Diffuse Mirrors

A light beam reflected from a difluse surface does not remain in the same plane, hut may be instead reflected omnidirectionally, i.e., in any spatial direction (e.g., [261]). Such behavior is ideally described by Lambert s cosine law. 

Diffuse reflectivity is caused by scattering centers which may be either on the reflecting surface or within the volume of the reflecting body and are usually subwavelength or mesoscopic. Multiple scattering tends to produce a dififrisely 

The total reflectance of a surface is the result of a combination of multiple scattering from the volume inclusions and from the reflector surface. These two components may be in any ratio. Multiple scattering by pigment particles within the coating volume readily achieve diffuse reflectances of 0.80-0.90. The values are much higher if the structure is optimized for diffuse reflectance [262]. Such optimization can be obtained for example by numerical techniques. 

Enhanced backscattering can lead to near-ideal Lambertian illumination and super-white coatings, or superdiffusers . Diffuse reflectors are described by the theory of disordered media. Generally, this theory is very complex and the methods 

Real reflectance can be described analytically or empirically [261]. There are several analytic reflectance models that can be used to describe various types of surfaces. The simplest diffuse source is Lambertian. The Mie theory can compute light scattering by spherical particles, as well as some other simple shapes like elongated ellipsoids [266]. 

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Equation (5-121) specifically includes those zones which may not have a direct view of the refractory. When Qr = 0, the refractory surface is said to be in radiative equilibrium with the entire enclosure. Equation (5-121) is indeterminate if = 0. If ,. = 0, rdoes indeed exist and may be evaluated with use of the statement Er = Hr = Wr. It transpires, however, that I, is independent of Erfor all 0 < , < 1. Moreover, since Wr = Hr when Q, = 0, for all 0 < ty < I, the value specified for , is irrelevant to radiative transfer in the entire enclosure. In particular it follows that if Qr = 0, then the vectors W, H, and Q for the entire enclosure are also independent of all 0 < e, < 1.0. A surface zone for which e, = 0 is termed a perfect diffuse mirror. A perfect diffuse mirror is thus also an adiabatic surface zone. The matrix method automatically deals with all options for flux and adiabatic refractory surfaces. 

Refractory Augmented Black View Factors Ftj Let M = Mr + Mi, where Mj is the number of black surface zones and Mr is the number of adiabatic refractory zones. Assume er = 0 or pr= 1 or, equivalently, that all adiabatic refractory surfaces are perfect diffuse mirrors. The view factor Ftj is then defined as the refractory augmented black view factor, i.e., the direct view factor between any two black source-sink zones, A, and Aj, with full allowance forreflections from all intervening refractory surfaces. The quantity Fy shall be referred to as F-bar, for expediency. 

A numerical solution of this equation for a constant surface concentration (infinite fluid volume) is given by Garg and Ruthven [Chem. Eng. ScL, 27, 417 (1972)]. The solution depends on the value of A. = n i — n )/ n — n ). Because of the effect of adsorbate concentration on the effective diffusivity, for large concentration steps adsorption is faster than desorption, while for small concentration steps, when D, can be taken to he essentially constant, adsorption and desorption curves are mirror images of each other as predicted by Eq. (16-96) see Ruthven, gen. refs., p. 175. 

Recent applications of e-beam and HF-plasma SNMS have been published in the following areas aerosol particles [3.77], X-ray mirrors [3.78, 3.79], ceramics and hard coatings [3.80-3.84], glasses [3.85], interface reactions [3.86], ion implantations [3.87], molecular beam epitaxy (MBE) layers [3.88], multilayer systems [3.89], ohmic contacts [3.90], organic additives [3.91], perovskite-type and superconducting layers [3.92], steel [3.93, 3.94], surface deposition [3.95], sub-surface diffusion [3.96], sensors [3.97-3.99], soil [3.100], and thermal barrier coatings [3.101]. 

In solvent-elimination LC-FTIR, basically three types of substrates and corresponding IR modes can be discerned, namely, powder substrates for diffuse reflectance (DRIFT) detection, metallic mirrors for reflection-absorption (R-A) spectrometry, and IR-transparent windows for transmission measurements [500]. The most favourable solvent-elimination LC-FTIR results have been obtained with IR-transparent deposition substrates that allow straightforward transmission measurements. Analyte morphology and/or transformation should always be taken into consideration during the interpretation of spectra obtained by solvent-elimination LC-FTIR. Dependent on the type of substrate and/or size of the deposited spots, often special optics such as a (diffuse) reflectance unit, a beam condenser or an FITR microscope are used to scan the deposited substances (typical diameter of the FITR beam, 20 pm). 

Fig. 6 A general pulse sequence (a) for spin diffusion or third-spin assisted mixing for polarization transfer between carbons (as shown) or carbon and nitrogen along with examples of homonuclear mixing elements and illustration of activated parts of H-13C-13C spin systems for PDSD, MIRROR, and PAR (b) (taken from [18] with permission), (c) Example of the application of PDSD for structure determination of the a-spectrin SH3 domain (taken from [133] with permission)...

Depth profiling of a solid sample may be performed by varying the interferometer moving-mirror velocity (modulated IR radiation). By increasing the mirror velocity, the sampling depth varies, and surface studies may be performed. Limitations do exist, but the technique has proven to be quite effective for solid samples [21]. In addition, unlike diffuse reflectance sampling techniques, particle size has a minimal effect upon the photoacoustic measurement. 

In the diffuse reflectance mode, samples can be measured as loose powders, with the advantages that not only is the tedious preparation of wafers unnecessary but also diffusion limitations associated with tightly pressed samples are avoided. Diffuse reflectance is also the indicated technique for strongly scattering or absorbing particles. The often-used acronyms DRIFT or DRIFTS stand for diffuse reflectance infrared Fourier transform spectroscopy. The diffusely scattered radiation is collected by an ellipsoidal mirror and focussed on the detector. The infrared absorption spectrum is described the Kubelka-Munk function ... 

In some situations measurement of the reflected, rather than the transmitted, radiation may be made to assess the amount of radiation that has been absorbed by the sample. There are two main ways by which radiation might be reflected. Specular reflection is similar to the reflection by a mirror and, for quantitative work, the angles of the incident and the reflected radiation are important. Diffuse reflection is from within the layers of the material and the reflected light is disbursed over a range of 180°. This type of reflection is measured in the thin films used in dry chemistry systems. The term reflectance density is often used, which is defined in a manner comparable to absorbance the logarithm of the ratio of incident to reflected light. 

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... 

Diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) is used to obtain spectra of powders and rough polymeric surfaces such as textiles and paper. IR radiation is focused onto the surface of the sample in a cup resulting in both specular reflectance (which directly reflects off the surface having equal angles of incidence and reflectance) and diffuse reflectance (which penetrates into the sample subsequently scattering in all angles). Special mirrors allow the specular reflectance to be minimized. 

Figure 5.23 — Flow-through ionophore-based sensor for the determination of lithium in serum. (A) Mechanism involved in the sensor response (symbol meanings as in Fig. 5.20). (B) Diffuse reflectance flow-cell (a) upper stainless steel cell body (A) silicon rubber packing (c) quartz glass window (d) Teflon spacer (0.05 mm thickness) (e) hydrophobic surface mirror (/) lower stainless steel cell body. For details, see text. (Reproduced from [90] with permission of the American Chemical Society).

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