Kramers-Kronig relation


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Kramers-Kronig relation

[′krā·mərz ′krō·nig ri‚lā·shən]
(optics)
A relation between the real and imaginary parts of the index of refraction of a substance, based on the causality principle and Cauchy's theorem.
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The quality of measurement data can be investigated by means of the Kramers-Kronig relation [4].
For example, the results of the Kramers-Kronig relation, applied on the measured impedance spectrum of wet crude sand, show data consistency only in the frequency range under 10 MHz (Fig.
Evaluation of consistency with the Kramers-Kronig Relations.
Cauchy's theorem may then be used to derive the relationship between the real and imaginary parts of such a function, known in physics as the Kramers-Kronig relation.
The f-sum rule may also be regarded as a high-frequency limit of the Kramers-Kronig relations (5); in this case, the multiplication by [omega] before Eq.
The aim of this work is to produce silicon thin layers of different thicknesses and other same deposition conditions (such as: deposition angle, deposition rate, deposition temperature and vacuum condition), calculate optical constants by using kramers-kronig relations on reflectivity curves and investigated about changes of optical properties as a function of film thickness.
The optical constants of our samples were derived on the basis of standard Kramers-Kronig relations using computer techniques.
In this work Kramers-Kronig relations were used to calculate the phase angle [theta] (E) [16]:
exist within some frequency bands for all dispersive media [5] as a consequence of Kramers-Kronig relations, which are applicable to all physically realizable, causal linear systems.
Then we apply Kramers-Kronig relations to determine corresponding causal amplitude responses for each phase characteristic.
Reflectance of produced layers were measured in VIS wave length range and by using Kramers-Kronig relations calculate other optical constants and investigate the relations between optical parameters and deposition angle of produced layers.
By using Kramers-Kronig relations for reflectivity curves, optical constants calculated.