Absolute reflectance measurements

Both the above techniques still require absolute reflectivity measurements to be made if quantitative results are to be obtained (chopping the light beam and using phase sensitive detection aids these determinations). Such measurements are notoriously difficult to make, and therefore multiple reflection and glancing incidence are both best suited to qualitative investigations of solution free species. The optical equipment required is essentially identical to that used for OTE studies, and data treatment is also similar. 

Absolute reflectance measurements can be made on front-surface opaque mirrors using the strong V-W reflectance attachment (16) diagrammed in Fig. 7. 

Comparison of telescopic spectra of asteroids (shown by dots and black curves) with meteorite spectra measured in the laboratory (gray curves). Spectral similarities can be used to estimate the compositions of asteroids and infer correlations. Because absolute reflectance (albedo) depends on particle sizes and packing in surface regoliths, it is permissible to translate asteroid spectra up or down in the diagram to obtain a match. 

In setting out to discover the relative positions of the atoms in a crystal, it is best, when the unit cell dimensions have been determined and the intensities of the reflections measured, to calculate F for each reflection. (See Chapter VII.) Absolute values of F, derived from intensities in relation to that of the primary beam, form the ideal experimental materisi, though very many structures have been determined from a set of relative F s. The reliability of the set-of figures depends on the success with which the corrections for thermal vibrations, absorption, and extinction effects have been estimated. 

The crystal structure of benzene itself is even more difficult, and it is only quite recently that accurate results have been obtained. The early work on naphthalene and anthracene was also inconclusive and did not at first lend any support to the idea of strictly planar molecules. The first really conclusive results were obtained for the molecule of hexamethylbenzene (Lonsdale, 1929). In the triclinic crystal structure the atoms occupy general positions, but a careful study of the intensities of the reflections, particularly those from the pronounced cleavage plane in which the molecule is found to lie, established that the molecule was planar to within narrow limits, and also that the benzene ring was a regular hexagon. Soon afterwards the more difficult structures of naphthalene and anthracene were fully analysed with the aid of absolute intensity measurements and the use of Fourier methods of analysis (Robertson, 1933a), and it was shown that the atoms were coplanar to within a few hundredths of an Angstrom unit. 

Once the complex reflectivity amplitude is known, the relation (2.121) determines e(a>). Nevertheless, the absolute reflectivity, unimportant as regards 0(cu) [see (2.120)] becomes essential for the permittivity. Earlier work on a number of crystal samples showed us that the maximum reflectivity at 4 K was greater than 90%. However, due to free sample mounting, the front face of the crystal is not perfectly planar, and accurate direct measurements of the absolute reflectivity are impossible. Fortunately, surface structures II and III allow probing the bulk reflectivity around 3982 A High-resolution spectra (0.3 cm 1) of structure II (cf. Section III) show the absence of any constructive intereference. This, together with numerical simulations,121 indicates that the bulk reflectivity should be very close to 100% (within 2%) at the maximum. 

Accuracy and linearity of the measured values of the reflectance p can be verified by measuring materials with known absolute reflectances of less than 100%. Examples of spectra of two such reference standards measured versus a 100% standard are shown in Figure 9. The reflectance of the two different standards is specified depending on the wavelength, as follows 48.5% at 250 nm, 46.8 at 350 nm (minimum), and 56.6% at 2500 nm 18.7% at 250 nm, 17.2% at 400 nm (minimum), and 26.3% at 2500 nm. It is evident from Figure 9 that the measured reflectance values do not correspond exactly to the specification. Furthermore, repeated measurements indicate less than perfect reproducibility. Analysis of the spectra in Figure 9 shows accuracy and precision of the measurements to be 2-5%. The deviations from the specified values could be caused by imperfect reference materials or could point towards a problem with the measurement apparatus (Thiede and Melsheimer, 2002). 

Since even a few percent error in R((o) is crucial to the Kramers-Kronig (K-K) analysis, extra care was taken in all procedures for obtaining absolute values for R(d)). Surface quality is essential for accurate reflectance measurements. Therefore, the surface morphology of each film was checked, both optically and using scanning electron microscopy [269], All the sample surfaces were of excellent optical quality and exhibited specular reflection. Thus, any scattering... 

The most convenient approximate solutions have been given by Kubelka and Munk 5 6) (cf. J>). These are valid only in the case of an ideal scattering medium without any regular reflection. While the so-called linear Eq. (3) is only valid at infinite thickness, the so-called hyperbolic solution (4) and (5) is of the greatest utility in TLC and HPTLC with a finite layer thickness d. It must be mentioned that in Eq. (3) is the absolute reflectance, while in optical in situ reflectance measurements in TLC and HPTLC only relative reflectances are accessible. 

In order to convert this number to the absolute reflectivity Rw, we need to know R0 Si. This can be done using equation 5.5 again. The result at 436nm is R0Si = 0.44. Thus, as an example, if the reflectivity relative to silicon is measured to be 40% than the absolute reflectivity is 0.4x0.44=0.18. The... 

Colour standards provide the references against which the colours of materials can be instramentally compared. They fall into two classes, primary standards and secondary standards. Primary standards are pressed powder tablets of fresh MgO, BaS04 or halon G-80 (pressed tetrafluoroethylene resin manufactured by the Allied Chemical Corporation) maintained by governmental standards agencies such as the National Bureau of Standards in Washington DC, USA or the National Physical Laboratory in Middlesex, England. These white standards are measured against a theoretical perfect white diffuser by means of an auxiliary sphere to derive an absolute reflectance value. Unfortunately, at the moment there is not a complete consensus between the various standards institutes on the perfect white diffuser values. 

Reflectivity measurements are, in principle, necessary to obtain the absorption coefficient from the transmission data. Such measurements are usually too difficult to perform directly for precise absolute values under high pressures in regions where absorption measurements are carried out. They... 

The reflectance, R, is defined as the ratio of the reflected light intensity to the intensity of the incident beam. Absolute reflectances are difficult to measure and are not necessarily of interest. Instead one is usually interested in the change in reflectance AT induced by some change in the system, for example, in electrode potential. Experimentally, one measures only the intensity of the reflected beam, 7r. Then if the incident intensity remains constant, a change A/r in the reflected beam gives l RIR = A/r//r. The basic data of reflectance experiments are plots of R R vs. the variable of interest, which may be frequency of incident light, potential, concentration of an electroactive species, etc. 

Figure 1 shows a solid electrode surface covered by an optically uniform film in contact with an electrolyte solution. The film actually corresponds to an adsorbed layer on the surface. When a light beam passing through the solution is reflected at the surface, the reflectivity is defined as the ratio of reflected light intensity to that of the incident beam. Because of the difficulty in measuring absolute reflectivity, relative reflectivity denoted as R/Ro is conveniently obtained and is the ratio of the reflectivities in the presence and absence of the film. R/Ra is simply reflectivity in this review. 

Under most circumstances, it is not convenient to measure the incident and reflected beams directly with the same detector because scintillator counters have a substantially smaller dynamic range than the 105- to 1010-fold difference between the direct beam flux and reflected beam flux. Instead, direct knowledge of the detector resolution, A(20), and the conversion factor between the monitor signal and the incident beam flux, amon, can be used to estimate the absolute reflectivity. Furthermore, the absolute reflectivity is well constrained by measurements close to bulk Bragg features or at the total external reflection condition near 20 0°. These intensities are dominated by bulk properties of the substrate and provide an independent calibration on the absolute reflectivity scale. 

With MRI, there is often a volume mismatch between tissue showing reduced water molecule diffusion (a signature for cell swelling and ischemic tissue) and a larger area of compromised tissue perfusion early after stroke onset - the so-called diffusion/perfusion mismatch. The difference, at least for all practical purposes, is believed to reflect the ischemic penumbra [138, 148-151]. Perfusion MRI currently affords a relative, rather than absolute, quantitative measure of cerebral tissue perfusion. Many studies have shown that the MRI-documented mismatch volume shrinks over time. However, mismatch may persist, for example those who present beyond 3 h and still have substantial mismatch [152], suggesting a longer window of therapeutic opportunity in select patients. 

Nevertheless, dc reflectance measurement can be accomplished if one is interested in the relative change of the reflectance but not in the absolute reflectance. Usually, the measured relative reflectance change is defined in a general form ... 

The modulation technique resolves the main technical difficulties of the constant potential spectral measurement at the electrode surface. Basically, in the modulation spectroscopic measurement, only the change associated with the change of the modulated parameter is detected. Thanks to lock-in ampHfication, we can significantly increase the sensitivity of the optical signal detection. It must be noted that what we can obtain is the change of the spectrum with respect to the modulated parameter but not the absolute reflection spectrum. In other words, modulation methods give the difference or differential spectrum. From the modulation spectrum, we cannot obtain explicitly the absolute spectrum at a unique condition unless a perfect reference absolute reflection spectrum is already in our hands. One should be careful in the interpretation of the spectral curves at this point. 

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