Fresnel reflection measurements

Fresnel reflection measurements are convenient for certain types of microsamples because essentially no sample preparation is required. Ideally, only radiation reflected from the front surface of the sample is measured at the detector in this type of measurement, so that the absorption spectrum may be calculated by the Kramers-Kronig transform, as described in Chapter 13. However, for scattering samples, diffusely reflected radiation (see Chapter 16) also contributes to the signal measured by the detector. When both mechanisms contribute significantly to the measured spectrum, no amount of data manipulation will allow an undistorted absorption spectrum to be calculated. 

To evaluate its capability for refractive index measurement, the fiber FPI device was tested using various liquids including methanol, acetone, and 2-propanol at room temperature. The interference spectra of the device immersed in various liquids are shown in Fig. 7.12 for comparison. The signal intensity dropped when the device was immersed in liquids as a result of the reduced refractive index contrast and thus lowered Fresnel reflections from the cavity endfaces. However, the interference fringes maintained a similar visibility. The spectral distance between the two adjacent valleys also decreased, indicating the increase of refractive index of the medium inside the cavity. Using (7.4), the refractive indices of the liquids were calculated to be nmethanoi = 1 -3283, acetone = 1 -3577, and n2-propanoi = 1.3739, which was close to the commonly accepted values. 

Here, n and n2 are the refractive indices of the interfacing materials. The surface reflectivity R, Equation 5, used by Robinson is the Fresnel reflectivity for normal light incidence (c.f. 4). Robinson s interpretation explains the well-known linear relationship between the specific surface area of a paper, as measured by gas adsorption, and its scattering coefficient (15. 28, 32). It also rationalizes the observed decrease in scattering and brightness of wet compared to dry pulp (33, 34). 

Ellipsometry grants the independent determination of two results per resolution element without changing the experimental geometry this technique is described in Sec. 6.4.4.2. More often however, the information on the phase shift is abandoned and just the reflectance is determined. Usually it is measured by comparing the signal caused by the reflected intensity with the one obtained when the sample is replaced by a mirror. Even without correcting for its reflectance such results can often be used for further mathematical evaluation. The Fresnel reflection coefficient r in the form given by Eq. 

In this expression Rp is the Fresnel reflectivity of the water-air interface, i.e., the reflectivity of an infinitely sharp interface between homogeneous media, p is the scattering-length density of the subphase and p(z) is that of the monolayer. In the measurements, the ratio R/Rp is determined as a function of... 

Pig. 19. Normalized absorbance vs. thickness plot for a layer of water in contact with a platinum reflector measured using an infrared beam at the wavelength of the maximum absorptin of the O-H stretching mode and incident at an angle of 45°, calculated using (a) Beer s Law and (b) the full Fresnel reflectance equations. 

Direct, in situ HPTLC-FTIR measurement is carried out by diffuse reflectance using a DRIFT (Diffuse Reflection Infrared Fourier Transform Spectroscopy) unit (Fig. 15) (40-45). It is necessary to take account of the fact that at wavelengths where the absorption is large and the refractive index is high, the incident radiation is almost 100% normally reflected at the surface so that there is scarcely any diffuse reflection, which is that part of the reflection that contains the spectral information concerning the sample, in contrast to the normal (Fresnel) reflection. This means that reflectance minima and not the expected reflectance maxima are obtained at wavelengths of strong absorption. With silica gel, the absorption maxima, also known as residual radiation bands, dominate appreciably in the 1300-... 

Measurement of the Fresnel reflectance spectrum is a very useful way of obtaining the spectrum of solids with flat surfaces when sample preparation is not possible. For example, to measure the spectrum of an oriented polymer, the sample cannot be melted, dissolved, or finely ground. A microscopic sample of a hard polymer may be available that is too thick for transmission spectrometry. If the sample is so hard, rough, and/or thick that a good transmission or attenuated total reflection (see Chapter 15) spectrum cannot be measured, Fresnel reflection spectrometry presents a very useful means of obtaining the spectrum. 

Fresnel reflection from the front surface of the film is usually measured along with the radiation that is transmitted through the film. The distortion of the spectrum that is caused by the Fresnel reflection will lead to deviations from Beer s law,... 

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