Kramers-Kronig relations for limited data point

[physengineer]

Hello,

I need to measure the complex-optical conductivity of some materials. The problem is that I can only measure the imaginary part of the complex conductivity only for limited wavelengths between 1030 nm and 2300 nm.

From Kramers-Kronig relations, we know that the real and imaginary parts of the optical conductivity are related but the required integrations are from $-\infty$ to
$+\infty$.

Is there any way to still be able to use Kramers-Kronig relations when I only know the imaginary part for just an interval rather than the whole spectrum.

I would appreciate any help in this regard!

 

[chrisbaird]

If you have enough data, you may be able to reasonably extrapolate to find the other values. Fit a curve to your data and use the curve for values you don't have.

Also, in practice, we can never acquire an infinite number of points in order to satisfy certain relations such as Kramers-Kronig or Fourier Transforms, and thus edge effects are inevitable. We can minimize edge effects by applying http://en.wikipedia.org/wiki/Window_function" .