Abstract

In optical tomography, it is challenging to obtain high-quality results for complex-structured objects which induce multiple scattering. Nonlinear reconstruction methods outperform linear ones in these situations. A promising nonlinear method is the approach based on beam propagation method, but its accuracy may decrease for complicated structures. In this paper, we describe a novel tomographic reconstruction method using multi-slice wave propagation method (WPM) as the forward model, which simulates the scattering process more precisely but has not been introduced in tomographic reconstruction before. The computational model of WPM is presented. To tackle the computational complexity, we propose an efficient scheme to compute the transmitted field and its derivative. We then use an iterative optimization method to recover the quantitative refraction index distribution. We also discuss the influences of the parameters in the method and how to determine their values. The experimental results demonstrate that this method can address multiple scattering problems and provide high accuracy for complex-structured objects.

© 2017 Optical Society of America

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References

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2017 (3)

2016 (8)

K. Kim, J. Yoon, and Y. Park, “Large-scale optical diffraction tomography for inspection of optical plastic lenses,” Opt. Lett. 41(5), 934–937 (2016).
[Crossref] [PubMed]

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

J. Kostencka, T. Kozacki, A. Kuś, B. Kemper, and M. Kujawińska, “Holographic tomography with scanning of illumination: space-domain reconstruction for spatially invariant accuracy,” Biomed. Opt. Express 7(10), 4086–4101 (2016).
[Crossref] [PubMed]

S. Schmidt, T. Tiess, S. Schröter, R. Hambach, M. Jäger, H. Bartelt, A. Tünnermann, and H. Gross, “Wave-optical modeling beyond the thin-element-approximation,” Opt. Express 24(26), 30188–30200 (2016).
[Crossref] [PubMed]

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

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]

2015 (2)

2014 (1)

2012 (2)

A. M. Maiden, M. J. Humphry, and J. M. Rodenburg, “Ptychographic transmission microscopy in three dimensions using a multi-slice approach,” J. Opt. Soc. Am. A 29(8), 1606–1614 (2012).
[Crossref] [PubMed]

J. Schäfer, S.-C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

2010 (2)

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

M. Fertig and K.-H. Brenner, “Vector wave propagation method,” J. Opt. Soc. Am. A 27(4), 709–717 (2010).
[Crossref] [PubMed]

2009 (5)

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]

E. V. Bekker, P. Sewell, T. M. Benson, and A. Vukovic, “Wide-angle alternating-direction implicit finite-difference beam propagation method,” J. Lightwave Technol. 27(14), 2595–2604 (2009).
[Crossref]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

2007 (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

2006 (2)

1995 (1)

1993 (1)

1982 (1)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4(4), 336–350 (1982).
[Crossref] [PubMed]

1978 (1)

Allain, M.

Badizadegan, K.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Bailleul, J.

Bartelt, H.

Beck, A.

A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Bekker, E. V.

Belkebir, K.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23(3), 586–595 (2006).
[Crossref] [PubMed]

Benson, T. M.

Brenner, K.-H.

Charrière, F.

Chaumet, P. C.

Choi, C.

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

Choi, W.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Colomb, T.

Dasari, R. R.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Debailleul, M.

Depeursinge, C.

Devaney, A. J.

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4(4), 336–350 (1982).
[Crossref] [PubMed]

Drsek, F.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Dudek, M.

Ecoffet, C.

Fang-Yen, C.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Feit, M. D.

Feld, M. S.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17(1), 266–277 (2009).
[Crossref] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Fertig, M.

Fleck, J. A.

Giovaninni, H.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

Giovannini, H.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Girard, J.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Godavarthi, C.

Goy, A.

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]

Gross, H.

Haeberlé, O.

B. Simon, M. Debailleul, M. Houkal, C. Ecoffet, J. Bailleul, J. Lambert, A. Spangenberg, H. Liu, O. Soppera, and O. Haeberlé, “Tomographic diffractive microscopy with isotropic resolution,” Optica 4(4), 460–463 (2017).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

Hambach, R.

Heger, T. J.

Heo, J.

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

Herkommer, A.

Houkal, M.

Humphry, M. J.

Jäger, M.

Jang, S.

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

Ji, M.

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

Jin, D.

Kamilov, U. S.

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]

Kemper, B.

Kienle, A.

J. Schäfer, S.-C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Kim, K.

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

K. Kim, J. Yoon, and Y. Park, “Large-scale optical diffraction tomography for inspection of optical plastic lenses,” Opt. Lett. 41(5), 934–937 (2016).
[Crossref] [PubMed]

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

Konan, D.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Kostencka, J.

Kozacki, T.

Kujawinska, M.

Kus, A.

Lambert, J.

Lee, S.

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

Lee, S.-C.

J. Schäfer, S.-C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Liu, H.

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Maiden, A. M.

Maire, G.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Marquet, P.

Mitchell, E. A. D.

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

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, H.

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

Park, Y.

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

K. Kim, J. Yoon, and Y. Park, “Large-scale optical diffraction tomography for inspection of optical plastic lenses,” Opt. Lett. 41(5), 934–937 (2016).
[Crossref] [PubMed]

Pavillon, N.

Psaltis, D.

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]

Rappaz, B.

Rodenburg, J. M.

Schäfer, J.

J. Schäfer, S.-C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Schmidt, S.

Schröter, S.

Sentenac, A.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

K. Belkebir, P. C. Chaumet, and A. Sentenac, “Influence of multiple scattering on three-dimensional imaging with optical diffraction tomography,” J. Opt. Soc. Am. A 23(3), 586–595 (2006).
[Crossref] [PubMed]

Sewell, P.

Shin, S.

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

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]

Simon, B.

Singer, W.

So, P. T. C.

Son, Y.

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

Soppera, O.

Spangenberg, A.

Sung, Y.

Talneau, A.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. Giovannini, A. Talneau, M. Allain, K. Belkebir, and A. Sentenac, “Far-field diffraction microscopy at λ/10 resolution,” Optica 3(6), 609–612 (2016).
[Crossref]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Teboulle, M.

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

Testorf, M.

Thiele, S.

Tian, L.

Tiess, T.

Tünnermann, A.

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]

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]

Vukovic, A.

Waller, L.

Yang, S.-A.

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

Yaqoob, Z.

Yoon, J.

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

K. Kim, J. Yoon, and Y. Park, “Large-scale optical diffraction tomography for inspection of optical plastic lenses,” Opt. Lett. 41(5), 934–937 (2016).
[Crossref] [PubMed]

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

Zhang, T.

Zhou, R.

Appl. Opt. (3)

Biomed. Opt. Express (1)

IEEE Trans. Comput. Imaging (1)

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]

IEEE Trans. Image Process. (1)

A. Beck and M. Teboulle, “Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,” IEEE Trans. Image Process. 18(11), 2419–2434 (2009).
[Crossref] [PubMed]

J. Biomed. Photonics Eng. (1)

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photonics Eng. 2, 20201 (2016).

J. Lightwave Technol. (1)

J. Mod. Opt. (1)

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, “Tomographic diffractive microscopy: basics, techniques and perspectives,” J. Mod. Opt. 57(9), 686–699 (2010).
[Crossref]

J. Opt. Soc. Am. A (3)

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

J. Quant. Spectrosc. Radiat. Transf. (1)

J. Schäfer, S.-C. Lee, and A. Kienle, “Calculation of the near fields for the scattering of electromagnetic waves by multiple infinite cylinders at perpendicular incidence,” J. Quant. Spectrosc. Radiat. Transf. 113(16), 2113–2123 (2012).
[Crossref]

Nat. Methods (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Optica (4)

Phys. Rev. Lett. (1)

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102(21), 213905 (2009).
[Crossref] [PubMed]

Sci. Rep. (2)

K. Kim, S. Lee, J. Yoon, J. Heo, C. Choi, and Y. Park, “Three-dimensional label-free imaging and quantification of lipid droplets in live hepatocytes,” Sci. Rep. 6(1), 36815 (2016).
[Crossref] [PubMed]

H. Park, S. Lee, M. Ji, K. Kim, Y. Son, S. Jang, and Y. Park, “Measuring cell surface area and deformability of individual human red blood cells over blood storage using quantitative phase imaging,” Sci. Rep. 6(1), 34257 (2016).
[Crossref] [PubMed]

SIAM J. Imaging Sci. (1)

A. Beck and M. Teboulle, “A fast iterative shrinkage-thresholding algorithm for linear inverse problems,” SIAM J. Imaging Sci. 2(1), 183–202 (2009).
[Crossref]

Ultrason. Imaging (1)

A. J. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4(4), 336–350 (1982).
[Crossref] [PubMed]

Other (3)

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Society for Industrial and Applied Mathematics, 2001).

H.-Y. Liu, D. Liu, H. Mansour, P. Boufounos, L. Waller, and U. S. Kamilov, “SEAGLE: Robust Computational Imaging under Multiple Scattering,” in Imaging and Applied Optics 2017, OSA Technical Digest (online) (Optical Society of America, 2017), paper MM4C.1.

G. L. Pedrola, Beam Propagation Method for Design of Optical Waveguide Devices (Wiley, 2015), Chap. 2.

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of WPM.

Fig. 2
Fig. 2

Propagation of a plane wave in simulation. (a) The object with fast-varying complex structures. (b) Beam amplitude computed with WPM. (c) Comparison of exit wave amplitude computed with WPM, BPM and the Mie theory.

Fig. 3
Fig. 3

Flow chart of the reconstruction algorithm.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup: M, mirror; PBS, polarizing beam splitter; λ/2, half-wave plate; SF, spatial filter with collimating lens; MPS, micro-positioning stage with the measured sample; C, cuvette containing RI-matching liquid; MO, microscope objective; TL, tube lens; BS, beam splitter; OB, object beam; RB, reference beam.

Fig. 5
Fig. 5

Reconstructions of the four-core fiber with different initial guesses in WPMA. (a) Reconstruction using FBP as a reference. (b, c) Reconstructions using WPMA initialized with the FBP result and a constant value (medium RI), respectively. (d) Cost function (τ = 0.7) value (logarithmic scale) as the function of iteration number. Scale bar: 30 μm.

Fig. 6
Fig. 6

Reconstructions of the four-core fiber with different constraints. (a) Reconstruction using FBP as a reference. (b, c) Reconstructions using WPMA with non-negativity constraint and no constraint, respectively. (d) Cost function (τ = 0.7) value (logarithmic scale) as the function of iteration number. Scale bar: 30 μm.

Fig. 7
Fig. 7

Reconstructions of the PCF with different amounts of regularization. (a-c) Reconstructions using WPMA with τ = 0, 0.1 and 3, respectively. (d) A cross section of PCF imaged with a scanning electron microscope (SEM). Scale bar: 60 μm.

Fig. 8
Fig. 8

Reconstructions of the PCF. (a-c) Results of FBP, BPMA and WPMA, respectively. (d) Cost function value as a function of iteration number. Scale bar: 60 μm.

Fig. 9
Fig. 9

Reconstructions of the PCF in diluted medium. (a-c) Results of FBP, BPMA and WPMA, respectively. (d) Cost function value as the function of iteration number. Scale bar: 60 μm.

Equations (21)

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U ˜ ( k x , k y ,z)= F x,y { U(x,y,z) }= U(x,y,z) e i( k x x+ k y y) dxdy
U(x,y,z+Δz)= U ˜ ( k x , k y ,z)φ(x,y,z, k x , k y ) e i( k x x+ k y y) d k x d k y
φ(x,y,z, k x , k y )= e iΔz k 0 2 n 2 (x,y,z+ Δz 2 ) k x 2 k y 2
U t = 1 P p=P/2 P/21 U ˜ t1 (p) h t (p)
( h t (p) ) ξ = e iΔz k 0 2 n t (ξ) 2 (pΔ k x ) 2 e i(ξΔxpΔ k x ) ,ξ=P/2,,P/21
U t = 1 P H t F U t1
H t = [ h t ( P 2 ), h t ( P 2 +1 ), ... , h t ( P 2 1 ) ] P×P
n ^ = argmin nΓ Γ{ Φ(n) }= argmin nΓ { D(n)+τR(n) }
D(n)= 1 N j=1 N D (j) (n) = 1 2N j=1 N U E (j) U T (j) 2 2
R(n)= j=1 P×T ( x n ) j 2 + ( z n ) j 2
D (j) (n)= 1 2 U E (j) U T (j) 2 2 ,j=1,2,,N
D(n)=( D(n) n 1 , D(n) n 2 ,, D(n) n P×T )=Re{ ( U T U E ) H U T n }
U T n = [ U T n 1 , U T n 2 ,, U T n P×T ] P×(P×T)
U T n j = [ ( U T ) 1 n j , ( U T ) 2 n j ,, ( U T ) P n j ] Tr ,j=1,2,,P×T
U t n = 1 P p=P/2 P/21 [ h t (p) n U ˜ t1 (p)+ h t (p) ( F U t1 n ) pth row ] ,t=1,2,,T
h t (p) n = [ O P×P diag( b t (p) ) O P×P ] P×(P×T)
( b t (p) ) ξ = ( h t (p)) ξ n t (ξ) = iΔz k 0 2 n t (ξ) k 0 2 n t (ξ) 2 (pΔ k x ) 2 e i( Δz k 0 2 n t (ξ) 2 (pΔ k x ) 2 +ξΔxpΔ k x ) ξ=P/2,,P/21
U t n = 1 P ( J t + H t F U t1 n )
J t = [ O P×P diag( B t F U t1 ) O P×P ] P×(P×T)
B t = [ b t ( P 2 ), b t ( P 2 +1 ), , b t ( P 2 1 ) ] P×P
U 0 n = O P×(P×T)

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