Abstract

Tomographic diffractive microscopy is a recent imaging technique that reconstructs quantitatively the three-dimensional permittivity map of a sample with a resolution better than that of conventional wide-field microscopy. Its main drawbacks lie in the complexity of the setup and in the slowness of the image recording as both the amplitude and the phase of the field scattered by the sample need to be measured for hundreds of successive illumination angles. In this Letter, we show that, using a wavefront sensor, tomographic diffractive microscopy can be implemented easily on a conventional microscope. Moreover, the number of illuminations can be dramatically decreased if a constrained reconstruction algorithm is used to recover the sample map of permittivity.

© 2012 Optical Society of America

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  2. O. Haeberlé, K. Belkebir, H. Giovannini, and A. Sentenac, J. Mod. Opt. 57, 686 (2010).
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  7. P. Bon, G. Maucort, B. Wattellier, and S. Monneret, Opt. Express 17, 13080 (2009).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  12. K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 22, 1889 (2005).
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2011

2010

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, Opt. Lett. 35, 1857 (2010).
[CrossRef]

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

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

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

2009

2008

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, Meas. Sci. Technol. 19, 074009 (2008).
[CrossRef]

2005

2002

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

Badizadegan, K.

Belkebir, K.

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

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, Opt. Lett. 35, 1857 (2010).
[CrossRef]

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

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

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 22, 1889 (2005).
[CrossRef]

Bon, P.

Chaumet, P. C.

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, Opt. Lett. 35, 1857 (2010).
[CrossRef]

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

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 22, 1889 (2005).
[CrossRef]

Choi, W.

Choi, Y.

Dasari, R.

Dasari, R. R.

Debailleul, M.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, Meas. Sci. Technol. 19, 074009 (2008).
[CrossRef]

Drsek, F.

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Fang-Yen, C.

Feld, M. S.

Fiolka, R.

Georges, V.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, Meas. Sci. Technol. 19, 074009 (2008).
[CrossRef]

Giovannini, H.

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

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

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

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Girard, J.

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

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Haeberlé, O.

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

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, Meas. Sci. Technol. 19, 074009 (2008).
[CrossRef]

Heintzmann, R.

Kim, M.

Konan, D.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Lauer, V.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, Meas. Sci. Technol. 19, 074009 (2008).
[CrossRef]

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

Maire, G.

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, Opt. Lett. 35, 1857 (2010).
[CrossRef]

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

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Maucort, G.

Monneret, S.

Mudry, E.

Sentenac, A.

E. Mudry, P. C. Chaumet, K. Belkebir, G. Maire, and A. Sentenac, Opt. Lett. 35, 1857 (2010).
[CrossRef]

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

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

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

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Opt. Soc. Am. A 22, 1889 (2005).
[CrossRef]

Simon, B.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, Meas. Sci. Technol. 19, 074009 (2008).
[CrossRef]

Stemmer, A.

Sung, Y.

Talneau, A.

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

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Wattellier, B.

Wicker, K.

J. Microsc.

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

J. Mod. Opt.

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

G. Maire, J. Girard, F. Drsek, H. Giovannini, A. Talneau, K. Belkebir, P. C. Chaumet, and A. Sentenac, J. Mod. Opt. 57, 746 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Meas. Sci. Technol.

M. Debailleul, B. Simon, V. Georges, O. Haeberlé, and V. Lauer, Meas. Sci. Technol. 19, 074009 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. Lett.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Schematic of the TDM setup. M, rotative mirror; BE, beam expander; D, diaphragm; BS, beam splitter; OL, objective lens; L1, tube lens; L2, L3, relay lenses (f=3.5 and 20 cm); WS, wavefront sensor.

Fig. 2.
Fig. 2.

(a), (c) Wavefront sensor, amplitude, and phase of the scattered far field (30° illumination angle); (b), (d) same data for phase-shifting interferometry. kx and ky, spatial frequencies; k0, wavenumber.

Fig. 3.
Fig. 3.

Comparison of the modulus of the 3D inverse Fourier transform of the data set (53 nm meshing) [(a), (b)] and of the permittivity map retrieved with the iterative inversion algorithm [(c), (d), (e), (f)]. (c), (d) The height of the investigating domain is 1.6 μm with a mesh size of 200 nm. (e), (f) Zoom on the sample with a height of 0.4 μm and a mesh size of 50 nm (dashed white line, actual geometry of the sample). The figures in the top row show transverse cuts at (a), z=53, (c) 100, and (e) 125 nm, and the ones in the bottom row longitudinal cuts at y=1μm. Cuts are along the white dotted lines.

Equations (3)

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

El=El0+χEl,
Eld=χEl,
F(χ,El)=CΓl=1LflχElΓ2+CWl=1LElEl0χElW2,

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