Effective absorption coefficient and effective thickness in attenuated total reflection spectroscopy

Since the introduction of attenuated total reflection (ATR) spectroscopy for characterization materials, attempts have been made to relate measured reflectivity ( R ) absorption coefficient ? absorbing material interest. The common approach is limited low case under assumption R ? exp ( ?<!-- ? <mml:msub> d e stretchy="false">) , where an effective thickness, which evaluated lossless case. In this Letter, a more detailed derivation leads = ?<!-- ? <mml:mi>p / 2 enabling definition ATR-effective and penetration depth electric field in material. It found that 4 ?<!-- ? <mml:mi>?<!-- ? <mml:mi>?<!-- ? imaginary part complex dielectric function material, wavelength. An alternative formulation <mml:mtext class="MJX-tex-mathit" mathvariant="italic">ef generalized thickness arbitrary strength reduces limit. experimental data water, biopolymer chitosan, soda-lime glass prove reliability infrared range.