Abstract

Optical microscopy is widely used to analyze the properties of materials and structures, to identify and classify these structures, and to understand and control their responses to external stimuli. The extent of available applications is determined largely by the resolution offered by a particular microscopy technique. Here we present an analytic description and an experimental realization of interscale mixing microscopy, a diffraction-based imaging technique that is capable of detecting and characterizing wavelength/10 objects in far-field measurements with both coherent and incoherent broadband light. This technique is aimed at analyzing subwavelength objects based on far-field measurements of the interference created by the objects and a finite diffraction grating. A single measurement, analyzing the multiple diffraction orders, is often sufficient to determine the parameters of the object. The presented formalism opens opportunities for spectroscopy of nanoscale objects in the far field.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Interscale mixing microscopy: numerically stable imaging of wavelength- scale objects with sub-wavelength resolution and far field measurements

Sandeep Inampudi, Nicholas Kuhta, and Viktor A. Podolskiy
Opt. Express 23(3) 2753-2763 (2015)

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)

Far-field photothermal microscopy beyond the diffraction limit

Vladimir P. Zharov
Opt. Lett. 28(15) 1314-1316 (2003)

References

  • View by:
  • |
  • |
  • |

  1. E. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für Mikroskopische Anatomie 9, 413–418 (1873).
    [Crossref]
  2. Lord Rayleigh, “On the theory of optical images, with special reference to the microscope,” Philos. Mag. 42 (255), 167–195 (1896).
    [Crossref]
  3. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference, and Diffraction of Light (Cambridge University, 1999).
  4. M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).
  5. E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
    [Crossref]
  6. S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
    [Crossref]
  7. S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
    [Crossref]
  8. M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
    [Crossref]
  9. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Academic, 1999).
  10. T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
    [Crossref]
  11. S. Durant, Z. Liu, J. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23, 2383–2392 (2006).
    [Crossref]
  12. 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]
  13. A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
    [Crossref]
  14. A. V. Zayats and D. Richards, eds., Nano-Optics and Near-Field Optical Microscopy (Artech, 2008).
  15. P. S. Carney, V. A. Markel, and J. C. Schotland, “Near-field tomography without phase retrieval,” Phys. Rev. Lett. 86, 5874–5877 (2001).
    [Crossref]
  16. A. A. Govyadinov, G. Y. Panasyuk, and J. C. Schotland, “Phaseless three-dimensional optical nanoimaging,” Phys. Rev. Lett. 103, 213901 (2009).
    [Crossref]
  17. A. Sentenac, P. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
    [Crossref]
  18. 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]
  19. S. Inampudi, N. Kuhta, and V. A. Podolskiy, “Interscale mixing microscopy: numerically stable imaging of wavelength-scale objects with sub-wavelength resolution and far field measurements,” Opt. Express 23, 2753–2763 (2015).
    [Crossref]
  20. E. E. Narimanov, “The resolution limit for far-field optical imaging,” in Conference on Lasers and Electro-Optics, Technical Digest (online) (Optical Society of America, 2013), paper QW3A.7.
  21. A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
    [Crossref]
  22. E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
    [Crossref]
  23. M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
    [Crossref]
  24. Z. Jacob, L. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
    [Crossref]
  25. A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
    [Crossref]
  26. Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
    [Crossref]
  27. M. A. Grimm and A. W. Lohmann, “Superresolution image for one-dimensional objects,” J. Opt. Soc. Am. 56, 1151–1156 (1966).
    [Crossref]
  28. W. Lukosz, “Optical systems with resolving powers exceeding the classical limit,” J. Opt. Soc. Am. 56, 1463–1471 (1966).
    [Crossref]
  29. R. M. Silver, B. M. Barnes, A. Ravikiran, J. Jun, M. Stocker, E. Marx, and H. J. Patrick, “Scatterfield microscopy for extending the limits of image-based optical metrology,“ Appl. Opt. 46, 4248–4257 (2007).
    [Crossref]
  30. 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, 6512–6522 (2013).
    [Crossref]
  31. E. Sabo, Z. Zalevsky, M. David, N. Konforti, and I. Kiryuschev, “Superresolution optical system using three fixed generalized gratings: experimental results,” J. Opt. Soc. Am. A 18, 514–520 (2001).
    [Crossref]
  32. M. G. L. Gustafsson, “Nonlinear structured-illumination microscopy: wide-field fluorescence imaging with theoretically unlimited resolution,” Proc. Natl. Acad. Sci. USA 102, 13081–13086 (2005).
    [Crossref]
  33. W. M. J. Coene, A. Thust, M. O. De Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
    [Crossref]

2015 (1)

2014 (1)

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

2013 (1)

2012 (2)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

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 (1)

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

2007 (3)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

R. M. Silver, B. M. Barnes, A. Ravikiran, J. Jun, M. Stocker, E. Marx, and H. J. Patrick, “Scatterfield microscopy for extending the limits of image-based optical metrology,“ Appl. Opt. 46, 4248–4257 (2007).
[Crossref]

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]

2006 (8)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[Crossref]

Z. Jacob, L. Alekseyev, and E. Narimanov, “Optical hyperlens: far-field imaging beyond the diffraction limit,” Opt. Express 14, 8247–8256 (2006).
[Crossref]

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[Crossref]

S. Durant, Z. Liu, J. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23, 2383–2392 (2006).
[Crossref]

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

A. Sentenac, P. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[Crossref]

2005 (1)

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

2001 (2)

2000 (1)

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

1996 (2)

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

W. M. J. Coene, A. Thust, M. O. De Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

1994 (1)

1966 (2)

1896 (1)

Lord Rayleigh, “On the theory of optical images, with special reference to the microscope,” Philos. Mag. 42 (255), 167–195 (1896).
[Crossref]

1873 (1)

E. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für Mikroskopische Anatomie 9, 413–418 (1873).
[Crossref]

Abbe, E. E.

E. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für Mikroskopische Anatomie 9, 413–418 (1873).
[Crossref]

Alekseyev, L.

Babacan, S. D.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Barnes, B. M.

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).

Belkebir, K.

A. Sentenac, P. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[Crossref]

Berry, M. V.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[Crossref]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Bonifacino, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Born, M.

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

Bullkich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Carney, P. S.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[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]

Chad, J.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

Chaumet, P.

A. Sentenac, P. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[Crossref]

Coene, W. M. J.

W. M. J. Coene, A. Thust, M. O. De Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Cohen, O.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Cohen-Hyams, T.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Dana, H.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

David, M.

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

De Beeck, M. O.

W. M. J. Coene, A. Thust, M. O. De Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Dennis, M.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

Durant, S.

Eldar, Y. C.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Engheta, N.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[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]

Gazit, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Girirajan, T. P. K.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

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.

Goddard, L. L.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

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]

Grimm, M. A.

Gustafsson, M. G. L.

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

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

Hell, S. W.

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Hess, S. T.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

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]

Inampudi, S.

Jacob, Z.

Jun, J.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Academic, 1999).

Kewitsch, A. S.

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

Kim, T.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Kiryuschev, I.

Kley, E. B.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Konforti, N.

Kuhta, N.

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]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

Lindberg, J.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

Lindwasser, O.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

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]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

S. Durant, Z. Liu, J. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23, 2383–2392 (2006).
[Crossref]

Lohmann, A. W.

Lord Rayleigh,

Lord Rayleigh, “On the theory of optical images, with special reference to the microscope,” Philos. Mag. 42 (255), 167–195 (1896).
[Crossref]

Lukosz, W.

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]

Marx, E.

Mason, M. D.

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

Mir, M.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Narimanov, E.

Narimanov, E. E.

E. E. Narimanov, “The resolution limit for far-field optical imaging,” in Conference on Lasers and Electro-Optics, Technical Digest (online) (Optical Society of America, 2013), paper QW3A.7.

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Osherovich, E.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[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.

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

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]

Podolskiy, V. A.

S. Inampudi, N. Kuhta, and V. A. Podolskiy, “Interscale mixing microscopy: numerically stable imaging of wavelength-scale objects with sub-wavelength resolution and far field measurements,” Opt. Express 23, 2753–2763 (2015).
[Crossref]

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]

Popescu, G.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Popescu, S.

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[Crossref]

Qin, J.

Ravikiran, A.

Rogers, E. T. F.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

Roy, T.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).

Sabo, E.

Salandrino, A.

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[Crossref]

Savo, S.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

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]

Segev, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Sentenac, A.

A. Sentenac, P. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[Crossref]

Shechtman, Y.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Shoham, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Sidorenko, P.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Silver, R. M.

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Academic, 1999).

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Steele, J.

Stiener, S.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Stocker, M.

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

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]

Szameit, A.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

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]

Thust, A.

W. M. J. Coene, A. Thust, M. O. De Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Van Dyck, D.

W. M. J. Coene, A. Thust, M. O. De Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Wichmann, J.

Wolf, E.

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

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]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

Yariv, A.

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

Yavneh, I.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Zalevsky, Z.

Zhang, X.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

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]

S. Durant, Z. Liu, J. Steele, and X. Zhang, “Theory of the transmission properties of an optical far-field superlens for imaging beyond the diffraction limit,” J. Opt. Soc. Am. B 23, 2383–2392 (2006).
[Crossref]

Zheludev, N. I.

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

Zhou, H.

Zhou, R.

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).

Zibulevsky, M.

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (2)

A. S. Kewitsch and A. Yariv, “Nonlinear optical properties of photoresists for projection lithography,” Appl. Phys. Lett. 68, 455–457 (1996).
[Crossref]

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]

Archiv für Mikroskopische Anatomie (1)

E. E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für Mikroskopische Anatomie 9, 413–418 (1873).
[Crossref]

Biophys. J. (1)

S. T. Hess, T. P. K. Girirajan, and M. D. Mason, “Ultra-high resolution imaging by fluorescence photoactivation localization microscopy,” Biophys. J. 91, 4258–4272 (2006).
[Crossref]

J. Microsc. (1)

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

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

M. V. Berry and S. Popescu, “Evolution of quantum superoscillations and optical superresolution without evanescent waves,” J. Phys. A 39, 6965–6977 (2006).
[Crossref]

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]

Nat. Mater. (2)

A. Szameit, Y. Shechtman, E. Osherovich, E. Bullkich, P. Sidorenko, H. Dana, S. Stiener, E. B. Kley, S. Gazit, T. Cohen-Hyams, S. Shoham, M. Zibulevsky, I. Yavneh, Y. C. Eldar, O. Cohen, and M. Segev, “Sparsity-based single-shot subwavelength coherent diffractive imaging,” Nat. Mater. 11, 455–459 (2012).
[Crossref]

E. T. F. Rogers, J. Lindberg, T. Roy, S. Savo, J. Chad, M. Dennis, and N. I. Zheludev, “A super-oscillatory lens optical microscope for subwavelength imaging,” Nat. Mater. 11, 432–435 (2012).
[Crossref]

Nat. Methods (1)

M. J. Rust, M. Bates, and X. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3, 793–796 (2006).

Nat. Photonics (1)

T. Kim, R. Zhou, M. Mir, S. D. Babacan, P. S. Carney, L. L. Goddard, and G. Popescu, “White-light diffraction tomography of unlabelled live cells,” Nat. Photonics 8, 256–263 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Philos. Mag. (1)

Lord Rayleigh, “On the theory of optical images, with special reference to the microscope,” Philos. Mag. 42 (255), 167–195 (1896).
[Crossref]

Phys. Rev. B (1)

A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy using metamaterial crystals: theory and simulations,” Phys. Rev. B 74, 075103 (2006).
[Crossref]

Phys. Rev. Lett. (3)

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

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. Chaumet, and K. Belkebir, “Beyond the Rayleigh criterion: grating assisted far-field optical diffraction tomography,” Phys. Rev. Lett. 97, 243901 (2006).
[Crossref]

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

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

Science (2)

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315, 1686 (2007).
[Crossref]

E. Betzig, G. H. Patterson, R. Sougrat, O. Lindwasser, S. Olenych, J. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313, 1642–1645 (2006).
[Crossref]

Ultramicroscopy (1)

W. M. J. Coene, A. Thust, M. O. De Beeck, and D. Van Dyck, “Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy,” Ultramicroscopy 64, 109–135 (1996).
[Crossref]

Other (4)

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

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (Academic, 1999).

E. E. Narimanov, “The resolution limit for far-field optical imaging,” in Conference on Lasers and Electro-Optics, Technical Digest (online) (Optical Society of America, 2013), paper QW3A.7.

A. V. Zayats and D. Richards, eds., Nano-Optics and Near-Field Optical Microscopy (Artech, 2008).

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 (5)

Fig. 1.
Fig. 1.

(a) (Magnetic) field of light scattered by an object (a slit in this example) can be represented as a collection of plane waves parameterized by the transverse wavevector k x . (b) The Fourier spectrum of a subwavelength object is dominated by evanescent modes with k x c / ω > 1 . (c) As the light propagates to the far-field of the object, the evanescent components get exponentially suppressed. (d) Attempts to optically re-construct the image in the far-field result in a diffraction-limited pattern. IMM mixes evanescent information into the propagating part of the spectrum [arrows in (b)], enabling to distinguish information about sub-wavelength features of the source with far-field measurements.

Fig. 2.
Fig. 2.

(a) Experimental optical imaging setup. (b)–(d) Fabricated gratings with Λ = 275    nm : (b) centered defect, (c) off-center defect, and (d) no defects.

Fig. 3.
Fig. 3.

IMM signal [Eq. (7)] from a 1D object that is being translated from one end of the finite diffraction grating to the other [inset in (a)]: (a) dependence of the IMM signal on defect position for object size l = λ 0 / 20 27    nm in Λ = 275    nm , w = 125    nm , N = 25 grating, illuminated with λ 0 = 532    nm light. (b) Dependence of the IMM maximum at a / Λ = 0 on object size l (black line); red line shows linear dependence. (c) Main panel: IMM signal for the grating in (a) for defects in neighboring apertures, inset: the IMM signal of the same sample and grating interrogated with λ 0 = 800    nm light. (d) IMM signal for the grating in (a) for objects within the same aperture (inset shows the signal in logarithmic scale).

Fig. 4.
Fig. 4.

IMM signal based on (a) a single experimental measurement corresponding to an incident angle of 21°, (b) postprocessed experimental data of nine different incident angles, and (c) theoretical predictions of I ( x ) according to Eq. (7). The positions of diffracted peaks and the ratio of their amplitudes represent position and relative dimensions of the objects, respectively. Thick lines and shaded areas in (b) represent the mean and standard deviation of postprocessed data, respectively; for all the panels, Λ = 275    nm and λ 0 = 532    nm . Inset in (a) illustrates the typical imaging processing routine: starting from the raw CCD image, we extract the transmission perpendicular to the grating and suppress the main diffraction peaks by multiplying the signal by sin ( k x Λ / 2 ) 2 , followed by Fourier transformation of the power spectrum.

Fig. 5.
Fig. 5.

(a), (c), (e) IMM signals extracted from experimental data obtained with broadband incoherent illumination and (b), (d), (f) calculated using Eq. (7) for samples with (a), (b) missing slit, (c), (d) shifted slit, and (e), (f) defect-free grating.

Equations (7)

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

F⃗ ( r⃗ ) = A⃗ ( k x ) e i k⃗ · r⃗ i ω t d k x ,
H y ( x ) = n = N 1 2 N 1 2 rect ( x w ) * δ ( x n Λ ) ,
H y ( k x ) = w sinc ( k x w 2 ) sin ( N k x Λ 2 ) sin ( k x Λ 2 ) .
H y ( k ) = w sinc ( k x w 2 ) sin ( N k x Λ 2 ) sin ( k x Λ 2 ) + l sinc ( k x l 2 ) e i k x a .
I ( k x ) | H y ( k x ) | 2 = I g ( k x ) + I d ( k x ) + I i ( k x ) sin 2 k x Λ 2 ,
I g ( k x ) = w 2 sinc 2 ( k x w 2 ) sin 2 ( N k x Λ 2 ) , I d ( k x ) = l 2 sinc 2 ( k x l 2 ) sin 2 ( k x Λ 2 ) , I i ( k x ) = 2 w l sinc ( k x w 2 ) sinc ( k x l 2 ) sin ( k x Λ 2 ) × sin ( N k x Λ 2 ) cos ( k x a ) .
I ( x ) = | F [ I ( k x ) sin 2 ( k x Λ 2 ) ] | 2 ,

Metrics