On the Robinson and Price (Kramers—Kronig) Method of Interpreting Reflection Data Taken through a Transparent Window

Abstract

It is shown that the usual integral formula used to obtain the phase shift from the reflectivity (at all frequencies) must be modified when the reflectivity is measured off a surface covered by a transparent window. The discussion is first restricted to reflection at normal incidence but is later generalized to include all possible angles of incidence. There are found to be three distinct cases defined by the conditions $\text{(1)}{\sin }^2{\text{α<1/ε}}_w{\text{,(2)\hspace{0.17em}1/ε}}_w<{\sin }^2{\mathrm{\alpha <\epsilon }}_0{\mathrm{/\epsilon }}_w\text{,(3)}{\sin }^2{\mathrm{\alpha >\epsilon }}_0{\mathrm{/\epsilon }}_w$ , where ε₀ is the static dielectric constant of the sample, ε_w is the dielectric constant of the window, and α is the angle of incidence. Case (1) involves the addition of an extra factor to the usual expression for the phase shift. This extra factor involves either zero, one, or two unknown parameters depending upon the particular values of α, ε_w and ε₀. In case (2) the expression for the phase shift is quite complicated and of doubtful practical value. In case (3), it was found possible to write a simple expression for the phase shift in terms of a different integral than the one ordinarily used.