Abstract

Intensity diffraction tomography (IDT) provides quantitative, volumetric refractive index reconstructions of unlabeled biological samples from intensity-only measurements. IDT is scanless and easily implemented in standard optical microscopes using an LED array but suffers from large data requirements and slow acquisition speeds. Here, we develop multiplexed IDT (mIDT), a coded illumination framework providing high volume-rate IDT for evaluating dynamic biological samples. mIDT combines illuminations from an LED grid using physical model-based design choices to improve acquisition rates and reduce dataset size with minimal loss to resolution and reconstruction quality. We analyze the optimal design scheme with our mIDT framework in simulation using the reconstruction error compared to conventional IDT and theoretical acquisition speed. With the optimally determined mIDT scheme, we achieve hardware-limited 4Hz acquisition rates enabling 3D refractive index distribution recovery on live Caenorhabditis elegans worms and embryos as well as epithelial buccal cells. Our mIDT architecture provides a 60 × speed improvement over conventional IDT and is robust across different illumination hardware designs, making it an easily adoptable imaging tool for volumetrically quantifying biological samples in their natural state.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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  1. T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
    [Crossref]
  2. D. Jin, R. Zhou, Z. Yaqoob, and P. So, “Tomographic phase microscopy: Principles and applications in bioimaging,” J. Opt. Soc. Am. B 34(5), B64–B77 (2017).
    [Crossref]
  3. V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
    [Crossref]
  4. Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
    [Crossref]
  5. P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).
  6. H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
    [Crossref]
  7. Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
    [Crossref]
  8. T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
    [Crossref]
  9. T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
    [Crossref]
  10. G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
    [Crossref]
  11. M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7(10), 3940–3950 (2016).
    [Crossref]
  12. L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an led array microscope,” Optica 2(2), 104–111 (2015).
    [Crossref]
  13. R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9(5), 2130 (2018).
    [Crossref]
  14. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
    [Crossref]
  15. J. Li, Q. Chen, J. Sun, J. Zhang, J. Ding, and C. Zuo, “Three-dimensional tomographic microscopy technique with multi-frequency combination with partially coherent illuminations,” Biomed. Opt. Express 9(6), 2526–2542 (2018).
    [Crossref]
  16. J. M. Soto, J. A. Rodrigo, and T. Alieva, “Optical diffraction tomography with fully and partially coherent illumination in high numerical aperture label-free microscopy,” Appl. Opt. 57(1), A205–A214 (2018).
    [Crossref]
  17. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
    [Crossref]
  18. L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23(9), 11394–11403 (2015).
    [Crossref]
  19. D. Hamilton and C. Sheppard, “Differential phase contrast in scanning optical microscopy,” J. Microsc. 133(1), 27–39 (1984).
    [Crossref]
  20. S. Mehta and C. Sheppard, “Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast,” Opt. Lett. 34(13), 1924–1926 (2009).
    [Crossref]
  21. M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging 5(3), 344–353 (2019).
    [Crossref]
  22. L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
    [Crossref]
  23. L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904–911 (2015).
    [Crossref]
  24. M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for fourier ptychographic microscopy,” in 2019 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2019), pp. 1–8.
  25. B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13(3), e0192937 (2018).
    [Crossref]
  26. Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cdpc),” PLoS One 12(2), e0171228 (2017).
    [Crossref]
  27. W. Lee, D. Jung, S. Ryu, and C. Joo, “Single-exposure quantitative phase imaging in color-coded led microscopy,” Opt. Express 25(7), 8398–8411 (2017).
    [Crossref]
  28. J. Li, Q. Chen, J. Zhang, Y. Zhang, L. Lu, and C. Zuo, “Efficient quantitative phase microscopy using programmable annular led illumination,” Biomed. Opt. Express 8(10), 4687–4705 (2017).
    [Crossref]
  29. H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophotonics 11(8), e201700364 (2018).
    [Crossref]
  30. Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
    [Crossref]
  31. R. Bridson, “Fast poisson disk sampling in arbitrary dimensions,” in SIGGRAPH sketches, (2007), p. 22.
  32. M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).
  33. J. Li, A. Matlock, Y. Li, Q. Chen, C. Zuo, and L. Tian, “High-speed in vitro intensity diffraction tomography,” arXiv preprint arXiv:1904.06004 (2019).
  34. Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19(10), 106002 (2014).
    [Crossref]
  35. G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
    [Crossref]
  36. A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
    [Crossref]
  37. Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
    [Crossref]
  38. T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for fourier ptychography microscopy,” Opt. Express 26(20), 26470–26484 (2018).
    [Crossref]
  39. Y. Xue, S. Cheng, Y. Li, and L. Tian, “Reliable deep-learning-based phase imaging with uncertainty quantification,” Optica 6(5), 618–629 (2019).
    [Crossref]
  40. U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
    [Crossref]
  41. U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
    [Crossref]
  42. W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1(03), 1 (2019).
    [Crossref]
  43. S. Chowdhury, M. Chen, R. Eckert, D. Ren, F. Wu, N. Repina, and L. Waller, “High-resolution 3d refractive index microscopy of multiple-scattering samples from intensity images,” Optica 6(9), 1211–1219 (2019).
    [Crossref]
  44. J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
    [Crossref]
  45. Y. Sun, Z. Xia, and U. S. Kamilov, “Efficient and accurate inversion of multiple scattering with deep learning,” Opt. Express 26(11), 14678–14688 (2018).
    [Crossref]
  46. S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
    [Crossref]
  47. Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
    [Crossref]
  48. A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
    [Crossref]

2019 (7)

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging 5(3), 344–353 (2019).
[Crossref]

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
[Crossref]

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1(03), 1 (2019).
[Crossref]

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

Y. Xue, S. Cheng, Y. Li, and L. Tian, “Reliable deep-learning-based phase imaging with uncertainty quantification,” Optica 6(5), 618–629 (2019).
[Crossref]

S. Chowdhury, M. Chen, R. Eckert, D. Ren, F. Wu, N. Repina, and L. Waller, “High-resolution 3d refractive index microscopy of multiple-scattering samples from intensity images,” Optica 6(9), 1211–1219 (2019).
[Crossref]

2018 (12)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

J. M. Soto, J. A. Rodrigo, and T. Alieva, “Optical diffraction tomography with fully and partially coherent illumination in high numerical aperture label-free microscopy,” Appl. Opt. 57(1), A205–A214 (2018).
[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9(5), 2130 (2018).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, J. Ding, and C. Zuo, “Three-dimensional tomographic microscopy technique with multi-frequency combination with partially coherent illuminations,” Biomed. Opt. Express 9(6), 2526–2542 (2018).
[Crossref]

Y. Sun, Z. Xia, and U. S. Kamilov, “Efficient and accurate inversion of multiple scattering with deep learning,” Opt. Express 26(11), 14678–14688 (2018).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for fourier ptychography microscopy,” Opt. Express 26(20), 26470–26484 (2018).
[Crossref]

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophotonics 11(8), e201700364 (2018).
[Crossref]

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13(3), e0192937 (2018).
[Crossref]

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

2017 (7)

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cdpc),” PLoS One 12(2), e0171228 (2017).
[Crossref]

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
[Crossref]

W. Lee, D. Jung, S. Ryu, and C. Joo, “Single-exposure quantitative phase imaging in color-coded led microscopy,” Opt. Express 25(7), 8398–8411 (2017).
[Crossref]

D. Jin, R. Zhou, Z. Yaqoob, and P. So, “Tomographic phase microscopy: Principles and applications in bioimaging,” J. Opt. Soc. Am. B 34(5), B64–B77 (2017).
[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
[Crossref]

J. Li, Q. Chen, J. Zhang, Y. Zhang, L. Lu, and C. Zuo, “Efficient quantitative phase microscopy using programmable annular led illumination,” Biomed. Opt. Express 8(10), 4687–4705 (2017).
[Crossref]

2016 (3)

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
[Crossref]

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7(10), 3940–3950 (2016).
[Crossref]

2015 (4)

2014 (3)

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19(10), 106002 (2014).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[Crossref]

2013 (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

2012 (1)

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

2009 (1)

2008 (1)

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

1984 (2)

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[Crossref]

D. Hamilton and C. Sheppard, “Differential phase contrast in scanning optical microscopy,” J. Microsc. 133(1), 27–39 (1984).
[Crossref]

1969 (1)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
[Crossref]

Akinwande, A. I.

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

Alieva, T.

Antoine, E. E.

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
[Crossref]

Arthur, K.

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

Ayoub, A. B.

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
[Crossref]

Babacan, S. D.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Barbastathis, G.

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
[Crossref]

Bertero, M.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

Boccacci, P.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

Bostan, E.

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging 5(3), 344–353 (2019).
[Crossref]

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for fourier ptychographic microscopy,” in 2019 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2019), pp. 1–8.

Bridson, R.

R. Bridson, “Fast poisson disk sampling in arbitrary dimensions,” in SIGGRAPH sketches, (2007), p. 22.

Bussey, K. J.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Carney, P. S.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Chen, H.-H.

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophotonics 11(8), e201700364 (2018).
[Crossref]

Chen, M.

S. Chowdhury, M. Chen, R. Eckert, D. Ren, F. Wu, N. Repina, and L. Waller, “High-resolution 3d refractive index microscopy of multiple-scattering samples from intensity images,” Optica 6(9), 1211–1219 (2019).
[Crossref]

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cdpc),” PLoS One 12(2), e0171228 (2017).
[Crossref]

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7(10), 3940–3950 (2016).
[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904–911 (2015).
[Crossref]

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for fourier ptychographic microscopy,” in 2019 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2019), pp. 1–8.

Chen, Q.

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, J. Ding, and C. Zuo, “Three-dimensional tomographic microscopy technique with multi-frequency combination with partially coherent illuminations,” Biomed. Opt. Express 9(6), 2526–2542 (2018).
[Crossref]

J. Li, Q. Chen, J. Zhang, Y. Zhang, L. Lu, and C. Zuo, “Efficient quantitative phase microscopy using programmable annular led illumination,” Biomed. Opt. Express 8(10), 4687–4705 (2017).
[Crossref]

J. Li, A. Matlock, Y. Li, Q. Chen, C. Zuo, and L. Tian, “High-speed in vitro intensity diffraction tomography,” arXiv preprint arXiv:1904.06004 (2019).

Cheng, S.

Choi, W.

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

Chowdhury, S.

Cotte, Y.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Davies, P. C.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Deng, M.

Depeursinge, C.

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

Diederich, B.

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13(3), e0192937 (2018).
[Crossref]

Diez-Silva, M.

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

Ding, J.

Eckert, R.

Equis, S.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Fan, Y.

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

Feld, M. S.

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

Frechin, M.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Goddard, L. L.

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Goy, A.

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Günaydin, H.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Hamilton, D.

D. Hamilton and C. Sheppard, “Differential phase contrast in scanning optical microscopy,” J. Microsc. 133(1), 27–39 (1984).
[Crossref]

Heintzmann, R.

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13(3), e0192937 (2018).
[Crossref]

Hernandez, K. F.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Jin, D.

Johnson, R. H.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Joo, C.

Jung, D.

Jung, W.

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

Kamilov, U. S.

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1(03), 1 (2019).
[Crossref]

Y. Sun, Z. Xia, and U. S. Kamilov, “Efficient and accurate inversion of multiple scattering with deep learning,” Opt. Express 26(11), 14678–14688 (2018).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Kandel, M. E.

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
[Crossref]

Kelbauskas, L.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Kellman, M.

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging 5(3), 344–353 (2019).
[Crossref]

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for fourier ptychographic microscopy,” in 2019 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2019), pp. 1–8.

Kim, G.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Kim, T.

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Kwon, D.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Lee, E.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Lee, H.

Lee, J.

Lee, M.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Lee, S.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Lee, W.

Lee, Y. S.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Li, J.

Li, S.

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
[Crossref]

Li, X.

Li, Y.

Lim, J.

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
[Crossref]

Lin, H.-Y.

Lin, Y.-Z.

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophotonics 11(8), e201700364 (2018).
[Crossref]

Ling, R.

Lintecum, K. M.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Liu, S.

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19(10), 106002 (2014).
[Crossref]

Liu, Z.

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904–911 (2015).
[Crossref]

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19(10), 106002 (2014).
[Crossref]

Lu, L.

Luo, Y.

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophotonics 11(8), e201700364 (2018).
[Crossref]

Lykotrafitis, G.

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

Ma, L.

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

Majeed, H.

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

Matlock, A.

J. Li, A. Matlock, Y. Li, Q. Chen, C. Zuo, and L. Tian, “High-speed in vitro intensity diffraction tomography,” arXiv preprint arXiv:1904.06004 (2019).

Mehta, S.

Meldrum, D. R.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Min, E.

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

Mir, M.

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Nandakumar, V.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Nehmetallah, G.

Nguyen, T.

Nguyen, T. H.

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
[Crossref]

Ozcan, A.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Pan, X.

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

Papadopoulos, I. N.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Park, Y.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

Phillips, Z. F.

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cdpc),” PLoS One 12(2), e0171228 (2017).
[Crossref]

Pollaro, L.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Pop, S.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Popescu, G.

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
[Crossref]

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

Psaltis, D.

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Ramchandran, K.

Ren, D.

Repina, N.

S. Chowdhury, M. Chen, R. Eckert, D. Ren, F. Wu, N. Repina, and L. Waller, “High-resolution 3d refractive index microscopy of multiple-scattering samples from intensity images,” Optica 6(9), 1211–1219 (2019).
[Crossref]

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging 5(3), 344–353 (2019).
[Crossref]

Rivenson, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Rodrigo, J. A.

Rubessa, M.

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
[Crossref]

Rughoobur, G.

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

Ryu, S.

Sandoz, P. A.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Schadwinkel, H.

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13(3), e0192937 (2018).
[Crossref]

Senechal, P.

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Sheppard, C.

Shin, J.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Shoreh, M. H.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Sinha, A.

So, P.

Soto, J. M.

Sridharan, S.

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[Crossref]

Sun, J.

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, J. Ding, and C. Zuo, “Three-dimensional tomographic microscopy technique with multi-frequency combination with partially coherent illuminations,” Biomed. Opt. Express 9(6), 2526–2542 (2018).
[Crossref]

Sun, Y.

Suresh, S.

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

Tahir, W.

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1(03), 1 (2019).
[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9(5), 2130 (2018).
[Crossref]

Teng, D.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Tian, L.

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1(03), 1 (2019).
[Crossref]

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

Y. Xue, S. Cheng, Y. Li, and L. Tian, “Reliable deep-learning-based phase imaging with uncertainty quantification,” Optica 6(5), 618–629 (2019).
[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for fourier ptychography microscopy,” Opt. Express 26(20), 26470–26484 (2018).
[Crossref]

R. Ling, W. Tahir, H.-Y. Lin, H. Lee, and L. Tian, “High-throughput intensity diffraction tomography with a computational microscope,” Biomed. Opt. Express 9(5), 2130 (2018).
[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7(10), 3940–3950 (2016).
[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904–911 (2015).
[Crossref]

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an led array microscope,” Optica 2(2), 104–111 (2015).
[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23(9), 11394–11403 (2015).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[Crossref]

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19(10), 106002 (2014).
[Crossref]

J. Li, A. Matlock, Y. Li, Q. Chen, C. Zuo, and L. Tian, “High-speed in vitro intensity diffraction tomography,” arXiv preprint arXiv:1904.06004 (2019).

Tremblay, C.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Unser, M.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Van Der Goot, G. F.

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

Vonesch, C.

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Learning approach to optical tomography,” Optica 2(6), 517–522 (2015).
[Crossref]

Waller, L.

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging 5(3), 344–353 (2019).
[Crossref]

S. Chowdhury, M. Chen, R. Eckert, D. Ren, F. Wu, N. Repina, and L. Waller, “High-resolution 3d refractive index microscopy of multiple-scattering samples from intensity images,” Optica 6(9), 1211–1219 (2019).
[Crossref]

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cdpc),” PLoS One 12(2), e0171228 (2017).
[Crossref]

M. Chen, L. Tian, and L. Waller, “3D differential phase contrast microscopy,” Biomed. Opt. Express 7(10), 3940–3950 (2016).
[Crossref]

L. Tian, Z. Liu, L.-H. Yeh, M. Chen, J. Zhong, and L. Waller, “Computational illumination for high-speed in vitro Fourier ptychographic microscopy,” Optica 2(10), 904–911 (2015).
[Crossref]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23(9), 11394–11403 (2015).
[Crossref]

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an led array microscope,” Optica 2(2), 104–111 (2015).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier ptychography with an LED array microscope,” Biomed. Opt. Express 5(7), 2376–2389 (2014).
[Crossref]

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19(10), 106002 (2014).
[Crossref]

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for fourier ptychographic microscopy,” in 2019 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2019), pp. 1–8.

Wartmann, R.

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13(3), e0192937 (2018).
[Crossref]

Wheeler, M. B.

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
[Crossref]

Wolf, E.

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
[Crossref]

Wu, F.

Xia, Z.

Xue, Y.

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Yaqoob, Z.

Yeh, L.-H.

Youn, S.

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Zhang, J.

Zhang, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

J. Li, Q. Chen, J. Zhang, Y. Zhang, L. Lu, and C. Zuo, “Efficient quantitative phase microscopy using programmable annular led illumination,” Biomed. Opt. Express 8(10), 4687–4705 (2017).
[Crossref]

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Zhong, J.

Zhou, R.

D. Jin, R. Zhou, Z. Yaqoob, and P. So, “Tomographic phase microscopy: Principles and applications in bioimaging,” J. Opt. Soc. Am. B 34(5), B64–B77 (2017).
[Crossref]

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

Zuo, C.

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

J. Li, Q. Chen, J. Sun, J. Zhang, J. Ding, and C. Zuo, “Three-dimensional tomographic microscopy technique with multi-frequency combination with partially coherent illuminations,” Biomed. Opt. Express 9(6), 2526–2542 (2018).
[Crossref]

J. Li, Q. Chen, J. Zhang, Y. Zhang, L. Lu, and C. Zuo, “Efficient quantitative phase microscopy using programmable annular led illumination,” Biomed. Opt. Express 8(10), 4687–4705 (2017).
[Crossref]

J. Li, A. Matlock, Y. Li, Q. Chen, C. Zuo, and L. Tian, “High-speed in vitro intensity diffraction tomography,” arXiv preprint arXiv:1904.06004 (2019).

Adv. Photonics (1)

W. Tahir, U. S. Kamilov, and L. Tian, “Holographic particle localization under multiple scattering,” Adv. Photonics 1(03), 1 (2019).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (5)

IEEE Trans. Comput. Imaging (2)

M. Kellman, E. Bostan, N. Repina, and L. Waller, “Physics-based learned design: Optimized coded-illumination for quantitative phase imaging,” IEEE Trans. Comput. Imaging 5(3), 344–353 (2019).
[Crossref]

U. S. Kamilov, I. N. Papadopoulos, M. H. Shoreh, A. Goy, C. Vonesch, M. Unser, and D. Psaltis, “Optical tomographic image reconstruction based on beam propagation and sparse regularization,” IEEE Trans. Comput. Imaging 2(1), 59–70 (2016).
[Crossref]

J. Biomed. Opt. (1)

Z. Liu, L. Tian, S. Liu, and L. Waller, “Real-time brightfield, darkfield, and phase contrast imaging in a light-emitting diode array microscope,” J. Biomed. Opt. 19(10), 106002 (2014).
[Crossref]

J. Biophotonics (2)

H.-H. Chen, Y.-Z. Lin, and Y. Luo, “Isotropic differential phase contrast microscopy for quantitative phase bio-imaging,” J. Biophotonics 11(8), e201700364 (2018).
[Crossref]

H. Majeed, S. Sridharan, M. Mir, L. Ma, E. Min, W. Jung, and G. Popescu, “Quantitative phase imaging for medical diagnosis,” J. Biophotonics 10(2), 177–205 (2017).
[Crossref]

J. Microsc. (1)

D. Hamilton and C. Sheppard, “Differential phase contrast in scanning optical microscopy,” J. Microsc. 133(1), 27–39 (1984).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (1)

T. Kim, R. Zhou, L. L. Goddard, and G. Popescu, “Solving inverse scattering problems in biological samples by quantitative phase imaging,” Laser Photonics Rev. 10(1), 13–39 (2016).
[Crossref]

Light: Sci. Appl. (2)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

J. Lim, A. B. Ayoub, E. E. Antoine, and D. Psaltis, “High-fidelity optical diffraction tomography of multiple scattering samples,” Light: Sci. Appl. 8(1), 1–12 (2019).
[Crossref]

Nat. Commun. (1)

T. H. Nguyen, M. E. Kandel, M. Rubessa, M. B. Wheeler, and G. Popescu, “Gradient light interference microscopy for 3D imaging of unlabeled specimens,” Nat. Commun. 8(1), 210 (2017).
[Crossref]

Nat. Photonics (3)

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12(10), 578–589 (2018).
[Crossref]

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8(3), 256–263 (2014).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref]

Opt. Commun. (2)

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1(4), 153–156 (1969).
[Crossref]

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Optica (8)

Photonics Res. (1)

Y. Fan, J. Sun, Q. Chen, X. Pan, L. Tian, and C. Zuo, “Optimal illumination scheme for isotropic quantitative differential phase contrast microscopy,” Photonics Res. 7(8), 890 (2019).
[Crossref]

PLoS One (3)

B. Diederich, R. Wartmann, H. Schadwinkel, and R. Heintzmann, “Using machine-learning to optimize phase contrast in a low-cost cellphone microscope,” PLoS One 13(3), e0192937 (2018).
[Crossref]

Z. F. Phillips, M. Chen, and L. Waller, “Single-shot quantitative phase microscopy with color-multiplexed differential phase contrast (cdpc),” PLoS One 12(2), e0171228 (2017).
[Crossref]

V. Nandakumar, L. Kelbauskas, K. F. Hernandez, K. M. Lintecum, P. Senechal, K. J. Bussey, P. C. Davies, R. H. Johnson, and D. R. Meldrum, “Isotropic 3D nuclear morphometry of normal, fibrocystic and malignant breast epithelial cells reveals new structural alterations,” PLoS One 7(1), e29230 (2012).
[Crossref]

Proc. Natl. Acad. Sci. (2)

Y. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by plasmodium falciparum,” Proc. Natl. Acad. Sci. 105(37), 13730–13735 (2008).
[Crossref]

A. Goy, G. Rughoobur, S. Li, K. Arthur, A. I. Akinwande, and G. Barbastathis, “High-resolution limited-angle phase tomography of dense layered objects using deep neural networks,” Proc. Natl. Acad. Sci. 116(40), 19848–19856 (2019).
[Crossref]

Sci. Rep. (1)

G. Kim, M. Lee, S. Youn, E. Lee, D. Kwon, J. Shin, S. Lee, Y. S. Lee, and Y. Park, “Measurements of three-dimensional refractive index tomography and membrane deformability of live erythrocytes from pelophylax nigromaculatus,” Sci. Rep. 8(1), 9192 (2018).
[Crossref]

Other (5)

P. A. Sandoz, C. Tremblay, S. Equis, S. Pop, L. Pollaro, Y. Cotte, G. F. Van Der Goot, and M. Frechin, “Label free 3D analysis of organelles in living cells by refractive index shows pre-mitotic organelle spinning in mammalian stem cells,” BioRxiv p. 407239 (2018).

M. Kellman, E. Bostan, M. Chen, and L. Waller, “Data-driven design for fourier ptychographic microscopy,” in 2019 IEEE International Conference on Computational Photography (ICCP), (IEEE, 2019), pp. 1–8.

R. Bridson, “Fast poisson disk sampling in arbitrary dimensions,” in SIGGRAPH sketches, (2007), p. 22.

M. Bertero and P. Boccacci, Introduction to Inverse Problems in Imaging (Taylor & Francis, 1998).

J. Li, A. Matlock, Y. Li, Q. Chen, C. Zuo, and L. Tian, “High-speed in vitro intensity diffraction tomography,” arXiv preprint arXiv:1904.06004 (2019).

Supplementary Material (3)

NameDescription
» Visualization 1       Visualization of the live Caenorhabditis elegans worm evaluated in Figure 5. The outsets show volumetric refractive index recovery of the worm's tissue structures.
» Visualization 2       Visualization of live C. elegans embryos volumetric refractive index distributions using mIDT. Video corresponds to Figure 6 in the main work. Embryo features are clearly recovered and could be tracked across time using our imaging technique.
» Visualization 3       Visualization of epithelial buccal cells and live native bacteria from Figure 7. Our imaging technique recovers bacteria motion across 3D space enabling the observation of bacteria-cell interactions in a natural, label-free environment.

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Figures (9)

Fig. 1.
Fig. 1. (a) mIDT imaging system composed of an inverted microscope equipped with an LED array. (b) mIDT reduces both acquisition speeds and image numbers. (c) Example mIDT ($N_m=6$,$L=16$) intensity images (top) and spectra (bottom) for a live C. elegans worm . (d) Example mIDT real and imaginary TFs across multiple depths. (e) Real and imaginary refractive index reconstructions and depth-coded projections of live C. elegans worm volumetric reconstructions, demonstrating minimal motion artifacts across a 1-minute acquisition period.
Fig. 2.
Fig. 2. (a) The in-focus weight distribution $W[0]$ of conventional IDT, Annular illumination IDT, and downsampled annular illumination TFs without multiplexing. Removing LEDs from the grid provides equivalent Fourier coverage while reducing the number of images required for IDT. (b) The real and imaginary TF behavior for multiplexed symmetric (top) and non-symmetric (bottom) illuminations. The loss of phase information for symmetric illumination necessitates geometric illumination constraints to maximize the object’s recovered phase. (c) The weight distribution and VMSE comparison of mIDT designs using pseudorandom and poisson disk random sampling for LED selection. Poisson disk sampling provides equivalent or lower VMSE to pseudorandom sampling because it reduces TF overlap by spatially separating multiplexed illuminations.
Fig. 3.
Fig. 3. (a) Depth-coded projections of conventional IDT (Upper Left) reconstructions compared with various mIDT designs. Each row is fixed with a specific multiplexing value and each column has a fixed downsampled LED grid. Downsampling without multiplexing preserves the reconstruction quality while multiplexing illuminations increases the reconstruction artifacts. (b) Volumetric mean-square errors (VMSEs) of mIDT designs using different downsampling and multiplexing conditions and their corresponding theoretical acquisition speed. Each mIDT case is compared to the conventional IDT reconstruction. The results show multiplexing and downsampling are necessary to achieve a theoretical 10Hz acquisition rate with our hardware setup.
Fig. 4.
Fig. 4. Depth-Coded Projections (Left) and Volumetric Mean-Square errors (Right) for conventional IDT and mIDT measurements under different SNR conditions. The $N_m=1, L=96$ case shows noise-limited reconstruction quality with increasingly underestimated object permittivity while both the mIDT and $N_m=1, L=16$ show higher contrast, better permittivity recovery with object-dependent structural artifacts. These artifacts cause the VMSE to increase with longer exposure times.
Fig. 5.
Fig. 5. Comparison of Phase Contrast (Top), conventional IDT (Middle), and mIDT (Bottom) measurements on two epithelial buccal cells. The phase contrast measurements show inverted phase information compared to IDT. mIDT recovers identical features to PhC and conventional IDT across different depths but includes slightly more artifacts as discussed in the main text.
Fig. 6.
Fig. 6. (a) Full-field refractive index reconstruction of a live C. elegans worm at the in-focus plane at time $T=0$s. The full video of the reconstruction is provided in Visualization 1. (b) Outsets at $T=0$s of the live worm across multiple depths. The markers highlight the following structures: lipid droplets and granular structures (red arrows), the grinder (white arrow), The pharyngeal-intestinal valve (white box), the intestinal tract (red bar), and wall muscle (white bar). mIDT reconstruction artifacts are more prominent at defocused slice reconstructions, but some structures are still recoverable. (c) Time lapse images of the C. elegans worm moving through outset regions at $Z=0\mu$m (Top), $Z=6\mu$m (Middle), and depth projections (Bottom) through the object volume. Lipid droplets (red arrows) and external native bacteria (blue arrows) are highlighted showing finely detailed features are captured with mIDT. The variouss in the depth projection show tissues and bacteria are recovered across the reconstructed volume.
Fig. 7.
Fig. 7. (Top) In-focus refractive index reconstruction of C. elegans embryo temporal measurement and (Bottom) depth-coded projections of volumetric reconstruction. The full video of the reconstruction is provided in Visualization 2. mIDT’s reconstruction quality enables the identification of the embryos in the three-fold (red arrow) and quickening (orange arrow) development stages. Individual developing tissues including the buccal cavity (white box), intestine (blue box), and native bacteria (blue arrow) are clearly recovered with mIDT.
Fig. 8.
Fig. 8. (a) Temporally-coded in-focus reconstruction of epithelial buccal cells and native bacteria. The volumetric reconstruction cross-sections capture moving bacteria across multiple depths. The full video of the reconstruction is provided in Visualization 3. (b) The refractive index reconstructions of diplococci bacteria (left) and a native bacterial cluster (right) across a one minute acquisition period. Both outsets show bacteria motion is quantitatively captured without artifacts using mIDT. The red arrow highlights a dynamic feature of the native bacterial cluster. (c) Maximum intensity projections of temporally encoded refractive index volume reconstructions of a single bacteria. The cross-sections recover 3D particle motion across multiple axial planes during the measurement highlighting mIDT’s potential for particle tracking.
Fig. 9.
Fig. 9. Predicted and manually determined Tikhonov regularization values for (a) fixed $N_m$ and variable $L$, (b) fixed $L$ and variable $N_m$, (c) fixed $L$ and $N_m$ with variable defocus, and (d) VMSEs comparing mIDT and conventional IDT using predicted and manually determined Tikhonov values. We observe linearly increasing $\tau$ with $L$ and linearly decreasing $\tau$ with $N_m$ as predicted from our derivations. Our VMSE is increased with our predictions but are still considered small for finding optimal mIDT designs.

Equations (15)

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I ^ ( u | u i ) = q = 0 N z 1 [ H r e ( u , q | u i ) Δ ϵ ^ r e ( u , q ) + H i m ( u , q | u i ) Δ ϵ ^ i m ( u , q ) ] ,
I ^ l ( u | N m l ) = q = 0 N z 1 { H r e , l ( u , q | N m l ) Δ ϵ ^ r e ( u , q ) + H i m , l ( u , q | N m l ) Δ ϵ ^ i m ( u , q ) } .
H r e ( i m ) , l ( u , q | N m l ) = m = 1 N m l H r e ( i m ) , l ( u , q | u m ) .
D = m a x q = 1 N z t r ( W [ q ] α ) q = 1 N z t r ( W [ q ] < α ) ,
Δ ϵ r e ( r ) = F 1 { 1 T [ ( l = 1 L | H i m , l | 2 + τ i m ) ( l = 1 L H r e , l I ^ l ) ( l = 1 L H r e , l H i m , l ) ( l = 1 L H i m , l I ^ l ) ] }
Δ ϵ i m ( r ) = F 1 { 1 T [ ( l = 1 L | H r e , l | 2 + τ r e ) ( l = 1 L H i m , l I ^ l ) ( l = 1 L H i m , l H r e , l ) ( l = 1 L H r e , l I ^ l ) ] }
τ = L γ / N m
H r e ( u , q | u i ) = j k 0 2 2 S ( u i ) P ( u i ) { P ( u u i ) e j [ η ( u u i ) η ( u i ) ] q Δ z η ( u u i ) P ( u + u i ) e j [ η ( u + u i ) η ( u i ) ] q Δ z η ( u + u i ) } ,
H i m ( u , q | u i ) = k 0 2 2 S ( u i ) P ( u i ) { P ( u u i ) e j [ η ( u u i ) η ( u i ) ] q Δ z η ( u u i ) + P ( u + u i ) e j [ η ( u + u i ) η ( u i ) ] q Δ z η ( u + u i ) } ,
I ^ = H Δ ϵ ^
H = [ H r e [ 1 , N m 1 ] H r e [ N z , N m 1 ] H i m [ 1 , N m 1 ] H i m [ N z , N m 1 ] H r e [ 1 , N m L ] H r e [ N z , N m L ] H i m [ 1 , N m L ] H i m [ N z , N m L ] ]
H q = [ H r e [ q , N m 1 ] H i m [ q , N m 1 ] H r e [ q , N m L ] H i m [ q , N m L ] ] .
W [ q ] = ( = 1 L | H r e [ q , N m ] | 2 ) ( = 1 L | H i m [ q , N m ] | 2 ) ( = 1 L H r e [ q , N m ] H i m [ q , N m ] ) ( = 1 L H r e [ q , N m ] H i m [ q , N m ] ) ,
D = a r g m i n G E { Δ ϵ ^ r e L G I ^ 2 }
G = H r e [ q , N m ] L | H r e [ q , N m ] | 2 + γ N m

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