Abstract

A recently developed optical diffraction tomography technique [J. Opt. Soc. Am. A 26, 19 (2009) ] is modified to handle the special case of a dispersionless scatterer, where the relative permittivity contrast of the object is independent of the operation frequency, allowing the fusion of multifrequency data. The modified technique is illustrated with a simulation scenario involving a dispersionless and lossless object being probed with plane waves of distinct incidence angles and frequencies. Superiority of the fusion of multifrequency data over the use of single-frequency data is demonstrated.

© 2009 Optical Society of America

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References

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  1. E. Karbeyaz and C. M. Rappaport, J. Opt. Soc. Am. A 26, 19 (2009).
    [CrossRef]
  2. T. Chu and K. Lee, IEEE Trans. Antennas Propag. 37, 515 (1989).
    [CrossRef]
  3. A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, Inverse Probl. 17, 1635 (2001).
    [CrossRef]
  4. M. L. Dennison and A. J. Devaney, Inverse Probl. 20, 1307 (2004).
    [CrossRef]
  5. A. J. Devaney, Ultrason. Imaging 4, 336 (1982).
    [CrossRef] [PubMed]
  6. A. J. Devaney and M. Dennison, Inverse Probl. 19, 855 (2003).
    [CrossRef]
  7. A. K. Dunn, “Light scattering properties of cells,” Ph.D dissertation (University of Texas at Austin, 1997).
  8. R. G. Driggers, Encyclopedia of Optical Engineering (CRC Press, 2003), Vol. 2.
  9. G. Hale and M. Querry, Appl. Opt. 12, 555 (1973).
    [CrossRef] [PubMed]
  10. H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
    [CrossRef] [PubMed]

2009

2006

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
[CrossRef] [PubMed]

2004

M. L. Dennison and A. J. Devaney, Inverse Probl. 20, 1307 (2004).
[CrossRef]

2003

A. J. Devaney and M. Dennison, Inverse Probl. 19, 855 (2003).
[CrossRef]

2001

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, Inverse Probl. 17, 1635 (2001).
[CrossRef]

1989

T. Chu and K. Lee, IEEE Trans. Antennas Propag. 37, 515 (1989).
[CrossRef]

1982

A. J. Devaney, Ultrason. Imaging 4, 336 (1982).
[CrossRef] [PubMed]

1973

Belkebir, K.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, Inverse Probl. 17, 1635 (2001).
[CrossRef]

Chu, T.

T. Chu and K. Lee, IEEE Trans. Antennas Propag. 37, 515 (1989).
[CrossRef]

de Hon, B. P.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, Inverse Probl. 17, 1635 (2001).
[CrossRef]

Dennison, M.

A. J. Devaney and M. Dennison, Inverse Probl. 19, 855 (2003).
[CrossRef]

Dennison, M. L.

M. L. Dennison and A. J. Devaney, Inverse Probl. 20, 1307 (2004).
[CrossRef]

Devaney, A. J.

M. L. Dennison and A. J. Devaney, Inverse Probl. 20, 1307 (2004).
[CrossRef]

A. J. Devaney and M. Dennison, Inverse Probl. 19, 855 (2003).
[CrossRef]

A. J. Devaney, Ultrason. Imaging 4, 336 (1982).
[CrossRef] [PubMed]

Ding, H.

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
[CrossRef] [PubMed]

Driggers, R. G.

R. G. Driggers, Encyclopedia of Optical Engineering (CRC Press, 2003), Vol. 2.

Dunn, A. K.

A. K. Dunn, “Light scattering properties of cells,” Ph.D dissertation (University of Texas at Austin, 1997).

Hale, G.

Hu, X. H.

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
[CrossRef] [PubMed]

Karbeyaz, E.

Kragel, P. J.

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
[CrossRef] [PubMed]

Lee, K.

T. Chu and K. Lee, IEEE Trans. Antennas Propag. 37, 515 (1989).
[CrossRef]

Litman, A. C. S.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, Inverse Probl. 17, 1635 (2001).
[CrossRef]

Lu, J. Q.

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
[CrossRef] [PubMed]

Querry, M.

Rappaport, C. M.

Tijhuis, A. G.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, Inverse Probl. 17, 1635 (2001).
[CrossRef]

Wooden, W. A.

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
[CrossRef] [PubMed]

Appl. Opt.

IEEE Trans. Antennas Propag.

T. Chu and K. Lee, IEEE Trans. Antennas Propag. 37, 515 (1989).
[CrossRef]

Inverse Probl.

A. G. Tijhuis, K. Belkebir, A. C. S. Litman, and B. P. de Hon, Inverse Probl. 17, 1635 (2001).
[CrossRef]

M. L. Dennison and A. J. Devaney, Inverse Probl. 20, 1307 (2004).
[CrossRef]

A. J. Devaney and M. Dennison, Inverse Probl. 19, 855 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Phys. Med. Biol.

H. Ding, J. Q. Lu, W. A. Wooden, P. J. Kragel, and X. H. Hu, Phys. Med. Biol. 51, 1479 (2006).
[CrossRef] [PubMed]

Ultrason. Imaging

A. J. Devaney, Ultrason. Imaging 4, 336 (1982).
[CrossRef] [PubMed]

Other

A. K. Dunn, “Light scattering properties of cells,” Ph.D dissertation (University of Texas at Austin, 1997).

R. G. Driggers, Encyclopedia of Optical Engineering (CRC Press, 2003), Vol. 2.

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Figures (4)

Fig. 1
Fig. 1

Investigated problem and the ODT setup.

Fig. 2
Fig. 2

Object function profile for the lossless, dispersionless dielectric phantom.

Fig. 3
Fig. 3

Multifrequency reconstruction at λ = 1.5 , 1.25, and 1 μ m ( I = 8 , T = 3 ).

Fig. 4
Fig. 4

Optimum single-frequency reconstruction at λ = 1.25 μ m ( I = 8 , T = 1 ).

Equations (10)

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O ( ρ , φ ) ε r ( ρ , φ ) 1 = m = 1 M n = N N c m n J 0 ( χ m a ρ ) exp ( j n φ ) .
m = 1 M n = N N c m n { 2 π k t η j u + 1 0 a F u n i , t ( ρ ) J 0 ( χ m a ρ ) J u ( k t ρ ) ρ d ρ } = α u i , t ; u [ k t a ] , 1 i I , 1 t T ,
α u i , t = 1 2 π A t 0 2 π f i , t ( φ ) exp ( j u φ ) d φ ,
f i , t ( φ ) = lim ρ { exp ( j k t ρ ) ρ E s i , t ( ρ , φ ) } ,
A t = η j k t 8 π .
F ν i , t ( ρ ) = j ν d ν i , t J ν ( n ν i , t k t ρ ) , ν [ k t a ] .
n ν i , t J ν 1 ( n ν i , t k t a ) J ν ( n ν i , t k t a ) = β ν i , t H ν 1 ( 2 ) ( k t a ) + J ν 1 ( k t a ) β ν i , t H ν ( 2 ) ( k t a ) + J ν ( k t a )
β ν i , t = 1 4 k t η α ν i , t exp ( j ν φ i ) .
d ν i , t = J ν ( k t a ) + β ν i , t H ν ( 2 ) ( k t a ) J ν ( n ν i , t k t a ) exp ( j ν φ i ) .
RMSE = object O r O a 2 d s object O a 2 d s .

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