Abstract

Tomographic diffraction microscopy is a three-dimensional quantitative optical imaging technique in which the sample is numerically reconstructed from tens of holograms recorded under different angles of incidence. We show that combining the measurement of the amplitude, the phase, and the polarization of the field scattered by the sample with an approximate knowledge of the sample permittivity allows reconstruction of spatially complex samples up to 50 nm resolution. This technique should be particularly useful for imaging objects made of known materials.

© 2016 Optical Society of America

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References

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2016 (1)

J. Qin, R. M. Silver, B. M. Barnes, H. Zhou, R. G. Dixson, and M.-A. Henn, Light Sci. Appl. 5, e16038 (2016).
[Crossref]

2015 (4)

2013 (5)

G. Maire, Y. Ruan, T. Zhang, P. C. Chaumet, H. Giovannini, D. Sentenac, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 30, 2133 (2013).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

2012 (2)

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, Inverse Probl. 28, 125008 (2012).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, Inverse Probl. 28, 065007 (2012).
[Crossref]

2010 (4)

H. Ayasso, B. Duchêne, and A. Mohammad-Djafari, J. Mod. Opt. 57, 765 (2010).
[Crossref]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. A 82, 061801 (2010).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, J. Mod. Opt. 57, 686 (2010).
[Crossref]

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).

2009 (4)

2007 (2)

2006 (4)

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[Crossref]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, J. Opt. Soc. Am. A 23, 3162 (2006).
[Crossref]

F. Simonetti, Phys. Rev. E 73, 036619 (2006).
[Crossref]

K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 23, 586 (2006).
[Crossref]

2004 (1)

G. Cox and C. J. R. Sheppard, Microsc. Res. Tech. 63, 18 (2004).
[Crossref]

2002 (1)

V. Lauer, J. Microsc. 205, 165 (2002).
[Crossref]

1998 (1)

A. Litman, D. Lesselier, and F. Santosa, Inverse Probl. 14, 685 (1998).
[Crossref]

1991 (1)

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251, 1468 (1991).
[Crossref]

Alexandrov, S. A.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[Crossref]

Aulbach, J.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

Ayasso, H.

H. Ayasso, B. Duchêne, and A. Mohammad-Djafari, J. Mod. Opt. 57, 765 (2010).
[Crossref]

Barnes, B. M.

J. Qin, R. M. Silver, B. M. Barnes, H. Zhou, R. G. Dixson, and M.-A. Henn, Light Sci. Appl. 5, e16038 (2016).
[Crossref]

Bartal, G.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).

Belkebir, K.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. G. Nnini, A. Talneau, C. Prada, A. Sentenac, and K. Belkebir, Opt. Lett. 40, 573 (2015).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 32, 287 (2015).
[Crossref]

G. Maire, Y. Ruan, T. Zhang, P. C. Chaumet, H. Giovannini, D. Sentenac, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 30, 2133 (2013).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, Inverse Probl. 28, 125008 (2012).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, Inverse Probl. 28, 065007 (2012).
[Crossref]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. A 82, 061801 (2010).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, J. Mod. Opt. 57, 686 (2010).
[Crossref]

P. C. Chaumet, K. Belkebir, and A. Sentenac, J. Appl. Phys. 106, 034901 (2009).
[Crossref]

K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 23, 586 (2006).
[Crossref]

Bertaux, N.

Betzig, E.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251, 1468 (1991).
[Crossref]

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

Chaumet, P. C.

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. G. Nnini, A. Talneau, C. Prada, A. Sentenac, and K. Belkebir, Opt. Lett. 40, 573 (2015).
[Crossref]

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 32, 287 (2015).
[Crossref]

G. Maire, Y. Ruan, T. Zhang, P. C. Chaumet, H. Giovannini, D. Sentenac, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 30, 2133 (2013).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, Inverse Probl. 28, 125008 (2012).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, Inverse Probl. 28, 065007 (2012).
[Crossref]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. A 82, 061801 (2010).
[Crossref]

P. C. Chaumet, K. Belkebir, and A. Sentenac, J. Appl. Phys. 106, 034901 (2009).
[Crossref]

A. Sentenac, C.-A. Guérin, P. C. Chaumet, F. Drsek, H. Giovannini, N. Bertaux, and M. Holschneider, Opt. Express 15, 1340 (2007).
[Crossref]

K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 23, 586 (2006).
[Crossref]

Choi, H.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).

Choi, W.

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

Cox, G.

G. Cox and C. J. R. Sheppard, Microsc. Res. Tech. 63, 18 (2004).
[Crossref]

Crocco, L.

A. Litman and L. Crocco, Inverse Probl. 25, 020201 (2009).
[Crossref]

Dasari, R. R.

Debailleul, M.

Depeursinge, C.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

Dixson, R. G.

J. Qin, R. M. Silver, B. M. Barnes, H. Zhou, R. G. Dixson, and M.-A. Henn, Light Sci. Appl. 5, e16038 (2016).
[Crossref]

Drsek, F.

Duchêne, B.

H. Ayasso, B. Duchêne, and A. Mohammad-Djafari, J. Mod. Opt. 57, 765 (2010).
[Crossref]

Fang-Yen, C.

Feld, M. S.

Garcia, J.

Garcia-Martinez, P.

Georges, V.

Giovaninni, H.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, J. Mod. Opt. 57, 686 (2010).
[Crossref]

Giovannini, H.

Girard, J.

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. A 82, 061801 (2010).
[Crossref]

Gjonaj, B.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

Godavarthi, C.

Goy, A.

Guérin, C.-A.

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[Crossref]

Haeberlé, O.

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, J. Mod. Opt. 57, 686 (2010).
[Crossref]

M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, Opt. Lett. 34, 79 (2009).
[Crossref]

Harris, T. D.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251, 1468 (1991).
[Crossref]

Henn, M.-A.

J. Qin, R. M. Silver, B. M. Barnes, H. Zhou, R. G. Dixson, and M.-A. Henn, Light Sci. Appl. 5, e16038 (2016).
[Crossref]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[Crossref]

Holschneider, M.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, Nat. Photonics 7, 739 (2013).
[Crossref]

Johnson, P. M.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

Kamilov, U. S.

Kostelak, R. L.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, Science 251, 1468 (1991).
[Crossref]

Kuipers, L.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

Lagendijk, A.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

Lauer, V.

V. Lauer, J. Microsc. 205, 165 (2002).
[Crossref]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[Crossref]

Lesselier, D.

A. Litman, D. Lesselier, and F. Santosa, Inverse Probl. 14, 685 (1998).
[Crossref]

Litman, A.

A. Litman and L. Crocco, Inverse Probl. 25, 020201 (2009).
[Crossref]

A. Litman, D. Lesselier, and F. Santosa, Inverse Probl. 14, 685 (1998).
[Crossref]

Liu, Z.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, Science 315, 1686 (2007).
[Crossref]

Magistretti, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

Maire, G.

Marquet, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

Mico, V.

Mohammad-Djafari, A.

H. Ayasso, B. Duchêne, and A. Mohammad-Djafari, J. Mod. Opt. 57, 765 (2010).
[Crossref]

Morin, R.

Mosk, A. P.

B. Gjonaj, J. Aulbach, P. M. Johnson, A. P. Mosk, L. Kuipers, and A. Lagendijk, Phys. Rev. Lett. 110, 266804 (2013).
[Crossref]

Mudry, E.

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, Inverse Probl. 28, 125008 (2012).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, Inverse Probl. 28, 065007 (2012).
[Crossref]

Nnini, H. G.

Papadopoulos, I. N.

Pavillon, N.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, Nat. Photonics 7, 113 (2013).
[Crossref]

Prada, C.

Psaltis, D.

Qin, J.

J. Qin, R. M. Silver, B. M. Barnes, H. Zhou, R. G. Dixson, and M.-A. Henn, Light Sci. Appl. 5, e16038 (2016).
[Crossref]

Rho, J.

J. Rho, Z. Ye, Y. Xiong, X. Yin, Z. Liu, H. Choi, G. Bartal, and X. Zhang, Nat. Commun. 1, 143 (2010).

Ruan, Y.

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

G. Maire, Y. Ruan, T. Zhang, P. C. Chaumet, H. Giovannini, D. Sentenac, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 30, 2133 (2013).
[Crossref]

Sampson, D. D.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
[Crossref]

Santosa, F.

A. Litman, D. Lesselier, and F. Santosa, Inverse Probl. 14, 685 (1998).
[Crossref]

Sentenac, A.

C. Godavarthi, T. Zhang, G. Maire, P. C. Chaumet, H. Giovannini, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 32, 287 (2015).
[Crossref]

T. Zhang, C. Godavarthi, P. C. Chaumet, G. Maire, H. G. Nnini, A. Talneau, C. Prada, A. Sentenac, and K. Belkebir, Opt. Lett. 40, 573 (2015).
[Crossref]

G. Maire, Y. Ruan, T. Zhang, P. C. Chaumet, H. Giovannini, D. Sentenac, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 30, 2133 (2013).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 111, 243904 (2013).
[Crossref]

T. Zhang, P. C. Chaumet, E. Mudry, A. Sentenac, and K. Belkebir, Inverse Probl. 28, 125008 (2012).
[Crossref]

E. Mudry, P. C. Chaumet, K. Belkebir, and A. Sentenac, Inverse Probl. 28, 065007 (2012).
[Crossref]

J. Girard, G. Maire, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. A 82, 061801 (2010).
[Crossref]

O. Haeberlé, K. Belkebir, H. Giovaninni, and A. Sentenac, J. Mod. Opt. 57, 686 (2010).
[Crossref]

P. C. Chaumet, K. Belkebir, and A. Sentenac, J. Appl. Phys. 106, 034901 (2009).
[Crossref]

A. Sentenac, C.-A. Guérin, P. C. Chaumet, F. Drsek, H. Giovannini, N. Bertaux, and M. Holschneider, Opt. Express 15, 1340 (2007).
[Crossref]

K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 23, 586 (2006).
[Crossref]

Sentenac, D.

G. Maire, Y. Ruan, T. Zhang, P. C. Chaumet, H. Giovannini, D. Sentenac, A. Talneau, K. Belkebir, and A. Sentenac, J. Opt. Soc. Am. A 30, 2133 (2013).
[Crossref]

T. Zhang, Y. Ruan, G. Maire, D. Sentenac, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 111, 243904 (2013).
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Supplementary Material (1)

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Figures (3)

Fig. 1.
Fig. 1. Reconstruction of three cubes of side λ / 20 and center-to-center distance λ / 10 and λ / 9 from synthetic data corrupted with 10% multiplicative noise. In (a) and (b), the cubes’ permittivity is 1.01. The single scattering approximation is valid. (a) Permittivity reconstruction obtained with HM using the positivity constraint. (b) Permittivity reconstruction with the BIM using the knowledge of target permittivity. (c) and (d) are same as (a) and (b), but the permittivity of the cubes is 4 and the single scattering approximation is no longer valid. BIM is always better than HM and is able, in the multiple scattering regime, to retrieve accurately the three cubes way beyond the Rayleigh limit. The mesh size of the reconstruction is λ / 60 .
Fig. 2.
Fig. 2. Images of a resin star sample of 97 nm wide rods of length 520 nm and height 140 nm on a Si substrate. (a) Scanning electronic microscope image. (b) Darkfield microscopy with NA = 0.95 . (c) Reconstruction obtained with HM from tomographic diffraction microscopy data with NA = 0.95 . (d) Permittivity reconstruction obtained with BIM using the knowledge of the resin permittivity from the same data as (c). (e) Permittivity distribution in the axial z direction versus the curvilinear abscissa of the dashed circle in (d). The mesh size taken for all the reconstructions is 20 nm. BIM is able to distinguish the rods down to an interspacing of about 50 nm. The width of the rods is estimated to 117 nm in average (between 5 and 6 pixels). The color code indicates the level of relative permittivity in (c) and (d).
Fig. 3.
Fig. 3. Same as Fig. 2, but the rod width is 76 nm and their length is 490 nm. BIM is able to distinguish the rods down to an interspacing of about 50 nm. The rods’ width is estimated to 87 nm on average (between 4 and 5 pixels).

Equations (2)

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F ( χ ) = l = 1 L m = 1 M f l , m mes f l , m sim ( χ ) 2 l = 1 L m = 1 M f l , m mes 2 .
χ = ( ε ref ε background ) [ 1 exp ( ξ 2 ) ] ,

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