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 Optical Society of America

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    [Crossref]
  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. 30, 331–345 (2012).
  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. 2, 23–39 (2006).
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    [Crossref] [PubMed]
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2013 (1)

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).

2012 (2)

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]

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).

2011 (2)

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]

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]

2010 (3)

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]

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]

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]

2009 (1)

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]

2006 (1)

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).

2001 (1)

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

1998 (1)

1996 (1)

Boone, B. G.

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).

Brockherde, W.

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).

Bruzzi, J. R.

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).

Buller, G. S.

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]

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]

Chiabrando, F.

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]

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]

Chiabrando, R.

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]

Cova, S.

Crotti, M.

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]

Dibi, Z.

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]

Diraco, G.

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]

Elkhalili, O.

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).

Ghioni, M.

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]

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]

Guerrieri, F.

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]

Hafiane, M. L.

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]

Hosticka, B.

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).

Kerem, S.

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).

König, B.

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).

Krichel, N. J.

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]

Lacaita, A.

Lange, R.

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

Layman, R. S.

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).

Leone, A.

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]

Listl, L.

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).

Manck, O.

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]

Markovic, B.

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).

Massa, J. S.

McCarthy, A.

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]

Mengel, P.

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).

Nex, F.

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]

Noble, M. W.

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).

Pellkofer, M.

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).

Piatti, D.

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]

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]

Rech, I.

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]

Rinaudo, F.

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]

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]

Samori, C.

Schrey, O.

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).

Seitz, P.

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

Siciliano, P.

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]

Strohbehn, K.

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).

Tisa, S.

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).

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]

Toepfer, C.

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).

Tosi, A.

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).

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]

Ulfig, W.

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).

Umasuthan, M.

Villa, F.A.

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).

Wagner, W.

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]

Walker, A. C.

Wallace, A. M.

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]

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]

Ye, J.

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]

Zappa, F.

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).

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. 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]

Adv. Microsyst. Automotive Appl. (1)

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).

Appl. Opt. (2)

IEEE J. Quantum Electron. (1)

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

IEEE J. Solid-state Circuits (1)

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]

IEEE Photonics J. (1)

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]

IEEE Trans. Circuits . Syst. I. Reg. Pap. (1)

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).

Johns Hopkins APL Tech. Dig. (1)

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).

Lect. Notes Comput. Sci. (1)

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]

Med. Eng. Phys. (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]

Proc. SPIE (1)

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]

Sens. Actuators A Phys. (1)

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]

Sensors (Basel) (1)

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]

Other (7)

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 .

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.

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.

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).

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Figures (15)

Fig. 1
Fig. 1 Long-shutter p-iTOF measurement principle, with light excitation pulses, integration time windows (synchronized to the excitation pulse and with durations twice the maximum round trip) and reflected light (with the delayed reflected pulsed signal and flat background).

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Fig. 2
Fig. 2 Long shutter iTOF measurement scheme, where the photon signal is counted in three different time-slots, Q0, Q1 and Qb. Note that the single photon detector can signal the detection of one and just the first one photon detected during the corresponding integration window. In a first phase, only W0 windows are enabled, then only W1 windows and finally only Wb windows.

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Fig. 3
Fig. 3 Long shutter (LST) iTOF measurement scheme, as in Fig. 2, but now the integration windows are enabled cyclically, i.e. W0, then W1, then Wb and then again W0, and so on.

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Fig. 4
Fig. 4 Double Sampling (DST) iTOF measurement principle, with the same light excitation (top) as the Long-Shutter case (Fig. 1), but different integration time windows (center) with shorter duration (equal just to the one-way trip of the light) and different synchronization patterns, and overall detected signal (bottom), with reflected light and background.

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Fig. 5
Fig. 5 Simulations for LST (left) and DST (right) methods of computed vs. real distance (top) at each distance and rms standard deviation (bottom). 100 trials have been considered, with an average of 1,000 signal photons per integration window and no background.

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Fig. 6
Fig. 6 Simulations for LST (left) and DST (right) methods of computed vs. real distance (top) at each distance and rms standard deviation (bottom). 100 trials have been considered, with an average of 100,000 signal photons and 100,000 background photons per integration window.

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Fig. 7
Fig. 7 3D acquisition system, based on a 2D camera employing a 32 × 32 pixel CMOS SPAD array (left), equipped with a pulsed-light illuminator based on LEDs for pulsed-light (right).

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Fig. 8
Fig. 8 Standard deviation of measurements for LST (left) and DST (right) methods, at the same detection conditions. The DST method shows better precision along the whole depth range.

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Fig. 9
Fig. 9 Computed (i.e. measured) vs. real distance for LST and DST pulsed-light iTOF methods.

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Fig. 10
Fig. 10 Relative error for DST and LST pulsed-light iTOF methods.

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Fig. 11
Fig. 11 Measured optical pulse (blue dots) vs. ideal one (red solid line).

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Fig. 12
Fig. 12 Scene under investigation, acquired with a standard color camera.

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Fig. 13
Fig. 13 Gray-scale precision (i.e. standard deviation) map of the measurements per each pixel of the sensor. Darker pixels show better precision (i.e. lower uncertainty). The DST method (right) shows both better precision and better uniformity compared to the LST one (left).

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Fig. 14
Fig. 14 Gray-scale 3D distance maps of the scene shown in Fig. 12 with a car at 5 m from the camera, for both the LST (left) and DST (right) methods.

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Fig. 15
Fig. 15 Some frames of a movie running at 25 fps in an indoor ambient: a person is walking forth and back from the camera, from 4 m to 14 m. Brighter pixels represent longer distances. The movie was acquired with the DST approach and the 32x32 pixels SPAD camera.

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Equations (7)

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d=D⋅[ ( Q 0 − Q b )−( Q 1 − Q b ) ( Q 0 − Q b ) ]=D⋅( Q 0 − Q 1 Q 0 − Q b )
( σ d d ¯ ) 2 = ( σ Q 0 − Q 1 Q ¯ 0 0 − Q ¯ 1 ) 2 + ( σ Q 0 − Q b Q ¯ 0 − Q ¯ b ) 2 −2⋅ σ Q 0 2 ( Q ¯ 0 − Q ¯ 1 )⋅( Q ¯ 0 − Q ¯ b ) .
σ d 2 = D 2 ( Q 0 ¯ − Q b ¯ ) 2 [ ( Q 0 ¯ − Q b ¯ )⋅( 2−3 d ¯ D + ( d ¯ D ) 2 ) + Q b ¯ ⋅( 2−2 d ¯ D +2 ( d ¯ D ) 2 ) ]
d=D⋅( Q 2 Q 2 + Q 3 )
σ d 2 = D 2 ⋅ ( Q 2 Q 2 + Q 3 ) 2 ⋅[ 1 Q 2 − 1 Q 2 + Q 3 ]
d=D⋅( Q 2 − Q b Q 2 + Q 3 −2 Q b )
σ d 2 = D 2 ( Q 2 ¯ + Q 3 ¯ −2 Q b ¯ ) 2 [ ( Q 2 ¯ + Q 3 ¯ −2 Q b ¯ )·( d ¯ D − ( d ¯ D ) 2 ) + Q b ¯ ·( 1−3 d ¯ D +3 ( d ¯ D ) 2 ) ]

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