Transmission oblique-incidence

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

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

Transmission through Homogeneous Materials at Oblique Incidence... 

In the following summary of contrast enhancement techniques, it is assumed that specimens are being observed in transmission, that they are not self-luminous, and that the light source is not imaged onto the specimen by the microscope condenser. All these assumptions describe typical conditions for LCP microscopy. Figures 5 and 6 show ray diagrams for a normally incident and obliquely incident beam of parallel rays, respectively. In both cases, the objective back focal plane contains the Fraunhofer diffraction pattern of the specimen. 

Fig. 30 Typical changes in FTIR transmission spectra of the PTFE films deposited on Si(100) substrates at Ts=RT by SR etching (a) and laser ablation (b). The bottom trace is a spectrum for the normal incidence (incident angle=0°) and the top trace is for the oblique incidence (incident angle=80°). Reproduced with permission from J Phys Chem 2000, B26, 6212-6217. Copyright 1998 Am Chem Soc...

By contrast with the transmission case, where the phase difference induced by birefringent materials is smooth and progressive, the phase and amplitude changes of the p and s components induced by reflection at a boundary between two materials are discontinuous. Figure 2 shows the effect of these stepwise changes on the polarization of light obliquely incident on a metallic mirror. 

The reflection and transmission (refraction) of light obliquely incident on the interface between two isotropic media is entirely controlled by the angle of incidence and the complex refractive indices of the media, being described by the Fresnel reflection and refraction equations (see Appendix). Originally worked out for transparent materials, these equations apply with complete generality when the refractive indices are complex rather than simple numbers. If the refractive indices are complex numbers, the angles of refraction must also be complex. For a description of the meaning of such quantities, see ref. 3. 

Under oblique incidence ( j=incidence angle, 2=refraction angle, with nisin i = n2 sin 2), the reflection and transmission coefficients depend on the polarization of the incident wave with respect to the incidence plane (see Fig. 6.1). If the polarization (direction of the electric field Eq) is perpendicular to the incidence plane (so-caUed s-polarization), the electric field is everywhere parallel to the interface, and using the same rules as above for the boundary conditions, its amplitude at the interface is now E()X2niCosi+n2Cosg>2), stiU much smaller than Eg [15]. However, if the polarization lies in the incidence plane (so-caUed p-polarization), the electric field has a component parallel to the interface and a component perpendicular to the interface. The parallel... 

Figure 2.1. Optical schemes for recording oblique-incidence transmission spectra of nanolayers, in which layer is located (a, b) on surface of hemicylinder, (c) on surface of plane-parallel plate, (d) between two hemicylinders (1) immersion medium with refractive index ni, (2) layer under investigation of thickness d2 and with optical constants 02 and kz, (3) transparent substrate with refractive index n%.

Figure 2.6. The s- and p-polarized oblique-incidence transmission spectra of 100-nm layer with optical parameters listed in Fig. 2.5. Layer is located on surface of 0.5-mm plane-parallel Si plate (ns = 3.4). Spectra are obtained at values of (a, d) 40°, b, e) 74°, and (c, f) 85°.

Since the substrate may influence the anisotropic optical properties of the overlying film [595], the method of Buffeteau et al. [247, 566-568, 593] is conceptually more reliable when the MO is studied on solid transparent substrates, whereas the initial anisotropic optical constants are extracted from normal- and oblique-incidence transmission or polarized reflection of the same film on the same substrate. In the case when different substrates participate into the measurements (e.g., when MO in monolayers at the AW interface is studied), the comparison of the simulated and experimental spectra can be used for distinguishing chemical effects generated by specific film-substrate interactions [568b]. In particular, the kmm values derived from spectra of monolayers at the AW interface obtained by IRRAS are usually larger than those obtained by eUipsometric measurements of thin films on solid supports [247]. This difference has been attributed to a gradient in the optical properties of the interfacial water [71]. 

High contrast and uniformity of transmission characteristics at oblique incidence are also beneficial features of the SBE mode which considerable improve the legibility of supertwist displays. Better viewing angles than that for the 90° twist structure seem to be a peculiar feature of highly twisted chiral nematics. Figure 4.23 demonstrates this for a 200° supertwist cell in comparison with the usual 90° twist cell [127]. 

Transmission characteristics at oblique incidence wideness of viewing angles (an example is shown in Fig. 4.27 for a twist cell). 

FIGURE 4.27. Transmission characteristics of a twist-cell in parallel polarizers at oblique incidence [159], ie = 30°. (a) Nematic mixture without dye and (b) dye-doped nematic mixture. Curves 1, 2, 3 correspond to different voltages Ui[Pg.185]

B. Wang, A. K. Otta and A. J. Chadwick, Transmission of obliquely incident waves at low-crested breaJswaters Theoretical interpretation of experimental observations, Coastal Eng. 54(4), 333-344 (2007). 

A review of various aspects of the normal beam technique, either pulse-echo or through-transmission is presented next along with sections on oblique incidence, guided waves and acoustic microscopy. 

A generalization of this approach is to deposit a quarterwave dielectric mirror onto a metal reflector. In this way, very high reflectance is obtained for near-normal incidence. For more oblique incident angles the aU-dielectric part will be transmissive, but in that case the metal part will reflect these beams, albeit with a lower reflectance. In this way the benefits of both types of the used structures are simultaneously employed. In [251] the authors mention the use of hybrid reflectors consisting of a Bragg-type dielectric mirror with an additional thin metal reflector deposited on its backside. 

For an obliquely incident light, as shown in Figure 7.7, the transmission T is... 

When the sound is incident obliquely on a plane interface (as shown in Fig.2a), and if both media support only one type of wave (a longitudinal wave if the medium is air or water), then Eg.15 can still be used to calculate the reflection and transmission coefficient. However, the expressions for Z and Z are modified as follows [2,7],... 

The FTIR spectrum of the PTFE film deposited by laser ablation was identical to that of the target [54], but that of the film produced by SR etching showed some visible differences (see Fig. 29). Obviously, the C-F2 deformation bands at 640 and 513 cm-1 appear much smaller in the bottom trace. To understand why these 640 and 513 cm-1 bands were so small in the SR case, we measured both normal and oblique transmission of FTIR with an incident angle of 0 and 80° [58]. Two FTIR spectrometers (PERKIN-ELMER and JASCO) were used to measure spectra in the range 400-3000 cm-1. For a cross-check, the film was also deposited on a metallic surface and infrared reflection absorption spectroscopy [62] was carried out to confirm our oblique transmission measurements. Typical changes in the FTIR transmission... 

Transmission spectra for the sample 1 in parallel and perpendicular polarizers were measured for different angles of incidence in visible and nesu infrared ranges. The obtained results indicate an optical axis lying along the pores. At oblique angles the anisotropy increases with increasing angle of incidence (Fig. 1). 

Fig. 2 presents transmission spectra for the light polarized perpendicular to the pores for the sample 2. The transmittance rises with increasing of the angle of incidence, whereas the transmission minimum has a red shift. At normal incidence PBG disappeared. The presence of PBG in the sample 2 at oblique angles indicates to its satisfactory optical quality and highly ordered pore structure. 

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