Abstract

We introduce a compact time-domain system for near-infrared spectroscopy using a spread spectrum technique. The proof-of-concept single channel instrument utilises a low-cost commercially available optical transceiver module as a light source, controlled by a Kintex 7 field programmable gate array (FPGA). The FPGA modulates the optical transceiver with maximum-length sequences at line rates up to 10Gb/s, allowing us to achieve an instrument response function with full width at half maximum under 600ps. The instrument is characterised through a set of detailed phantom measurements as well as proof-of-concept in vivo measurements, demonstrating performance comparable with conventional pulsed time-domain near-infrared spectroscopy systems.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]

2017 (3)

M. Alayed and M. J. Deen, “Time-resolved diffuse optical spectroscopy and imaging using solid-state detectors: characteristics, present status, and research challenges,” Sensors 17, 2115 (2017).
[Crossref]

K. Mehta, A. Hasnain, X. Zhou, J. Luo, T. B. Penney, and N. Chen, “Spread spectrum time-resolved diffuse optical measurement system for enhanced sensitivity in detecting human brain activity,” J. Biomed. Opt. 22, 045005 (2017).
[Crossref]

P. Chen, Y.-Y. Hsiao, Y.-S. Chung, W. X. Tsai, and J.-M. Lin, “A 2.5-ps bin size and 6.7-ps resolution FPGA time-to-digital converter based on delay wrapping and averaging,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems 25, 114–124 (2017).
[Crossref]

2016 (2)

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

D. Chitnis, R. J. Cooper, L. Dempsey, S. Powell, S. Quaggia, D. Highton, C. Elwell, J. C. Hebden, and N. L. Everdell, “Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system,” Biomed. Opt. Express 7, 4275–4288 (2016).
[Crossref] [PubMed]

2014 (4)

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” Neuroimage 85, 28–50 (2014).
[Crossref]

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

2013 (1)

2012 (1)

M. Ferrari and V. Quaresima, “A brief review on the history of human functional near-infrared spectroscopy (fNIRS) development and fields of application,” Neuroimage 63, 921–935 (2012).
[Crossref] [PubMed]

2010 (2)

S. Lloyd-Fox, A. Blasi, and C. Elwell, “Illuminating the developing brain: the past, present and future of functional near-infrared spectroscopy,” Neuroscience & Biobehavioral Reviews 34, 269–284 (2010).
[Crossref]

Q. Zhang, L. Chen, and N. Chen, “Pseudo-random single photon counting: a high-speed implementation,” Biomed. Opt. Express 1, 41–46 (2010).
[Crossref]

2008 (2)

2006 (2)

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near-infrared spectroscopy,” Optics Express 14, 5418–5432 (2006).
[Crossref] [PubMed]

I. Rech, I. Labanca, M. Ghioni, and S. Cova, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[Crossref]

2005 (1)

A. Gibson, J. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1 (2005).
[Crossref] [PubMed]

2004 (2)

2003 (1)

2002 (1)

2000 (1)

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse problems 15, R41 (1999).
[Crossref]

1996 (1)

S. G. Simonson and C. A. Piantadosi, “Near-infrared spectroscopy: clinical applications,” Critical care clinics 12, 1019–1029 (1996).
[Crossref]

1992 (1)

S. R. Arridge, M. Cope, and D. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531 (1992).
[Crossref]

1989 (1)

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Applied optics 28, 2331–2336 (1989).
[Crossref]

Airantzis, D.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

Alayed, M.

M. Alayed and M. J. Deen, “Time-resolved diffuse optical spectroscopy and imaging using solid-state detectors: characteristics, present status, and research challenges,” Sensors 17, 2115 (2017).
[Crossref]

An, Q.

J. Zheng, P. Cao, D. Jiang, and Q. An, “Low-cost FPGA TDC with high resolution and density,” IEEE Transactions on Nuclear Science (2017).

Arridge, S. R.

A. Gibson, J. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1 (2005).
[Crossref] [PubMed]

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse problems 15, R41 (1999).
[Crossref]

S. R. Arridge, M. Cope, and D. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531 (1992).
[Crossref]

S. Powell, R. J. Cooper, J. C. Hebden, and S. R. Arridge, “Dynamic image reconstruction in time-resolved diffuse optical tomography,” in “Optical Tomography and Spectroscopy of Tissue XI,”, vol. 9319 (International Society for Optics and Photonics, 2015), vol. 9319, p. 93191I.

Blasi, A.

S. Lloyd-Fox, A. Blasi, and C. Elwell, “Illuminating the developing brain: the past, present and future of functional near-infrared spectroscopy,” Neuroscience & Biobehavioral Reviews 34, 269–284 (2010).
[Crossref]

Boas, D. A.

D. A. Boas, C. E. Elwell, M. Ferrari, and G. Taga, Twenty Years of Functional Near-infrared Spectroscopy: Introduction for the Special Issue (Elsevier2014).

Caffini, M.

Cao, P.

J. Zheng, P. Cao, D. Jiang, and Q. An, “Low-cost FPGA TDC with high resolution and density,” IEEE Transactions on Nuclear Science (2017).

Carmichael, C.

R. Monreal, C. Carmichael, and G. Swift, “Single-event characterization of multi-gigabit transceivers (MGT) in space-grade Virtex-5QV field programmable gate arrays (FPGA),” in “Radiation Effects Data Workshop (REDW), 2011 IEEE,” (IEEE, 2011), pp. 1–8.

Chance, B.

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Applied optics 28, 2331–2336 (1989).
[Crossref]

Chen, L.

Chen, N.

K. Mehta, A. Hasnain, X. Zhou, J. Luo, T. B. Penney, and N. Chen, “Spread spectrum time-resolved diffuse optical measurement system for enhanced sensitivity in detecting human brain activity,” J. Biomed. Opt. 22, 045005 (2017).
[Crossref]

Q. Zhang, L. Chen, and N. Chen, “Pseudo-random single photon counting: a high-speed implementation,” Biomed. Opt. Express 1, 41–46 (2010).
[Crossref]

W. Mo and N. Chen, “Fast time-domain diffuse optical tomography using pseudorandom bit sequences,” Opt. Express 16, 13643–13650 (2008).
[Crossref] [PubMed]

H. Tian, S. Fernando, H. W. Soon, Y. Ha, and N. Chen, “Design of a high speed pseudo-random bit sequence based time resolved single photon counter on FPGA,” in “Field Programmable Logic and Applications, 2008. FPL 2008. International Conference on,” (IEEE, 2008), pp. 583–586.

Chen, N. G.

Chen, P.

P. Chen, Y.-Y. Hsiao, Y.-S. Chung, W. X. Tsai, and J.-M. Lin, “A 2.5-ps bin size and 6.7-ps resolution FPGA time-to-digital converter based on delay wrapping and averaging,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems 25, 114–124 (2017).
[Crossref]

Chitnis, D.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

D. Chitnis, R. J. Cooper, L. Dempsey, S. Powell, S. Quaggia, D. Highton, C. Elwell, J. C. Hebden, and N. L. Everdell, “Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system,” Biomed. Opt. Express 7, 4275–4288 (2016).
[Crossref] [PubMed]

Chung, Y.-S.

P. Chen, Y.-Y. Hsiao, Y.-S. Chung, W. X. Tsai, and J.-M. Lin, “A 2.5-ps bin size and 6.7-ps resolution FPGA time-to-digital converter based on delay wrapping and averaging,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems 25, 114–124 (2017).
[Crossref]

Contini, D.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” Neuroimage 85, 28–50 (2014).
[Crossref]

R. Re, D. Contini, M. Turola, L. Spinelli, L. Zucchelli, M. Caffini, R. Cubeddu, and A. Torricelli, “Multi-channel medical device for time domain functional near-infrared spectroscopy based on wavelength space multiplexing,” Biomed. Opt. Express 4, 2231–2246 (2013).
[Crossref] [PubMed]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near-infrared spectroscopy,” Optics Express 14, 5418–5432 (2006).
[Crossref] [PubMed]

Cooper, R. J.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

D. Chitnis, R. J. Cooper, L. Dempsey, S. Powell, S. Quaggia, D. Highton, C. Elwell, J. C. Hebden, and N. L. Everdell, “Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system,” Biomed. Opt. Express 7, 4275–4288 (2016).
[Crossref] [PubMed]

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

S. Powell, R. J. Cooper, J. C. Hebden, and S. R. Arridge, “Dynamic image reconstruction in time-resolved diffuse optical tomography,” in “Optical Tomography and Spectroscopy of Tissue XI,”, vol. 9319 (International Society for Optics and Photonics, 2015), vol. 9319, p. 93191I.

Cope, M.

S. R. Arridge, M. Cope, and D. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531 (1992).
[Crossref]

Cova, S.

I. Rech, I. Labanca, M. Ghioni, and S. Cova, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[Crossref]

Cubeddu, R.

Deen, M. J.

M. Alayed and M. J. Deen, “Time-resolved diffuse optical spectroscopy and imaging using solid-state detectors: characteristics, present status, and research challenges,” Sensors 17, 2115 (2017).
[Crossref]

Dehghani, H.

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

Delpy, D.

S. R. Arridge, M. Cope, and D. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531 (1992).
[Crossref]

Delpy, D. T.

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

Dempsey, L.

Dixon, R. C.

R. C. Dixon, Spread Spectrum Systems: With Commercial Applications, vol. 994 (Wiley , 1994).

Dorai, A.

A. Dorai, O. Sentieys, and H. Dubois, “Evaluation of noc on multi-FPGA interconnection using GTX transceiver,” in “24th IEEE International Conference on Electronics, Circuits and Systems (ICECS),” (2017).

Dubois, H.

A. Dorai, O. Sentieys, and H. Dubois, “Evaluation of noc on multi-FPGA interconnection using GTX transceiver,” in “24th IEEE International Conference on Electronics, Circuits and Systems (ICECS),” (2017).

Dunne, L.

F. Lange, L. Dunne, and I. Tachtsidis, “Evaluation of haemoglobin and cytochrome responses during forearm ischaemia using multi-wavelength time domain NIRS,” in “Oxygen Transport to Tissue XXXIX,” (Springer, 2017), pp. 67–72.

Elwell, C.

D. Chitnis, R. J. Cooper, L. Dempsey, S. Powell, S. Quaggia, D. Highton, C. Elwell, J. C. Hebden, and N. L. Everdell, “Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system,” Biomed. Opt. Express 7, 4275–4288 (2016).
[Crossref] [PubMed]

S. Lloyd-Fox, A. Blasi, and C. Elwell, “Illuminating the developing brain: the past, present and future of functional near-infrared spectroscopy,” Neuroscience & Biobehavioral Reviews 34, 269–284 (2010).
[Crossref]

Elwell, C. E.

D. A. Boas, C. E. Elwell, M. Ferrari, and G. Taga, Twenty Years of Functional Near-infrared Spectroscopy: Introduction for the Special Issue (Elsevier2014).

Everdell, N.

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

Everdell, N. L.

Fernando, S.

Q. Zhang, H. W. Soon, H. Tian, S. Fernando, Y. Ha, and N. G. Chen, “Pseudo-random single photon counting for time-resolved optical measurement,” Opt. Express 16, 13233–13239 (2008).
[Crossref] [PubMed]

H. Tian, S. Fernando, H. W. Soon, Y. Ha, and N. Chen, “Design of a high speed pseudo-random bit sequence based time resolved single photon counter on FPGA,” in “Field Programmable Logic and Applications, 2008. FPL 2008. International Conference on,” (IEEE, 2008), pp. 583–586.

Ferrari, M.

M. Ferrari and V. Quaresima, “A brief review on the history of human functional near-infrared spectroscopy (fNIRS) development and fields of application,” Neuroimage 63, 921–935 (2012).
[Crossref] [PubMed]

M. Ferrari, L. Mottola, and V. Quaresima, “Principles, techniques, and limitations of near-infrared spectroscopy,” Canadian journal of applied physiology 29, 463–487 (2004).
[Crossref] [PubMed]

D. A. Boas, C. E. Elwell, M. Ferrari, and G. Taga, Twenty Years of Functional Near-infrared Spectroscopy: Introduction for the Special Issue (Elsevier2014).

Finger, A.

H.-J. Zepernick and A. Finger, Pseudo Random Signal processing: Theory and Application (John Wiley & Sons, 2013).

Ghioni, M.

I. Rech, I. Labanca, M. Ghioni, and S. Cova, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[Crossref]

Giagka, V.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

Gibson, A.

A. Gibson, J. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1 (2005).
[Crossref] [PubMed]

Gibson, A. P.

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

Ha, Y.

Q. Zhang, H. W. Soon, H. Tian, S. Fernando, Y. Ha, and N. G. Chen, “Pseudo-random single photon counting for time-resolved optical measurement,” Opt. Express 16, 13233–13239 (2008).
[Crossref] [PubMed]

H. Tian, S. Fernando, H. W. Soon, Y. Ha, and N. Chen, “Design of a high speed pseudo-random bit sequence based time resolved single photon counter on FPGA,” in “Field Programmable Logic and Applications, 2008. FPL 2008. International Conference on,” (IEEE, 2008), pp. 583–586.

Hasnain, A.

K. Mehta, A. Hasnain, X. Zhou, J. Luo, T. B. Penney, and N. Chen, “Spread spectrum time-resolved diffuse optical measurement system for enhanced sensitivity in detecting human brain activity,” J. Biomed. Opt. 22, 045005 (2017).
[Crossref]

Hebden, J.

A. Gibson, J. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol. 50, R1 (2005).
[Crossref] [PubMed]

Hebden, J. C.

D. Chitnis, R. J. Cooper, L. Dempsey, S. Powell, S. Quaggia, D. Highton, C. Elwell, J. C. Hebden, and N. L. Everdell, “Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system,” Biomed. Opt. Express 7, 4275–4288 (2016).
[Crossref] [PubMed]

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

S. Powell, R. J. Cooper, J. C. Hebden, and S. R. Arridge, “Dynamic image reconstruction in time-resolved diffuse optical tomography,” in “Optical Tomography and Spectroscopy of Tissue XI,”, vol. 9319 (International Society for Optics and Photonics, 2015), vol. 9319, p. 93191I.

Highton, D.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

D. Chitnis, R. J. Cooper, L. Dempsey, S. Powell, S. Quaggia, D. Highton, C. Elwell, J. C. Hebden, and N. L. Everdell, “Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system,” Biomed. Opt. Express 7, 4275–4288 (2016).
[Crossref] [PubMed]

Hillman, E. M.

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

Hsiao, Y.-Y.

P. Chen, Y.-Y. Hsiao, Y.-S. Chung, W. X. Tsai, and J.-M. Lin, “A 2.5-ps bin size and 6.7-ps resolution FPGA time-to-digital converter based on delay wrapping and averaging,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems 25, 114–124 (2017).
[Crossref]

Jelzow, A.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

Jiang, D.

J. Zheng, P. Cao, D. Jiang, and Q. An, “Low-cost FPGA TDC with high resolution and density,” IEEE Transactions on Nuclear Science (2017).

Kacprzak, M.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

Kleiser, S.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

Labanca, I.

I. Rech, I. Labanca, M. Ghioni, and S. Cova, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[Crossref]

Lange, F.

F. Lange, L. Dunne, and I. Tachtsidis, “Evaluation of haemoglobin and cytochrome responses during forearm ischaemia using multi-wavelength time domain NIRS,” in “Oxygen Transport to Tissue XXXIX,” (Springer, 2017), pp. 67–72.

Liebert, A.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43, 3037–3047 (2004).
[Crossref] [PubMed]

Lin, J.-M.

P. Chen, Y.-Y. Hsiao, Y.-S. Chung, W. X. Tsai, and J.-M. Lin, “A 2.5-ps bin size and 6.7-ps resolution FPGA time-to-digital converter based on delay wrapping and averaging,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems 25, 114–124 (2017).
[Crossref]

Lloyd-Fox, S.

S. Lloyd-Fox, A. Blasi, and C. Elwell, “Illuminating the developing brain: the past, present and future of functional near-infrared spectroscopy,” Neuroscience & Biobehavioral Reviews 34, 269–284 (2010).
[Crossref]

Luo, J.

K. Mehta, A. Hasnain, X. Zhou, J. Luo, T. B. Penney, and N. Chen, “Spread spectrum time-resolved diffuse optical measurement system for enhanced sensitivity in detecting human brain activity,” J. Biomed. Opt. 22, 045005 (2017).
[Crossref]

Macdonald, R.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43, 3037–3047 (2004).
[Crossref] [PubMed]

Magazov, S.

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

Magee, E.

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

Mazurenka, M.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

Mehta, K.

K. Mehta, A. Hasnain, X. Zhou, J. Luo, T. B. Penney, and N. Chen, “Spread spectrum time-resolved diffuse optical measurement system for enhanced sensitivity in detecting human brain activity,” J. Biomed. Opt. 22, 045005 (2017).
[Crossref]

Metz, A. J.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

Milej, D.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

Mo, W.

Möller, M.

Monreal, R.

R. Monreal, C. Carmichael, and G. Swift, “Single-event characterization of multi-gigabit transceivers (MGT) in space-grade Virtex-5QV field programmable gate arrays (FPGA),” in “Radiation Effects Data Workshop (REDW), 2011 IEEE,” (IEEE, 2011), pp. 1–8.

Mottola, L.

M. Ferrari, L. Mottola, and V. Quaresima, “Principles, techniques, and limitations of near-infrared spectroscopy,” Canadian journal of applied physiology 29, 463–487 (2004).
[Crossref] [PubMed]

Obrig, H.

Paglia, F.

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near-infrared spectroscopy,” Optics Express 14, 5418–5432 (2006).
[Crossref] [PubMed]

Patterson, M. S.

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Applied optics 28, 2331–2336 (1989).
[Crossref]

Pavia, J. M.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

Penney, T. B.

K. Mehta, A. Hasnain, X. Zhou, J. Luo, T. B. Penney, and N. Chen, “Spread spectrum time-resolved diffuse optical measurement system for enhanced sensitivity in detecting human brain activity,” J. Biomed. Opt. 22, 045005 (2017).
[Crossref]

Phan, P.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

Piantadosi, C. A.

S. G. Simonson and C. A. Piantadosi, “Near-infrared spectroscopy: clinical applications,” Critical care clinics 12, 1019–1029 (1996).
[Crossref]

Pifferi, A.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” Neuroimage 85, 28–50 (2014).
[Crossref]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near-infrared spectroscopy,” Optics Express 14, 5418–5432 (2006).
[Crossref] [PubMed]

Powell, S.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

D. Chitnis, R. J. Cooper, L. Dempsey, S. Powell, S. Quaggia, D. Highton, C. Elwell, J. C. Hebden, and N. L. Everdell, “Functional imaging of the human brain using a modular, fibre-less, high-density diffuse optical tomography system,” Biomed. Opt. Express 7, 4275–4288 (2016).
[Crossref] [PubMed]

S. Powell, R. J. Cooper, J. C. Hebden, and S. R. Arridge, “Dynamic image reconstruction in time-resolved diffuse optical tomography,” in “Optical Tomography and Spectroscopy of Tissue XI,”, vol. 9319 (International Society for Optics and Photonics, 2015), vol. 9319, p. 93191I.

Quaggia, S.

Quaresima, V.

M. Ferrari and V. Quaresima, “A brief review on the history of human functional near-infrared spectroscopy (fNIRS) development and fields of application,” Neuroimage 63, 921–935 (2012).
[Crossref] [PubMed]

M. Ferrari, L. Mottola, and V. Quaresima, “Principles, techniques, and limitations of near-infrared spectroscopy,” Canadian journal of applied physiology 29, 463–487 (2004).
[Crossref] [PubMed]

Re, R.

Rech, I.

I. Rech, I. Labanca, M. Ghioni, and S. Cova, “Modified single photon counting modules for optimal timing performance,” Rev. Sci. Instrum. 77, 033104 (2006).
[Crossref]

Rinneberg, H.

Sawosz, P.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

Schmidt, F. E.

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

Scholkmann, F.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

Schweiger, M.

E. M. Hillman, J. C. Hebden, F. E. Schmidt, S. R. Arridge, M. Schweiger, H. Dehghani, and D. T. Delpy, “Calibration techniques and datatype extraction for time-resolved optical tomography,” Rev. Sci. Instrum. 71, 3415–3427 (2000).
[Crossref]

Sentieys, O.

A. Dorai, O. Sentieys, and H. Dubois, “Evaluation of noc on multi-FPGA interconnection using GTX transceiver,” in “24th IEEE International Conference on Electronics, Circuits and Systems (ICECS),” (2017).

Simonson, S. G.

S. G. Simonson and C. A. Piantadosi, “Near-infrared spectroscopy: clinical applications,” Critical care clinics 12, 1019–1029 (1996).
[Crossref]

Smith, M.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

Soon, H. W.

Q. Zhang, H. W. Soon, H. Tian, S. Fernando, Y. Ha, and N. G. Chen, “Pseudo-random single photon counting for time-resolved optical measurement,” Opt. Express 16, 13233–13239 (2008).
[Crossref] [PubMed]

H. Tian, S. Fernando, H. W. Soon, Y. Ha, and N. Chen, “Design of a high speed pseudo-random bit sequence based time resolved single photon counter on FPGA,” in “Field Programmable Logic and Applications, 2008. FPL 2008. International Conference on,” (IEEE, 2008), pp. 583–586.

Spinelli, L.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” Neuroimage 85, 28–50 (2014).
[Crossref]

R. Re, D. Contini, M. Turola, L. Spinelli, L. Zucchelli, M. Caffini, R. Cubeddu, and A. Torricelli, “Multi-channel medical device for time domain functional near-infrared spectroscopy based on wavelength space multiplexing,” Biomed. Opt. Express 4, 2231–2246 (2013).
[Crossref] [PubMed]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near-infrared spectroscopy,” Optics Express 14, 5418–5432 (2006).
[Crossref] [PubMed]

Steinbrink, J.

Steinkellner, O.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

Swift, G.

R. Monreal, C. Carmichael, and G. Swift, “Single-event characterization of multi-gigabit transceivers (MGT) in space-grade Virtex-5QV field programmable gate arrays (FPGA),” in “Radiation Effects Data Workshop (REDW), 2011 IEEE,” (IEEE, 2011), pp. 1–8.

Tachtsidis, I.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

F. Lange, L. Dunne, and I. Tachtsidis, “Evaluation of haemoglobin and cytochrome responses during forearm ischaemia using multi-wavelength time domain NIRS,” in “Oxygen Transport to Tissue XXXIX,” (Springer, 2017), pp. 67–72.

Taga, G.

D. A. Boas, C. E. Elwell, M. Ferrari, and G. Taga, Twenty Years of Functional Near-infrared Spectroscopy: Introduction for the Special Issue (Elsevier2014).

Taubert, D. R.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

Tian, H.

Q. Zhang, H. W. Soon, H. Tian, S. Fernando, Y. Ha, and N. G. Chen, “Pseudo-random single photon counting for time-resolved optical measurement,” Opt. Express 16, 13233–13239 (2008).
[Crossref] [PubMed]

H. Tian, S. Fernando, H. W. Soon, Y. Ha, and N. Chen, “Design of a high speed pseudo-random bit sequence based time resolved single photon counter on FPGA,” in “Field Programmable Logic and Applications, 2008. FPL 2008. International Conference on,” (IEEE, 2008), pp. 583–586.

Torricelli, A.

A. Torricelli, D. Contini, A. Pifferi, M. Caffini, R. Re, L. Zucchelli, and L. Spinelli, “Time domain functional NIRS imaging for human brain mapping,” Neuroimage 85, 28–50 (2014).
[Crossref]

R. Re, D. Contini, M. Turola, L. Spinelli, L. Zucchelli, M. Caffini, R. Cubeddu, and A. Torricelli, “Multi-channel medical device for time domain functional near-infrared spectroscopy based on wavelength space multiplexing,” Biomed. Opt. Express 4, 2231–2246 (2013).
[Crossref] [PubMed]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, F. Paglia, and R. Cubeddu, “Multi-channel time-resolved system for functional near-infrared spectroscopy,” Optics Express 14, 5418–5432 (2006).
[Crossref] [PubMed]

Tsai, W. X.

P. Chen, Y.-Y. Hsiao, Y.-S. Chung, W. X. Tsai, and J.-M. Lin, “A 2.5-ps bin size and 6.7-ps resolution FPGA time-to-digital converter based on delay wrapping and averaging,” IEEE Transactions on Very Large Scale Integration (VLSI) Systems 25, 114–124 (2017).
[Crossref]

Turola, M.

Varela, M.

R. J. Cooper, E. Magee, N. Everdell, S. Magazov, M. Varela, D. Airantzis, A. P. Gibson, and J. C. Hebden, “MONSTIR II: a 32-channel, multispectral, time-resolved optical tomography system for neonatal brain imaging,” Rev. Sci. Instrum. 85, 053105 (2014).
[Crossref] [PubMed]

Villringer, A.

Wabnitz, H.

H. Wabnitz, D. R. Taubert, M. Mazurenka, O. Steinkellner, A. Jelzow, R. Macdonald, D. Milej, P. Sawosz, M. Kacprzak, A. Liebert, and et al., “Performance assessment of time-domain optical brain imagers, part 1: basic instrumental performance protocol,” J. Biomed. Opt. 19, 086010 (2014).
[Crossref] [PubMed]

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, R. Macdonald, A. Villringer, and H. Rinneberg, “Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons,” Appl. Opt. 43, 3037–3047 (2004).
[Crossref] [PubMed]

Williams, R.

D. Chitnis, D. Airantzis, D. Highton, R. Williams, P. Phan, V. Giagka, S. Powell, R. J. Cooper, I. Tachtsidis, M. Smith, and et al., “Towards a wearable near-infrared spectroscopic probe for monitoring concentrations of multiple chromophores in biological tissue in vivo,” Rev. Sci. Instrum. 87, 065112 (2016).
[Crossref] [PubMed]

Wilson, B. C.

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Applied optics 28, 2331–2336 (1989).
[Crossref]

Wolf, M.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

Wolf, U.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

Zepernick, H.-J.

H.-J. Zepernick and A. Finger, Pseudo Random Signal processing: Theory and Application (John Wiley & Sons, 2013).

Zhang, Q.

Zheng, J.

J. Zheng, P. Cao, D. Jiang, and Q. An, “Low-cost FPGA TDC with high resolution and density,” IEEE Transactions on Nuclear Science (2017).

Zhou, X.

K. Mehta, A. Hasnain, X. Zhou, J. Luo, T. B. Penney, and N. Chen, “Spread spectrum time-resolved diffuse optical measurement system for enhanced sensitivity in detecting human brain activity,” J. Biomed. Opt. 22, 045005 (2017).
[Crossref]

Zhu, Q.

Zimmermann, R.

F. Scholkmann, S. Kleiser, A. J. Metz, R. Zimmermann, J. M. Pavia, U. Wolf, and M. Wolf, “A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology,” Neuroimage 85, 6–27 (2014).
[Crossref]

Zucchelli, L.

Appl. Opt. (1)

Applied optics (1)

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Figures (11)

Fig. 1
Fig. 1 A schematic representation of the implemented TD NIRS system. At the bottom of the Figure, a simplified timing diagram demonstrating the relationship between the operating clock of the GTX transmitters and the outputs of the GTX SMA and the GTX SFP+ ports.
Fig. 2
Fig. 2 A simplified representation of the internal architecture of the ROM file loaded into the FPGA, in order to generate 127-bit sequences, i.e. pulses and MLSs. With this structure a 127-bit MLS and a single pulse were generated, both having a 12.7ns period. In dark grey the full 127-bit transmitted sequences are highlighted, split into two or three TX words.
Fig. 3
Fig. 3 Flow diagram of the five post-processing stages been followed after the collection of the raw MLS data from the TCSPC acquisition board.
Fig. 4
Fig. 4 (a) An indicative MLS response as recorded by the TCSPC card using an IRF setup and (b) the resulting IRF after cross-correlation (in linear- and log-scale).
Fig. 5
Fig. 5 Stability experiment for (a) the intensity and (b) the photon relative mean TOF, using the proposed system over eight hours.
Fig. 6
Fig. 6 Linearity for the (a) absorption and (b) reduced scattering coefficients at 850nm. The error bars demonstrate the standard deviation between repeated measurements (10 for each point) and the dashed lines represent the first order linear fit of their mean values.
Fig. 7
Fig. 7 Noise properties of the proposed system. (a) Indicative TPSF from slab with ∼106 counts/sec. (b) The relationship between CV and SNR with integration time for the ∼106 counts/sec case. (c) Indicative TPSF from slab with ∼105 counts/sec. (d) The relationship between CV and SNR with integration time for the ∼105 counts/sec case.
Fig. 8
Fig. 8 (a) Intensity and (b) relative mean TOF changes during tissue-equivalent rod phantom experiments.
Fig. 9
Fig. 9 Phase angle changes of the FFT performed on the captured TPSFs for different frequency components for the tissue-equivalent rod phantom experiments.
Fig. 10
Fig. 10 (a) Intensity and (b) relative mean TOF changes during cuff occlusion measurement.
Fig. 11
Fig. 11 Phase angle changes of the FFT performed on the captured TPSFs for different frequency components for the cuff occlusion measurement.

Tables (1)

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Table 1 Properties of the VCSEL light source.

Equations (5)

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TPSF Meas . PE ( t ) = IRF PE ( t ) * TPSF Real ( t ) ,
IRF PE ( t ) = Laser Pulse ( t ) * Source IRF ( t ) * Detector IRF ( t ) ,
G SS ( t ) = IRF SS ( t ) * P ( t ) * TPSF Real ( t ) ,
R X X ( τ ) = 1 T 0 T P ( t ) P * ( t τ ) d t = { 1 , for τ / T = 0 1 N MLS , otherwsise
TPSF SS ( τ ) = G SS ( t ) P ( t τ ) = IRF SS ( τ ) * R X X ( τ ) * TPSF Real ( τ ) ,