Abstract

A recent paper [J. Opt. Soc. Am. A 26, 1147 (2009)] proposed a new criterion to identify the validity of the Born approximation. In this paper, we present our doubts on the mathematical basis and the applicability of this criterion.

© 2011 Optical Society of America

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References

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  1. S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156(2009).
    [CrossRef]
  2. B. Chen and J. J. Stamnes, “Validity of diffraction tomography based on the first Born and the first Rytov approximations,” Appl. Opt. 37, 2996–3006 (1998).
    [CrossRef]
  3. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  4. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
  5. W. C. Chew, Waves and Fields in Inhomogeneous Media(Van Nostrand Reinhold, 1990).
  6. S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Proceedings of the IEEE 11th International Conference on Computer Vision (IEEE, 2007), Vol.  14, pp. 1–8.
    [CrossRef]
  7. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
  8. L. Zapalowski, M. A. Fiddy, and S. Leeman, “On the Born Rytov controversy,” in Proceedings of the Ultrasonics Symposium (IEEE, 1983), pp. 928–930.
  9. E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, 1978).
  10. J. Li, X. Wang, and T. Wang, “On the validity of Born approximation,” PIER 107, 219–237 (2010).
    [CrossRef]

2010 (1)

J. Li, X. Wang, and T. Wang, “On the validity of Born approximation,” PIER 107, 219–237 (2010).
[CrossRef]

2009 (1)

1998 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

Chen, B.

Chew, W. C.

W. C. Chew, Waves and Fields in Inhomogeneous Media(Van Nostrand Reinhold, 1990).

Feigin, M.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156(2009).
[CrossRef]

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Proceedings of the IEEE 11th International Conference on Computer Vision (IEEE, 2007), Vol.  14, pp. 1–8.
[CrossRef]

Fiddy, M. A.

L. Zapalowski, M. A. Fiddy, and S. Leeman, “On the Born Rytov controversy,” in Proceedings of the Ultrasonics Symposium (IEEE, 1983), pp. 928–930.

Greenspan, H.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156(2009).
[CrossRef]

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Proceedings of the IEEE 11th International Conference on Computer Vision (IEEE, 2007), Vol.  14, pp. 1–8.
[CrossRef]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Kreyszig, E.

E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, 1978).

Leeman, S.

L. Zapalowski, M. A. Fiddy, and S. Leeman, “On the Born Rytov controversy,” in Proceedings of the Ultrasonics Symposium (IEEE, 1983), pp. 928–930.

Li, J.

J. Li, X. Wang, and T. Wang, “On the validity of Born approximation,” PIER 107, 219–237 (2010).
[CrossRef]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Sochen, N.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156(2009).
[CrossRef]

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Proceedings of the IEEE 11th International Conference on Computer Vision (IEEE, 2007), Vol.  14, pp. 1–8.
[CrossRef]

Stamnes, J. J.

Trattner, S.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156(2009).
[CrossRef]

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Proceedings of the IEEE 11th International Conference on Computer Vision (IEEE, 2007), Vol.  14, pp. 1–8.
[CrossRef]

Wang, T.

J. Li, X. Wang, and T. Wang, “On the validity of Born approximation,” PIER 107, 219–237 (2010).
[CrossRef]

Wang, X.

J. Li, X. Wang, and T. Wang, “On the validity of Born approximation,” PIER 107, 219–237 (2010).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

Zapalowski, L.

L. Zapalowski, M. A. Fiddy, and S. Leeman, “On the Born Rytov controversy,” in Proceedings of the Ultrasonics Symposium (IEEE, 1983), pp. 928–930.

Appl. Opt. (1)

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

PIER (1)

J. Li, X. Wang, and T. Wang, “On the validity of Born approximation,” PIER 107, 219–237 (2010).
[CrossRef]

Other (7)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

W. C. Chew, Waves and Fields in Inhomogeneous Media(Van Nostrand Reinhold, 1990).

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Proceedings of the IEEE 11th International Conference on Computer Vision (IEEE, 2007), Vol.  14, pp. 1–8.
[CrossRef]

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).

L. Zapalowski, M. A. Fiddy, and S. Leeman, “On the Born Rytov controversy,” in Proceedings of the Ultrasonics Symposium (IEEE, 1983), pp. 928–930.

E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, 1978).

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Equations (15)

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U ( s ) ( r , ω ) = V F ( r , ω ) G ( r , r , ω ) [ U ( i ) ( r , ω ) + U ( s ) ( r , ω ) ] d 3 r ,
( H U ) ( r , ω ) = V F ( r , ω ) G ( r , r , ω ) U ( r , ω ) d 3 r ,
U ( s ) = H U ( i ) + H U ( s ) .
U ( s ) = ( I H ) 1 H U i = H U ( i ) + H 2 U ( i ) + + H n U ( i ) + m = 1 U m ( s ) ,
U ( s ) ( r , ω ) U 1 ( s ) ( r , ω ) = H U ( i ) ( r , ω ) = V F ( r , ω ) G ( r , r , ω ) U ( i ) ( r , ω ) d 3 r .
| m = 2 U m ( s ) ( r , ω ) | | U 1 ( s ) ( r , ω ) | , r     at the reciever .
| U ( s ) ( r , ω ) | | U ( i ) ( r , ω ) | , r V .
U 1 ( s ) ( r , ω ) = ( H U ( i ) ) ( r , ω ) = V F ( r , ω ) G ( r , r , ω ) U ( i ) ( r , ω ) d 3 r ,
m = 2 U m ( s ) ( r , ω ) = ( H U ( s ) ) ( r , ω ) = V F ( r , ω ) G ( r , r , ω ) U ( s ) ( r , ω ) d 3 r .
| U 1 ( s ) ( r , ω ) | | U ( i ) ( r , ω ) | , r V .
| k 2 4 π r Δ n 2 V | 1 .
r | k 2 4 π Δ n 2 V | .
| U ( s ) ( r ) | | U ( i ) ( r ) | , r V ,
| ( H U ( s ) ) ( r , ω ) | | ( H U ( i ) ) ( r , ω ) | .
| m = 2 U m ( s ) ( r , ω ) | | U 1 ( s ) ( r , ω ) | .

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