Abstract

Light-in-flight imaging enables the visualization and characterization of light propagation, which provides essential information for the study of the fundamental phenomena of light. A camera images an object by sensing the light emitted or reflected from it, and interestingly, when a light pulse itself is to be imaged, the relativistic effects, caused by the fact that the distance a pulse travels between consecutive frames is of the same scale as the distance that scattered photons travel from the pulse to the camera, must be accounted for to acquire accurate space–time information of the light pulse. Here, we propose a computational light-in-flight imaging scheme that records the projection of light-in-flight on a transverse xy plane using a single-photon avalanche diode camera, calculates z and t information of light-in-flight via an optical model, and therefore reconstructs its accurate (x, y, z, t) four-dimensional information. The proposed scheme compensates the temporal distortion in the recorded arrival time to retrieve the accurate time of a light pulse, with respect to its corresponding spatial location, without performing any extra measurements. Experimental light-in-flight imaging in a three-dimensional space of 375  mm×75  mm×50  mm is performed, showing that the position error is 1.75 mm, and the time error is 3.84 ps despite the fact that the camera time resolution is 55 ps, demonstrating the feasibility of the proposed scheme. This work provides a method to expand the recording and measuring of repeatable transient events with extremely weak scattering to four dimensions and can be applied to the observation of optical phenomena with ps temporal resolution.

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2019 (1)

T. G. Etoh, T. Okinaka, Y. Takano, K. Takehara, H. Nakano, K. Shimonomura, T. Ando, N. Ngo, Y. Kamakura, V. T. S. Dao, A. Q. Nguyen, E. Charbon, C. Zhang, P. De Moor, P. Goetschalckx, and L. Haspeslagh, “Light-in-flight imaging by a silicon image sensor: toward the theoretical highest frame rate,” Sensors 19, 2247 (2019).
[Crossref]

2018 (2)

I. Gyongy, N. Calder, A. Davies, N. A. W. Dutton, R. R. Duncan, C. Rickman, P. Dalgarno, and R. K. Henderson, “A 256 × 256, 100-kfps, 61% fill-factor SPAD image sensor for time-resolved microscopy applications,” IEEE Trans. Electron. Devices 65, 547–554 (2018).
[Crossref]

J. Liang and L. V. Wang, “Single-shot ultrafast optical imaging,” Optica 5, 1113–1127 (2018).
[Crossref]

2016 (6)

T. L. Cocker, D. Peller, P. Yu, J. Repp, and R. Huber, “Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging,” Nature 539, 263–267 (2016).
[Crossref]

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 3, 694–697 (2016).
[Crossref]

M. Clerici, G. C. Spalding, R. Warburton, A. Lyons, C. Aniculaesei, J. M. Richards, J. Leach, R. Henderson, and D. Faccio, “Observation of image pair creation and annihilation from superluminal scattering sources,” Sci. Adv. 2, e1501691 (2016).
[Crossref]

M. Laurenzis, J. Klein, and E. Bacher, “Relativistic effects in imaging of light in flight with arbitrary paths,” Opt. Lett. 41, 2001–2004 (2016).
[Crossref]

M. Laurenzis, J. Klein, E. Bacher, N. Metzger, and F. Christnacher, “Sensing and reconstruction of arbitrary light-in-flight paths by a relativistic imaging approach,” Proc. SPIE 9988, 998804 (2016).
[Crossref]

2015 (3)

A. Jarabo, B. Masia, A. Velten, C. Barsi, R. Raskar, and D. Gutierrez, “Relativistic effects for time-resolved light transport,” Comput. Graph. Forum. 34, 1–12 (2015).
[Crossref]

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

M. Laurenzis, J. Klein, E. Bacher, and N. Metzger, “Multiple-return single-photon counting of light in flight and sensing of non-line-of-sight objects at shortwave infrared wavelengths,” Opt. Lett. 40, 4815–4818 (2015).
[Crossref]

2014 (3)

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

2013 (3)

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, C. Joshi, E. Lawson, M. Bawendi, D. Gutierrez, and R. Raskar, “Femto-photography: capturing and visualizing the propagation of light,” ACM Trans. Graph. 32, 44 (2013).
[Crossref]

F. Heide, M. B. Hullin, J. Gregson, and W. Heidrich, “Low-budget transient imaging using photonic mixer devices,” ACM Trans. Graph. 32, 45 (2013).
[Crossref]

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Coded time of flight cameras: sparse deconvolution to address multipath interference and recover time profiles,” ACM Trans. Graph. 32, 167 (2013).
[Crossref]

2012 (3)

T. Kakue, K. Tosa, J. Yuasa, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, and T. Kubota, “Digital light-in-flight recording by holography by use of a femtosecond pulsed laser,” IEEE J. Sel. Top. Quantum Electron. 18, 479–485 (2012).
[Crossref]

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

J. M. Hill and B. J. Cox, “Einstein’s special relativity beyond the speed of light,” Proc. R. Soc. A 468, 4174–4192 (2012).
[Crossref]

2009 (2)

M. B. Bouchard, B. R. Chen, S. A. Burgess, and E. M. C. Hillman, “Ultra-fast multispectral optical imaging of cortical oxygenation, blood flow, and intracellular calcium dynamics,” Opt. Express 17, 15670–15678 (2009).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

2007 (2)

C. Niclass, M. Gersbach, R. Henderson, L. Grant, and E. Charbon, “A single photon avalanche diode implemented in 130-nm CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 13, 863–869 (2007).
[Crossref]

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

1984 (1)

1978 (1)

1967 (1)

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[Crossref]

Abramson, N.

Adolph, M.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Ando, T.

T. G. Etoh, T. Okinaka, Y. Takano, K. Takehara, H. Nakano, K. Shimonomura, T. Ando, N. Ngo, Y. Kamakura, V. T. S. Dao, A. Q. Nguyen, E. Charbon, C. Zhang, P. De Moor, P. Goetschalckx, and L. Haspeslagh, “Light-in-flight imaging by a silicon image sensor: toward the theoretical highest frame rate,” Sensors 19, 2247 (2019).
[Crossref]

Aniculaesei, C.

M. Clerici, G. C. Spalding, R. Warburton, A. Lyons, C. Aniculaesei, J. M. Richards, J. Leach, R. Henderson, and D. Faccio, “Observation of image pair creation and annihilation from superluminal scattering sources,” Sci. Adv. 2, e1501691 (2016).
[Crossref]

Aquila, A.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Awatsuji, Y.

T. Kakue, K. Tosa, J. Yuasa, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, and T. Kubota, “Digital light-in-flight recording by holography by use of a femtosecond pulsed laser,” IEEE J. Sel. Top. Quantum Electron. 18, 479–485 (2012).
[Crossref]

Bacher, E.

Barsi, C.

A. Jarabo, B. Masia, A. Velten, C. Barsi, R. Raskar, and D. Gutierrez, “Relativistic effects for time-resolved light transport,” Comput. Graph. Forum. 34, 1–12 (2015).
[Crossref]

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, C. Joshi, E. Lawson, M. Bawendi, D. Gutierrez, and R. Raskar, “Femto-photography: capturing and visualizing the propagation of light,” ACM Trans. Graph. 32, 44 (2013).
[Crossref]

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Coded time of flight cameras: sparse deconvolution to address multipath interference and recover time profiles,” ACM Trans. Graph. 32, 167 (2013).
[Crossref]

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, E. Lawson, C. Joshi, D. Gutierrez, M. G. Bawendi, and R. Raskar, “Relativistic ultrafast rendering using time-of-flight imaging,” in ACM SIGGRAPH 2012 (2012), paper 41.

Bawendi, M.

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, C. Joshi, E. Lawson, M. Bawendi, D. Gutierrez, and R. Raskar, “Femto-photography: capturing and visualizing the propagation of light,” ACM Trans. Graph. 32, 44 (2013).
[Crossref]

Bawendi, M. G.

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, E. Lawson, C. Joshi, D. Gutierrez, M. G. Bawendi, and R. Raskar, “Relativistic ultrafast rendering using time-of-flight imaging,” in ACM SIGGRAPH 2012 (2012), paper 41.

Bhandari, A.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Coded time of flight cameras: sparse deconvolution to address multipath interference and recover time profiles,” ACM Trans. Graph. 32, 167 (2013).
[Crossref]

Bostedt, C.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Bouchard, M. B.

Bozek, J. D.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Brockherde, W.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

Broky, J.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Bronzi, D.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

Buller, G. S.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Burgess, S. A.

Calder, N.

I. Gyongy, N. Calder, A. Davies, N. A. W. Dutton, R. R. Duncan, C. Rickman, P. Dalgarno, and R. K. Henderson, “A 256 × 256, 100-kfps, 61% fill-factor SPAD image sensor for time-resolved microscopy applications,” IEEE Trans. Electron. Devices 65, 547–554 (2018).
[Crossref]

Charbon, E.

T. G. Etoh, T. Okinaka, Y. Takano, K. Takehara, H. Nakano, K. Shimonomura, T. Ando, N. Ngo, Y. Kamakura, V. T. S. Dao, A. Q. Nguyen, E. Charbon, C. Zhang, P. De Moor, P. Goetschalckx, and L. Haspeslagh, “Light-in-flight imaging by a silicon image sensor: toward the theoretical highest frame rate,” Sensors 19, 2247 (2019).
[Crossref]

C. Niclass, M. Gersbach, R. Henderson, L. Grant, and E. Charbon, “A single photon avalanche diode implemented in 130-nm CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 13, 863–869 (2007).
[Crossref]

Chen, B. R.

Chen, Y.

Christnacher, F.

M. Laurenzis, J. Klein, E. Bacher, N. Metzger, and F. Christnacher, “Sensing and reconstruction of arbitrary light-in-flight paths by a relativistic imaging approach,” Proc. SPIE 9988, 998804 (2016).
[Crossref]

Christodoulides, D. N.

G. A. Siviloglou, J. Broky, A. Dogariu, and D. N. Christodoulides, “Observation of accelerating Airy beams,” Phys. Rev. Lett. 99, 213901 (2007).
[Crossref]

Chu, X.

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Clerici, M.

M. Clerici, G. C. Spalding, R. Warburton, A. Lyons, C. Aniculaesei, J. M. Richards, J. Leach, R. Henderson, and D. Faccio, “Observation of image pair creation and annihilation from superluminal scattering sources,” Sci. Adv. 2, e1501691 (2016).
[Crossref]

Cocker, T. L.

T. L. Cocker, D. Peller, P. Yu, J. Repp, and R. Huber, “Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging,” Nature 539, 263–267 (2016).
[Crossref]

Coffee, R.

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T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Spalding, G. C.

M. Clerici, G. C. Spalding, R. Warburton, A. Lyons, C. Aniculaesei, J. M. Richards, J. Leach, R. Henderson, and D. Faccio, “Observation of image pair creation and annihilation from superluminal scattering sources,” Sci. Adv. 2, e1501691 (2016).
[Crossref]

Stern, S.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Streeter, L.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Coded time of flight cameras: sparse deconvolution to address multipath interference and recover time profiles,” ACM Trans. Graph. 32, 167 (2013).
[Crossref]

Strüder, L.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Tahara, T.

T. Kakue, K. Tosa, J. Yuasa, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, and T. Kubota, “Digital light-in-flight recording by holography by use of a femtosecond pulsed laser,” IEEE J. Sel. Top. Quantum Electron. 18, 479–485 (2012).
[Crossref]

Takano, Y.

T. G. Etoh, T. Okinaka, Y. Takano, K. Takehara, H. Nakano, K. Shimonomura, T. Ando, N. Ngo, Y. Kamakura, V. T. S. Dao, A. Q. Nguyen, E. Charbon, C. Zhang, P. De Moor, P. Goetschalckx, and L. Haspeslagh, “Light-in-flight imaging by a silicon image sensor: toward the theoretical highest frame rate,” Sensors 19, 2247 (2019).
[Crossref]

Takehara, K.

T. G. Etoh, T. Okinaka, Y. Takano, K. Takehara, H. Nakano, K. Shimonomura, T. Ando, N. Ngo, Y. Kamakura, V. T. S. Dao, A. Q. Nguyen, E. Charbon, C. Zhang, P. De Moor, P. Goetschalckx, and L. Haspeslagh, “Light-in-flight imaging by a silicon image sensor: toward the theoretical highest frame rate,” Sensors 19, 2247 (2019).
[Crossref]

Thomson, R. R.

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Tisa, S.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

Tosa, K.

T. Kakue, K. Tosa, J. Yuasa, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, and T. Kubota, “Digital light-in-flight recording by holography by use of a femtosecond pulsed laser,” IEEE J. Sel. Top. Quantum Electron. 18, 479–485 (2012).
[Crossref]

Tosi, A.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

Tsia, K. K.

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

Tsukamoto, A.

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Ullrich, J.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Ura, S.

T. Kakue, K. Tosa, J. Yuasa, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, and T. Kubota, “Digital light-in-flight recording by holography by use of a femtosecond pulsed laser,” IEEE J. Sel. Top. Quantum Electron. 18, 479–485 (2012).
[Crossref]

Ushida, T.

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Velten, A.

A. Jarabo, B. Masia, A. Velten, C. Barsi, R. Raskar, and D. Gutierrez, “Relativistic effects for time-resolved light transport,” Comput. Graph. Forum. 34, 1–12 (2015).
[Crossref]

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, C. Joshi, E. Lawson, M. Bawendi, D. Gutierrez, and R. Raskar, “Femto-photography: capturing and visualizing the propagation of light,” ACM Trans. Graph. 32, 44 (2013).
[Crossref]

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, E. Lawson, C. Joshi, D. Gutierrez, M. G. Bawendi, and R. Raskar, “Relativistic ultrafast rendering using time-of-flight imaging,” in ACM SIGGRAPH 2012 (2012), paper 41.

Villa, F.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

Wang, B.

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Wang, L. V.

Warburton, R.

M. Clerici, G. C. Spalding, R. Warburton, A. Lyons, C. Aniculaesei, J. M. Richards, J. Leach, R. Henderson, and D. Faccio, “Observation of image pair creation and annihilation from superluminal scattering sources,” Sci. Adv. 2, e1501691 (2016).
[Crossref]

Wecht, K. W.

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[Crossref]

Weidenspointner, G.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Weyers, S.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

White, B.

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Whyte, R.

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Coded time of flight cameras: sparse deconvolution to address multipath interference and recover time profiles,” ACM Trans. Graph. 32, 167 (2013).
[Crossref]

Wong, T.

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Wu, D.

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, C. Joshi, E. Lawson, M. Bawendi, D. Gutierrez, and R. Raskar, “Femto-photography: capturing and visualizing the propagation of light,” ACM Trans. Graph. 32, 44 (2013).
[Crossref]

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, E. Lawson, C. Joshi, D. Gutierrez, M. G. Bawendi, and R. Raskar, “Relativistic ultrafast rendering using time-of-flight imaging,” in ACM SIGGRAPH 2012 (2012), paper 41.

Wu, E.

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Xu, Q.

Yiu, S.-M.

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Yu, C.

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Yu, P.

T. L. Cocker, D. Peller, P. Yu, J. Repp, and R. Huber, “Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging,” Nature 539, 263–267 (2016).
[Crossref]

Yuasa, J.

T. Kakue, K. Tosa, J. Yuasa, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, and T. Kubota, “Digital light-in-flight recording by holography by use of a femtosecond pulsed laser,” IEEE J. Sel. Top. Quantum Electron. 18, 479–485 (2012).
[Crossref]

Zappa, F.

D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

Zhang, C.

T. G. Etoh, T. Okinaka, Y. Takano, K. Takehara, H. Nakano, K. Shimonomura, T. Ando, N. Ngo, Y. Kamakura, V. T. S. Dao, A. Q. Nguyen, E. Charbon, C. Zhang, P. De Moor, P. Goetschalckx, and L. Haspeslagh, “Light-in-flight imaging by a silicon image sensor: toward the theoretical highest frame rate,” Sensors 19, 2247 (2019).
[Crossref]

Zhao, K.

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Zhu, L.

ACM Trans. Graph. (3)

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, C. Joshi, E. Lawson, M. Bawendi, D. Gutierrez, and R. Raskar, “Femto-photography: capturing and visualizing the propagation of light,” ACM Trans. Graph. 32, 44 (2013).
[Crossref]

F. Heide, M. B. Hullin, J. Gregson, and W. Heidrich, “Low-budget transient imaging using photonic mixer devices,” ACM Trans. Graph. 32, 45 (2013).
[Crossref]

A. Kadambi, R. Whyte, A. Bhandari, L. Streeter, C. Barsi, A. Dorrington, and R. Raskar, “Coded time of flight cameras: sparse deconvolution to address multipath interference and recover time profiles,” ACM Trans. Graph. 32, 167 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. A. Giordmaine, P. M. Rentzepis, S. L. Shapiro, and K. W. Wecht, “Two-photon excitation of fluorescence by picosecond light pulses,” Appl. Phys. Lett. 11, 216–218 (1967).
[Crossref]

Bioinformatics (1)

C.-M. Liu, T. Wong, E. Wu, R. Luo, S.-M. Yiu, Y. Li, B. Wang, C. Yu, X. Chu, K. Zhao, R. Li, and T.-W. Lam, “SOAP3: ultra-fast GPU-based parallel alignment tool for short reads,” Bioinformatics 28, 878–879 (2012).
[Crossref]

Comput. Graph. Forum. (1)

A. Jarabo, B. Masia, A. Velten, C. Barsi, R. Raskar, and D. Gutierrez, “Relativistic effects for time-resolved light transport,” Comput. Graph. Forum. 34, 1–12 (2015).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

C. Niclass, M. Gersbach, R. Henderson, L. Grant, and E. Charbon, “A single photon avalanche diode implemented in 130-nm CMOS technology,” IEEE J. Sel. Top. Quantum Electron. 13, 863–869 (2007).
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D. Bronzi, F. Villa, S. Tisa, A. Tosi, F. Zappa, D. Durini, S. Weyers, and W. Brockherde, “100000 frames/s 64 × 32 single-photon detector array for 2-D imaging and 3-D ranging,” IEEE J. Sel. Top. Quantum Electron. 20, 354–363 (2014).
[Crossref]

T. Kakue, K. Tosa, J. Yuasa, T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, and T. Kubota, “Digital light-in-flight recording by holography by use of a femtosecond pulsed laser,” IEEE J. Sel. Top. Quantum Electron. 18, 479–485 (2012).
[Crossref]

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I. Gyongy, N. Calder, A. Davies, N. A. W. Dutton, R. R. Duncan, C. Rickman, P. Dalgarno, and R. K. Henderson, “A 256 × 256, 100-kfps, 61% fill-factor SPAD image sensor for time-resolved microscopy applications,” IEEE Trans. Electron. Devices 65, 547–554 (2018).
[Crossref]

Nat. Commun. (1)

G. Gariepy, N. Krstajić, R. Henderson, C. Li, R. R. Thomson, G. S. Buller, B. Heshmat, R. Raskar, J. Leach, and D. Faccio, “Single-photon sensitive light-in-fight imaging,” Nat. Commun. 6, 6021 (2015).
[Crossref]

Nat. Photonics (2)

K. Nakagawa, A. Iwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

T. Gorkhover, S. Schorb, R. Coffee, M. Adolph, L. Foucar, D. Rupp, A. Aquila, J. D. Bozek, S. W. Epp, B. Erk, L. Gumprecht, L. Holmegaard, A. Hartmann, R. Hartmann, G. Hauser, P. Holl, A. Hömke, P. Johnsson, N. Kimmel, K.-U. Kühnel, M. Messerschmidt, C. Reich, A. Rouzée, B. Rudek, C. Schmidt, J. Schulz, H. Soltau, S. Stern, G. Weidenspointner, B. White, J. Küpper, L. Strüder, I. Schlichting, J. Ullrich, D. Rolles, A. Rudenko, T. Möller, and C. Bostedt, “Femtosecond and nanometre visualization of structural dynamics in superheated nanoparticles,” Nat. Photonics 10, 93–97 (2016).
[Crossref]

Nature (3)

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

T. L. Cocker, D. Peller, P. Yu, J. Repp, and R. Huber, “Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging,” Nature 539, 263–267 (2016).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

Opt. Express (1)

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Proc. SPIE (1)

M. Laurenzis, J. Klein, E. Bacher, N. Metzger, and F. Christnacher, “Sensing and reconstruction of arbitrary light-in-flight paths by a relativistic imaging approach,” Proc. SPIE 9988, 998804 (2016).
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Sci. Adv. (1)

M. Clerici, G. C. Spalding, R. Warburton, A. Lyons, C. Aniculaesei, J. M. Richards, J. Leach, R. Henderson, and D. Faccio, “Observation of image pair creation and annihilation from superluminal scattering sources,” Sci. Adv. 2, e1501691 (2016).
[Crossref]

Sensors (1)

T. G. Etoh, T. Okinaka, Y. Takano, K. Takehara, H. Nakano, K. Shimonomura, T. Ando, N. Ngo, Y. Kamakura, V. T. S. Dao, A. Q. Nguyen, E. Charbon, C. Zhang, P. De Moor, P. Goetschalckx, and L. Haspeslagh, “Light-in-flight imaging by a silicon image sensor: toward the theoretical highest frame rate,” Sensors 19, 2247 (2019).
[Crossref]

Other (1)

A. Velten, D. Wu, A. Jarabo, B. Masia, C. Barsi, E. Lawson, C. Joshi, D. Gutierrez, M. G. Bawendi, and R. Raskar, “Relativistic ultrafast rendering using time-of-flight imaging,” in ACM SIGGRAPH 2012 (2012), paper 41.

Supplementary Material (1)

NameDescription
» Visualization 1       Computational 4D imaging of light-in-flight

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Figures (6)

Fig. 1.
Fig. 1. Schematics of difference between imaging (a) a moving car and (b) a flying light pulse. Δt stands for the time during which the object moves from position A to position B, and t1 and t2 denote the time of flight for the scattered photons to propagate to the camera from positions A and B, respectively.
Fig. 2.
Fig. 2. Experimental system for light-in-flight measurement and data processing. (a) In the experiment, the pulsed laser and the SPAD camera are synchronized via a trigger generator. Placed at z=0  mm, a 636 nm pulsed laser emits pulses across the field of view of the SPAD camera. The SPAD camera, with a lens of 3.5 mm focal length, is located at z=535  mm. The object focal plane of the camera is the xy plane at z=0  mm, having a field of view of 245  mm×245  mm. The SPAD camera collects the scattered photons from the propagating laser pulses and records a histogram at each pixel using TCSPC mode. (b) The raw data of the histograms is fitted with a Gaussian distribution. Histograms with widths too large or too small are discarded (pixels 1 and 2). Malfunctioning pixels with abnormally large counts are also discarded (pixel 4), leaving only effective pixels (pixel 3). (c) The arrival time of the scattered photons ta in the effective pixels is determined as the peak position of the fitted Gaussian distribution, and a pixel versus arrival time can be obtained. Consequently, the projection of the light path on the xy plane, as well as the arrival times along the path is obtained, forming the (x, y, ta) three-dimensional data of light-in-flight.
Fig. 3.
Fig. 3. Optical model for the computation of propagation time t. α and θ are the angles of CBG and BAF, respectively. s and l are the lengths of BA and BE, respectively. BE is the projection of BD on the reference plane (RP).
Fig. 4.
Fig. 4. Reconstruction procedure for consecutive light paths. (a) For light path 1 (LP1), the reference plane (RP1) is the xy plane containing the starting point 1 (S1). The spatial location of the projection (PP1), propagation angle, and ending point (E1) of LP1 are determined using the proposed geometric model. (b) E1 is used as S2 for the reconstruction of LP2, and RP2 is the xy plane containing S2. The equation of LP2 and the position of E2 can be obtained. (c) In the same manner, LP3 and E3 are determined with RP3.
Fig. 5.
Fig. 5. Experimental results of the propagation angle estimation. (a) Angle error resulting from using different numbers of tai for the estimation of α. (b) Calculated propagation time t with respect to arrival time ta at different propagation angles. (c) The variation of measured full width at half maximum for a laser pulse with respect to its propagation angle α, caused by the relativistic effects.
Fig. 6.
Fig. 6. Experimental 4D reconstruction of light-in-flight. (a) A reconstruction of a laser pulse reflected by two mirrors is demonstrated. The RMSEs of the reconstruction (red line) to the ground truth (dashed line) in position and time are 1.75 mm and 3.84 ps, respectively. (b) The difference between the calculated propagation time t (red line) and measured arrival time ta (blue line) at each recorded frame. The propagation time is in good agreement with the ground truth (dashed line), demonstrating a feasible compensation for the relativistic effects via the proposed scheme.

Equations (2)

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ta=t+s2/c2+t22stsin(α+θ)/c,
t=1cs·l·cosθl·sinα+s·cos(α+θ),

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