Abstract

We reply to a comment by Wang et al. [J. Opt. Soc. Am. A 28, 662 (2011)] on the paper of Trattner et al. [J. Opt. Soc. Am. A 26, 1147 (2009)]. Although we agree with some of the points raised, we show that there is imprecision in the comment. We emphasize again the use of the necessary condition for the use of the Born approximation and refer the reader to an error analysis that supported our criterion.

© 2011 Optical Society of America

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  1. X. Wang, J. Li., T. Wang, and S. Xiao, “Validity criterion for the Born approximation convergence in microscopy imaging: comment,” J. Opt. Soc. Am. A 28, 662–664 (2011).
    [CrossRef]
  2. S. Trattner, M. Feigin, M. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in DIC microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156 (2009).
    [CrossRef]
  3. S. Trattner, M. Feigin, M. Greenspan, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of the 3rd Workshop on Microsopic Image Analysis with Applications in Biology (in conjunction with MICCAI’08 NY) (2008), pp. 103–110.

2011

2009

Feigin, M.

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

S. Trattner, M. Feigin, M. Greenspan, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of the 3rd Workshop on Microsopic Image Analysis with Applications in Biology (in conjunction with MICCAI’08 NY) (2008), pp. 103–110.

Greenspan, M.

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

S. Trattner, M. Feigin, M. Greenspan, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of the 3rd Workshop on Microsopic Image Analysis with Applications in Biology (in conjunction with MICCAI’08 NY) (2008), pp. 103–110.

Li., J.

Sochen, N.

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

S. Trattner, M. Feigin, M. Greenspan, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of the 3rd Workshop on Microsopic Image Analysis with Applications in Biology (in conjunction with MICCAI’08 NY) (2008), pp. 103–110.

Trattner, S.

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

S. Trattner, M. Feigin, M. Greenspan, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of the 3rd Workshop on Microsopic Image Analysis with Applications in Biology (in conjunction with MICCAI’08 NY) (2008), pp. 103–110.

Wang, T.

Wang, X.

Xiao, S.

J. Opt. Soc. Am. A

Other

S. Trattner, M. Feigin, M. Greenspan, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of the 3rd Workshop on Microsopic Image Analysis with Applications in Biology (in conjunction with MICCAI’08 NY) (2008), pp. 103–110.

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Equations (11)

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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 r .
H f ( r , ω ) = V F ( r , ω ) G ( r r , ω ) f ( r , ω ) d r ,
U ( s ) ( r , ω ) = H U ( i ) ( r , ω ) + H U ( s ) ( r , ω ) .
| U ( s ) ( r , ω ) | | U ( i ) ( r , ω ) | , r V ,
| H ( U ( s ) ) ( r , ω ) | | H ( U ( i ) ) ( r , ω ) | .
| U ( s ) ( r , ω ) | | U ( i ) ( r , ω ) | , r V ,
| H ( U ( s ) ) ( r , ω ) | | H ( U ( i ) ) ( r , ω ) | .
| H ( U ( s ) ) ( r , ω ) | | H ( U ( i ) ) ( r , ω ) |
| U ( s ) ( r , ω ) | | U ( i ) ( r , ω ) | , r V ,
f ( s ) ( r ) = 1 ( 2 π σ 2 ) 3 / 2 e x 2 + y 2 + z 2 2 σ 2
| m = 2 ( U m ( s ) ) ( r , ω ) | | U 1 ( s ) ) ( r , ω ) | .

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