The quality of measurement data can be investigated by means of the Kramers-Kronig relation .
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.
Since this is not possible, the Kramers-Kronig relation
is numerically integrated over a truncated frequency range thus providing an approximation for the phase factor.
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 dielectric function [epsilon]([omega]) is an example of such a function.
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.
Indeed and in accordance with the Kramers-Kronig relations, a significant metallic content increases the effective refractive index at the expense of low transmittance, as seen in all spectra presented in this paper.
Vartiainen, "Kramers-Kronig Relations in Optical Materials Research," Springer, 2005.
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.
exist within some frequency bands for all dispersive media  as a consequence of Kramers-Kronig relations
, which are applicable to all physically realizable, causal linear systems.
Also the materials were assumed lossless in a wide range in frequency domain which is in contrast to the dependency of real and imaginary parts of [epsilon] and [mu] via Kramers-Kronig relations
The inductance of the spiral using a mathematical model with Kramers-Kronig relations
are proposed in .
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.