OSA's Digital Library

Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry M. Van Driel
  • Vol. 25, Iss. 4 — Apr. 1, 2008
  • pp: 609–613

Differential multiply subtractive Kramers–Kronig relations

Er’el Granot, Yossi Ben-Aderet, and Shmuel Sternklar  »View Author Affiliations

JOSA B, Vol. 25, Issue 4, pp. 609-613 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (186 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We apply the multiply subtractive Kramers–Kronig (MSKK) method to the derivative of a medium’s optical transfer function. That is, the phase “difference” or derivative Δ θ (instead of the phase) can be evaluated from the measurements of the relative derivative of the intensity Δ ln [ I ( ω ) ] = Δ I ( ω ) I ( ω ) with the aid of a few Δ θ measurements. As a result, we obtain a method that integrates two different techniques, MSKK and spectral ballistic imaging. We show that the transfer function can be evaluated with great accuracy without the need to measure the phases at all but rather its derivative, which is a much simpler process.

© 2008 Optical Society of America

OCIS Codes
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(100.5070) Image processing : Phase retrieval
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

ToC Category:
Imaging Systems

Original Manuscript: December 6, 2007
Manuscript Accepted: January 6, 2008
Published: March 27, 2008

Er'el Granot, Yossi Ben-Aderet, and Shmuel Sternklar, "Differential multiply subtractive Kramers-Kronig relations," J. Opt. Soc. Am. B 25, 609-613 (2008)

Sort:  Year  |  Journal  |  Reset  


  1. R. Kronig, “On the theory of dispersion of X-rays,” J. Opt. Soc. Am. 12, 547-557 (1926). [CrossRef]
  2. H. A. Kramers, Estratto dagli Atti del Congresso Internazionale di Fisici Como (Nicolo Zonichello, 1927).
  3. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer-Verlag, 2005).
  4. E. Granot and S. Sternklar, “Reconstructing the impulse response of a diffusive medium with the Kramers-Kronig relations,” J. Opt. Soc. Am. B (to be published).
  5. L. Wang, P. P. Ho, F. Liu, G. Zhang, and R. R. Alfano, “Ballistic 2-D imaging through scattering walls using an ultrafast optical Kerr gate,” Science 253, 769-771 (1991). [CrossRef] [PubMed]
  6. J. C. Hebden and D. T. Delpy, “Enhanced time-resolved imaging with a diffusion model of photon transport,” Opt. Lett. 19, 311-313 (1994). [CrossRef] [PubMed]
  7. G. M. Turner, G. Zacharakis, A. Soubret, J. Ripoll, and V. Ntziachristos, “Complete-angle projection diffuse optical tomography by use of early photons,” Opt. Lett. 30, 409-411 (2005). [CrossRef] [PubMed]
  8. A. Ya. Polishchuk, J. Dolne, F. Liu, and R. R. Alfano, “Average and most-probable photon paths in random media,” Opt. Lett. 22, 430-432 (1997). [CrossRef] [PubMed]
  9. L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano, “True scattering coefficients of turbid matter measured by early-time gating,” Opt. Lett. 20, 913-915 (1995). [CrossRef] [PubMed]
  10. 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]
  11. R. Z. Bachrach and F. C. Brown, “Exciton-optical properties of TlBr and TlCl,” Phys. Rev. B 1, 818-831 (1970). [CrossRef]
  12. R. K. Ahrenkiel, “Modified Kramers-Kronig analysis of optical spectra,” J. Opt. Soc. Am. 61, 1651-1655 (1971). [CrossRef]
  13. K. F. Palmer, M. Z. Williams, and B. A. Budde, “Multiply subtractive Kramers-Kronig analysis of optical data,” Appl. Opt. 37, 2660-2673 (1998). [CrossRef]
  14. 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]
  15. 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]
  16. 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited