Abstract

In this paper we report a unique approach to measuring oxygen saturation levels by utilising the wavelength of the haemoglobin instead of the conventional absorption difference. Two experiments are set up to measure the wavelength of the haemoglobin bound to oxygen at different oxygen saturation levels with the help of a spectrometer. We report a unique low cost and robust wavelength monitoring SpO2 sensor that measures the SpO2 by using the colour of the blood and not the absorption difference of oxyhaemoglobin and deoxyhaemoglobin. With use of a spectrometer, we show that the wavelength of the oxygen-bound haemoglobin has a relation to the oxygen saturation level. The proposed device is designed and experimentally implemented with a colour sensor to measure the SpO2 level of the blood.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Non-contact measurement of oxygen saturation with an RGB camera

Alessandro R. Guazzi, Mauricio Villarroel, João Jorge, Jonathan Daly, Matthew C. Frise, Peter A. Robbins, and Lionel Tarassenko
Biomed. Opt. Express 6(9) 3320-3338 (2015)

Bedside monitoring of patients with shock using a portable spatially-resolved near-infrared spectroscopy

Ting Li, Meixue Duan, Kai Li, Guoqiang Yu, and Zhengshang Ruan
Biomed. Opt. Express 6(9) 3431-3436 (2015)

Blood oxygenation and flow measurements using a single 720-nm tunable V-cavity laser

Yafei Feng, Haoyu Deng, Xin Chen, and Jian-Jun He
Biomed. Opt. Express 8(8) 3516-3525 (2017)

References

  • View by:
  • |
  • |
  • |

  1. A. Gawande, Being Mortal (Metropolitan Books 2014), pp. 6.
  2. M. Mosely, “Are Health Tests Really A Good Idea?” (BBC Horizon, August2015).
  3. S. Iguchi, K. Mitsubayashi, T. Uehara, and M. Ogawa, “A wearable oxygen sensor for transcutaneous blood gas monitoring at the conjunctiva,” Sens. Actuators B Chem. 108(1-2), 733–737 (2005).
    [Crossref]
  4. B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
    [Crossref]
  5. L. Atallah, B. Lo, R. King, and G.-Z. Yang, “Sensor positioning for activity recognition using wearable accelerometers,” IEEE Trans. Biomed. Circuits Syst. 5(4), 320–329 (2011).
    [Crossref] [PubMed]
  6. P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
    [Crossref] [PubMed]
  7. J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
    [Crossref] [PubMed]
  8. Withings, “What does SpO2 mean? What is the normal blood oxygen level?” Available from: https://withings.zendesk.com/hc/en-us/articles/201494667-Whatdoes-SpO2-mean-What-is-the-normal-blood-oxygen-level-
  9. R. Ortega, C. Hansen, K. Elterman, and A. Woo, “Pulse Oximetry” The New England Journal of Medicine. Available from: https://www.youtube.com/watch?v=2v3rae-73jc . (2014).
  10. G. Sagar, “Introduction to Pulse Oximetry” Available from: http://chips.ece.iisc.ernet.in/images/a/a1/Pulse_oximetry.pdf . 1 (2012).
  11. A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).
  12. A. Kishimoto, O. Tochikubo, K. Ohshige, and A. Yanaga, “Ring-shaped pulse oximeter and its application: measurement of SpO2 and blood pressure during sleep and during flight,” Clin. Exp. Hypertens. 27(2-3), 279–288 (2005).
    [Crossref] [PubMed]
  13. Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
    [Crossref] [PubMed]
  14. J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
    [Crossref] [PubMed]
  15. F. Adochiei, C. Rotariu, R. Ciobotariu, and H. Costin, “A wireless low-power pulse oximetry system for patient telemonitoring,” Sens. Actuators B Chem. 7, 1–4 (2011).
  16. M. Rothmaier, B. Selm, S. Spichtig, D. Haensse, and M. Wolf, “Photonic textiles for pulse oximetry,” Opt. Express 16(17), 12973–12986 (2008).
    [Crossref] [PubMed]
  17. S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
    [Crossref]
  18. Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).
  19. UCSB ScienceLine, “Why is blood red?”, Availiable from: http://scienceline.ucsb.edu/getkey.php?key=2419 .
  20. W. Nahm and H. Gehring, “Non-invasive in vivo measurement of blood spectrum by time-resolved near-infrared spectroscopy,” Sens. Actuators B Chem. 29(1-3), 174–179 (1995).
    [Crossref]
  21. Public Lab, “Foldable Mini-Spectrometer”, http://publiclab.org/wiki/foldable-spec .
  22. Texas Advanced Optoelectronic Solutions, “TCS3200, TCS3210 Programmable Color Light-To-Frequency Converter” 4 (2009).
  23. M. J. Campbell, ed., “Swinscow TDV,” in Statistics at Square One, 9th ed. (BMJ Publishing Group 1997).

2015 (1)

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

2014 (2)

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

2013 (1)

S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
[Crossref]

2011 (3)

F. Adochiei, C. Rotariu, R. Ciobotariu, and H. Costin, “A wireless low-power pulse oximetry system for patient telemonitoring,” Sens. Actuators B Chem. 7, 1–4 (2011).

L. Atallah, B. Lo, R. King, and G.-Z. Yang, “Sensor positioning for activity recognition using wearable accelerometers,” IEEE Trans. Biomed. Circuits Syst. 5(4), 320–329 (2011).
[Crossref] [PubMed]

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

2008 (1)

2006 (1)

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

2005 (2)

S. Iguchi, K. Mitsubayashi, T. Uehara, and M. Ogawa, “A wearable oxygen sensor for transcutaneous blood gas monitoring at the conjunctiva,” Sens. Actuators B Chem. 108(1-2), 733–737 (2005).
[Crossref]

A. Kishimoto, O. Tochikubo, K. Ohshige, and A. Yanaga, “Ring-shaped pulse oximeter and its application: measurement of SpO2 and blood pressure during sleep and during flight,” Clin. Exp. Hypertens. 27(2-3), 279–288 (2005).
[Crossref] [PubMed]

2003 (1)

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

1995 (1)

W. Nahm and H. Gehring, “Non-invasive in vivo measurement of blood spectrum by time-resolved near-infrared spectroscopy,” Sens. Actuators B Chem. 29(1-3), 174–179 (1995).
[Crossref]

Aaron, M.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Abraham, W. T.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Adamson, P. B.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Adochiei, F.

F. Adochiei, C. Rotariu, R. Ciobotariu, and H. Costin, “A wireless low-power pulse oximetry system for patient telemonitoring,” Sens. Actuators B Chem. 7, 1–4 (2011).

Aranda, J. M.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Atallah, L.

L. Atallah, B. Lo, R. King, and G.-Z. Yang, “Sensor positioning for activity recognition using wearable accelerometers,” IEEE Trans. Biomed. Circuits Syst. 5(4), 320–329 (2011).
[Crossref] [PubMed]

Bauman, J. G.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Bourge, R. C.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Castoldi, S.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Chang, C. S.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Chapman, J.

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

Chen, M. J.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Chételat, O.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Ciobotariu, R.

F. Adochiei, C. Rotariu, R. Ciobotariu, and H. Costin, “A wireless low-power pulse oximetry system for patient telemonitoring,” Sens. Actuators B Chem. 7, 1–4 (2011).

Correvon, M.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Costin, H.

F. Adochiei, C. Rotariu, R. Ciobotariu, and H. Costin, “A wireless low-power pulse oximetry system for patient telemonitoring,” Sens. Actuators B Chem. 7, 1–4 (2011).

Dasen, S.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Ding, X. R.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Droz, S.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Ferrario, D.

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

Gehring, H.

W. Nahm and H. Gehring, “Non-invasive in vivo measurement of blood spectrum by time-resolved near-infrared spectroscopy,” Sens. Actuators B Chem. 29(1-3), 174–179 (1995).
[Crossref]

Guardino, J. M.

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

Haensse, D.

Han, C. C.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Huang, W. L.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Iguchi, S.

S. Iguchi, K. Mitsubayashi, T. Uehara, and M. Ogawa, “A wearable oxygen sensor for transcutaneous blood gas monitoring at the conjunctiva,” Sens. Actuators B Chem. 108(1-2), 733–737 (2005).
[Crossref]

Ischer, R.

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

Jacob, N.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Jang, I. H.

S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
[Crossref]

Kahrilas, P. J.

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

Kim, J. Y.

S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
[Crossref]

King, R.

L. Atallah, B. Lo, R. King, and G.-Z. Yang, “Sensor positioning for activity recognition using wearable accelerometers,” IEEE Trans. Biomed. Circuits Syst. 5(4), 320–329 (2011).
[Crossref] [PubMed]

Kishimoto, A.

A. Kishimoto, O. Tochikubo, K. Ohshige, and A. Yanaga, “Ring-shaped pulse oximeter and its application: measurement of SpO2 and blood pressure during sleep and during flight,” Clin. Exp. Hypertens. 27(2-3), 279–288 (2005).
[Crossref] [PubMed]

Kiyoko, M.

A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).

Ko, K. E.

S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
[Crossref]

Kormann, R.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Lin, J. Y.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Liu, S. M.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Lo, B.

L. Atallah, B. Lo, R. King, and G.-Z. Yang, “Sensor positioning for activity recognition using wearable accelerometers,” IEEE Trans. Biomed. Circuits Syst. 5(4), 320–329 (2011).
[Crossref] [PubMed]

Lo, B. P. L.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Mitsubayashi, K.

S. Iguchi, K. Mitsubayashi, T. Uehara, and M. Ogawa, “A wearable oxygen sensor for transcutaneous blood gas monitoring at the conjunctiva,” Sens. Actuators B Chem. 108(1-2), 733–737 (2005).
[Crossref]

Miyae, Y.

A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).

Nahm, W.

W. Nahm and H. Gehring, “Non-invasive in vivo measurement of blood spectrum by time-resolved near-infrared spectroscopy,” Sens. Actuators B Chem. 29(1-3), 174–179 (1995).
[Crossref]

Neumann, V.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Nobuyuki, A.

A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).

Ogawa, M.

S. Iguchi, K. Mitsubayashi, T. Uehara, and M. Ogawa, “A wearable oxygen sensor for transcutaneous blood gas monitoring at the conjunctiva,” Sens. Actuators B Chem. 108(1-2), 733–737 (2005).
[Crossref]

Ohshige, K.

A. Kishimoto, O. Tochikubo, K. Ohshige, and A. Yanaga, “Ring-shaped pulse oximeter and its application: measurement of SpO2 and blood pressure during sleep and during flight,” Clin. Exp. Hypertens. 27(2-3), 279–288 (2005).
[Crossref] [PubMed]

Ours, T.

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

Pandolfino, J. E.

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

Park, S. M.

S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
[Crossref]

Pasche, S.

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

Perrenoud, A.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Pilloud, P.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Poon, C. C. Y.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Richter, J. E.

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

Rotariu, C.

F. Adochiei, C. Rotariu, R. Ciobotariu, and H. Costin, “A wireless low-power pulse oximetry system for patient telemonitoring,” Sens. Actuators B Chem. 7, 1–4 (2011).

Rothmaier, M.

Sawaguchi, Y.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Schyrr, B.

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

Scolan, E.

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

Selm, B.

Sim, K.-B.

S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
[Crossref]

Smith, A.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Solà, J.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Spichtig, S.

Stevenson, L. W.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Su, C. Y.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Taiki, T.

A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).

Terumasa, H.

A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).

Tochikubo, O.

A. Kishimoto, O. Tochikubo, K. Ohshige, and A. Yanaga, “Ring-shaped pulse oximeter and its application: measurement of SpO2 and blood pressure during sleep and during flight,” Clin. Exp. Hypertens. 27(2-3), 279–288 (2005).
[Crossref] [PubMed]

Uehara, T.

S. Iguchi, K. Mitsubayashi, T. Uehara, and M. Ogawa, “A wearable oxygen sensor for transcutaneous blood gas monitoring at the conjunctiva,” Sens. Actuators B Chem. 108(1-2), 733–737 (2005).
[Crossref]

Verjus, C.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Viardot, G.

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

Voirin, J. A. P. G.

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

Wolf, M.

Wu, Y.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Yadav, J. S.

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

Yanaga, A.

A. Kishimoto, O. Tochikubo, K. Ohshige, and A. Yanaga, “Ring-shaped pulse oximeter and its application: measurement of SpO2 and blood pressure during sleep and during flight,” Clin. Exp. Hypertens. 27(2-3), 279–288 (2005).
[Crossref] [PubMed]

Yang, G. Z.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Yang, G.-Z.

L. Atallah, B. Lo, R. King, and G.-Z. Yang, “Sensor positioning for activity recognition using wearable accelerometers,” IEEE Trans. Biomed. Circuits Syst. 5(4), 320–329 (2011).
[Crossref] [PubMed]

Yasuhiro, N.

A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).

Yu, W. C.

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Zhang, H.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Zhang, Y. T.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Zhao, N.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Zheng, Y. L.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Zhou, X. L.

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

Am. J. Gastroenterol. (1)

J. E. Pandolfino, J. E. Richter, T. Ours, J. M. Guardino, J. Chapman, and P. J. Kahrilas, “Ambulatory Esophageal pH Monitoring Using a Wireless System,” Am. J. Gastroenterol. 98(4), 740–749 (2003).
[Crossref] [PubMed]

Clin. Exp. Hypertens. (1)

A. Kishimoto, O. Tochikubo, K. Ohshige, and A. Yanaga, “Ring-shaped pulse oximeter and its application: measurement of SpO2 and blood pressure during sleep and during flight,” Clin. Exp. Hypertens. 27(2-3), 279–288 (2005).
[Crossref] [PubMed]

Comput. Ind. (1)

Y. Wu, C. S. Chang, Y. Sawaguchi, W. C. Yu, M. J. Chen, J. Y. Lin, S. M. Liu, C. C. Han, W. L. Huang, and C. Y. Su, “A mobile-phone-based health management system,” Comput. Ind. 69, 3–11 (2015).

Conf. Proc. IEEE Eng. Med. Biol. Soc. (1)

J. Solà, S. Castoldi, O. Chételat, M. Correvon, S. Dasen, S. Droz, N. Jacob, R. Kormann, V. Neumann, A. Perrenoud, P. Pilloud, C. Verjus, and G. Viardot, “SpO2 Sensor Embedded in a Finger Ring: design and implementation,” Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 4295–4298 (2006).
[Crossref] [PubMed]

IEEE Trans. Biomed. Circuits Syst. (1)

L. Atallah, B. Lo, R. King, and G.-Z. Yang, “Sensor positioning for activity recognition using wearable accelerometers,” IEEE Trans. Biomed. Circuits Syst. 5(4), 320–329 (2011).
[Crossref] [PubMed]

IEEE Trans. Biomed. Eng. (1)

Y. L. Zheng, X. R. Ding, C. C. Y. Poon, B. P. L. Lo, H. Zhang, X. L. Zhou, G. Z. Yang, N. Zhao, and Y. T. Zhang, “Unobtrusive Sensing and Wearable Devices for Health Informatics,” IEEE Trans. Biomed. Eng. 61(5), 1538–1554 (2014).
[Crossref] [PubMed]

J. Card. Fail. (1)

P. B. Adamson, W. T. Abraham, M. Aaron, J. M. Aranda, R. C. Bourge, A. Smith, L. W. Stevenson, J. G. Bauman, and J. S. Yadav, “CHAMPION trial rationale and design: the long-term safety and clinical efficacy of a wireless pulmonary artery pressure monitoring system,” J. Card. Fail. 17(1), 3–10 (2011).
[Crossref] [PubMed]

J. Electr. Eng. Technol. (1)

S. M. Park, J. Y. Kim, K. E. Ko, I. H. Jang, and K.-B. Sim, “Real-time heart rate monitoring system based on ring-type pulse oximeter sensor,” J. Electr. Eng. Technol. 8(2), 376–384 (2013).
[Crossref]

Opt. Express (1)

Sens. Actuators B Chem. (4)

F. Adochiei, C. Rotariu, R. Ciobotariu, and H. Costin, “A wireless low-power pulse oximetry system for patient telemonitoring,” Sens. Actuators B Chem. 7, 1–4 (2011).

S. Iguchi, K. Mitsubayashi, T. Uehara, and M. Ogawa, “A wearable oxygen sensor for transcutaneous blood gas monitoring at the conjunctiva,” Sens. Actuators B Chem. 108(1-2), 733–737 (2005).
[Crossref]

B. Schyrr, S. Pasche, E. Scolan, R. Ischer, D. Ferrario, and J. A. P. G. Voirin, “Development of a polymer optical fiber pH sensor for on-body monitoring application,” Sens. Actuators B Chem. 194, 238–248 (2014).
[Crossref]

W. Nahm and H. Gehring, “Non-invasive in vivo measurement of blood spectrum by time-resolved near-infrared spectroscopy,” Sens. Actuators B Chem. 29(1-3), 174–179 (1995).
[Crossref]

Other (10)

Public Lab, “Foldable Mini-Spectrometer”, http://publiclab.org/wiki/foldable-spec .

Texas Advanced Optoelectronic Solutions, “TCS3200, TCS3210 Programmable Color Light-To-Frequency Converter” 4 (2009).

M. J. Campbell, ed., “Swinscow TDV,” in Statistics at Square One, 9th ed. (BMJ Publishing Group 1997).

UCSB ScienceLine, “Why is blood red?”, Availiable from: http://scienceline.ucsb.edu/getkey.php?key=2419 .

A. Gawande, Being Mortal (Metropolitan Books 2014), pp. 6.

M. Mosely, “Are Health Tests Really A Good Idea?” (BBC Horizon, August2015).

Withings, “What does SpO2 mean? What is the normal blood oxygen level?” Available from: https://withings.zendesk.com/hc/en-us/articles/201494667-Whatdoes-SpO2-mean-What-is-the-normal-blood-oxygen-level-

R. Ortega, C. Hansen, K. Elterman, and A. Woo, “Pulse Oximetry” The New England Journal of Medicine. Available from: https://www.youtube.com/watch?v=2v3rae-73jc . (2014).

G. Sagar, “Introduction to Pulse Oximetry” Available from: http://chips.ece.iisc.ernet.in/images/a/a1/Pulse_oximetry.pdf . 1 (2012).

A. Nobuyuki, N. Yasuhiro, T. Taiki, Y. Miyae, M. Kiyoko, and H. Terumasa, “Trial of Measurement of Sleep Apnoea Syndrome with Sound Monitoring and SpO2 at home.” e-Health Networking, Applications and Services, 2009. Healthcom 2009. 11th International Conference 66–69 (2012).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (18)

Fig. 1
Fig. 1

Schematic of the spectrometer set up.

Fig. 2
Fig. 2

Photograph of the spectrometer measurement attached to the index finger with a phone’s bright LED on the nail side and the SpO2 monitor attached to the middle finger.

Fig. 3
Fig. 3

Graph of the first participants’ wavelength when the SpO2 level was at 97% with the peak wavelength at 632nm. Values below 600nm can be ignored as only the red light wavelengths are relevant for measuring pulsative blood need detection.

Fig. 4
Fig. 4

Graph of the second participant’s wavelength when their SpO2 level is at 96%. Sharp peak at 624nm. This suggests a lower SpO2.

Fig. 5
Fig. 5

(a) Graph showing the first and second participant’s wavelength when both participant’s SpO2 levels were at 97%. They both have the same wavelength peak but a different intensity level. Figure 5(b) Graph showing five different spectrometer readings with different participants. Each participant has a difference in intensity and wavelength.

Fig. 6
Fig. 6

Graph showing the change in wavelength over level of SpO2. The higher the peak wavelength, the higher the SpO2 value.

Fig. 7
Fig. 7

(a) Back view of 3D printed spectrograph with slit (15mm x 2.5mm). (b) Front view of spectrograph with diffracting grating (15mm x 15mm).

Fig. 8
Fig. 8

Image of 10.1 MP camera attached to the spectrograph. The diffracted light entering the slit can be captured.

Fig. 9
Fig. 9

(a) An image captured by the camera of white light through the slit. It shows the visible spectrum. 9 (b) An image of the index finger’s blood colour. The image’s colour can be analysed to work out its corresponding wavelength and thus SpO2 value at that moment in time.

Fig. 10
Fig. 10

(a) A photograph of the colour sensor attached to the elastic for the ring. (b) Shows the colour sensor attached to the Arduino Uno. After the red value has been found, it is printed onto an LCD screen and updated every second.

Fig. 11
Fig. 11

Shows the index finger holding the colour sensor with the bright LED being fed to the Arduino micro controller to store the data and the SpO2 sensor attached to the middle finger being read by the SpO2 monitor.

Fig. 12
Fig. 12

A graph of the change in Red value as oxygen levels changed. It shows the higher the red value, the lower the SpO2.

Fig. 13
Fig. 13

(a). A graph representing the average SpO2’s corresponding red value. As the red value increases, the SpO2 decreases proportionally. Figure 13(b). A graph of a participant’s SpO2 values ranging from 99% to 95% in SpO2 and 20700 to 23450 in red value. The graph shows that each value of SpO2 has a range of ~540µW/cm2.

Fig. 14
Fig. 14

A graph representing the correlation between the wavelength and red value as SpO2 changed. As SpO2 increases, the red value decreases and the wavelength increases. This shows that the higher the red value, the lower the wavelength.

Fig. 15
Fig. 15

Left: Ringed device reading the SpO2 value and transmitting the value to the receiving device via a MX-FS-03V transmitter. Right: Receiving device displaying the SpO2 value via a MX-05V receiver.

Fig. 16
Fig. 16

Shows a photograph of the accuracy testing with the SpO2 monitor and ringed device on the same finger. The serial monitor is reading the values from the program, ready to send to the server.

Fig. 17
Fig. 17

Two images of the ring device, (a) with the ring off and (b) with the ring on the index finger.

Fig. 18
Fig. 18

(a). Person 1’s accuracy testing. Absolute error no more than 1%. 60% matching with real value. Figure 18(b) Person 2’s accuracy testing. Absolute error no more than 1%. 90% matching with real value. Figure 18(c) Person 3′s accuracy testing. Absolute error no more than 1%. 80% matching with real value.

Tables (2)

Tables Icon

Table 1 the X and Y values used to work out the product moment correlation coefficient.

Tables Icon

Table 2 the sum products and n used for the formulas.

Equations (2)

Equations on this page are rendered with MathJax. Learn more.

S xy = Σxy Σx Σy n , S xx = Σ x 2 (Σ x 2 ) n , S yy = Σy (Σ y 2 ) n
r= ( Σxy Σx Σy n ) ( Σ x 2 ( Σ x 2 ) n ) ×(  Σy ( Σ y 2 ) n )

Metrics