Abstract

The computational power required to classify cell holograms is a major limit to the throughput of label-free cell sorting based on digital holographic microscopy. In this work, a simple integrated photonic stage comprising a collection of silica pillar scatterers is proposed as an effective nonlinear mixing interface between the light scattered by a cell and an image sensor. The light processing provided by the photonic stage allows for the use of a simple linear classifier implemented in the electric domain and applied on a limited number of pixels. A proof-of-concept of the presented machine learning technique, which is based on the extreme learning machine (ELM) paradigm, is provided by the classification results on samples generated by 2D FDTD simulations of cells in a microfluidic channel.

© 2017 Optical Society of America

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References

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  1. D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
    [Crossref] [PubMed]
  2. L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.
  3. B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.
  4. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Publishers, 2005).
  5. G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: Theory and applications,” Neurocomputing 70(1), 489–501 (2006).
    [Crossref]
  6. G. Huang, G.-B. Huang, S. Song, and K. You, “Trends in extreme learning machines: A review,” Neural Networks 61, 32–48 (2015).
    [Crossref]
  7. M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Computer Science Review 3(3), 127–149 (2009).
    [Crossref]
  8. K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
    [Crossref] [PubMed]
  9. K.-W. Wong, C.-S. Leung, and S.-J. Chang, “Use of periodic and monotonic activation functions in multilayer feedforward neural networks trained by extended Kalman filter algorithm,” in Proceedings of IEEE Conference on Vision, Image, and Signal Processing (IEEE, 2002), pp. 217–224.
  10. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).
  11. D. Zink, A. H. Fischer, and J. A Nickerson, “Nuclear structure in cancer cells,” Nat. Rev. Cancer 4(9), 677–687 (2004).
    [Crossref] [PubMed]
  12. S. M. Lewis, B. J. Bain, I. Bates, and J. V. Dacie, Dacie and Lewis practical haematology (Churchill Livingstone, 2011), Chap 5.

2015 (1)

G. Huang, G.-B. Huang, S. Song, and K. You, “Trends in extreme learning machines: A review,” Neural Networks 61, 32–48 (2015).
[Crossref]

2014 (1)

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

2011 (1)

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

2010 (1)

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

2009 (1)

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Computer Science Review 3(3), 127–149 (2009).
[Crossref]

2006 (1)

G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: Theory and applications,” Neurocomputing 70(1), 489–501 (2006).
[Crossref]

2004 (1)

D. Zink, A. H. Fischer, and J. A Nickerson, “Nuclear structure in cancer cells,” Nat. Rev. Cancer 4(9), 677–687 (2004).
[Crossref] [PubMed]

Amini, H.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Bain, B. J.

S. M. Lewis, B. J. Bain, I. Bates, and J. V. Dacie, Dacie and Lewis practical haematology (Churchill Livingstone, 2011), Chap 5.

Bates, I.

S. M. Lewis, B. J. Bain, I. Bates, and J. V. Dacie, Dacie and Lewis practical haematology (Churchill Livingstone, 2011), Chap 5.

Bienstman, P.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.

Blondel, M.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Brucher, M.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Carlo, D. D.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Chang, S.-J.

K.-W. Wong, C.-S. Leung, and S.-J. Chang, “Use of periodic and monotonic activation functions in multilayer feedforward neural networks trained by extended Kalman filter algorithm,” in Proceedings of IEEE Conference on Vision, Image, and Signal Processing (IEEE, 2002), pp. 217–224.

Cournapeau, D.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Dacie, J. V.

S. M. Lewis, B. J. Bain, I. Bates, and J. V. Dacie, Dacie and Lewis practical haematology (Churchill Livingstone, 2011), Chap 5.

Dambre, J.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.

de Wijs, K.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Dubourg, V.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Duchesnay, É.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Dusa, A.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Fiers, M.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Fischer, A. H.

D. Zink, A. H. Fischer, and J. A Nickerson, “Nuclear structure in cancer cells,” Nat. Rev. Cancer 4(9), 677–687 (2004).
[Crossref] [PubMed]

Gossett, D. R.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Gramfort, A.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Grisel, O.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Publishers, 2005).

Huang, G.

G. Huang, G.-B. Huang, S. Song, and K. You, “Trends in extreme learning machines: A review,” Neural Networks 61, 32–48 (2015).
[Crossref]

Huang, G.-B.

G. Huang, G.-B. Huang, S. Song, and K. You, “Trends in extreme learning machines: A review,” Neural Networks 61, 32–48 (2015).
[Crossref]

G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: Theory and applications,” Neurocomputing 70(1), 489–501 (2006).
[Crossref]

Hur, S. C.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Jaeger, H.

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Computer Science Review 3(3), 127–149 (2009).
[Crossref]

Lagae, L.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.

Lee, W.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Leung, C.-S.

K.-W. Wong, C.-S. Leung, and S.-J. Chang, “Use of periodic and monotonic activation functions in multilayer feedforward neural networks trained by extended Kalman filter algorithm,” in Proceedings of IEEE Conference on Vision, Image, and Signal Processing (IEEE, 2002), pp. 217–224.

Lewis, S. M.

S. M. Lewis, B. J. Bain, I. Bates, and J. V. Dacie, Dacie and Lewis practical haematology (Churchill Livingstone, 2011), Chap 5.

Li, Y.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Liu, C.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Lukoševicius, M.

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Computer Science Review 3(3), 127–149 (2009).
[Crossref]

Mach, A. J.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Majeed, B.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Mechet, P.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Michel, V.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Morthier, G.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Nickerson, J. A

D. Zink, A. H. Fischer, and J. A Nickerson, “Nuclear structure in cancer cells,” Nat. Rev. Cancer 4(9), 677–687 (2004).
[Crossref] [PubMed]

Passos, A.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Pedregosa, F.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Perrot, M.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Peumans, P.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Prettenhofer, P.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Schneider, B.

B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.

Schrauwen, B.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Siew, C.-K.

G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: Theory and applications,” Neurocomputing 70(1), 489–501 (2006).
[Crossref]

Song, S.

G. Huang, G.-B. Huang, S. Song, and K. You, “Trends in extreme learning machines: A review,” Neural Networks 61, 32–48 (2015).
[Crossref]

Stahl, R.

B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Publishers, 2005).

Thirion, B.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Tse, H. T. K.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Vaerenbergh, T. V.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Vanderplas, J.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Vandoorne, K.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Vanmeerbeeck, G.

B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Varoquaux, G.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Vercruysse, D.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

Verstraeten, D.

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Weaver, W. M.

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Weiss, R.

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Wong, K.-W.

K.-W. Wong, C.-S. Leung, and S.-J. Chang, “Use of periodic and monotonic activation functions in multilayer feedforward neural networks trained by extended Kalman filter algorithm,” in Proceedings of IEEE Conference on Vision, Image, and Signal Processing (IEEE, 2002), pp. 217–224.

You, K.

G. Huang, G.-B. Huang, S. Song, and K. You, “Trends in extreme learning machines: A review,” Neural Networks 61, 32–48 (2015).
[Crossref]

Zhu, Q.-Y.

G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: Theory and applications,” Neurocomputing 70(1), 489–501 (2006).
[Crossref]

Zink, D.

D. Zink, A. H. Fischer, and J. A Nickerson, “Nuclear structure in cancer cells,” Nat. Rev. Cancer 4(9), 677–687 (2004).
[Crossref] [PubMed]

Anal. Bioanal. Chem. (1)

D. R. Gossett, W. M. Weaver, A. J. Mach, S. C. Hur, H. T. K. Tse, W. Lee, H. Amini, and D. D. Carlo, “Label-free cell separation and sorting in microfluidic systems,” Anal. Bioanal. Chem. 397(8), 3249–3267 (2010).
[Crossref] [PubMed]

Computer Science Review (1)

M. Lukoševičius and H. Jaeger, “Reservoir computing approaches to recurrent neural network training,” Computer Science Review 3(3), 127–149 (2009).
[Crossref]

J. Mach. Learn. Res. (1)

F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and É. Duchesnay, “Scikit-learn: Machine Learning in Python,” J. Mach. Learn. Res. 12, 2825–2830 (2011).

Nat. Commun. (1)

K. Vandoorne, P. Mechet, T. V. Vaerenbergh, M. Fiers, G. Morthier, D. Verstraeten, B. Schrauwen, J. Dambre, and P. Bienstman, “Experimental demonstration of reservoir computing on a silicon photonics chip,” Nat. Commun. 5, 3541 (2014).
[Crossref] [PubMed]

Nat. Rev. Cancer (1)

D. Zink, A. H. Fischer, and J. A Nickerson, “Nuclear structure in cancer cells,” Nat. Rev. Cancer 4(9), 677–687 (2004).
[Crossref] [PubMed]

Neural Networks (1)

G. Huang, G.-B. Huang, S. Song, and K. You, “Trends in extreme learning machines: A review,” Neural Networks 61, 32–48 (2015).
[Crossref]

Neurocomputing (1)

G.-B. Huang, Q.-Y. Zhu, and C.-K. Siew, “Extreme learning machine: Theory and applications,” Neurocomputing 70(1), 489–501 (2006).
[Crossref]

Other (5)

K.-W. Wong, C.-S. Leung, and S.-J. Chang, “Use of periodic and monotonic activation functions in multilayer feedforward neural networks trained by extended Kalman filter algorithm,” in Proceedings of IEEE Conference on Vision, Image, and Signal Processing (IEEE, 2002), pp. 217–224.

L. Lagae, D. Vercruysse, A. Dusa, C. Liu, K. de Wijs, R. Stahl, G. Vanmeerbeeck, B. Majeed, Y. Li, and P. Peumans, “High throughput cell sorter based on lensfree imaging of cells,” in Proceedings of IEEE International Electron Devices Meeting (IEEE, 2015), pp. 333–336.

B. Schneider, G. Vanmeerbeeck, R. Stahl, L. Lagae, J. Dambre, and P. Bienstman, “Neural network for blood cell classification in a holographic microscopy system,” in Proceedings of 17th International Conference on Transparent Optical Networks (ICTON, 2015), pp. 1–4.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House Publishers, 2005).

S. M. Lewis, B. J. Bain, I. Bates, and J. V. Dacie, Dacie and Lewis practical haematology (Churchill Livingstone, 2011), Chap 5.

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Figures (8)

Fig. 1
Fig. 1 Schematic of the classification process. From right to left: a monochromatic plane wave impinges on a microfluidic channel containing a cell in water ( n H 2 O ~ 1.34 ), which has a low refractive index contrast (ncytoplasm = 1.37, nnucleus = 1.39); the forward scattered light passes through a collection of silica scatterers ( n S i O 2 ~ 1.461 ) embedded in silicon nitride ( n S i 3 N 4 ~ 2.027 ) and organized in layers; the radiation intensity is then collected by a far-field monitor, which is divided into bins (pixels); each pixel value is fed into a trained logistic regression, which classifies the cell as a “normal” cell (small nucleus) or as a “cancer” cell (big nucleus). The logistic regression consists of a weighted sum of the pixel values. The weights are trained so that the sum exceeds a threshold value only if a certain input class is recognized.
Fig. 2
Fig. 2 Examples of cells automatically generated by the employed randomized models. a) Comparison between generated examples of “normal” cell and “cancer” cell. b) Comparison between generated examples of “lymphocyte” and “neutrophil”.
Fig. 3
Fig. 3 Far-field intensity profiles of the light scattered by a cell: a) without the presence of scatterers, the interference pattern is relatively simple and smooth, most of the intensity is confined between −6° and 6°; b) with 1 layer of scatterers, the far-field intensity is distributed around periodically placed peaks, most of the field stays between −40° and 40°; c) with 4 layers of scatterers, the far-field intensity is distributed in a complex pattern mostly between −60° and 60°.
Fig. 4
Fig. 4 Comparison between the test error rates of “normal” and “cancer” cell classification, corresponding to the absence (in red) and the presence (in blue) of scatterers (4 layers, Ar = 150nm, D = 1.846µm). A green laser source (λ = 532nm) is employed. a) Test error rate as a function of the number of employed pixels, with 5% added white noise. The darker and the lighter versions of the two line colors respectively represent the mean value and the confidence interval (of 2 standard deviations) over the 20 sample sets generated for validation. b) Test error rate (averaged on the values obtained considering Npix = 250, 260, , 300) as a function of the added noise percentage. In order to avoid error bar overlap, some of the blue points are slightly shifted to the right. Both the plots show that the scatterers’ presence allows for an error rate reduction up to ∼ 50%, provided that a sufficient number of pixels and a low enough noise level are considered.
Fig. 5
Fig. 5 Two equivalent schematics of the proposed classifying system. At the top, a physical schema shows an example of amplitude and phase evolution along 3 optical paths that end up impinging on the same pixel of the image sensor. The acquired light intensity is then weighted and summed by a linear classifier. At the bottom, a diagram (under the form of a neural network architecture) represents the corresponding mathematical operations on the light phase accumulated through the cell refractive index structure (see Eq. (7)). For simplicity’s sake, the light deflection due to the cell presence is neglected and thus the amplitudes An and the factors Anm, Bnm and C are considered as constants with respect to the inputs θn.
Fig. 6
Fig. 6 Change in the acquired diffraction pattern due to small increases (130 nm) of the nucleus size as a function of the starting nucleus size. The change between two interference patterns has been calculated by summing the absolute values of the elements of their point-wise difference vector. It can be noted that the smaller the employed wavelength is, the larger the pattern modifications become, implying an easier classification task.
Fig. 7
Fig. 7 Comparison between the test error rates of “normal” and “cancer” cell classification, corresponding to the absence (in red) and the presence (in blue) of scatterers (4 layers, Ar = 150nm, D = 2.85µm). An UV laser source (λ = 337.1nm) is employed. a) Test error rate as a function of the number of employed pixels, with 5% added white noise. The darker and the lighter versions of the two line colors respectively represent the mean value and the confidence interval (of 2 standard deviations) over the 20 sample sets generated for validation. b) Test error rate (averaged on the values obtained considering Npix = 250, 260, …, 300) as a function of the added noise percentage. Both the plots show that the scatterers presence allows for a considerable error rate reduction (up to an order of magnitude) in the whole investigated ranges of pixel number and noise level.
Fig. 8
Fig. 8 Comparison between the test error rates of “lymphocyte” and “neutrophil” cell classification, corresponding to the absence (in red) and the presence (in blue) of scatterers. The scatterers configuration and the light source are the same as in Fig. 4. a) Test error rate as a function of the number of employed pixels, with 5% added white noise. The darker and the lighter versions of the two line colors respectively represent the mean value and the confidence interval (of 2 standard deviations) over the 20 sample sets generated for validation. b) Test error rate (averaged on the values obtained considering Npix = 250, 260, , 300) as a function of the added noise percentage. In order to avoid error bar overlap, some of the blue points are slightly shifted to the right. Both the plots show that the scatterers’ presence allows for an error rate reduction greater than 50%, provided that a sufficient number of pixels and a low enough noise level are considered.

Equations (8)

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

ρ 2 cos 2 θ a 2 + ρ 2 sin 2 θ b 2 = 1
ρ ρ ( 1 + A cos ( ω θ ) )
ρ ρ + B ε s
a n = b n = { 1.2 × ( 1 + 0.1 ε ) μ m normal calls 2.5 × ( 1 + 01 ε ) μ m cancer calls
a n = b n = { 3.5 × ( 1 + 0.2 ε ) μ m lymphocytes 3.5 / 3 × ( 1 + 02 ε ) μ m neutrophils
a n = b n = { x n = x c + a c × 0.2 ε and y n = y c + b c × 0.2 ε lymphocytes x n = x c + r cos ( α k + β ) and y n = y c + r sin ( α k + β ) neutrophils
I | n A n e i ( θ n + ϕ n ) | 2 = C + m < n [ A n m cos ( θ n θ m ) + B n m sin ( θ n θ m ) ]
Δ I A [ sin ( Δ θ c ) sin ( Δ θ n ) ] + B [ cos ( Δ θ c ) cos ( Δ θ n ) ] with Δ θ c = 2 π D c λ ( n n u c l e u s n c y t o p l a s m ) and Δ θ n = 2 π D n λ ( n n u c l e u s n c y t o p l a s m )

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