]

## 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.

### Figures

Fig. 1 |
Fig. 2 |
Fig. 3 |

Fig. 4 |
Fig. 5 |
Fig. 6 |

Fig. 7 |
Fig. 8 |
Fig. 9 |

Fig. 10 |
Fig. 11 |
Fig. 12 |

Fig. 13 |
Fig. 14 |
Fig. 15 |

« Previous Article | Next Article »

OSA is a member of CrossRef.