Abstract

The differential multiply subtractive Kramers–Kronig (DMSKK) method is utilized for deriving the optical spectral response of a 1D scattering medium. The technique is based on the multiply subtractive Kramers–Kronig technique, where the phase spectrum is reconstructed from the amplitude spectrum in a finite spectral range with the aid of one or more phase-anchoring values. We employ a new phase-anchoring technique in the DMSKK method to partially mitigate the finite-range effects. This method incorporates spectral ballistic imaging to anchor the phase difference (instead of the phase directly) at one or more reference wavelengths. The simplicity of phase derivative measurements and its utilization in the DMSKK method are emphasized by a simple experiment.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. E. Granot, S. Sternklar, Y. Ben-Aderet, and D. Schermann, “Quasi-ballistic imaging through a dynamic scattering medium with optical-field averaging using spectral-ballistic-imaging,” Opt. Express 14, 8598-8603 (2006).
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2008 (1)

2007 (1)

2006 (2)

E. Granot, S. Sternklar, D. Schermann, Y. Ben-Aderet, and M. H. Itzhaq, “200 femtosecond impulse response of a Fabry-Perot etalon with the spectral ballistic imaging technique,” Appl. Phys. B 82, 359-362 (2006).
[CrossRef]

E. Granot, S. Sternklar, Y. Ben-Aderet, and D. Schermann, “Quasi-ballistic imaging through a dynamic scattering medium with optical-field averaging using spectral-ballistic-imaging,” Opt. Express 14, 8598-8603 (2006).
[CrossRef] [PubMed]

2003 (3)

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive Kramers-Kronig relations for arbitrary order harmonic generation susceptibilities,” Opt. Commun. 218, 409-414 (2003).
[CrossRef]

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane,” J. Chem. Phys. 119, 11095-11098 (2003).
[CrossRef]

E. Granot and S. Sternklar, “Spectral ballistic imaging: a novel technique for viewing through turbid or obstructing media,” J. Opt. Soc. Am. A 20, 1595-1599 (2003).
[CrossRef]

2001 (1)

1998 (1)

1996 (1)

1995 (1)

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34-40 (1995).
[CrossRef]

1971 (1)

1970 (1)

R. Z. Bachrach and F. C. Brown, “Exciton-optical properties of TlBr and TlCl,” Phys. Rev. B 1, 818-831 (1970).
[CrossRef]

1965 (1)

1926 (1)

Ahrenkiel, R. K.

Andermann, G.

Bachrach, R. Z.

R. Z. Bachrach and F. C. Brown, “Exciton-optical properties of TlBr and TlCl,” Phys. Rev. B 1, 818-831 (1970).
[CrossRef]

Ben-Aderet, Y.

Brown, F. C.

R. Z. Bachrach and F. C. Brown, “Exciton-optical properties of TlBr and TlCl,” Phys. Rev. B 1, 818-831 (1970).
[CrossRef]

Budde, B. A.

Caron, A.

Chance, B.

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34-40 (1995).
[CrossRef]

Dows, D. A.

Granot, E.

Itzhaq, M. H.

E. Granot, S. Sternklar, D. Schermann, Y. Ben-Aderet, and M. H. Itzhaq, “200 femtosecond impulse response of a Fabry-Perot etalon with the spectral ballistic imaging technique,” Appl. Phys. B 82, 359-362 (2006).
[CrossRef]

Jiang, H.

Jiang, S.

Kronig, R.

Lucarini, V.

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive Kramers-Kronig relations for arbitrary order harmonic generation susceptibilities,” Opt. Commun. 218, 409-414 (2003).
[CrossRef]

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane,” J. Chem. Phys. 119, 11095-11098 (2003).
[CrossRef]

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).

McBride, T. O.

Osterberg, U. L.

Palmer, K. F.

Patterson, M. S.

Paulsen, K. D.

Peiponen, K. E.

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive Kramers-Kronig relations for arbitrary order harmonic generation susceptibilities,” Opt. Commun. 218, 409-414 (2003).
[CrossRef]

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane,” J. Chem. Phys. 119, 11095-11098 (2003).
[CrossRef]

Peiponen, K.-E.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).

Pogue, B. W.

Poplack, S. P.

Saarinen, J. J.

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane,” J. Chem. Phys. 119, 11095-11098 (2003).
[CrossRef]

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive Kramers-Kronig relations for arbitrary order harmonic generation susceptibilities,” Opt. Commun. 218, 409-414 (2003).
[CrossRef]

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).

Schermann, D.

E. Granot, S. Sternklar, Y. Ben-Aderet, and D. Schermann, “Quasi-ballistic imaging through a dynamic scattering medium with optical-field averaging using spectral-ballistic-imaging,” Opt. Express 14, 8598-8603 (2006).
[CrossRef] [PubMed]

E. Granot, S. Sternklar, D. Schermann, Y. Ben-Aderet, and M. H. Itzhaq, “200 femtosecond impulse response of a Fabry-Perot etalon with the spectral ballistic imaging technique,” Appl. Phys. B 82, 359-362 (2006).
[CrossRef]

Sternklar, S.

Vartiainen, E. M.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).

Williams, M. Z.

Yodh, A.

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34-40 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

E. Granot, S. Sternklar, D. Schermann, Y. Ben-Aderet, and M. H. Itzhaq, “200 femtosecond impulse response of a Fabry-Perot etalon with the spectral ballistic imaging technique,” Appl. Phys. B 82, 359-362 (2006).
[CrossRef]

J. Chem. Phys. (1)

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive generalized Kramers-Kronig relations: application on third-harmonic generation susceptibility on polysilane,” J. Chem. Phys. 119, 11095-11098 (2003).
[CrossRef]

J. Opt. Soc. Am. (3)

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

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

Opt. Commun. (1)

V. Lucarini, J. J. Saarinen, and K. E. Peiponen, “Multiply subtractive Kramers-Kronig relations for arbitrary order harmonic generation susceptibilities,” Opt. Commun. 218, 409-414 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

R. Z. Bachrach and F. C. Brown, “Exciton-optical properties of TlBr and TlCl,” Phys. Rev. B 1, 818-831 (1970).
[CrossRef]

Phys. Today (1)

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34-40 (1995).
[CrossRef]

Other (1)

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).

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Figures (5)

Fig. 1
Fig. 1

Block diagram of the SPEBI system.

Fig. 2
Fig. 2

Comparison between the SPEBI phase-difference spectrum measurements (top graph) and the reconstruction of the phase difference by the conventional KK method (second graph), the DSSKK method (third graph), and DMSKK method (fourth graph).

Fig. 3
Fig. 3

Comparison of the spectra at the boundaries: SPEBI phase-difference spectral measurements (solid curve) and the reconstruction of the phase difference by the conventional KK method (dashed-dotted curve), the DSSKK method (dotted curve), and DMSKK method (dashed curve).

Fig. 4
Fig. 4

Reconstruction of the phase difference by the DMSKK method (dashed curve), the DSSKK (dotted curve), and its comparison to the SPEBI measurements (solid curve), in the region of the second anchoring point.

Fig. 5
Fig. 5

Difference spectrum Δ ( ω ) for the KK-derived techniques.

Equations (8)

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θ ( ω ) = 2 ω π P 0 ln H ( ω ) ω 2 ω 2 d ω ,
θ ( ω ) ω = θ ( ω 1 ) ω 1 2 π ( ω 2 ω 1 2 ) P 0 ln H ( ω ) ( ω 2 ω 2 ) ( ω 2 ω 1 2 ) d ω ,
θ ( ω ) ω = θ ( ω 1 ) ω 1 ( ω 2 ω 2 2 ) ( ω 2 ω 3 2 ) ( ω 2 ω Q 2 ) ( ω 1 2 ω 2 2 ) ( ω 1 2 ω 3 2 ) ( ω 1 2 ω Q 2 ) + θ ( ω j ) ω j ( ω 2 ω 1 2 ) ( ω 2 ω j 1 2 ) ( ω 2 ω j + 1 2 ) ( ω 2 ω Q 2 ) ( ω j 2 ω 1 2 ) ( ω j 2 ω j 1 2 ) ( ω j 2 ω j + 1 2 ) ( ω j 2 ω Q 2 ) + θ ( ω Q ) ω Q ( ω 2 ω 1 2 ) ( ω 2 ω 2 2 ) ( ω 2 ω Q 1 2 ) ( ω 1 2 ω 1 2 ) ( ω 1 2 ω 2 2 ) ( ω Q 2 ω Q 1 2 ) 2 π ( ω 2 ω 1 2 ) ( ω 2 ω 2 2 ) ( ω 2 ω Q 2 ) P 0 ln H ( ω ) ( ω 2 ω 2 ) ( ω 2 ω 1 2 ) ( ω 2 ω Q 2 ) d ω ,
θ ( ω ) ω = j = 1 Q θ ( ω j ) ω j n = 1 j Q ( ω 2 ω n 2 ) ( ω j 2 ω n 2 ) 2 π n = 1 Q ( ω 2 ω n 2 ) P 0 d ln H ( ϖ ) d ϖ ϖ = ω ( ω 2 ω 2 ) n = 1 Q ( ω 2 ω n 2 ) d ω ,
θ ( ω ) ω = θ ( ω 1 ) ω 1 2 π ( ω 2 ω 1 2 ) P 0 d ln H ( ϖ ) d ϖ ϖ = ω ( ω 2 ω 2 ) ( ω 2 ω 1 2 ) d ω ,
θ ( ω M ) = j = 1 M Δ θ ( ω j ) ,
Δ ( ω ) θ SPEBI ( ω ) θ KK ( ω ) .
PEM ( ω ) m ( Δ θ SPEBI ( ω ) Δ θ KK ( ω ) ) 2 ,

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