INDEX homogeneous substrate

A quantitative description does become possible, however, if the system under examination satisfies special conditions. These include diffuse, monochromatic illumination, homogeneous pigmentation, isotropic scattering in the coating, no difference in refractive index between vehicle and air, and a coating so thick that the substrate has no effect on the exiting radiation. This is the special case treated by the Kubelka-Munk theory. 

In order to interpret the reflectance spectrum, modeling of the interface is the key issue. For example, in the simulation above, we tacitly made some assumptions. One is that the change of the optical properties of the substrate and refractive index of the solution immediately adjacent to the film surface are independent of potential and the presence of the film. The use of the Fresnel model with optical constants is based on the assumption that the phases in the three-strata model are two-dimen-sionally homogeneous continua. However, if the adsorbed molecule is a globular polymer which possesses a chromophore at its core, a better model of the adsorption layer would be a homogeneously distributed point dipole incorporated in a colorless medium. To gain closer access to the interpretation of the spectrum, a more precise and detailed model would be necessary. But this may increase the number of adjustable parameters and may demand a too complex optical treatment to calculate mathematically. Moreover, one has to pile up approximations, the validity of which cannot easily be confirmed experimentally. 

Although the optical properties of the adsorbed layer by evaluation of the ellipsometric data obtained are quite interesting for its characterization, for inter-facial science the information about the amount adsorbed at an interface is especially important. In the calculation of this quantity, however, the problem appears to be of a proper proportionality between the layer properties provided by ellipsometry and the adsorbed amount. Recently, it was shown that for ultrathin adsorbed layers of conventional soluble surfactants ellipsometry is insufficient and additional experimental methods are required (245,250). Relatively thick layers are also often not homogeneous in the bulk (substrate) normal to the interface. In this case the refractive index and the thickness of the layer calculated from the experimental values of 8 A and 8 A represent mean optical quantities. If, additionally, the relractive index n is a linear function of the solute concentration in the layer ... 

For multilayer quarter-wavelength antireflection films with homogeneous strata (step-down refiactive index film) [156, 157], the amplimde reflection coefificient determined for the whole structure in the aforementioned manner is made equal to zero (the condition of reflection minimum) and numerical optimization is further performed to obtain the strata parameters. In that case, the above-mentioned step-down condition is applied that refractive index decreases in steps from the value at the substrate surface to the no value of the surrounding medium [155]. 

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