Differential multiply subtractive Kramers-Kronig relations

We apply the multiply subtractive Kramers-Kronig (MSKK) method to the derivative of a medium's optical transfer function. That is, the phase "difference" or derivative Δθ (instead of the phase) can be evaluated from the measurements of the relative derivative of the intensity Δ ln[I(ω)]=ΔI(ω)/I(ω) with the aid of a few Δθ measurements. As a result, we obtain a method that integrates two different techniques, MSKK and spectral ballistic imaging. We show that the transfer function can be evaluated with great accuracy without the need to measure the phases at all but rather its derivative, which is a much simpler process.