Abstract

In this paper we present a super-resolving approach for detecting an axially moving target that is based upon a time-multiplexing concept and that overcomes the diffraction limit set by the optics of an imaging camera by a priori knowledge of the high-resolution background in front of which the target is moving. As the movement trajectory is axial, the approach can be applied to targets that are approaching or moving away from the camera. By recording a set of low-resolution images at different target axial positions, the super-resolving algorithm weights each image by demultiplexing them using the high-resolution background image and provides a super-resolved image of the target. Theoretical analyses as well as simulations and preliminary experimental validation are presented to validate the proposed approach.

© 2013 Optical Society of America

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2012

2011

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Z. X. Pan, H. J. Huang, and W. D. Sun, “Super resolution of remote sensing image based on structure similarity in CS frame,” Proc. SPIE 8002, 80020H (2011).
[CrossRef]

B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

2010

2009

Z. Zalevsky, E. Fish, N. Shachar, Y. Vexberg, V. Micó, and J. Garcia, “Super-resolved imaging with randomly distributed, time- and size-varied particles,” J. Opt. A 11, 1–6 (2009).

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[CrossRef]

2008

2007

2006

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

Z. Zalevsky, J. Garcia, and C. Ferreira, “Super resolved imaging of remote moving targets,” Opt. Lett. 31, 586–588 (2006).
[CrossRef]

2005

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]

K. Puschmann and F. Kneer, “On super-resolution in astronomical imaging.” Astron. Astrophys. 436, 373–378 (2005).
[CrossRef]

2003

U. C. Fischer, J. Heimel, H.-J. Maas, H. Fuchs, J. C. Weeber, and A. Dereux, “Super-resolution scanning near-field optical microscopy,” Opt. Nanotech. 88, 141–153 (2003).
[CrossRef]

1998

1997

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy and undersampled measured images,” IEEE Trans. Image Process. 6, 1646–1658(1997).
[CrossRef]

C. C. Schmullius and D. L. Evans, “Review article synthetic aperture radar (SAR) frequency and polarization requirements for applications in ecology, geology, hydrology, and oceanography: a tabular status quo after SIR-C/X-SAR,” Int. J. Remote Sens. 18, 2713–2722 (1997).
[CrossRef]

1994

1991

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef]

Bates, M.

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[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).
[CrossRef]

Bertero, M.

M. Bertero and C. De Mol, “Super-resolution by data inversion,” in Progress in Optics, E. Wolf, ed. (Elsevier North-Holland, 1996), Vol. 36, Chap. 3, pp. 129–178.

Betzig, E.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef]

Chen, Z.

B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Chiu, S. J.

M. D. Robinson, S. J. Chiu, C. A. Toth, J. Izatt, J. Y. Lo, and S. Farsiu, “Novel applications of super-resolution in medical imaging,” in Super-Resolution Imaging, P. Milanfar, ed. (CRC, 2010), pp. 383–412.

Choi, W.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Choi, Y.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Courjon, D.

D. Courjon, Near-Field Microscopy and Near-Field Optics(Imperial College, 2003).

Curlander, J. C.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley-Interscience, 1991).

Dasari, R. R.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

De Mol, C.

M. Bertero and C. De Mol, “Super-resolution by data inversion,” in Progress in Optics, E. Wolf, ed. (Elsevier North-Holland, 1996), Vol. 36, Chap. 3, pp. 129–178.

Dereux, A.

U. C. Fischer, J. Heimel, H.-J. Maas, H. Fuchs, J. C. Weeber, and A. Dereux, “Super-resolution scanning near-field optical microscopy,” Opt. Nanotech. 88, 141–153 (2003).
[CrossRef]

Du, Y.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31, 5023–5040 (2010).
[CrossRef]

Elad, M.

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy and undersampled measured images,” IEEE Trans. Image Process. 6, 1646–1658(1997).
[CrossRef]

Evans, D. L.

C. C. Schmullius and D. L. Evans, “Review article synthetic aperture radar (SAR) frequency and polarization requirements for applications in ecology, geology, hydrology, and oceanography: a tabular status quo after SIR-C/X-SAR,” Int. J. Remote Sens. 18, 2713–2722 (1997).
[CrossRef]

Fang-Yen, C.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Farsiu, S.

M. D. Robinson, S. J. Chiu, C. A. Toth, J. Izatt, J. Y. Lo, and S. Farsiu, “Novel applications of super-resolution in medical imaging,” in Super-Resolution Imaging, P. Milanfar, ed. (CRC, 2010), pp. 383–412.

Feld, M. S.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Ferreira, C.

Feuer, A.

M. Elad and A. Feuer, “Restoration of a single superresolution image from several blurred, noisy and undersampled measured images,” IEEE Trans. Image Process. 6, 1646–1658(1997).
[CrossRef]

Fischer, U. C.

U. C. Fischer, J. Heimel, H.-J. Maas, H. Fuchs, J. C. Weeber, and A. Dereux, “Super-resolution scanning near-field optical microscopy,” Opt. Nanotech. 88, 141–153 (2003).
[CrossRef]

Fish, E.

Z. Zalevsky, E. Fish, N. Shachar, Y. Vexberg, V. Micó, and J. Garcia, “Super-resolved imaging with randomly distributed, time- and size-varied particles,” J. Opt. A 11, 1–6 (2009).

Fixler, D.

Fuchs, H.

U. C. Fischer, J. Heimel, H.-J. Maas, H. Fuchs, J. C. Weeber, and A. Dereux, “Super-resolution scanning near-field optical microscopy,” Opt. Nanotech. 88, 141–153 (2003).
[CrossRef]

Garcia, J.

García, J.

Grossman, E.

Gur, A.

Gur, E.

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]

Harris, T. D.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef]

Heimel, J.

U. C. Fischer, J. Heimel, H.-J. Maas, H. Fuchs, J. C. Weeber, and A. Dereux, “Super-resolution scanning near-field optical microscopy,” Opt. Nanotech. 88, 141–153 (2003).
[CrossRef]

Hell, S. W.

Hong, M.

B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Huang, B.

B. Huang, M. Bates, and X. Zhuang, “Super resolution fluorescence microscopy,” Annu. Rev. Biochem. 78, 993–1016 (2009).
[CrossRef]

Huang, H. J.

Z. X. Pan, H. J. Huang, and W. D. Sun, “Super resolution of remote sensing image based on structure similarity in CS frame,” Proc. SPIE 8002, 80020H (2011).
[CrossRef]

Hunt, B. R.

Ilovitsh, A.

Izatt, J.

M. D. Robinson, S. J. Chiu, C. A. Toth, J. Izatt, J. Y. Lo, and S. Farsiu, “Novel applications of super-resolution in medical imaging,” in Super-Resolution Imaging, P. Milanfar, ed. (CRC, 2010), pp. 383–412.

Jacquinot, P.

P. Jacquinot and B. Roizen-Dossier, “Apodization,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1964), Vol. 3, Chap. 2, pp. 29–186.

Kang, P.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Khan, A.

B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Kneer, F.

K. Puschmann and F. Kneer, “On super-resolution in astronomical imaging.” Astron. Astrophys. 436, 373–378 (2005).
[CrossRef]

Kostelak, R. L.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef]

Lee, K. J.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Limon, O.

Lin, Y.-H.

Lindberg, J.

J. Lindberg, “Mathematical concepts of optical super resolution,” J. Opt. 14, 083001 (2012).
[CrossRef]

Ling, F.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31, 5023–5040 (2010).
[CrossRef]

Liu, Z.

B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Lo, J. Y.

M. D. Robinson, S. J. Chiu, C. A. Toth, J. Izatt, J. Y. Lo, and S. Farsiu, “Novel applications of super-resolution in medical imaging,” in Super-Resolution Imaging, P. Milanfar, ed. (CRC, 2010), pp. 383–412.

Lohmann, A. W.

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2000), Vol. 40, pp. 271–341.

Luk’yanchuk, B.

B. Luk’yanchuk, A. Khan, Z. Liu, Z. Chen, and M. Hong, “Optical virtual imaging at 50 nm lateral resolution with a white-light nanoscope,” Nat. Commun. 2, 218 (2011).
[CrossRef]

Maas, H.-J.

U. C. Fischer, J. Heimel, H.-J. Maas, H. Fuchs, J. C. Weeber, and A. Dereux, “Super-resolution scanning near-field optical microscopy,” Opt. Nanotech. 88, 141–153 (2003).
[CrossRef]

Marcellin, M. W.

McDonough, R. N.

J. C. Curlander and R. N. McDonough, Synthetic Aperture Radar: Systems and Signal Processing (Wiley-Interscience, 1991).

Meller, M.

Mendlovic, D.

Z. Zalevsky and D. Mendlovic, Optical Super Resolution (Springer-Verlag, 2003).

Z. Zalevsky, D. Mendlovic, and A. W. Lohmann, “Optical systems with improved resolving power,” in Progress in Optics, E. Wolf, ed. (Elsevier, 2000), Vol. 40, pp. 271–341.

Merino, M. T.

M. T. Merino and J. Núñez, “Super-resolution of remotely sensed images with variable-pixel linearreconstruction,” IEEE Trans. Geosci. Remote Sens. 45, 1446–1457 (2007).
[CrossRef]

Mico, V.

Micó, V.

Núñez, J.

M. T. Merino and J. Núñez, “Super-resolution of remotely sensed images with variable-pixel linearreconstruction,” IEEE Trans. Geosci. Remote Sens. 45, 1446–1457 (2007).
[CrossRef]

Orbach, S.

Pan, Z. X.

Z. X. Pan, H. J. Huang, and W. D. Sun, “Super resolution of remote sensing image based on structure similarity in CS frame,” Proc. SPIE 8002, 80020H (2011).
[CrossRef]

Puschmann, K.

K. Puschmann and F. Kneer, “On super-resolution in astronomical imaging.” Astron. Astrophys. 436, 373–378 (2005).
[CrossRef]

Robinson, M. D.

M. D. Robinson, S. J. Chiu, C. A. Toth, J. Izatt, J. Y. Lo, and S. Farsiu, “Novel applications of super-resolution in medical imaging,” in Super-Resolution Imaging, P. Milanfar, ed. (CRC, 2010), pp. 383–412.

Roizen-Dossier, B.

P. Jacquinot and B. Roizen-Dossier, “Apodization,” in Progress in Optics, E. Wolf, ed. (North-Holland, 1964), Vol. 3, Chap. 2, pp. 29–186.

Rozental, S.

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).
[CrossRef]

Saat, E.

Schmullius, C. C.

C. C. Schmullius and D. L. Evans, “Review article synthetic aperture radar (SAR) frequency and polarization requirements for applications in ecology, geology, hydrology, and oceanography: a tabular status quo after SIR-C/X-SAR,” Int. J. Remote Sens. 18, 2713–2722 (1997).
[CrossRef]

Shachar, N.

Z. Zalevsky, E. Fish, N. Shachar, Y. Vexberg, V. Micó, and J. Garcia, “Super-resolved imaging with randomly distributed, time- and size-varied particles,” J. Opt. A 11, 1–6 (2009).

Sheppard, C. J.

T. Wilson and C. J. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Sheppard, D. G.

Sun, W. D.

Z. X. Pan, H. J. Huang, and W. D. Sun, “Super resolution of remote sensing image based on structure similarity in CS frame,” Proc. SPIE 8002, 80020H (2011).
[CrossRef]

Toth, C. A.

M. D. Robinson, S. J. Chiu, C. A. Toth, J. Izatt, J. Y. Lo, and S. Farsiu, “Novel applications of super-resolution in medical imaging,” in Super-Resolution Imaging, P. Milanfar, ed. (CRC, 2010), pp. 383–412.

Trautman, J. K.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef]

Tsai, D. P.

Tzioni, R.

Vexberg, Y.

Z. Zalevsky, E. Fish, N. Shachar, Y. Vexberg, V. Micó, and J. Garcia, “Super-resolved imaging with randomly distributed, time- and size-varied particles,” J. Opt. A 11, 1–6 (2009).

Weeber, J. C.

U. C. Fischer, J. Heimel, H.-J. Maas, H. Fuchs, J. C. Weeber, and A. Dereux, “Super-resolution scanning near-field optical microscopy,” Opt. Nanotech. 88, 141–153 (2003).
[CrossRef]

Weiner, J. S.

E. Betzig, J. K. Trautman, T. D. Harris, J. S. Weiner, and R. L. Kostelak, “Breaking the diffraction barrier: optical microscopy on a nanometric scale,” Science 251, 1468–1470 (1991).
[CrossRef]

Wichmann, J.

Wilson, T.

T. Wilson and C. J. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984).

Wu, S.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31, 5023–5040 (2010).
[CrossRef]

Xiao, F.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31, 5023–5040 (2010).
[CrossRef]

Xue, H.

F. Ling, Y. Du, F. Xiao, H. Xue, and S. Wu, “Super-resolution land-cover mapping using multiple sub-pixel shifted remotely sensed images,” Int. J. Remote Sens. 31, 5023–5040 (2010).
[CrossRef]

Yang, T. D.

Y. Choi, T. D. Yang, C. Fang-Yen, P. Kang, K. J. Lee, R. R. Dasari, M. S. Feld, and W. Choi, “Overcoming the diffraction limit using multiple light scattering in a highly disordered medium,” Phys. Rev. Lett. 107, 023902 (2011).
[CrossRef]

Zach, S.

Zalevsky, Z.

A. Ilovitsh, S. Zach, and Z. Zalevsky, “Contour superresolved imaging of static ground targets using satellite platform,” Appl. Opt. 51, 5863–5868 (2012).
[CrossRef]

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Z. Zalevsky, E. Fish, N. Shachar, Y. Vexberg, V. Micó, and J. Garcia, “Super-resolved imaging with randomly distributed, time- and size-varied particles,” J. Opt. A 11, 1–6 (2009).

Z. Zalevsky, E. Saat, S. Orbach, V. Mico, and J. Garcia, “Exceeding the resolving imaging power using environmental conditions,” Appl. Opt. 47, A1–A6 (2008).
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Z. Zalevsky, J. García, and V. Micó, “Transversal superresolution with noncontact axial movement of periodic structures,” J. Opt. Soc. Am. A 24, 3220–3225 (2007).
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Figures (2)

Fig. 1.
Fig. 1.

(a) Best low-resolution image without background. (b) Integration of all low-resolution images (with background). (c) One low-resolution image out of the set of captured images (with background). (d) Super-resolved reconstruction.

Fig. 2.
Fig. 2.

Experimental results: (a) Background at high resolution. (b) Left: low-resolution image out of the captured set of images; Right: super-resolved reconstruction.

Equations (9)

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g(x)=(1s1(xβt))b(x)+s(xβt),
I(x)=((1s1(xβt))b(x)+s(xβt))p(xx)dx=βt((1s1(x))b(βtx)+s(x))p(xβtx)dx,
r(x)=I(βtx)b(βtx)dt,
I(βtx)=βt((1s1(x))b(βtx)+s(x))p(βtxβtx)dx((1s1(x))b(βtx)+s(x))p(xx)dx.
r(x)=((1s1(x))b(βtx)+s(x))p(xx)b(βtx)dxdt=(1s1(x))p(xx)(b(βtx)b(βtx)dt)dx+s(x)p(xx)dxb(βtx)dt.
b(βtx)b(βtx)dtδ(xx).
b(βtx)dtΔTb(x),
p(xx)δ(xx)p(0)δ(xx),
r(x)=p(0)p(0)s1(x)+ΔTb(x)s(x)p(xx)dx.

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