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Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 25 — Sep. 1, 2006
  • pp: 6519–6524

Comparison of subtractive Kramers–Kronig analysis and maximum entropy model in resolving phase from finite spectral range reflectance data

Evgeny Gornov, Erik M. Vartiainen, and Kai-Erik Peiponen  »View Author Affiliations

Applied Optics, Vol. 45, Issue 25, pp. 6519-6524 (2006)

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The maximum entropy model (MEM) and Kramers–Kronig (K-K) analysis were compared with the aim of phase retrieval from reflectance. The object was to test two different phase-retrieval methods when reflectance is known at a finite frequency range and data fitting is not performed beyond the finite frequency band. In addition, it was assumed that the phase is known only at one or two anchor points. As an example, we study the terahertz reflection spectrum related to a semiconductor and an optical spectrum of potassium chloride. It is shown that the MEM resolves the complex refractive index of a medium, in the vicinity of initial and final points of the spectra, better than singly and doubly subtractive K-K relations. Both methods give only satisfactory results in the event of one anchor point, but in the case of two anchor points, the MEM is better than doubly subtractive K-K. It is proposed that the MEM should be used instead of K-K analysis, for a priori information of phase at two anchor points, for the purpose of resolving the complex refractive index of a medium from reflectance with high accuracy.

© 2006 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(000.4430) General : Numerical approximation and analysis
(300.0300) Spectroscopy : Spectroscopy

Original Manuscript: March 3, 2006
Manuscript Accepted: May 14, 2006

Evgeny Gornov, Erik M. Vartiainen, and Kai-Erik Peiponen, "Comparison of subtractive Kramers-Kronig analysis and maximum entropy model in resolving phase from finite spectral range reflectance data," Appl. Opt. 45, 6519-6524 (2006)

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