Abstract

We report the experimental observation of systematically occurring phase singularities in coherent imaging of sub-Rayleigh distanced objects. A theory that relates the observation to the sub-Rayleigh distance is presented and compared with experimental measurements. As a consequence, the limit of resolution with coherent illumination is extended by a factor of 1.64×.

© 2010 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1987).
  2. S. Vyas and P. Senthilkumaran, Appl. Opt. 46, 7862 (2007).
    [CrossRef] [PubMed]
  3. M. Totzeck and H. J. Tiziani, Opt. Commun. 138, 365 (1997).
    [CrossRef]
  4. H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
    [CrossRef] [PubMed]
  5. Y. Cotte and C. Depeursinge, in Proceedings of Focus on Microscopy, Advanced Linear and Non-Linear Imaging (2009), paper TU-AF2–PAR-D.
  6. E. Cuche, P. Marquet, and C. Depeursinge, Appl. Opt. 38, 6994 (1999).
    [CrossRef]
  7. A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
    [CrossRef] [PubMed]
  8. X. Heng, X. Q. Cui, D. W. Knapp, J. G. Wu, Z. Yaqoob, E. J. McDowell, D. Psaltis, and C. H. Yang, Opt. Express 14, 10410 (2006).
    [CrossRef] [PubMed]
  9. M. G. L. Gustafsson, Proc. Natl. Acad. Sci. USA 102, 13081 (2005).
    [CrossRef] [PubMed]

2009 (1)

Y. Cotte and C. Depeursinge, in Proceedings of Focus on Microscopy, Advanced Linear and Non-Linear Imaging (2009), paper TU-AF2–PAR-D.

2007 (2)

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

S. Vyas and P. Senthilkumaran, Appl. Opt. 46, 7862 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (1)

M. G. L. Gustafsson, Proc. Natl. Acad. Sci. USA 102, 13081 (2005).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

1997 (1)

M. Totzeck and H. J. Tiziani, Opt. Commun. 138, 365 (1997).
[CrossRef]

1987 (1)

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1987).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1987).

Charrière, F.

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

Colomb, T.

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

Cotte, Y.

Y. Cotte and C. Depeursinge, in Proceedings of Focus on Microscopy, Advanced Linear and Non-Linear Imaging (2009), paper TU-AF2–PAR-D.

Cuche, E.

Cui, X. Q.

Depeursinge, C.

Y. Cotte and C. Depeursinge, in Proceedings of Focus on Microscopy, Advanced Linear and Non-Linear Imaging (2009), paper TU-AF2–PAR-D.

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, Appl. Opt. 38, 6994 (1999).
[CrossRef]

Gbur, G.

Gustafsson, M. G. L.

M. G. L. Gustafsson, Proc. Natl. Acad. Sci. USA 102, 13081 (2005).
[CrossRef] [PubMed]

Heng, X.

Knapp, D. W.

Kühn, J.

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

Marian, A.

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

Marquet, P.

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

E. Cuche, P. Marquet, and C. Depeursinge, Appl. Opt. 38, 6994 (1999).
[CrossRef]

McDowell, E. J.

Montfort, F.

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

Psaltis, D.

Schouten, H. F.

Senthilkumaran, P.

Tiziani, H. J.

M. Totzeck and H. J. Tiziani, Opt. Commun. 138, 365 (1997).
[CrossRef]

Totzeck, M.

M. Totzeck and H. J. Tiziani, Opt. Commun. 138, 365 (1997).
[CrossRef]

Visser, T. D.

Vyas, S.

Wolf, E.

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, Opt. Lett. 28, 968 (2003).
[CrossRef] [PubMed]

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1987).

Wu, J. G.

Yang, C. H.

Yaqoob, Z.

Appl. Opt. (2)

J. Microsc. (1)

A. Marian, F. Charrière, T. Colomb, F. Montfort, J. Kühn, P. Marquet, and C. Depeursinge, J. Microsc. 225, 156 (2007).
[CrossRef] [PubMed]

Opt. Commun. (1)

M. Totzeck and H. J. Tiziani, Opt. Commun. 138, 365 (1997).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. Natl. Acad. Sci. USA (1)

M. G. L. Gustafsson, Proc. Natl. Acad. Sci. USA 102, 13081 (2005).
[CrossRef] [PubMed]

Other (2)

Y. Cotte and C. Depeursinge, in Proceedings of Focus on Microscopy, Advanced Linear and Non-Linear Imaging (2009), paper TU-AF2–PAR-D.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Cambridge U. Press, 1987).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Experimental SEM images of test targets (a), (d), and (g) and their experimental DHM images [(b) and (c), (e) and (f), (h) and (i)] in the focal plane for λ = 532 nm and NA eff = 0.83 . The test targets are couples of nanoholes drilled by FIB in an aluminum film and are pictured at 100 , 000 × magnification with corresponding scale bars. Respectively displayed in (b) and (c) are the imaged amplitudes and their corresponding phases of test target (a), with nanohole ctc distance d = 500 nm . (d)–(f) are the corresponding results for d = 400 nm , and (g)–(i) are for d = 300 nm .

Fig. 2
Fig. 2

Schematic illustration of image plane in phase with Δ ϕ = 0 . Circles show contours of equal phase emitted from two point sources located the circles’ center.

Fig. 3
Fig. 3

Deduction of nanohole distances from angle θ of phase singularities for λ = 532 nm and NA eff = 0.83 . The line plot indicates the theoretical relation for different reference radii r. The points and gray bars indicate the experimental results from Table 1 and their corresponding ranges of trust.

Tables (1)

Tables Icon

Table 1 Results of Angle Measurements of Experimental Data for λ = 532   nm and NA eff = 0.83

Equations (7)

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

d min , coh = 0.82 λ NA .
s = Δ Φ k max = π ( 2 π / λ ) NA = λ 2 NA ,
s 0 = s ± Δ s = s ( 1 ± NA Δ ϕ / π ) ,
x 2 + ( a / 2 ) 2 = r 2 2 , ( d x ) 2 + ( a / 2 ) 2 = r 1 2 ,
tan θ = x d / 2 a / 2 .
d ( θ , r , s 0 ) = { 2 r 2 + 2 r s 0 + s 0 2 [ 4 r 2 ( r + s 0 ) 2 s 0 2 ( 2 r + s 0 ) 2 cot 2 θ ] 1 / 2 } 1 / 2 .
θ max = π / 2 d min = s .

Metrics