Abstract

The linear systems optical resolution limit is a dense grating pattern at a λ/2 pitch or a critical dimension (resolution) of λ/4. However, conventional microscopy provides a (Rayleigh) resolution of only ~ 0.6λ/NA, approaching λ/1.67 as NA → 1. A synthetic aperture approach to reaching the λ/4 linear-systems limit, extending previous developments in imaging-interferometric microscopy, is presented. Resolution of non-periodic 180-nm features using 633-nm illumination (λ/3.52) and of a 170-nm grating (λ/3.72) is demonstrated. These results are achieved with a 0.4-NA optical system and retain the working distance, field-of-view, and depth-of-field advantages of low-NA systems while approaching ultimate resolution limits.

© 2007 Optical Society of America

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  1. G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
    [CrossRef] [PubMed]
  2. V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94, 143903 (2005).
    [CrossRef] [PubMed]
  3. 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] [PubMed]
  4. W. Lukosz and M. Marchant, "Optischen Abbildung Unter Ueberschreitung der Beugungsbedingten Aufloesungsgrenze," Optica Acta  10, 241-255 (1963).
    [CrossRef]
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    [CrossRef]
  6. X. Chen and S. R. J. Brueck, "Imaging interferometric lithography - approaching the resolution limits of optics," Opt. Lett. 24, 124-126 (1999).
    [CrossRef]
  7. C. J. Schwarz, Y. Kuznetsova, and S. R. J. Brueck, "Imaging interferometric microscopy," Opt. Lett. 28, 1424-1426 (2003).
    [CrossRef] [PubMed]
  8. 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] [PubMed]
  9. 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]
  10. V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, "Single-step superresolution by interferometric imaging," Opt. Express. 12, 2589-2596 (2004).
    [CrossRef] [PubMed]
  11. V. Mico, Z. Zalevsky, P. Garcia-Martinez and J. Garcia "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
    [CrossRef] [PubMed]
  12. V. Mico, Z. Zalevsky and J. Garcia, "Superresolution optical system by common-path interferometry," Opt. Express. 14, 5168-5177 (2006).
    [CrossRef] [PubMed]
  13. V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia "Synthetic aperture superresolution with multiple off-axis holograms," J. Opt. Soc. Am. A 23, 3162-3170 (2006).
    [CrossRef]
  14. J. W. Goodman, Introduction to Fourier Optics, 2nd Ed. (John Wiley and Sons, 1998).

2006 (5)

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

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] [PubMed]

V. Mico, Z. Zalevsky and J. Garcia, "Superresolution optical system by common-path interferometry," Opt. Express. 14, 5168-5177 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez and J. Garcia "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia "Synthetic aperture superresolution with multiple off-axis holograms," J. Opt. Soc. Am. A 23, 3162-3170 (2006).
[CrossRef]

2005 (3)

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]

V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef] [PubMed]

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] [PubMed]

2004 (1)

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, "Single-step superresolution by interferometric imaging," Opt. Express. 12, 2589-2596 (2004).
[CrossRef] [PubMed]

2003 (1)

1999 (1)

1967 (1)

1963 (1)

W. Lukosz and M. Marchant, "Optischen Abbildung Unter Ueberschreitung der Beugungsbedingten Aufloesungsgrenze," Optica Acta  10, 241-255 (1963).
[CrossRef]

Alexandrov, S. A.

Andrei, M. A.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Brueck, S. R. J.

Chen, X.

Donnert, G.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Eggeling, C.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Garcia, J.

V. Mico, Z. Zalevsky and J. Garcia, "Superresolution optical system by common-path interferometry," Opt. Express. 14, 5168-5177 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia "Synthetic aperture superresolution with multiple off-axis holograms," J. Opt. Soc. Am. A 23, 3162-3170 (2006).
[CrossRef]

V. Mico, Z. Zalevsky, P. Garcia-Martinez and J. Garcia "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, "Single-step superresolution by interferometric imaging," Opt. Express. 12, 2589-2596 (2004).
[CrossRef] [PubMed]

Garcia-Martinez, P.

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] [PubMed]

Hell, S. W.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef] [PubMed]

Hillman, T. R.

Jahn, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Keller, J.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Kuznetsova, Y.

Lucosz, W.

Lührmann, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Lukosz, W.

W. Lukosz and M. Marchant, "Optischen Abbildung Unter Ueberschreitung der Beugungsbedingten Aufloesungsgrenze," Optica Acta  10, 241-255 (1963).
[CrossRef]

Marchant, M.

W. Lukosz and M. Marchant, "Optischen Abbildung Unter Ueberschreitung der Beugungsbedingten Aufloesungsgrenze," Optica Acta  10, 241-255 (1963).
[CrossRef]

Medda, R.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Mico, V.

V. Mico, Z. Zalevsky and J. Garcia, "Superresolution optical system by common-path interferometry," Opt. Express. 14, 5168-5177 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia "Synthetic aperture superresolution with multiple off-axis holograms," J. Opt. Soc. Am. A 23, 3162-3170 (2006).
[CrossRef]

V. Mico, Z. Zalevsky, P. Garcia-Martinez and J. Garcia "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, "Single-step superresolution by interferometric imaging," Opt. Express. 12, 2589-2596 (2004).
[CrossRef] [PubMed]

Rizzoli, S. O.

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Sampson, D. D.

Schwarz, C. J.

Westphal, V.

V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef] [PubMed]

Zalevsky, Z.

V. Mico, Z. Zalevsky, P. Garcia-Martinez and J. Garcia "Superresolved imaging in digital holography by superposition of tilted wavefronts," Appl. Opt. 45, 822-828 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia "Synthetic aperture superresolution with multiple off-axis holograms," J. Opt. Soc. Am. A 23, 3162-3170 (2006).
[CrossRef]

V. Mico, Z. Zalevsky and J. Garcia, "Superresolution optical system by common-path interferometry," Opt. Express. 14, 5168-5177 (2006).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, "Single-step superresolution by interferometric imaging," Opt. Express. 12, 2589-2596 (2004).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

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

Opt. Express. (2)

V. Mico, Z. Zalevsky, P. Garcia-Martinez, and J. Garcia, "Single-step superresolution by interferometric imaging," Opt. Express. 12, 2589-2596 (2004).
[CrossRef] [PubMed]

V. Mico, Z. Zalevsky and J. Garcia, "Superresolution optical system by common-path interferometry," Opt. Express. 14, 5168-5177 (2006).
[CrossRef] [PubMed]

Opt. Lett. (3)

Optica Acta (1)

W. Lukosz and M. Marchant, "Optischen Abbildung Unter Ueberschreitung der Beugungsbedingten Aufloesungsgrenze," Optica Acta  10, 241-255 (1963).
[CrossRef]

Phys. Rev. Lett. (2)

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] [PubMed]

V. Westphal and S. W. Hell, "Nanoscale resolution in the focal plane of an optical microscope," Phys. Rev. Lett. 94, 143903 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA (2)

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] [PubMed]

G. Donnert, J. Keller, R. Medda, M. A. Andrei, S. O. Rizzoli, R. Lührmann, R. Jahn, C. Eggeling, and S. W. Hell, "Macromolecular-scale resolution in biological fluorescence microscopy," Proc. Natl. Acad. Sci. USA 103, 11440-11445 (2006).
[CrossRef] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics, 2nd Ed. (John Wiley and Sons, 1998).

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Figures (13)

Fig. 1.
Fig. 1.

Optical arrangement for imaging interferometric microscopy: α = sin-1(NA), β is the incident beam angle of incidence, and βref is the angle of the reference beam onto the image plane.

Fig. 2.
Fig. 2.

(a). Manhattan geometry pattern used for image resolution exploration consisting of five nested “ells” and a large box. The lines and spaces of the “ells” are 240 nm. (b). intensity Fourier space components of the pattern, mapped onto the frequency space coverage of the imaging system.

Fig. 3.
Fig. 3.

Experimental setup for off-axis images and interferometric reconstruction.

Fig. 4.
Fig. 4.

(a). Low-frequency and (b) reconstructed images with the high frequency images taken at an offset illumination of 53, (c) reconstructed image with high frequency images taken at 53° and 80° without filtering, and d) reconstructed image using electronic spatial filtering.

Fig. 5.
Fig. 5.

Optical arrangement using a tilted object (with respect to the objective image plane) to enhance the frequency space information.

Fig. 6.
Fig. 6.

Frequency space coverage with tilted mask, a) for 180-nm CD structure, b) location of high frequency spectral components for a 170-nm CD structure.

Fig. 7.
Fig. 7.

Range of captured frequencies versus tilt mask angle, β = 80°. The vertical dashed line corresponds to the present experiment. The shaded region is the accessible frequency space coverage along the tilt direction.

Fig. 8.
Fig. 8.

Mapping between spatial frequencies in tilted/offset image and actual object spatial frequencies. Curves correspond to the indicated spatial frequencies in the y-direction. The decreasing extent of the curves with increasing transverse wave vector is a result of the circular aperture of the objective.

Fig. 9.
Fig. 9.

Experiment for a 180-nm CD: a) reconstructed image, b) reconstructed model

Fig. 10.
Fig. 10.

Comparison of cross cuts for the experiment (reconstructed total image) and a Fourier optics model (along the line indicated line in Fig. 8).

Fig. 11.
Fig. 11.

Reconstructed images of: a) a 170-nm CD structure; b) a 170-nm CD grating, obtained using multiple partial images including one with a tilted object plane.

Fig. 12.
Fig. 12.

Experiment (a, c) and simulation (b, d) results showing the impact of the frequency restoration on the high frequency partial image. The dotted lines are visual guides showing the significant shift of the out-of-focus object (left) in the laboratory frame.

Fig. 13.
Fig. 13.

Reconstructed image, 180- and 170-nm structures illustrating the restoration of the field of view achieved by transforming the laboratory frame spatial frequencies to the image frame.

Tables (1)

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Table I: Scalability of resolution including immersion microscopy

Equations (2)

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f y = f y
f x = f x cos θ tilt + 1 f x ′2 f y ′2 sin θ tilt

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