Abstract

We present an imaging technique that allows the recovery of the profile of wavelength-scale objects with deep subwavelength resolution based on far-field intensity measurements. The approach, interscale mixing microscopy (IMM), relies on diffractive elements positioned in the near-field proximity of an object in order to scatter information carried by evanescent waves into propagating part of the spectrum. A combination of numerical solutions of Maxwell equations and nonlinear fitting is then used to recover the information about the object based on far-field intensity measurements. It is demonstrated that IMM has the potential to recover wavelength/20 features of wavelength-scale objects in the presence of 10% noise.

© 2015 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Interscale mixing microscopy: far-field imaging beyond the diffraction limit

Christopher M. Roberts, Nicolas Olivier, William P. Wardley, Sandeep Inampudi, Wayne Dickson, Anatoly V. Zayats, and Viktor A. Podolskiy
Optica 3(8) 803-808 (2016)

Super-resolution and reconstruction of sparse sub-wavelength images

Snir Gazit, Alexander Szameit, Yonina C. Eldar, and Mordechai Segev
Opt. Express 17(26) 23920-23946 (2009)

Experimental studies of far-field superlens for sub-diffractional optical imaging

Zhaowei Liu, Stéphane Durant, Hyesog Lee, Yuri Pikus, Yi Xiong, Cheng Sun, and Xiang Zhang
Opt. Express 15(11) 6947-6954 (2007)

References

  • View by:
  • |
  • |
  • |

  1. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
    [Crossref]
  2. E. E. Narimanov, “The resolution limit for far-field optical imaging,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper QW3A.7.
  3. S. M. Mansfield and G. S. Kino, “Solid immersion microscopy,” Appl. Phys. Lett. 57, 2615–2616 (1990).
  4. S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17, 23920–23946 (2009)
    [Crossref]
  5. M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Micr. 198, 82–87 (2000).
    [Crossref]
  6. M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
    [Crossref] [PubMed]
  7. Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
    [Crossref] [PubMed]
  8. T. Wilson, Confocal Microscopy (Academic Press, 1990).
  9. R.M. Silver, B.M. Barnes, R. Attota, J. Jun, M. Stocker, E. Marx, and H.J. Patrick, “Scatterfield microscopy for extending the limits of image-based optical metrology,” Appl. Opt. 46, 4248 (2007).
    [Crossref] [PubMed]
  10. J. Qin, R.M. Silver, B.M. Barnes, H. Zhou, and F. Goasmat, “Fourier domain optical tool normalization for quantitative parametric image reconstruction,” Appl. Opt. 52, 6512 (2013).
    [Crossref] [PubMed]
  11. U. Durig, D. W. Pohl, and F. Rohner, “Nearfield optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).
  12. P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev Lett. 86, 5874–5877 (2001).
    [Crossref] [PubMed]
  13. A. A. Govyadinov, G. Y. Panasyuk, and J. C. Schotland, “Phaseless three-dimensional optical nanoimaging,” Phys. Rev. Lett. 103, 213901 (2009).
    [Crossref]
  14. A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev Lett. 97, 243901 (2009).
    [Crossref]
  15. S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
    [Crossref]
  16. G. P. Agrawal and C. L. Mehta, “Evanescent waves and the van Cittert Zernike theorem in cylindrical geometry,” Pramana 9, 155 (1977).
    [Crossref]
  17. COMSOL Multiphysics, COMSOL AB, 2013.
  18. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [Crossref]
  19. R.H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large-scale nonlinear programming,” SIAM Journal on Optimization 9, 877 (1999).
    [Crossref]
  20. Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26, 1424–1426 (2001).
  21. B. Memarzadeh and H. Mosallei, “Array of planar plasmonic scatterers functioning as light concentrator,” Opt. Lett. 36, 2569 (2011).
    [Crossref] [PubMed]
  22. N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
    [Crossref] [PubMed]
  23. X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
    [Crossref]

2013 (1)

2012 (1)

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
[Crossref]

2011 (2)

B. Memarzadeh and H. Mosallei, “Array of planar plasmonic scatterers functioning as light concentrator,” Opt. Lett. 36, 2569 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

2010 (1)

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

2009 (3)

A. A. Govyadinov, G. Y. Panasyuk, and J. C. Schotland, “Phaseless three-dimensional optical nanoimaging,” Phys. Rev. Lett. 103, 213901 (2009).
[Crossref]

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev Lett. 97, 243901 (2009).
[Crossref]

S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17, 23920–23946 (2009)
[Crossref]

2007 (2)

2005 (1)

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[Crossref] [PubMed]

2001 (2)

P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev Lett. 86, 5874–5877 (2001).
[Crossref] [PubMed]

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26, 1424–1426 (2001).

2000 (1)

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Micr. 198, 82–87 (2000).
[Crossref]

1999 (1)

R.H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large-scale nonlinear programming,” SIAM Journal on Optimization 9, 877 (1999).
[Crossref]

1990 (1)

S. M. Mansfield and G. S. Kino, “Solid immersion microscopy,” Appl. Phys. Lett. 57, 2615–2616 (1990).

1986 (1)

U. Durig, D. W. Pohl, and F. Rohner, “Nearfield optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).

1981 (1)

1977 (1)

G. P. Agrawal and C. L. Mehta, “Evanescent waves and the van Cittert Zernike theorem in cylindrical geometry,” Pramana 9, 155 (1977).
[Crossref]

Agrawal, G. P.

G. P. Agrawal and C. L. Mehta, “Evanescent waves and the van Cittert Zernike theorem in cylindrical geometry,” Pramana 9, 155 (1977).
[Crossref]

Aieta, F.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

Attota, R.

Barnes, B.M.

Belkebir, K.

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev Lett. 97, 243901 (2009).
[Crossref]

Boltasseva, A.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
[Crossref]

Bomzon, Z.

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

Byrd, R.H.

R.H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large-scale nonlinear programming,” SIAM Journal on Optimization 9, 877 (1999).
[Crossref]

Capasso, F

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

Carney, P. S.

P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev Lett. 86, 5874–5877 (2001).
[Crossref] [PubMed]

Chaumet, P. C.

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev Lett. 97, 243901 (2009).
[Crossref]

Durant, S.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Durig, U.

U. Durig, D. W. Pohl, and F. Rohner, “Nearfield optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).

Eldar, Y. C.

Emani, N. K.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
[Crossref]

Escarra, M. D.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

Fang, N.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

Gaylord, T. K.

Gazit, S.

Genevet, P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

Gmachl, C. F.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

Goasmat, F.

Govyadinov, A. A.

A. A. Govyadinov, G. Y. Panasyuk, and J. C. Schotland, “Phaseless three-dimensional optical nanoimaging,” Phys. Rev. Lett. 103, 213901 (2009).
[Crossref]

Gustafsson, M. G.

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[Crossref] [PubMed]

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Micr. 198, 82–87 (2000).
[Crossref]

Hasman, E.

Hoffman, A. J.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

Hribar, M. E.

R.H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large-scale nonlinear programming,” SIAM Journal on Optimization 9, 877 (1999).
[Crossref]

Jun, J.

Kats, M. A.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

Kildishev, A. V.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
[Crossref]

Kino, G. S.

S. M. Mansfield and G. S. Kino, “Solid immersion microscopy,” Appl. Phys. Lett. 57, 2615–2616 (1990).

Kleiner, V.

Kuhta, N. A.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

Lee, H.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Mansfield, S. M.

S. M. Mansfield and G. S. Kino, “Solid immersion microscopy,” Appl. Phys. Lett. 57, 2615–2616 (1990).

Markel, V. A.

P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev Lett. 86, 5874–5877 (2001).
[Crossref] [PubMed]

Marx, E.

Mehta, C. L.

G. P. Agrawal and C. L. Mehta, “Evanescent waves and the van Cittert Zernike theorem in cylindrical geometry,” Pramana 9, 155 (1977).
[Crossref]

Memarzadeh, B.

Moharam, M. G.

Mosallei, H.

Narimanov, E. E.

E. E. Narimanov, “The resolution limit for far-field optical imaging,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper QW3A.7.

Ni, X.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
[Crossref]

Nocedal, J.

R.H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large-scale nonlinear programming,” SIAM Journal on Optimization 9, 877 (1999).
[Crossref]

Panasyuk, G. Y.

A. A. Govyadinov, G. Y. Panasyuk, and J. C. Schotland, “Phaseless three-dimensional optical nanoimaging,” Phys. Rev. Lett. 103, 213901 (2009).
[Crossref]

Patrick, H.J.

Pikus, Y.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Podolskiy, V. A.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

Pohl, D. W.

U. Durig, D. W. Pohl, and F. Rohner, “Nearfield optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).

Qin, J.

Rohner, F.

U. Durig, D. W. Pohl, and F. Rohner, “Nearfield optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).

Schotland, J. C.

A. A. Govyadinov, G. Y. Panasyuk, and J. C. Schotland, “Phaseless three-dimensional optical nanoimaging,” Phys. Rev. Lett. 103, 213901 (2009).
[Crossref]

P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev Lett. 86, 5874–5877 (2001).
[Crossref] [PubMed]

Segev, M.

Sentenac, A.

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev Lett. 97, 243901 (2009).
[Crossref]

Shalaev, V. M.

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
[Crossref]

Silver, R.M.

Stocker, M.

Sun, C.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Szameit, A.

Tetienne, J.P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

Thongrattanasiri, S.

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

Wilson, T.

T. Wilson, Confocal Microscopy (Academic Press, 1990).

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

Xiong, Y.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Yu, N.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

Zhang, X.

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Zhou, H.

Appl. Opt. (2)

Appl. Phys. Lett. (2)

S. Thongrattanasiri, N. A. Kuhta, M. D. Escarra, A. J. Hoffman, C. F. Gmachl, and V. A. Podolskiy, “Analytical technique for subwavelength far field imaging,” Appl. Phys. Lett. 97, 101103 (2010).
[Crossref]

S. M. Mansfield and G. S. Kino, “Solid immersion microscopy,” Appl. Phys. Lett. 57, 2615–2616 (1990).

J. Appl. Phys. (1)

U. Durig, D. W. Pohl, and F. Rohner, “Nearfield optical scanning microscopy,” J. Appl. Phys. 59, 3318–3327 (1986).

J. Micr. (1)

M. G. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Micr. 198, 82–87 (2000).
[Crossref]

J. Opt. Soc. Am. (1)

Nano Lett. (1)

Z. Liu, S. Durant, H. Lee, Y. Pikus, N. Fang, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical superlens,” Nano Lett. 7, 403–408 (2007).
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev Lett. (2)

A. Sentenac, P. C. Chaumet, and K. Belkebir, “Beyond the rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev Lett. 97, 243901 (2009).
[Crossref]

P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev Lett. 86, 5874–5877 (2001).
[Crossref] [PubMed]

Phys. Rev. Lett. (1)

A. A. Govyadinov, G. Y. Panasyuk, and J. C. Schotland, “Phaseless three-dimensional optical nanoimaging,” Phys. Rev. Lett. 103, 213901 (2009).
[Crossref]

Pramana (1)

G. P. Agrawal and C. L. Mehta, “Evanescent waves and the van Cittert Zernike theorem in cylindrical geometry,” Pramana 9, 155 (1977).
[Crossref]

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

M. G. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
[Crossref] [PubMed]

Science (2)

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.P. Tetienne, F Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science,  334, 333 (2011).
[Crossref] [PubMed]

X. Ni, N. K. Emani, A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Broadband light bending with plasmonic nanoantennas,” Science,  335, 427 (2012).
[Crossref]

SIAM Journal on Optimization (1)

R.H. Byrd, M. E. Hribar, and J. Nocedal, “An interior point algorithm for large-scale nonlinear programming,” SIAM Journal on Optimization 9, 877 (1999).
[Crossref]

Other (4)

COMSOL Multiphysics, COMSOL AB, 2013.

T. Wilson, Confocal Microscopy (Academic Press, 1990).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University, 1999).
[Crossref]

E. E. Narimanov, “The resolution limit for far-field optical imaging,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper QW3A.7.

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 (6)

Fig. 1
Fig. 1 Schematic of IMM; Main figure: the diffraction-based high-resolution imaging setup; inset: line object represented as a set of pixels with amplitudes bi
Fig. 2
Fig. 2 Image reconstruction using pixel basis expansion; (a) The far-field intensity pattern created by the three subwavelength sources λ /20,λ /10, and λ /5 in length [green line in panels (d)…(f)]; (b) typical distribution of angle-dependent random noise (inset) and noise-affected far-field intensity pattern corresponding to noise level of 10% (main panel); (c) transfer function of the particular diffraction grating used in computational experiments (parameters presented in the text). Panels (d), (e), and (f) represent recoveries corresponding to 5%, 10%, and 20% noise level respectively; blue lines and shaded areas represent mean and standard deviation of recoveries representing different realizations of noise; red lines represent noise-less recoveries; green lines correspond to actual configuratoin of the sources
Fig. 3
Fig. 3 Similar to Fig. 2(d)–2(f), but with recoveries based on field (as opposed to intensity) measurements; panels (a), (b), and (c) represent recoveries of the same set of objects when the noise with magnitude of 5%, 10%, and 20% (in terms of maximum value of the field amplitude) is added to the “measured” field
Fig. 4
Fig. 4 Image reconstruction of scattering objects (blocks) (a) Distribution of electromagnetic field across the system; inset highlights the compex interaction between the incident field and the scattering objects; position of objects (modeled as PEC lines) indicated by black lines in inset; (b) transfer function of the grating used in recovery; Panels (c), (d) correspond to recovery of the objects that fit inside the gap of the grating (h = 0.5λ) with 2% (c) and 4% (d) random noise respectively; panels (e,f) represent recoveries of objects with compound size greater than air gap of periodic grating that are recovered using a two arm grating system with arm separation h = 0.55λ; in panels (c…f) blue lines and shaded areas represent mean and standard deviation of the distribution of recovered objects; red lines represent noiseless recoveries; black horizontal lines represent positions of the objects in the FEM setup
Fig. 5
Fig. 5 (a) reconstruction of the two-block system, as described in Fig. 4 with PEC lines replaced with thin (λ/50) objects with finite permittivity ε; lines of different color represent blocks of different permittivity (b,c) Image reconstruction of (b) light emitting sources and (c) light scattering objects (blocks) using dielectric gratings.
Fig. 6
Fig. 6 Image reconstruction using aperiodic diffractive elements. Image recoveries of dense object (a)–(c) [λ/10 sized sources with λ/10 spacing]and sparse object (d)–(f) [λ/10 sized sources with λ /2 spacing] using three types of gratings with decreasing periodicity from center to ends (a,d), equal periodicity from center to ends (b,e) and increasing periodicity from center to ends (c,f). While all grating systems are able to recover all three objects, the system with decreasing periodicity tends to minimize the appearance of parasitic objects in the case of noisy measurements. Panel (g) quantifies the quality of image recovery via mean square deviation between recovered and original fields.

Equations (8)

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

H s c ( r ) = a ( k ) exp ( i k r ) d k .
k 2 + k z 2 = n 2 ω 2 c 2 .
I p ( θ p , θ i ) = | k x = k max k max τ ( k x , θ p ) a ( k x k i ) | 2 ,
θ i θ p | I p ( θ p , θ i ) I m e a s ( θ p , θ i ) | 2 min .
a ( k x k i ) = sin [ ( k x k i ) p x / 2 ] 2 π ( k x k i ) exp ( i k y y 0 ) n = 1 N b n exp [ i ( k x k i ) x n ]
I m e a s ( θ p , θ i ) | I m e a s ( θ p , θ i ) + δ r n max ( I m e a s ) | ,
I p ( θ p , θ i ) = | H g ( θ p , θ i ) + k x = k max k max τ ( k x , θ p ) a ( k x k i ) | 2
Δ d e v = 1 N n = 1 N | H e ( x n ) H s c ( x n ) | 2

Metrics