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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 [itex]-\infty[/itex] to

[itex]+\infty[/itex].

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!