Abstract

We used a rotating slit placed at the back focal plane of the microscope’s objective lens to scan the light diffracted by a plasmonic crystal, which had a period smaller than the resolution limit of the optical microscope. A set of images were collected at different orientations of the slit. A high-resolution image of the plasmonic crystal was obtained by processing the experimental images using a numerical Fourier ptychographic algorithm. Supporting simulations of the experiments are also presented.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]

2018 (1)

H. Farooq, S. Skinner-Ramos, H. Alghasham, and L. de Peralta, “Improving the resolution of an optical microscope using ring-like illumination and scanning the direction of the diffracted light with a slit,” Opt. Commun. 426, 201–205 (2018).
[Crossref]

2017 (2)

M. Alotaibi, S. Skinner-Ramos, A. Alamri, B. Alharbi, M. Alfarraj, and L. Grave de Peralta, “Illumination-direction multiplexing Fourier ptychographic microscopy using hemispherical digital condensers,” Appl. Opt. 56(14), 4052–4057 (2017).
[Crossref] [PubMed]

S. Skinner-Ramos, H. Farooq, H. Alghasham, and L. Grave de Peralta, “Toward phase-recovery optical nanoscopes,” Journal of Physical Science and Application 7, 19–27 (2017).

2015 (4)

2014 (4)

2013 (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

2012 (1)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (1)

2008 (1)

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

2007 (1)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

2004 (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[Crossref] [PubMed]

1982 (1)

1981 (1)

H. Köheler, “On Abbe’s theory of image formation in the microscope,” Opt. Acta (Lond.) 28(12), 1691–1701 (1981).
[Crossref]

1978 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–245 (1972).

1952 (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952).
[Crossref]

1950 (1)

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. 63(10), 737–744 (1950).
[Crossref]

Alamri, A.

Alfarraj, M.

Alghasham, H.

H. Farooq, S. Skinner-Ramos, H. Alghasham, and L. de Peralta, “Improving the resolution of an optical microscope using ring-like illumination and scanning the direction of the diffracted light with a slit,” Opt. Commun. 426, 201–205 (2018).
[Crossref]

S. Skinner-Ramos, H. Farooq, H. Alghasham, and L. Grave de Peralta, “Toward phase-recovery optical nanoscopes,” Journal of Physical Science and Application 7, 19–27 (2017).

Alharbi, B.

Alharbi, N.

D. Dominguez, M. Alhusain, N. Alharbi, A. A. Bernussi, and L. Grave de Peralta, “Fourier plane imaging microscopy for detection of plasmonic crystals with periods beyond the optical diffraction limit,” Plasmonics 10(6), 1337–1344 (2015).
[Crossref]

Alhusain, M.

D. Dominguez, M. Alhusain, N. Alharbi, A. A. Bernussi, and L. Grave de Peralta, “Fourier plane imaging microscopy for detection of plasmonic crystals with periods beyond the optical diffraction limit,” Plasmonics 10(6), 1337–1344 (2015).
[Crossref]

Alotaibi, M.

Aussenegg, F. R.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Barham, P. M.

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. 63(10), 737–744 (1950).
[Crossref]

Bernussi, A. A.

D. Dominguez, M. Alhusain, N. Alharbi, A. A. Bernussi, and L. Grave de Peralta, “Fourier plane imaging microscopy for detection of plasmonic crystals with periods beyond the optical diffraction limit,” Plasmonics 10(6), 1337–1344 (2015).
[Crossref]

D. B. Desai, D. Dominguez, A. A. Bernussi, and L. de Peralta, “Ultra-thin condensers for optical subwavelength resolution microscopy,” J. Appl. Phys. 115(9), 093103 (2014).
[Crossref]

Bian, Z.

Bunk, O.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Cullis, A. G.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

David, C.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

de Peralta, L.

H. Farooq, S. Skinner-Ramos, H. Alghasham, and L. de Peralta, “Improving the resolution of an optical microscope using ring-like illumination and scanning the direction of the diffracted light with a slit,” Opt. Commun. 426, 201–205 (2018).
[Crossref]

D. B. Desai, D. Dominguez, A. A. Bernussi, and L. de Peralta, “Ultra-thin condensers for optical subwavelength resolution microscopy,” J. Appl. Phys. 115(9), 093103 (2014).
[Crossref]

Desai, D. B.

D. B. Desai, D. Dominguez, A. A. Bernussi, and L. de Peralta, “Ultra-thin condensers for optical subwavelength resolution microscopy,” J. Appl. Phys. 115(9), 093103 (2014).
[Crossref]

Ditlbacher, H.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Dobson, B. R.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Dominguez, D.

D. Dominguez, M. Alhusain, N. Alharbi, A. A. Bernussi, and L. Grave de Peralta, “Fourier plane imaging microscopy for detection of plasmonic crystals with periods beyond the optical diffraction limit,” Plasmonics 10(6), 1337–1344 (2015).
[Crossref]

D. B. Desai, D. Dominguez, A. A. Bernussi, and L. de Peralta, “Ultra-thin condensers for optical subwavelength resolution microscopy,” J. Appl. Phys. 115(9), 093103 (2014).
[Crossref]

Dong, S.

Drezet, A.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Farooq, H.

H. Farooq, S. Skinner-Ramos, H. Alghasham, and L. de Peralta, “Improving the resolution of an optical microscope using ring-like illumination and scanning the direction of the diffracted light with a slit,” Opt. Commun. 426, 201–205 (2018).
[Crossref]

S. Skinner-Ramos, H. Farooq, H. Alghasham, and L. Grave de Peralta, “Toward phase-recovery optical nanoscopes,” Journal of Physical Science and Application 7, 19–27 (2017).

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Fienup, J. R.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–245 (1972).

Grave de Peralta, L.

S. Skinner-Ramos, H. Farooq, H. Alghasham, and L. Grave de Peralta, “Toward phase-recovery optical nanoscopes,” Journal of Physical Science and Application 7, 19–27 (2017).

M. Alotaibi, S. Skinner-Ramos, A. Alamri, B. Alharbi, M. Alfarraj, and L. Grave de Peralta, “Illumination-direction multiplexing Fourier ptychographic microscopy using hemispherical digital condensers,” Appl. Opt. 56(14), 4052–4057 (2017).
[Crossref] [PubMed]

L. Grave de Peralta, “Metal slab superlens-negative refractive index versus inclined illumination: discussion,” J. Opt. Soc. Am. A 32(9), 1729–1735 (2015).
[Crossref] [PubMed]

D. Dominguez, M. Alhusain, N. Alharbi, A. A. Bernussi, and L. Grave de Peralta, “Fourier plane imaging microscopy for detection of plasmonic crystals with periods beyond the optical diffraction limit,” Plasmonics 10(6), 1337–1344 (2015).
[Crossref]

Gryczynski, I.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[Crossref] [PubMed]

Gryczynski, Z.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[Crossref] [PubMed]

Guo, K.

Hohenau, A.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Hopkins, H. H.

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. 63(10), 737–744 (1950).
[Crossref]

Horstmeyer, R.

Humphry, M. J.

Hurst, A. C.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730 (2012).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Jefimovs, K.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Johnson, I.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Köheler, H.

H. Köheler, “On Abbe’s theory of image formation in the microscope,” Opt. Acta (Lond.) 28(12), 1691–1701 (1981).
[Crossref]

Koller, D.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Kraus, B.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730 (2012).
[Crossref] [PubMed]

Krenn, J. R.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Lakowicz, J. R.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[Crossref] [PubMed]

Leitner, A.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Li, X.

Maiden, A. M.

Malicka, J.

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[Crossref] [PubMed]

Nanda, P.

Ou, X.

Pfeiffer, F.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Ramchandran, K.

Rodenburg, J. M.

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730 (2012).
[Crossref] [PubMed]

A. M. Maiden, M. J. Humphry, F. Zhang, and J. M. Rodenburg, “Superresolution imaging via ptychography,” J. Opt. Soc. Am. A 28(4), 604–612 (2011).
[Crossref] [PubMed]

A. M. Maiden, J. M. Rodenburg, and M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–245 (1972).

Sayre, D.

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952).
[Crossref]

Shiradkar, R.

Skinner-Ramos, S.

H. Farooq, S. Skinner-Ramos, H. Alghasham, and L. de Peralta, “Improving the resolution of an optical microscope using ring-like illumination and scanning the direction of the diffracted light with a slit,” Opt. Commun. 426, 201–205 (2018).
[Crossref]

S. Skinner-Ramos, H. Farooq, H. Alghasham, and L. Grave de Peralta, “Toward phase-recovery optical nanoscopes,” Journal of Physical Science and Application 7, 19–27 (2017).

M. Alotaibi, S. Skinner-Ramos, A. Alamri, B. Alharbi, M. Alfarraj, and L. Grave de Peralta, “Illumination-direction multiplexing Fourier ptychographic microscopy using hemispherical digital condensers,” Appl. Opt. 56(14), 4052–4057 (2017).
[Crossref] [PubMed]

Steinberger, B.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Stepanov, A.

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Tian, L.

Waller, L.

Wang, Y. M.

Yang, C.

Zhang, F.

Zheng, G.

Acta Crystallogr. (1)

D. Sayre, “Some implications of a theorem due to Shannon,” Acta Crystallogr. 5(6), 843 (1952).
[Crossref]

Appl. Opt. (2)

Biomed. Opt. Express (3)

J. Appl. Phys. (1)

D. B. Desai, D. Dominguez, A. A. Bernussi, and L. de Peralta, “Ultra-thin condensers for optical subwavelength resolution microscopy,” J. Appl. Phys. 115(9), 093103 (2014).
[Crossref]

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

J. Phys. Chem. B (1)

I. Gryczynski, J. Malicka, Z. Gryczynski, and J. R. Lakowicz, “Surface plasmon-coupled emission with gold films,” J. Phys. Chem. B 108(33), 12568–12574 (2004).
[Crossref] [PubMed]

Journal of Physical Science and Application (1)

S. Skinner-Ramos, H. Farooq, H. Alghasham, and L. Grave de Peralta, “Toward phase-recovery optical nanoscopes,” Journal of Physical Science and Application 7, 19–27 (2017).

Mater. Sci. Eng. B (1)

A. Drezet, A. Hohenau, D. Koller, A. Stepanov, H. Ditlbacher, B. Steinberger, F. R. Aussenegg, A. Leitner, and J. R. Krenn, “Leakage radiation microscopy of surface plasmon polaritons,” Mater. Sci. Eng. B 149(3), 220–229 (2008).
[Crossref]

Nat. Commun. (1)

M. J. Humphry, B. Kraus, A. C. Hurst, A. M. Maiden, and J. M. Rodenburg, “Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging,” Nat. Commun. 3(1), 730 (2012).
[Crossref] [PubMed]

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Opt. Acta (Lond.) (1)

H. Köheler, “On Abbe’s theory of image formation in the microscope,” Opt. Acta (Lond.) 28(12), 1691–1701 (1981).
[Crossref]

Opt. Commun. (1)

H. Farooq, S. Skinner-Ramos, H. Alghasham, and L. de Peralta, “Improving the resolution of an optical microscope using ring-like illumination and scanning the direction of the diffracted light with a slit,” Opt. Commun. 426, 201–205 (2018).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Optik (Stuttg.) (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–245 (1972).

Phys. Rev. Lett. (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: A novel phase retrieval algorithm,” Phys. Rev. Lett. 93(2), 023903 (2004).
[Crossref] [PubMed]

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Plasmonics (1)

D. Dominguez, M. Alhusain, N. Alharbi, A. A. Bernussi, and L. Grave de Peralta, “Fourier plane imaging microscopy for detection of plasmonic crystals with periods beyond the optical diffraction limit,” Plasmonics 10(6), 1337–1344 (2015).
[Crossref]

Proc. Phys. Soc. (1)

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. 63(10), 737–744 (1950).
[Crossref]

Other (4)

E. Hetcht, Optics 3rd ed. (Addison Wesley, 1998).

M. Born and E. Wolf, Principles of Optics 5th ed. (Pergamon Press, 1975).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

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Figures (7)

Fig. 1
Fig. 1 (a) Schematic illustration of the experimental setup. (b) Cross-sectional schematic of the plasmonic UTC structure with a periodic array of Cr pillars.
Fig. 2
Fig. 2 Experimental (a) FP and (b) RP images of the sample obtained without the slit. Typical examples of experimental pairs of (c, f) FP and (d, g) RP images obtained with the slit at the back focal plane of the objective lens oriented (c-d) perpendicularly to the sample’s periodicity with px = 940 nm, and (f-g) after rotating the slit at an angle of 80 degrees. (e) and (h) Images obtained after zooming in the square regions shown in (d) and (g), respectively.
Fig. 3
Fig. 3 Flowchart of the IDM-SDLM algorithm.
Fig. 4
Fig. 4 (a-b) Instances of simulated IDM FP images corresponding to Θj = (a) 0 and (b) 80 degrees. (c-f) Results obtained after processing the nine simulated FP images of the sample using the FPIM technique. (c) Diffraction rings of radii equal to NAc = 1.25, (d) fraction of the first-order diffraction rings visible with NAo = 0.65 objective lens, (e) respective centers of the diffraction rings separated by a distance λ/px = 0.6, and λ/py = 1.6 and, (f) IFPIM.
Fig. 5
Fig. 5 IDM-SDLM simulation results. Exact (a) amplitude and (b) phase of the RP-OD. (c) Sampled region of the FP and (d) simulated low-resolution IDM RP image obtained when the slit oriented at Θ = 80 degrees. (e) Amplitude and (f) phase of the simulated RP-OD obtained after 10 iterations of the IDM-SDLM algorithm.
Fig. 6
Fig. 6 Results obtained after processing with the FPIM technique the nine experimental FP images (a) Diffraction rings with radius equal to NAc = 1.25, (b) superposition of the sum of all FP images and the first-order diffraction rings, (c) centers of the diffraction rings separated by a distance λ/px = 0.6, and λ/py = 1.6. (d) Amplitude square of the Fourier transform of (c) containing both periodic structures with px = 940 nm and py = 360 nm.
Fig. 7
Fig. 7 Results obtained after processing the experimental low-resolution IDM RP images using the IDM-SDLM algorithm. (a) Synthetic FP image with NAs = NAo + NAc = 1.9. Amplitude (b) and (c) phase corresponding to the obtained RP- OD. (d) Magnified imaged of (b).

Equations (7)

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A m,j act (k) e i P m,j act (k) =F[ a m=0 (r) e i p m=0 (r) ],
A m,j,q (k) e i P m,j,q (k) = A m,j act (k k q ) e i P m,j act (k k q ) W S ( Θ j ).
a m,j,q (r) e i p m,j,q (r) = F 1 [ A m,j,q (k) e i P m,j,q (k) ].
a m,j,q mod (r)= I RP,j I RPT a m,j,q (r), I RPT = q=1 N I RP,j,q , I RP,j,q = [ a m,j,q (r)] 2 ,
A m,j,q rec (k) e i P m,j,q rec (k) =F[ a m,j,q mod (r) e i p m,j,q (r) ] W S ( Θ j .
A m,j upd (k) e i P m,j upd (k) = A m,j act (k) e i P m,j act (k) +α q=1 N [ γ A m,j,q rec (k+ k q ) e i P m,j,q rec (k+ k q ) β A m,j,q (k+ k q ) e i P m,j ,q (k+ k q ) ] .
a m=0 (r)= c 1 I RP, + c 2 I RPIM ,

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