Abstract

We demonstrate that the axial resolution of a reflection tomographic diffractive microscope is drastically improved when the sample is placed in front of a perfect mirror. We show analytically and with rigorous simulations that this approach permits us to obtain images with the same isotropic resolution as that obtained when the sample is illuminated and observed from every possible angle. The main difficulty lies in accounting properly for the mirror in the inversion algorithm.

© 2010 Optical Society of America

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References

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  2. W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
    [CrossRef]
  3. M. Debailleul, V. Georges, B. Simon, R. Morin, and O. Haeberlé, Opt. Lett. 34, 79 (2009).
    [CrossRef]
  4. S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, Phys. Rev. Lett. 97, 168102 (2006).
    [CrossRef] [PubMed]
  5. 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] [PubMed]
  6. Y. Sung, W. Choi, C. Fang-Yen, K. B. zadegan, R. R. Dasari, and M. S. Feld, Opt. Express 17, 266 (2009).
    [CrossRef] [PubMed]
  7. R. Fiolka, K. Wicker, R. Heintzmann, and A. Stemmer, Opt. Express 17, 12407 (2009).
    [CrossRef] [PubMed]
  8. F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, Opt. Express 14, 7005 (2006).
    [CrossRef] [PubMed]
  9. S. S. Kou and C. J. R. Sheppard, Opt. Lett. 33, 2362 (2008).
    [CrossRef] [PubMed]
  10. S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, Cent. Eur. J. Phys. 7, 22 (2009).
    [CrossRef]
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    [CrossRef]
  12. C. J. Nolan, M. Cheney, T. Dowling, and R. Gaburro, Inverse Probl. 22, 1817 (2006).
    [CrossRef]
  13. A. J. Devaney, J. Opt. Soc. Am. A 21, 2216 (2004).
    [CrossRef]
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    [CrossRef]
  15. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).
  16. P. C. Chaumet, K. Belkebir, and A. Sentenac, Opt. Lett. 29, 2740 (2004).
    [CrossRef] [PubMed]
  17. P. C. Chaumet, K. Belkebir, and A. Sentenac, J. Appl. Phys. 106, 034901 (2009).
    [CrossRef]

2009 (6)

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

Y. Sung, W. Choi, C. Fang-Yen, K. B. zadegan, R. R. Dasari, and M. S. Feld, Opt. Express 17, 266 (2009).
[CrossRef] [PubMed]

R. Fiolka, K. Wicker, R. Heintzmann, and A. Stemmer, Opt. Express 17, 12407 (2009).
[CrossRef] [PubMed]

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, Cent. Eur. J. Phys. 7, 22 (2009).
[CrossRef]

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

2008 (2)

2007 (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

2006 (3)

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

F. Charrière, N. Pavillon, T. Colomb, C. Depeursinge, T. J. Heger, E. A. D. Mitchell, P. Marquet, and B. Rappaz, Opt. Express 14, 7005 (2006).
[CrossRef] [PubMed]

C. J. Nolan, M. Cheney, T. Dowling, and R. Gaburro, Inverse Probl. 22, 1817 (2006).
[CrossRef]

2005 (1)

2004 (2)

2002 (1)

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

Alexandrov, S. A.

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

Badizadegan, K.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Belkebir, K.

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] [PubMed]

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 22, 1889 (2005).
[CrossRef]

P. C. Chaumet, K. Belkebir, and A. Sentenac, Opt. Lett. 29, 2740 (2004).
[CrossRef] [PubMed]

Charrière, F.

Chaumet, P. C.

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

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

P. C. Chaumet, K. Belkebir, and A. Sentenac, Opt. Lett. 29, 2740 (2004).
[CrossRef] [PubMed]

Cheney, M.

C. J. Nolan, M. Cheney, T. Dowling, and R. Gaburro, Inverse Probl. 22, 1817 (2006).
[CrossRef]

Choi, W.

Y. Sung, W. Choi, C. Fang-Yen, K. B. zadegan, R. R. Dasari, and M. S. Feld, Opt. Express 17, 266 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Colomb, T.

Dasari, R. R.

Y. Sung, W. Choi, C. Fang-Yen, K. B. zadegan, R. R. Dasari, and M. S. Feld, Opt. Express 17, 266 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Debailleul, M.

Delaunay, J.-J.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, Cent. Eur. J. Phys. 7, 22 (2009).
[CrossRef]

Depeursinge, C.

Devaney, A. J.

Dowling, T.

C. J. Nolan, M. Cheney, T. Dowling, and R. Gaburro, Inverse Probl. 22, 1817 (2006).
[CrossRef]

Drsek, F.

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] [PubMed]

Fang-Yen, C.

Y. Sung, W. Choi, C. Fang-Yen, K. B. zadegan, R. R. Dasari, and M. S. Feld, Opt. Express 17, 266 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Feld, M. S.

Y. Sung, W. Choi, C. Fang-Yen, K. B. zadegan, R. R. Dasari, and M. S. Feld, Opt. Express 17, 266 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Fiolka, R.

Gaburro, R.

C. J. Nolan, M. Cheney, T. Dowling, and R. Gaburro, Inverse Probl. 22, 1817 (2006).
[CrossRef]

Georges, V.

Giovannini, H.

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] [PubMed]

Girard, J.

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] [PubMed]

Gutzler, T.

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

Haeberlé, O.

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

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, Cent. Eur. J. Phys. 7, 22 (2009).
[CrossRef]

Heger, T. J.

Heintzmann, R.

Hillman, T. R.

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

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

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] [PubMed]

Kou, S. S.

Lauer, V.

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

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Maire, G.

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] [PubMed]

Marquet, P.

Mitchell, E. A. D.

Morin, R.

Natterer, F.

F. Natterer, Wave Motion 45, 776 (2008).
[CrossRef]

Nolan, C. J.

C. J. Nolan, M. Cheney, T. Dowling, and R. Gaburro, Inverse Probl. 22, 1817 (2006).
[CrossRef]

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Pavillon, N.

Rappaz, B.

Sampson, D. D.

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

Sentenac, A.

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] [PubMed]

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 22, 1889 (2005).
[CrossRef]

P. C. Chaumet, K. Belkebir, and A. Sentenac, Opt. Lett. 29, 2740 (2004).
[CrossRef] [PubMed]

Sheppard, C. J. R.

Simon, B.

Stemmer, A.

Sung, Y.

Talneau, A.

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] [PubMed]

Vertu, S.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, Cent. Eur. J. Phys. 7, 22 (2009).
[CrossRef]

Wicker, K.

Yamada, I.

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, Cent. Eur. J. Phys. 7, 22 (2009).
[CrossRef]

zadegan, K. B.

Cent. Eur. J. Phys. (1)

S. Vertu, J.-J. Delaunay, I. Yamada, and O. Haeberlé, Cent. Eur. J. Phys. 7, 22 (2009).
[CrossRef]

Inverse Probl. (1)

C. J. Nolan, M. Cheney, T. Dowling, and R. Gaburro, Inverse Probl. 22, 1817 (2006).
[CrossRef]

J. Appl. Phys. (1)

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

J. Microsc. (1)

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

J. Opt. Soc. Am. A (2)

Nat. Meth. (1)

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, and M. S. Feld, Nat. Meth. 4, 717 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. Lett. (2)

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

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] [PubMed]

Wave Motion (1)

F. Natterer, Wave Motion 45, 776 (2008).
[CrossRef]

Other (1)

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, 1975).

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Figures (3)

Fig. 1
Fig. 1

Description of different TDM con figurations (insets, accessible Fourier domain). (a) Reflection (half-sphere of radius 2 k 0 ). (b) Transmission (tore with cir cular section of radius k 0 ). (c) Isotropic (sphere of radius 2 k 0 ). (d) Mirror-assisted reflection configuration (sphere of radius 2 k 0 ).

Fig. 2
Fig. 2

PSFs of the different TDM configurations represented in Fig. 1 (NA is equal to 1 in all cases). (a) Transmission. (b) Complete isotropic configuration. This plot also represents the real part of the PSF in the reflection configuration and the PSF of the mirror-assisted reflection configuration if the pointlike object is placed at one wavelength, at least, above the mirror. (c) Imaginary part of the PSF of the reflection configuration.

Fig. 3
Fig. 3

Real and imaginary parts of the reconstructed permittivity for (a) and (b) transmission setup, (c) and (d) reflection setup, and (e) and (f) mirror setup (the sample is placed at λ / 10 above the mirror), (g) and (h) complete free-space configuration.

Equations (8)

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E d ( k ) = G ( k , r ) α ( r ) E ref ( r ) d r ,
E d ( k ) = e i k 0 R R α ˜ ( k k inc ) [ k × ( k × E 0 ) ] ,
F iso ( r ) = 1 2 π 2 r 3 [ sin ( 2 k 0 r ) 2 k 0 r cos ( 2 k 0 r ) ] .
α ( k z , k ) = d r 0 α ( r ) cos ( k z z ) exp ( i k . r ) d z ,
E d ( k ) = e i k 0 R R ( A f + B f + ) ,
f ± = α ( k z + k z inc , k k inc ) ± α ( k z k z inc , k k inc ) ,
A = k × ( k × E 0 ) , B = E z 0 k × ( k × z ^ ) .
F mirror ( r , z , h ) = F iso ( r 2 + ( z h ) 2 ) + F iso ( r 2 + ( z + h ) 2 ) .

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