Abstract

Imaging interferometric nanoscopy (IIN) is a synthetic aperture approach offering the potential of optical resolution to the linear-system limit of optics (λ/4n). The immersion advantages of IIN can be realized if the object is in close proximity to a solid-immersion medium with illumination and collection through the substrate and coupling this radiation to air by a grating on the medium surface opposite the object. The spatial resolution as a function of the medium thickness and refractive index as well as the field-of-view of the objective optical system is derived and applied to simulations.

© 2012 Optical Society of America

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2009 (4)

2008 (9)

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express 16, 2555–2569 (2008).
[CrossRef]

Y. Kuznetsova, A. Neumann, and S. R. J. Brueck, “Imaging interferometric microscopy,” J. Opt. Soc. Am. A 25, 811–822 (2008).
[CrossRef]

A. Neumann, Y. Kusnetsova, and S. R. J. Brueck, “Structured illumination for the extension of imaging interferometric lithography,” Opt. Express 16, 6785–6793 (2008).
[CrossRef]

V. Mico, Z. Zalevsky, C. Ferreira, and J. García, “Superresolution digital holographic microscopy for three-dimensional samples,” Opt. Express 16, 19260–19270 (2008).
[CrossRef]

A. Neumann, Y. Kuznetsova, and S. R. J. Brueck, “Optical resolution below λ/4 using synthetic aperture microscopy and evanescent-wave illumination,” Opt. Express 16, 20477–20485 (2008).
[CrossRef]

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors 8, 3903–3931 (2008).
[CrossRef]

S. A. Alexandrov and D. D. Sampson, “Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency,” J. Opt. A. 10, 025304 (2008).
[CrossRef]

V. Mico, Z. Zalevsky, and J. García, “Common-path phase-shifting digital holographic microscopy: a way to quantitative imaging and superresolution,” Opt. Commun. 281, 4273–4281 (2008).
[CrossRef]

V. Micó, J. García, and Z. Zalevsky, “Axial superresolution by synthetic aperture generation,” J. Opt. A. 10, 125001 (2008).
[CrossRef]

2007 (5)

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Digital Fourier holography enables wide-field, superresolved, microscopic characterization,” Opt. Photon. News 18, 29 (2007).
[CrossRef]

S. W. Hell, “Far-field optical nanoscopy (review),” Science 316, 1153–1158 (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]

Y. Kuznetsova, A. Neumann, and S. R. J. Brueck, “Imaging interferometric microscopy—approaching the linear systems limits of optical resolution,” Opt. Express 15, 6651–6663 (2007).
[CrossRef]

2006 (8)

2005 (2)

2004 (1)

2003 (1)

2002 (2)

J. H. Massig, “Digital off-axis holography with a synthetic aperture,” Opt. Lett. 27, 2179–2181 (2002).
[CrossRef]

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef]

2001 (1)

1999 (1)

1998 (1)

1992 (1)

1990 (1)

1987 (1)

1986 (1)

1969 (1)

1967 (1)

1964 (1)

1960 (1)

A. I. Kartashev, “Optical system with enhanced resolving power,” Opt. Spectrosc. 9, 204–206 (1960).

1955 (1)

1952 (1)

M. Françon, “Amélioration de la reśolution ďoptique,” Nuovo Cimento Suppl. 9, 283–287 (1952).
[CrossRef]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopichen Wahrnehmung,” Arch. Mikrosk. Anat. Entwichlungsmech 9, 413–468 (1873).
[CrossRef]

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopichen Wahrnehmung,” Arch. Mikrosk. Anat. Entwichlungsmech 9, 413–468 (1873).
[CrossRef]

Alekseyev, L. V.

Alexandrov, S. A.

S. A. Alexandrov and D. D. Sampson, “Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency,” J. Opt. A. 10, 025304 (2008).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Digital Fourier holography enables wide-field, superresolved, microscopic characterization,” Opt. Photon. News 18, 29 (2007).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
[CrossRef]

Angell, D.

Belkebir, K.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (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 (2006).
[CrossRef]

Boppart, S. A.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors 8, 3903–3931 (2008).
[CrossRef]

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express 16, 2555–2569 (2008).
[CrossRef]

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
[CrossRef]

Brueck, S. R. J.

Carney, P. S.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors 8, 3903–3931 (2008).
[CrossRef]

Carney, S.

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express 16, 2555–2569 (2008).
[CrossRef]

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
[CrossRef]

Chaumet, P. C.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (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 (2006).
[CrossRef]

Collot, L.

Cox, I. J.

Davis, B. J.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors 8, 3903–3931 (2008).
[CrossRef]

Drsek, F.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Ferreira, C.

Françon, M.

M. Françon, “Amélioration de la reśolution ďoptique,” Nuovo Cimento Suppl. 9, 283–287 (1952).
[CrossRef]

Garcia, J.

García, J.

Garcia-Martinez, P.

García-Martínez, P.

Giovannini, H.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Girard, J.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Goldberg, B. B.

Granero, L.

Gross, M.

Gutzler, T.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Digital Fourier holography enables wide-field, superresolved, microscopic characterization,” Opt. Photon. News 18, 29 (2007).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

Hegedus, Z.

Hell, S. W.

S. W. Hell, “Far-field optical nanoscopy (review),” Science 316, 1153–1158 (2007).
[CrossRef]

Hillman, T. R.

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Digital Fourier holography enables wide-field, superresolved, microscopic characterization,” Opt. Photon. News 18, 29 (2007).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
[CrossRef]

Ippolito, S. B.

Jacob, Z.

Kartashev, A. I.

A. I. Kartashev, “Optical system with enhanced resolving power,” Opt. Spectrosc. 9, 204–206 (1960).

Koklu, F. H.

Konan, D.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Kuei, C.-P.

Kusnetsova, Y.

Kuznetsova, Y.

Lauer, V.

V. Lauer, “New approach to optical diffraction tomography yielding a vector equation of diffraction tomography and a novel tomographic microscope,” J. Microsc. 205, 165–176 (2002).
[CrossRef]

Le, F.

Lee, H.

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]

Leith, E. N.

Liu, Z.

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]

Lohmann, A. W.

A. W. Lohmann and D. P. Parish, “Superresolution for nonbirefringent objects,” Appl. Opt. 3, 1037–1043 (1964).
[CrossRef]

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power,” in Progress in Optics, Vol. 15, E. Wolf, ed. (1999), Chap. 4.

Lukosz, W.

Maire, G.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Marks, D. L.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors 8, 3903–3931 (2008).
[CrossRef]

Marks, P.

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express 16, 2555–2569 (2008).
[CrossRef]

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
[CrossRef]

Marom, E.

Massig, J. H.

Mendlovic, D.

A. Shemer, D. Mendlovic, Z. Zalevsky, J. Garcia, and P. García-Martínez, “Superresolving optical system with time multiplexing and computer decoding,” Appl. Opt. 38, 7245–7251 (1999).
[CrossRef]

Z. Zalevsky and D. Mendlovic, Optical Super Resolution(Springer, 2002).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power,” in Progress in Optics, Vol. 15, E. Wolf, ed. (1999), Chap. 4.

Mico, V.

Micó, V.

Narimanov, E.

Neumann, A.

Parish, D. P.

Pustovyy, O.

Ralston, D. L.

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express 16, 2555–2569 (2008).
[CrossRef]

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
[CrossRef]

Ralston, T. S.

B. J. Davis, D. L. Marks, T. S. Ralston, P. S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy: computed imaging for scanned coherent microscopy,” Sensors 8, 3903–3931 (2008).
[CrossRef]

Sampson, D. D.

S. A. Alexandrov and D. D. Sampson, “Spatial information transmission beyond a systems diffraction limit using optical spectral encoding of the spatial frequency,” J. Opt. A. 10, 025304 (2008).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Digital Fourier holography enables wide-field, superresolved, microscopic characterization,” Opt. Photon. News 18, 29 (2007).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, T. Gutzler, and D. D. Sampson, “Synthetic aperture Fourier holographic optical microscopy,” Phys. Rev. Lett. 97, 168102 (2006).
[CrossRef]

S. A. Alexandrov, T. R. Hillman, and D. D. Sampson, “Spatially resolved Fourier holographic light scattering angular spectroscopy,” Opt. Lett. 30, 3305–3307 (2005).
[CrossRef]

Schwarz, C. J.

Sentenac, A.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (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 (2006).
[CrossRef]

Shemer, A.

Sheppard, C. J. R.

Sheppard, J. R.

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]

Sun, P. C.

Talneau, A.

G. Maire, F. Drsek, J. Girard, H. Giovannini, A. Talneau, D. Konan, K. Belkebir, P. C. Chaumet, and A. Sentenac, “Experimental demonstration of quantitative imaging beyond Abbe’s limit with optical diffraction tomography,” Phys. Rev. Lett. 102, 213905 (2009).
[CrossRef]

Toraldo di Francia, G.

Tyler, S.

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Real-time interferometric synthetic aperture microscopy,” Opt. Express 16, 2555–2569 (2008).
[CrossRef]

S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
[CrossRef]

Unlu, M. S.

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[CrossRef]

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Appl. Opt. (5)

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S. Tyler, D. L. Ralston, P. Marks, S. Carney, and S. A. Boppart, “Interferometric synthetic aperture microscopy,” Nat. Phys. 3, 129–134 (2007).
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Opt. Express (9)

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Figures (12)

Fig. 1.
Fig. 1.

IIN optical arrangement (described in detail in [41]).

Fig. 2.
Fig. 2.

a) Illumination and collection configurations: A—objective normal to the substrate surface, image frequencies up to (n+NA)/λ can be captured; B—objective with tilt away from the optic axis, frequencies up to (n+1)/λ; C—objective on the side of the substrate with grating, frequencies between (n+1)/λ and 2n/λ. b) spatial frequency-space coverage with regions collected with various geometries indicated.

Fig. 3.
Fig. 3.

Geometry shows the collection of high-spatial-frequency information propagating in the substrate that corresponds to small features.

Fig. 4.
Fig. 4.

Resolution restriction: normalized HP versus index of refraction for different NAs (0.4, 0.8, 1.2) with a fixed substrate thickness (t=50μm) and FOV (F=32μm). Solid lines, dependence described by the lower part of Eq. (6); dashed lines, dependence described by the upper part of Eq. (6).

Fig. 5.
Fig. 5.

Resolution restriction: normalized HP versus index of refraction for different substrate thicknesses: 10, 30, 100, 300 μm calculated with NA=0.4, F=32μm in different synthetic aperture steps: long dashed lines, inside of synthetic aperture up to λ/[2(n+3NA)]; dashed lines, inside of synthetic aperture up to λ/[2(n+5NA)]; dotted lines, inside of synthetic aperture up to λ/[2(n+7NA)].

Fig. 6.
Fig. 6.

a) SEM image of periodic structure, HP=120nm and b) IIN subimage for t=2mm and decoupling grating HP of 280 nm.

Fig. 7.
Fig. 7.

a) Model CD=120nm structures, b) x-direction high-frequency image.

Fig. 8.
Fig. 8.

Difference in expansion of spectral package (120 nm features) for different substrate thicknesses (n=1.5, F=64μm): a) t=1μm, image expansion 3 times; b) t=5μm, image expansion 10 times; comparison of filtered image crosscuts (blue) with crosscuts of images (red) distorted by substrate propagation with: c) t=1μm, d) t=5μm.

Fig. 9.
Fig. 9.

Synthetic aperture guideline: normalized subimage bandwidth 2NAsub versus normalized FOV for different extraction gratings represented by center frequency HPc (gnHPc/λ).

Fig. 10.
Fig. 10.

Restored images (CD=120nm, n=1.5), crosscuts and crosscut differences: a) t=1μm, F=16μm—quality of the resorted image is good, b) t=5μm, F=16μm—quality of the resorted image is poor due to increased substrate thickness, c) t=5μm, F=32μm—quality of the resorted image is improved as the result of increasing FOV.

Fig. 11.
Fig. 11.

MSE versus HP of a 10-line pattern for different substrate thicknesses, n=1.5; F=32μm; λ=633nm. 3% MSE considered as images with acceptable quality. 0.5 μm substrates allows restoration of images with 112 nm features, 1μm113.5nm, 3μm118nm, 5μm120nm, 10μm124nm.

Fig. 12.
Fig. 12.

HP versus n for different substrate thicknesses: 1, 5, 10 μm (F=32μm), λ=633nm. Substrates with higher n allow resolution and restoration of images with smaller features.

Tables (2)

Tables Icon

Table 1. Wavelength-Dependent Resolution on a Si Substrate for Different Techniques

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Table 2. Examples of Possible Combinations of Materials and Wavelength for Enhanced Resolution

Equations (16)

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

d=λnsinα1+NA.
d=λ2NA.
kα1=k0NA=nk0sinα1=nk0sin[sin1(NA/n)]
sin(α1)=NAn=bb2+t2;b=t[(nNA)21]1/2,
sin(α2)=b+F(b+F)2+t2=[1+(b+Ft)2]1/2,={1+[Ft+((nNA)21)1/2]2}1/2
HPmin=MAX{λ2(n+3NA);λ2n{1+{1+[Ft+((nNA)21)1/2]2}1/2}}.
sinα0=λnd=2NAn.
sinα2=1n(λd+sinθ).
L0=tcosα0=t1sin2α0=t1(λnd)2,
L=tcosα2=t1sin2α2=t1[1n(λd+sinθ)],
Δφ=φφ0=2πntλ[11[1n(λd+sinθ)]211(λnd)2].
Ft=tanα2tanα1.
sinα2=sinαc+NAsub,
sinα1=sinαcNAsub,
sinαc+sinβ=λ2nHPc.
Ft=sinαc+NAsubn1(sinαc+NAsubn)2sinαcNAsubn1(sinαcNAsubn)2.

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