Multiply subtractive kramers-kronig analysis of optical data.
Abstract
We describe a new, multiply subtractive Kramers-Kronig (MSKK)method to find the optical constants of a material from a singletransmittance or reflectance spectrum covering a small frequencydomain. The MSKK method incorporates independent measurements ofn and k at one or more reference wave-numbervalues to minimize errors due to extrapolations of the data. Anunexpected connection between the MSKK equations and the interpolationtheory allows us to derive the equations from an interpolationtheorem. We found that the locations of the reference points affectthe accuracy of the values determined for the optical constants andthat the optimal spacing of N reference data points isrelated to the zeros of a suitably transformed Chebychev polynomial oforder N. We discuss our efforts to optimize both the numberand the spacing of these reference points and apply our method to sometest spectra.
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Existing computational techniques such as MEM, SSKK, MSKK, and DMSKK require heavy iterations or knowledge of anchor points to converge to accurate values.
“These techniques require heavy iterations or the knowledge of socalled 'anchor points' (i.e., points where the properties of the samples are known) to converge to accurate values.”
From Robust phase correction techniques for terahertz time-domain reflection spectroscopy (2024) · cites this paper as [23]
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“To this end, several computational techniques have been developed, such as the maximum entropy method (MEM) [20, 21], singly sub-tractive Kramers-Kronig (SSKK) [22], multiply subtractive Kramers-Kronig (MSKK) [23], differential multiply subtractive Kramers-Kronig (DMSKK) [24].”
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X-Ray Microscope Instrumentation
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Appendix A X-Ray Data Tabulations
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Inverse engineering of optical constants in photochromic micron-scale hybrid films
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- Authors
- Palmer, K. F., Williams, M. Z., & Budde, B. A.
- Affiliations
- Westminster College - Missouri (US)
- Venue
- Applied Optics
- Publisher
- Optica Publishing Group
- Published
- 1998-05-01
- Volume
- 37
- Issue
- 13
- Pages
- 2660
- ISSN
- 0003-6935 (ISSN-L)
- 1539-4522
- OpenAlex
- W2028432570
- Cited by
- 90
- References
- 15
- Citations by year
- 2026: 1 · 2025: 1 · 2022: 4 · 2021: 5 · 2020: 1 · 2019: 18 · 2018: 3 · 2017: 2 · 2016: 2 · 2015: 2 · 2014: 1 · 2013: 5 · 2012: 2
- FWCI
- 0.98
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Applied Optics (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Optical and Acousto-Optic Technologies
- Physical Sciences › Chemistry › Analytical Chemistry › Spectroscopy and Chemometric Analyses
- Physical Sciences › Engineering › Biomedical Engineering › Optical Polarization and Ellipsometry
- Keywords
- Kramers-Kronig relations, optical constants, refractive index, extinction coefficient, transmission spectra, spectral reflectance, reference points, interpolation theorem
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