Abstract

We have developed a superresolution vibrational imaging method by simultaneous detection of Raman and hyper-Raman scattering. Raman and hyper-Raman images obtained with the same laser spot carry independent information on the sample spatial distribution, owing to different signal dependence (linear in Raman and quadratic in hyper-Raman) on the incident light intensity. This information can be quantitatively analyzed to recover the incident light intensity distribution at the focal plane. A superresolution vibrational image is then derived by the constrained deconvolution of the images by the obtained incident light intensity distribution. This method has been applied to a TiO2 nanostructure and the obtained superresolution image was compared with a scanning electron microscopy image. The spatial resolution achieved by the present method is evaluated to be 160nm, which is more than twice better than the diffraction limited resolution.

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M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

B. Hofmann and L. v. Wolfersdorf, Numer. Funct. Anal. Optim. 27, 357 (2006).
[CrossRef]

R. Shimada, H. Kano, and H. Hamaguchi, Opt. Lett. 31, 320 (2006).
[CrossRef] [PubMed]

2002

2001

J. Squier and M. Muller, Rev. Sci. Instrum. 72, 2855 (2001).
[CrossRef]

1999

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

T. A. Klar and S. W. Hell, Opt. Lett. 24, 954 (1999).
[CrossRef]

1997

R. J. Gonzalez, R. Zallen, and H. Berger, Phys. Rev. B 55, 7014 (1997).
[CrossRef]

1994

1993

P. C. Hansen and D. P. O’Leary, SIAM J. Sci. Comput. 14, 1487 (1993).
[CrossRef]

1988

1984

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984), p. 39.

1978

T. Ohsaka, F. Izumi, and Y. Fujiki, J. Raman Spectrosc. 7, 321 (1978).
[CrossRef]

1965

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 14, 681 (1965).
[CrossRef]

Bates, M.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

Berger, H.

R. J. Gonzalez, R. Zallen, and H. Berger, Phys. Rev. B 55, 7014 (1997).
[CrossRef]

Bovik, A. C.

Conchello, J. A.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Cooper, J.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Fujiki, Y.

T. Ohsaka, F. Izumi, and Y. Fujiki, J. Raman Spectrosc. 7, 321 (1978).
[CrossRef]

Gonzalez, R. J.

R. J. Gonzalez, R. Zallen, and H. Berger, Phys. Rev. B 55, 7014 (1997).
[CrossRef]

Hamaguchi, H.

Hansen, P. C.

P. C. Hansen and D. P. O’Leary, SIAM J. Sci. Comput. 14, 1487 (1993).
[CrossRef]

Hecht, E.

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), p. 472.

Hell, S. W.

Hofmann, B.

B. Hofmann and L. v. Wolfersdorf, Numer. Funct. Anal. Optim. 27, 357 (2006).
[CrossRef]

Izumi, F.

T. Ohsaka, F. Izumi, and Y. Fujiki, J. Raman Spectrosc. 7, 321 (1978).
[CrossRef]

Kano, H.

Karpova, T.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Kawata, S.

Klar, T. A.

Ling, J.

Maker, P. D.

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 14, 681 (1965).
[CrossRef]

McNally, J. G.

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Miller, M. A.

Minami, S.

Moore, R. V.

Muller, M.

J. Squier and M. Muller, Rev. Sci. Instrum. 72, 2855 (2001).
[CrossRef]

Nakamura, O.

O’Leary, D. P.

P. C. Hansen and D. P. O’Leary, SIAM J. Sci. Comput. 14, 1487 (1993).
[CrossRef]

Ohsaka, T.

T. Ohsaka, F. Izumi, and Y. Fujiki, J. Raman Spectrosc. 7, 321 (1978).
[CrossRef]

Rust, M. J.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

Savage, C. M.

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 14, 681 (1965).
[CrossRef]

Sheppard, C.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984), p. 39.

Shimada, R.

Squier, J.

J. Squier and M. Muller, Rev. Sci. Instrum. 72, 2855 (2001).
[CrossRef]

Terhune, R. W.

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 14, 681 (1965).
[CrossRef]

Weitman, S. D.

Wichmann, J.

Wilson, T.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984), p. 39.

Wolfersdorf, L. v.

B. Hofmann and L. v. Wolfersdorf, Numer. Funct. Anal. Optim. 27, 357 (2006).
[CrossRef]

Zallen, R.

R. J. Gonzalez, R. Zallen, and H. Berger, Phys. Rev. B 55, 7014 (1997).
[CrossRef]

Zhuang, X.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

Appl. Opt.

J. Opt. Soc. Am. A

J. Raman Spectrosc.

T. Ohsaka, F. Izumi, and Y. Fujiki, J. Raman Spectrosc. 7, 321 (1978).
[CrossRef]

Methods

J. G. McNally, T. Karpova, J. Cooper, and J. A. Conchello, Methods 19, 373 (1999).
[CrossRef] [PubMed]

Nat. Meth.

M. J. Rust, M. Bates, and X. Zhuang, Nat. Meth. 3, 793(2006).
[CrossRef]

Numer. Funct. Anal. Optim.

B. Hofmann and L. v. Wolfersdorf, Numer. Funct. Anal. Optim. 27, 357 (2006).
[CrossRef]

Opt. Lett.

Phys. Rev. B

R. J. Gonzalez, R. Zallen, and H. Berger, Phys. Rev. B 55, 7014 (1997).
[CrossRef]

Phys. Rev. Lett.

R. W. Terhune, P. D. Maker, and C. M. Savage, Phys. Rev. Lett. 14, 681 (1965).
[CrossRef]

Rev. Sci. Instrum.

J. Squier and M. Muller, Rev. Sci. Instrum. 72, 2855 (2001).
[CrossRef]

SIAM J. Sci. Comput.

P. C. Hansen and D. P. O’Leary, SIAM J. Sci. Comput. 14, 1487 (1993).
[CrossRef]

Other

E. Hecht, Optics, 4th ed. (Addison-Wesley, 2002), p. 472.

T. Wilson and C. Sheppard, Theory and Practice of Scanning Optical Microscopy (Academic, 1984), p. 39.

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Figures (4)

Fig. 1
Fig. 1

Simultaneous Raman and hyper-Raman microspectroscopic imaging system.

Fig. 2
Fig. 2

(a) Raman and (b) hyper-Raman spectra of anatase-type TiO 2 .

Fig. 3
Fig. 3

(a) Raman and (b) hyper-Raman images of the TiO 2 standard sample, (c) incident light intensity distribution, (d) superresolution, and (e) SEM images of the TiO 2 standard sample.

Fig. 4
Fig. 4

Intensity cross sections of Raman, hyper-Raman, superresolution, and SEM images along the dotted lines in Fig. 3.

Equations (4)

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

R = χ * I , H = χ * I 2 ,
R * I 2 = H * I = χ * I * I 2 .
ε = | R * I 2 H * I | 2 + γ | I I 0 | 2 .
ε = | R χ * I | 2 + | H χ * I 2 | 2 + γ | χ | 2 .

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