Home

Optical Impulse Response Reconstruction of a Scattering Medium with the Differential Multiply Subtractive Kramers-Kronig Method


  Yossi Ben-Aderet [1,2]  ,  Er'el Granot [1]  ,  Shmuel Sternklar [1]  ,  Tzachi Tal [1]  
 [1] Ariel University Center of Samaria, Dept. of Electrical and Electronic Engineering
[2] Department of Electrooptical Engineering, Ben Gurion University of the Negev, Beer-Sheva, Israel.

 

            Spectral analysis of scattering media is not a trivial task. Further complications arise if it is desired to acquire the phase spectrum in addition to the amplitude spectrum, since direct measurements of phase, especially on scattering media, can be quite cumbersome. This is unfortunate, since the phase spectrum holds significant information on the medium which should not be neglected. For example, an inverse-Fourier-transform of the complex spectral response gives the impulse response, which can be used to image into the medium. In principle, it is possible to directly measure the optical impulse response, however it requires fast (sub-ps) sources and detectors. In this work, we introduce new frequency-domain techniques for reconstructing the phase spectrum and impulse response of a scattering medium with high temporal resolution.

In the current study, we introduce the Differential Multiply Subtractive Kamers-Kronig (DMSKK) method. The technique is based on the Multiply Subtractive Kramers-Kronig (MSKK) technique [1-2], 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.

The simplicity of phase-derivative measurements and its utilization in the DMSKK method are emphasized by a simple experiment which employs the Spectral Ballistic Imaging (SPEBI) method [4] to measure the phase-difference spectrum. We then apply the DMSKK method to derive the phase spectrum and impulse response of a 1D scattering medium.

References

[1] K.F. Palmer, M. Z. Williams, and B.A. Budde, "Multiply subtractive Kramers-Kronig analysis

     of optical data," Appl. Opt. 37, 2660-2673 (1998)

[2] V. Lucarini, J. J. Saarinen, and K-E. Peiponen, "Multiply_subtractive generalized Kramers-

    Kronig relations: application on third harmonic_generation susceptibility on polysilane"

[3] E. Granot, Y. Ben-Aderet, and S. Sternklar, "Differential multiply subtractive Kramers-

      Kronig relations," J. Opt. Soc. Am. B 25, 609-613 (2008)

[4 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 (2003)