Retrieval of Linear Optical Functions from Finite Range Spectra

Abstract

There are many experimental situations in which infrared reflectivity spectra can be acquired only over a limited spectral range. It is therefore necessary to find computing procedures that allow the efficient analysis of such data. In this paper, we propose a new procedure labeled constrained finite range correction (CFRC) that can be advantageously substituted to multiply subtractive Kramers-Kronig relations. The constrained finite range correction is able to produce realistic results even when very little supplementary information is available. For semitransparent crystals, the hypothesis of the phase spectrum positiveness alone is often sufficient to compute satisfactory approximations of the optical functions. The efficiency of the new method is shown through the analysis of several synthetic and experimental spectra.

Mid-infrared optical properties of pyrolytic boron nitride in the 390–1050 °C temperature range using spectral emissivity measurements

“…Contrary to the model-fitting approach, this method involves purely mathematical operations on the data without any physical input. The imaginary part of the Fresnel reflection coefficient ( * = θ r re i ) is calculated from the real part ( = r R) by means of the following equation [48]: where P stands for principal value of the integral.…”

Theory of Midinfrared Absorption Microspectroscopy: I. Homogeneous Samples

“…These effects produce apparent deviations from Beer's law if the simple model of eq 33 is applied. The importance of optical effects has been recognized for some time, [49][50][51] particularly in reflection-based modalities, and algorithms 38,52,53 have been developed to calculate the complex refractive index from certain types of data measured in bulk spectroscopy. In systems without tight focusing, this type of approach has been applied to correct for the apparent artifacts 21,39,40,54-59 and should be used where possible.…”

Far-and mid-infrared properties of carbon layers elaborated by plasma sputtering

“…The advantage of this model is that it does not require any knowledge of the microscopic mechanisms of absorption responsible for the infrared response. Of course, it had been shown for several materials that the shape of the dielectric function given by the piecewise polynomials dielectric function model is exactly the same as the one obtained by classical method (Kramers-Kronig inversion) applied on dielectric compounds[28]. More details on this mathematical way of retrieving the optical function can be found in Ref [28]…”