Abstract

We consider an imaging problem that aims to identify the profile of a reflective surface by the scattered wave measured in the near field. Potential applications include nondestructive detection of micro devices, subwavelength imaging techniques in nano-optics. When the height of the imaging target is small, the connection between the localized evanescent wave modes of the measurement and the high spatial frequency components of the structure is characterized explicitly, which leads to a natural reconstruction method with super resolution images. A novel multiple frequency approach is also presented that captures both the main features as well as the fine details of the structure.

© 2012 Optical Society of America

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References

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    [CrossRef]
  13. G. Bao and P. Li, Opt. Lett. 32, 1465 (2007).
    [CrossRef]
  14. G. Bao and P. Li, Inverse Probl. 20, L1 (2004).
    [CrossRef]
  15. Y. Chen, Inverse Probl. 13, 1 (1997).
    [CrossRef]

2011 (1)

G. Bao and J. Lin, SIAM J. Appl. Math. 71, 1733 (2011).
[CrossRef]

2007 (1)

2006 (1)

G. Derveaux, G. Papanicolaou, and C. Tsogka, Inverse Probl. 22, 1437 (2006).
[CrossRef]

2004 (1)

G. Bao and P. Li, Inverse Probl. 20, L1 (2004).
[CrossRef]

2001 (1)

2000 (1)

P. Carney and J. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

1999 (1)

R. Dunn, Chem. Rev. 99, 2891 (1999).
[CrossRef]

1997 (1)

Y. Chen, Inverse Probl. 13, 1 (1997).
[CrossRef]

1995 (1)

1994 (1)

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

1992 (1)

1990 (1)

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, and T. L. Ferrel, Rev. Sci. Instrum. 61, 3669 (1990).
[CrossRef]

1989 (1)

D. Courjon, K. Sarayeddine, and M. Spajer, Opt. Commun. 71, 23 (1989).
[CrossRef]

Bainier, C.

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

Bao, G.

G. Bao and J. Lin, SIAM J. Appl. Math. 71, 1733 (2011).
[CrossRef]

G. Bao and P. Li, Opt. Lett. 32, 1465 (2007).
[CrossRef]

G. Bao and P. Li, Inverse Probl. 20, L1 (2004).
[CrossRef]

G. Bao and J. Lin, “Near-field imaging of the surface displacement on an infinite ground plane,” Inverse Probl. Imag. (to be published).

Barchiesi, D.

Carminati, R.

Carney, P.

P. Carney and J. Schotland, Opt. Lett. 26, 1072 (2001).
[CrossRef]

P. Carney and J. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

Chen, Y.

Y. Chen, Inverse Probl. 13, 1 (1997).
[CrossRef]

Chilcott, D. W.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, and T. L. Ferrel, Rev. Sci. Instrum. 61, 3669 (1990).
[CrossRef]

Colton, D.

D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, 1983).

Courjon, D.

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

D. Courjon, K. Sarayeddine, and M. Spajer, Opt. Commun. 71, 23 (1989).
[CrossRef]

Derveaux, G.

G. Derveaux, G. Papanicolaou, and C. Tsogka, Inverse Probl. 22, 1437 (2006).
[CrossRef]

Dunn, R.

R. Dunn, Chem. Rev. 99, 2891 (1999).
[CrossRef]

Ferrel, T. L.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, and T. L. Ferrel, Rev. Sci. Instrum. 61, 3669 (1990).
[CrossRef]

Greffet, J.

Kress, R.

D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, 1983).

Labeke, D.

Li, P.

G. Bao and P. Li, Opt. Lett. 32, 1465 (2007).
[CrossRef]

G. Bao and P. Li, Inverse Probl. 20, L1 (2004).
[CrossRef]

Lin, J.

G. Bao and J. Lin, SIAM J. Appl. Math. 71, 1733 (2011).
[CrossRef]

G. Bao and J. Lin, “Near-field imaging of the surface displacement on an infinite ground plane,” Inverse Probl. Imag. (to be published).

Papanicolaou, G.

G. Derveaux, G. Papanicolaou, and C. Tsogka, Inverse Probl. 22, 1437 (2006).
[CrossRef]

Reddick, R. C.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, and T. L. Ferrel, Rev. Sci. Instrum. 61, 3669 (1990).
[CrossRef]

Sarayeddine, K.

D. Courjon, K. Sarayeddine, and M. Spajer, Opt. Commun. 71, 23 (1989).
[CrossRef]

Schotland, J.

P. Carney and J. Schotland, Opt. Lett. 26, 1072 (2001).
[CrossRef]

P. Carney and J. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

Sharp, S. L.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, and T. L. Ferrel, Rev. Sci. Instrum. 61, 3669 (1990).
[CrossRef]

Spajer, M.

D. Courjon, K. Sarayeddine, and M. Spajer, Opt. Commun. 71, 23 (1989).
[CrossRef]

Tsogka, C.

G. Derveaux, G. Papanicolaou, and C. Tsogka, Inverse Probl. 22, 1437 (2006).
[CrossRef]

Warmack, R. J.

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, and T. L. Ferrel, Rev. Sci. Instrum. 61, 3669 (1990).
[CrossRef]

Appl. Phys. Lett. (1)

P. Carney and J. Schotland, Appl. Phys. Lett. 77, 2798 (2000).
[CrossRef]

Chem. Rev. (1)

R. Dunn, Chem. Rev. 99, 2891 (1999).
[CrossRef]

Inverse Probl. (3)

G. Bao and P. Li, Inverse Probl. 20, L1 (2004).
[CrossRef]

Y. Chen, Inverse Probl. 13, 1 (1997).
[CrossRef]

G. Derveaux, G. Papanicolaou, and C. Tsogka, Inverse Probl. 22, 1437 (2006).
[CrossRef]

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

Opt. Commun. (1)

D. Courjon, K. Sarayeddine, and M. Spajer, Opt. Commun. 71, 23 (1989).
[CrossRef]

Opt. Lett. (2)

Rep. Prog. Phys. (1)

D. Courjon and C. Bainier, Rep. Prog. Phys. 57, 989 (1994).
[CrossRef]

Rev. Sci. Instrum. (1)

R. C. Reddick, R. J. Warmack, D. W. Chilcott, S. L. Sharp, and T. L. Ferrel, Rev. Sci. Instrum. 61, 3669 (1990).
[CrossRef]

SIAM J. Appl. Math. (1)

G. Bao and J. Lin, SIAM J. Appl. Math. 71, 1733 (2011).
[CrossRef]

Other (2)

D. Colton and R. Kress, Integral Equation Methods in Scattering Theory (Wiley, 1983).

G. Bao and J. Lin, “Near-field imaging of the surface displacement on an infinite ground plane,” Inverse Probl. Imag. (to be published).

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Figures (3)

Fig. 1.
Fig. 1.

Problem geometry.

Fig. 2.
Fig. 2.

Near-field image (dotted curve) and the real profile (solid curve).

Fig. 3.
Fig. 3.

Evolution of the reconstruction at k=5, 20, 40. The dash line is the reconstruction, and the solid line is the real image.

Equations (12)

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

Δu+k2u=0above the ground plane.
us(x)=ΓG(x,y)ψ(y)dsy
G(x,y)Φ(x,y)Φ(xr,y).
Φ(x,y)=i4π1k2(κ)ei(x1y1)·κeik2(κ)|x2y2|dκ,
u^s(κ,d)eik2(κ)d(fφ^)(κ),κ(,),
Id(κ)={eik2(κ)d|κ|kc,0|κ|>kc,
h^(κ)=Id(κ)u^s(κ,d).
minKfφ+gfL2(γ)whereφis a continuous function that satisfiesfφ=h.
(Kfφ)(x1)γ¯G˜(x1y1;f(x1),f(y1))φ(y1)dy1,
min12S(Γ)umeasL2(BR+)2minJ(Γ).
Γ(V·n)·Real{unu¯adjn}ds<0,
{Δuadj+k2uadj=0above the ground plane,uadj=0onΓ,uadjn=T*(uadj)+uumeasonBR+,

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