Specular external reflection

The above theory may be developed in two different ways, depending on the experimental arrangement. We first consider the case of specular external reflection and then extend the theory to internal reflection. 

In the presence of a thin film, as shown in Fig. 3, the situation becomes more complex. For the case of specular reflection, with the electric field polarised in the x direction (i.e. perpendicular to the plane of reflection), the continuity conditions at the (1, 2) interface demand that 

By using the continuity conditions and relating the electric field at (1,2) and (2, 3) through eqn. (1), we find that 

From these two expressions, we can calculate the changes in reflectance and transmittance that occur on film formation. We find 

Provided the film is non-absorbing, then, whilst both AR and AT are finite conservation of energy ensures that A ft = — AT18, as may be verified from eqns. (23) and (24). In addition, if l , or, equivalently, nx n2, then it is evident that AR 0. In other words, even if the film does not absorb in the IR region being examined, some changes in reflectance and transmittance will occur on film formation. 

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With temperature control and anaerobic considerations in mind, we designed a variable-temperature thin-layer specular (external) reflectance spectroelectro-chemical cell (Figure 5.1). The cell design is such that the incident light from the spectrometer reflects off the working electrode, ensuring that the species detected... 

Due to its very nature, the electrode/electrolyte interface may conveniently be studied by reflection-absorption spectroscopy. The first attempts in the infrared wavelength range were made with internal reflection spectroscopy. This allows multiple reflections at the electrode surface to increase the signal, which was otherwise too weak for direct measurement.However, due to inherent difficulties of this method (e.g., the need for a transparent substrate, the necessity for a thin metal layer as electrode), specular external reflection spectroscopy now is preferred for the in situ investigation of electrode processes. 

A majority of traditional NIR measurements are made on solid materials and these involve reflectance measurements, notably via diffuse reflectance. Likewise, in the mid-IR not all spectral measurements involve the transmission of radiation. Such measurements include internal reflectance (also known as attenuated total reflectance, ATR), external reflectance (front surface, mirror -style or specular reflectance), bulk diffuse reflectance (less common in the mid-IR compared to NIR), and photoacoustic determinations. Photoacoustic detection has been applied to trace-level gas measurements and commercial instruments are available based on this mode of detection. It is important to note that the photoacoustic spectrum is a direct measurement of infrared absorption. While most infrared spectra are either directly or indirectly correlated... 

Figure 3.17. (a) Specular X-ray intensity of a DIP trim with 20.6 nm thickness. Bragg reflections up to the seventh order are seen, (b) Magnification of the specular scan from the region of total external reflection across the first specular DIP Bragg reflection. The inset displays a rocking scan across the DIP(OOl) reflection which exhibits FWHM as small as 0.0087°. Reprinted with permission from A. C. Diirr, F. Schreiber, M. Mtinch, N. Karl, B. Krause, V. Kruppa and H. Dosch. Applied Physics Letters, 81, 2276 (2002). Copyright 2002, American Institute of Physics. 

The other two types of external reflection microspectroscopy are less well suited to the characterization of tissue samples. In the first type, which is variously called specular reflection, front-surface reflection or Kramers-Kronig reflection, the reflectance... 

External reflection techniques like specular reflection and diffuse reflection are less suitable for studying hydrogels. There are a number of disadvantages of external reflection compared to transmission and ATR techniques. First, for the same acquisition time, the signal-to noise ratio is lower than in transmission or ATR. It is difficult to determine the path length of the light inside the sample making quantitative information difficult. 

In situ electro-optical reflection is a very promising means for meeting this need. There are two such methods, internal and external reflection methods the latter includes specular reflection spectroscopy, ellip-sometry, IR reflection spectroscopy, and surface enhanced Raman scattering (SERS). 

In external reflectance the incident radiation is focused on to the sample, and two forms of reflectance can occur, namely specular and diffuse. External reflectance measures the radiation reflected from a surface. The material must therefore be reflective, or be attached to a reflective backing. A particularly useful application of this technique is the study of surfaces. 

Reflection measurements at optically flat interfaces can be performed in two basic configurations, external and internal reflection. In the case of external reflection (also called specular reflection) the light propagates in the optically rare medium (e. g. air), whereas in the case of internal reflection (usually employed as attenuated total reflection (ATR)) the hght propagates in the optically dense medium (Fig. 5.3). 

External reflection IR (ERS) the techniques in this category can be a single reflection setup (reflection-absorption IR, RAIR, or grazing incidence reflection IR, GIR) or a multireflection setup (MRAIR). The single reflection technique is also frequently referred to as specular reflectance IR. 

Reflectance techniques may be used for samples that are difficult to analyze by the conventional transmittance method. In all, reflectance techniques can be divided into two categories internal reflection and external reflection. In internal reflection method, interaction of the electromagnetic radiation on the interface between the sample and a meditnn with a higher refraction index is studied, while external reflectance techniques arise from the radiation reflected from the sample surface. External reflection covers two different types of reflection specular (regular) reflection and diffuse reflection. The former usually associated with reflection from smooth, polished surfaces Hke mirror, and the latter associated with the reflection from rough surfaces. 

The incident radiation focused onto the sample may be directly reflected by the sample surface, giving rise to specular reflection, and it may also undergo multiple reflections at the sample, resulting in diffuse reflection. In external reflectance techniques, the radiation reflected from a surface is evaluated (Figure 8). 

The reflection from the boundary when medium 1 is optically rarer than medium 2 (pi < U2) is called the external or specular s reflection (Fig. 1.8). When the radiation travels from an optically denser to optically rarer medium, that is, when n > n2, it is said that internal reflection takes place (see Fig. 1.10 below). 

FTIR spectroscopy can be used in diffuse reflectance, specular reflectance, and external reflectance in grazing angle reflectance mode [23]. It enables the analysis of functional group and specific bonds of surface species. Particles can be measured separately (diffuse reflectance mode) after being scraped from composite electrodes [24]. 

External reflection. This is not as well developed a technique as internal reflection the physics of reflection of light from surfaces is less accommodating to the infrared spectroscopist. Smooth or shiny surfaces are particular problems. Specular reflection from the surface itself is governed by Fresnel s equations—the reflectance depends on a complicated combination of refractive index, sample absorbance and polarisation. Consequently, samples where the reflectance is mainly from the surface give rise to spectra which bear little relation to conventional transmission spectra. A transformation known as the Kramers-Kronig transformation does exist which attempts to convert a specular reflectance spectrum into a conventional-looking one. It is not 100% successful, and also very computer-intensive. For these reasons, specular reflectance is not commonly used by the analyst. 

There are surface-oriented sampling techniques such as internal reflectance (ATR) and external (specular) reflectance, both providing data that are influenced in one way or another by the sample s refractive index (at the measurement wavelength), the refractive index of the sampling medium (in particular, ATR), and the polarization of the infrared beam (in particular, external reflectance). For ideal cases, the mathematical relationship between the recorded spectrum and an idealized absorption (or transmission) spectrum is understood. In these situations, a correction algorithm can be... 

Specular, external (or regular) reflectance (R,) is described by the use of the Fresnel equation as... 

External reflectance spectroscopy (ERS) techniques, which can be combined with IR microscopy are specular reflection spectroscopy (SRS) and reflection-absorption spectroscopy (RAS). These techniques vary in the way the irradiated IR radiation on the surface is reflected from the surface. 

IR reflection spectroscopy is normally used for samples which are difficult to analyze in transmission, such as bulk samples or thin layers on nontransparent substrates. In this case, the IR radiation is directed at a sample surface, usually at an angle larger than 0° off-normal, with the attenuated radiation, reflected back from that surface, being detected. Reflection techniques can be based on specular reflection (internal or external reflection), where the reflectivity R, at normal incidence, is given by... 

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