Causality calculations in the time domain: An efficient alternative to the Kramers–Kronig method*

Peterson, C. W.; Knight, Bruce W.

doi:10.1364/josa.63.001238

Cited by 80 publications

(27 citation statements)

References 4 publications

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“…[nðñ nÞ: refractive index, imaginary part; K ðñ nÞ: absorption index] for the bulk n n bulk ðñ nÞ and the thin layern n layer ðñ nÞ, respectively, have to be derived from the corresponding ERA and ATR spectra via the Kramers-Kronig transformation [38], integrated in the FSOS software package [39]. This procedure, called ''backward spectra calculation'', is well-proven and was successfully employed in the case of thin epoxy films [40].…”

Section: Comparison Between the Bulk And The Adsorption Statementioning

confidence: 99%

Adhesive Interactions of Polyurethane Monomers with Native Metal Surfaces

Nies

Wehlack

Ehbing

et al. 2012

The Journal of Adhesion

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Understanding of fundamental adhesion is a key issue for bonding, polymer composites, and coatings. In this study, diluted solutions of polyurethane monomers (methylene diphenyl diisocyanate isomer mixture-MDI, polypropylene ether triol-PPET) are exposed to the native surfaces of Au, Al, and Cu. The adsorption state of the molecules (from multi-to sub-monolayers) is investigated in situ by infrared external reflection absorption spectroscopy (IR-ERAS). A sequence of solvent rinsing steps helps to distinguish physisorbed from chemisorbed molecules. PPET sticks very weakly to the metals. The spectra reveal a bulk-like state. MDI adsorbs weakly on Au but the spectra differ significantly from the bulk state. On Al and Cu, MDI establishes strong adhesion. Rich new spectral features indicate a probably chemical nature of adhesion, and a specific structure in the neighboring adsorbate layer. However, detailed final conclusions on the adhesion mechanisms must not be derived without appropriate quantum mechanical modeling.

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Section: Comparison Between the Bulk And The Adsorption Statementioning

confidence: 99%

Adhesive Interactions of Polyurethane Monomers with Native Metal Surfaces

Nies

Wehlack

Ehbing

et al. 2012

The Journal of Adhesion

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“…Stated more fully, the Kramers-Kronig transform is equivalent to the infinite Hilbert transform, provided that the real variable is an even function of wavenumber and the imaginary variable is an odd function of wavenumber, i.e., n(5) = +IT(-5) and k(5) = -k(-5). Further, the Hilbert transform is equivalent to the allied Fourier integrals (6,(14)(15)(16)(17)(18) I-.…”

Section: Introductionmentioning

confidence: 99%

Infrared intensities of liquids. IX. The Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms

Bertie¹,

Zhang²

1992

Can. J. Chem.

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. Can. J . Chem. 70, 520 (1992). It is well known that the infinite Kramers-Kronig transform is equivalent to the infinite Hilbert transform, which is equivalent to the allied Fourier integrals. The Hilbert transform can thus be implemented using fast Fourier transform routines. Such implemcntation is usually some 60 times faster than the Kramers-Kronig transform for a data file containing about 7 points. This paper reports that, for transformations between the real and imaginary refractive indices, n(C) and k(C) in A = n(S) + ik(5), the FFT-based Hilbert transform can be much less accurate than, or as accurate as, the Kramers-Kronig transform, depending on the algorithm used. The Kramers-Kronig transform, incorporating Mclaurin's formula for finding the principal value of the integral, transforms k(G) spectra into n ( 5 ) spectra that are accurate to about 0.05%. Some Hilbert transform algorithms in the literature yield only about 470 accuracy. The BZ algorithm for the Hilbert transform is presented, for use on a laboratory computer running under DOS, that yields n(C) spectra accurate to 0.05%. For the transform from n(C) to k ( + ) , the BZ algorithm gives k ( 5 ) accurate to about -0.2% of the largest k value in the spectrum. This compares with an accuracy of 0.5% for the Kramers-Kronig transform. In cases where the k(D) spectrum is truncated at low wavenumbers, a simple method is presented that improves by a factor of -10 the accuracy at low wavenumber of the n(G) spectrum obtained by Hilbert or Kramers-Kronig transforms of the k(G) spectrum. Il est bien connu que la transformation infinie de Kramers-Kronig est 1'Cquivalent d'une transformation infinie de Hilbert qui est elle-m&me 1'Cquivalent des intCgrales allied Fourier. On peut donc rkaliser une transformation de Hilbert en utilisant des routines rapides de transformation de Fourier. Pour une base de donnees contenant 7000 points, une telle realisation est generalement 60 fois plus rapide qu'une transformation de Kramers-Kronig. Dans ce travail, on montre que, pour des transformations entre des indices de rkfraction reels et imaginaires, IT(:) , la transformation de Hilbert basCe sur FFT est beaucoup moins ou aussi prCcise que la transformation de Kramers-Kronig suivant I'algorithme utilise. La transformation de Kramers-Kronig, incorporant les formules de McLaurin pour trouver la valeur principale de I'integrale, transforme des spectres k ( 5 ) en spectres n(:) qui sont prCcis environ 0,05%. Quelques algorithmes rapportts dans la litterature pour la transformation de Hilbert ne conduisent qu'i une precision de 4%. On prCsente I'algorithme BZ qui peut &tre utilise sur un ordinateur de laboratoire, operant sous DOS, qui permet d'effectuer la transformation de Hilbert et qui donne des spectres n(:) precis h 0,05%. Pour la transformation n(C) en k(ij), I'algorithme BZ conduit i une precision d'environ -0,2% pour la valeur la plus importante du spectre. Cette valeur se compare h une prkcision de 0,5% pour la transformation de Kramers-Kronig. Pour les cas ou ...

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“…Moreover, in the case that ω goes to infinity and χ ( ω ) approaches zero, ln | χ ( ω )| goes to negative infinity. To resolve these problems, an alternative form of TDKK using the Fourier series approach was reported (69). The spectral phase as a function of the signal modulus is represented in the time domain as

φ (ω) = \frac{- 1}{π} P true \int_{- \infty}^{+ \infty} \frac{l n | χ (ω^{'}) |}{ω^{'} - ω} d ω^{'} = 2 I m [ψ (l n | χ (ω) |) - \frac{l n | χ (ω) |}{2}],

where the operator ψ ( f ( ω )) is defined as

ψ (f (ω)) = \frac{1}{\sqrt{2 π}} F [u (t)] * F [F^{- 1} [f (ω)]] = \frac{1}{\sqrt{2 π}} F [u (t)] * f (ω),

and u ( t ) is the Heaviside step function (41).…”

Section: Hyperspectral Coherent Raman Scattering Image Analysismentioning

confidence: 99%

In Situ and In Vivo Molecular Analysis by Coherent Raman Scattering Microscopy

Liao

Cheng

2016

Annual Rev. Anal. Chem.

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Coherent Raman scattering (CRS) microscopy is a high-speed vibrational imaging platform with the ability to visualize the chemical content of a living specimen by using molecular vibrational fingerprints. We review technical advances and biological applications of CRS microscopy. The basic theory of CRS and the state-of-the-art instrumentation of a CRS microscope are presented. We further summarize and compare the algorithms that are used to separate the Raman signal from the nonresonant background, to denoise a CRS image, and to decompose a hyperspectral CRS image into concentration maps of principal components. Important applications of single-frequency and hyperspectral CRS microscopy are highlighted. Potential directions of CRS microscopy are discussed.

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Causality calculations in the time domain: An efficient alternative to the Kramers–Kronig method*

Cited by 80 publications

References 4 publications

Adhesive Interactions of Polyurethane Monomers with Native Metal Surfaces

Adhesive Interactions of Polyurethane Monomers with Native Metal Surfaces

Infrared intensities of liquids. IX. The Kramers–Kronig transform, and its approximation by the finite Hilbert transform via fast Fourier transforms

In Situ and In Vivo Molecular Analysis by Coherent Raman Scattering Microscopy

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