Transmission and Reflection

Modulation techniques have been used to eliminate the structureless background of the optical spectra and to enhance structure connected with the critical points. 

PMR (polarization modulated magneto reflection) measures the difference between sample reflectivity for periodically changed right (-1-) and left (-) circularly polarized light, ARp/R = (R+-R )/R, where R is the reflectivity for unpolarized light, Pidgeon etal. [51,52]. 

WMR (wavelength modulated reflection) the Incident light is modulated with A X 5 to 10 nm at 18.5 Hz, Lbfgren [11]. 

ER (electroreflection) an electric field across the crystal Is modulated with a beat frequency oscillator [11]. 

MR (magnetic field-modulated reflection) a magnetic field Is modulated with AH 140 Oe at 210 Hz In the Faraday geometry, Mitani, Koda [53], and with AH 120Oe In the Voigt geometry, Silberstein etal. [54]. 

The reflectance of a boundary plane between two non-absorbing media is a function of the refractive indices of the media examined. When light moves from a medium of refractive index rii into a second medium with refractive index n2, both reflection and transmission of the light may occur (Fig. 10.1). The relationship between 9 and 0, is given by Snellius law (angles are defined as the angle between the beam and the normal on the interface) 

on the other hand, in two non-absorbing media the light beam is polarised parallel to the plane of incidence (p-polarised) the reflectance is 

If in non-absorbing media the incident light is non-polarised, the reflectance is equal to R = Vl(Rs + Rp)- Both reflectance coefficients rs and rp are equal to the square roots of their corresponding reflectances Rs and Rp. 

For near-normal incidence, i.e. 0 0t 0, it follows quite easily for non-absorbing media 

From Eq. (10.17) an important conclusion maybe derived, namely that there must exist an angle at which 0 + 0r =Vm rad, so that Rp 0. Hence, the reflected beam is completely s-polarised. This angle is coined the polarising angle or Brewster angle 0B (see Fig. 10.2), for which holds 

Reflected and transmitted radiation from a powder layer can be either specular or diffuse (Fig. 1.22). The specular (Fresnel) component Isr reflected from the external boundary, which is comprised of all parts of the interface that have faces oriented in the direction of the averaged common interface. The magnitude of this component and its angular dependence can be determined by the Fresnel formulas (1.62). The specular (regular) transmission 7rt is the fraction of radiation that travels through the sample without any inclination. The other fractions of the radiation, the so-called diffuse reflection and transmission, /dr and /dt. respectively, are generated by the incoherent (independent) scattering and absorption by particles and do not satisfy the Fresnel formulas. 

One can distinguish the surface and volume components in the diffuse transmission /dt and the diffuse reflection /dr (Fig. 1.22) [224-227]. The surface component, which is referred to as Fresnel diffiise reflectance, is the radiation undergoing mirrorlike reflection and still obeying the Fresnel reflection law but arising from randomly oriented faces. This phenomenon was first described by Lambert in 1760 [228] to account for the colors of opaque materials. The volume, or Kubelka-Munk (KM), component is the radiation transmitted through at least one particle or a bump on the surface (Fig. 1.22). 

All the components mentioned interact with the powder and, therefore, contain information about its absorption coefficient. However, only the specular transmission and volume KM components give the absorptionlike spectra of the powder directly. The Fresnel components produce specular reflection (first derivative or inverted) specha [which can be converted into the spectra of the absorption coefficient using the KK transformation (1.1.13°)]. Therefore, to obtain the absorption spectrum of a powder, the Fresnel components must be eliminated from the final spectrum. In practice, this can be achieved by immersion of the sample in a hansparent matrix with a refractive index close to that of the powder, selection of appropriate powder size, or special construction of reflection accessories (Section 4.2). 

ABSORPTION AND REFLECTION OF INFRARED RADIATION BY ULTRATHIN FILMS 

There is no general theory for diffuse reflection and transmission [176, 229-232]. The intensity of radiation traveling through a layer of particles is attenuated by incoherent scattering and absorption as well. Provided the particles are well separated so that multiple scattering may be neglected, this intensity can be approximated by [233] 

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Now let us use the wavepackets just discussed to extract the physically measurable infomration about our problem, namely, the probabilities of reflection and transmission. As long as the wavepackets do not spread much during the collision, these probabilities are given by the general definition ... 

The ordered structure and molecule orientation in the monolayers, as suggested by the Hardy model, have been studied by various means. Electron diffraction techniques, for example, including both reflection and transmission, have been employed to examine the molecular orientation of adsorbed monolayers or surface hlms. The observations from these studies can be summarized as follows [3]. 

FIG. 3. Absolute atomic concentrations in units of 10 al./cm. determined by ERD. RBS, and optical reflection and transmission spectroscopy, of (a) hydrogen, (b) carbon, and (c) silicon as a function of the carbon fraction. v. Results are presented for the series ASTI (filled circles), AST2 (filled triangles), ATLl (open circles), and ATL2 (open triangles). (From R. A. C. M. M. van Swaaij. Ph.D. Thesis, Universiteit Utrecht. Utrecht, the Netherlands, 1994. with permission.)... 

Figure 9.8 Second-harmonic generation from thin film (or surface). Fundamental beam at frequency > i p or. v polarized) is incident on film at angle 0. The p- and. s-polarized second-harmonic fields (frequency 2 co) are generated in reflection and transmission. 

Measurements of supported catalysts in diffuse reflection and transmission mode are in practice limited to frequencies above those where the support absorbs (below about 1250 cm-1). Infrared Emission Spectroscopy (IRES) offers an alternative in this case. When a material is heated to about 100 °C or higher, it emits a spectrum of infrared radiation in which all the characteristic vibrations appear as clearly recognizable peaks. Although measuring in this mode offers the attractive advantage that low frequencies such as those of metal-oxygen or sulfur-sulfur bonds are easily accessible, the technique has hardly been explored for the purpose of catalyst characterization. An in situ cell for IRES measurements and some experiments on Mo-O-S clusters of interest for hydrodesulfurization catalysts have been described by Weber etal. [11],... 

Dielectric constant (DE) values are reported as permittivity with the symbol e or K The polymer cylindrical donuts were used for the measurement of DE on a Hewlett-Packard 8510 automated network analyzer. The analyzer is capable of measuring 401 data points over a frequency band of 500 MHz to 18.5GHz. Typically Sll and S21 values, which correspond to reflection and transmission, respectively, are measured and then these values are used to calculate the permittivity and permeability. 

The depth in the sample surface from which the PA signal comes depends on the beam chopping frequency. At low chopping frequencies spectral information comes from greater depths in the sample. In other words, if one speeds up the motor of the device, such as a fan blade, that is chopping the incident light beam, not only will S/N diminish, but the sample will also be probed at a shallower depth below its surface. This ability to yield subsurface spectral and thermal information is a peculiar advantage of PAS over reflectance and transmission spectroscopies that still remains to be widely exploited (5). 

Illumination is a relevant parameter in the electrochemistry of silicon because photogenerated carriers may initiate or contribute to the charge exchange at the electrolyte-silicon interface. If an electrode is illuminated, photogenerated electron-hole pairs are generated corresponding to the number of absorbed photons. This number depends on spectral distribution, total illumination intensity and losses due to optical reflection and transmission. The number of electron-hole... 

Quantitative determination of the absolute distance from the surface to a labeled cell membrane at a cell/substrate contact region can be based on the variation of F(d) with 0.(1O6) This effort is challenging because corrections have to be made for 0-dependent reflection and transmission through four stratified layers (glass, culture medium, membrane, and cytoplasm), all with different refractive indices. For 3T3 cells, Lanni et a//1065 derived a plasma membrane/substrate spacing of 49 nm for focal contacts and 69 nm for close contacts elsewhere. They were also able to calculate an approximate refractive index for the cytoplasm of 1.358 to 1.374. 

The earliest applications for quantitative analysis of liquid samples and solid preparations entailed sample dissolution in an appropriate solvent. A number of moisture determinations in APIs and pharmaceutical preparations based on both reflectance and transmission measurements have been reported. Their results are comparable to those of the KF method. The high sensitivity provided by the NIR technique has fostered its use in the determination of moisture in freeze-dried pharmaceuticals. ° The noninvasive nature of NIR has been exploited in determination of moisture in sealed glass vials. " " ... 

The particular colour which we see from objects coloured with dyes and pigments arises from the absorption and selective reflection and transmission of light from the materials containing the colorants into our eyes, there to be received by the photoreceptors and interpreted by the brain. 

Photoresists. These are used in holography because they can be employed to map holographic exposures into surface relief. This property is utilised in the production of embossing masters, reflection and transmission gratings and in computer generated holograms. 

The considerations in the preceding section make it worthwhile to discuss reflection and transmission at plane boundaries first, one plane boundary separating infinite media, then in the next section two successive plane boundaries forming a slab. In addition to providing useful results for bulk materials, these relatively simple boundary-value problems illustrate methods used in more complicated small-particle problems. Also, the optical properties of slabs often will be compared to those of small particles—both similarities and differences—to develop intuitive thinking about particles by way of the more familiar properties of bulk matter. 

Figure 2.5 Reflection and transmission of obliquely incident light for electric vector parallel (a) and perpendicular (b) to the plane of incidence.

Equations (2.63) and (2.65) are readily solved for the reflection and transmission coefficients... 

Equations (2.67)-(2.70) are the Fresnel formulas for reflection and transmission of light obliquely incident on a plane boundary. 

We now consider reflection and transmission of a wave Eiexp[iu(N2z/c — 0] normally incident on a plane-parallel slab of arbitrary material embedded in a nonabsorbing medium (Fig. 2.7). The reflected and transmitted waves are... 

The field amplitudes are written as scalars because reflection and transmission at normal incidence are independent of polarization. At the first boundary (z = 0), the amplitudes satisfy the usual boundary conditions ... 

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